HEAT TRANSFER STUDY OF A TRIPLE ROW IMPINGEMENT CHANNEL AT
LARGE IMPINGEMENT HEIGHTS
by
ROBERTO CLARETTI
A thesis submitted in partial fulfillment of the requirements
for the Honors in the Major Program in Mechanical Engineering
in the College of Engineering and Computer Science
and in The Burnett Honors College
at the University of Central Florida
Orlando Florida
Spring Term 2011
Thesis Chair Dr Jay Kapat
ii
ABSTRACT
Advanced cooling techniques are required to increase the Brayton cycle
temperature ratio necessary for the increase of the overall cyclersquos efficiency Current
turbine components are cooled with an array of internal cooling channels in the midchord
section of the blade pin fin arrays at the trailing edge and impingement channels in the
leading edge Impingement channels provide the designer with high convective
coefficients on the target surface Increasing the heat transfer coefficient of these
channels has been a subject of research for the past 20 years In the current study a triple
row impingement channel is studied with a jet to target spacing of 6 8 and 10 The
effects of sidewalls are also analyzed Temperature sensitive paint alongside thin foil
heaters are used to obtain heat transfer distributions throughout the target and side walls
of the three different channels Thermal performances were also calculated for the two
largest channels It was found that the side walls provide a significant amount of cooling
especially when the channels are mounted side by side so that their sidewalls behave as
fins Similar to literature it was found that an increase in ZD decreases heat transfer
coefficient and provides a more uniform profile It was also found that the ZD = 6 and 8
target wall heat transfer profiles are very similar hinting to the fact that successful
potential core impingement may have occurred at height of eight diameters A
Computational Fluid Dynamics or CFD study was also performed to provide better
insight into the flow field that creates such characteristic heat transfer profiles The
Realizable k-ε solution with enhanced wall functions gave surface heat transfer
coefficients 30 off from the experimental data
iii
DEDICATED TO ENNIO MAMA Y PAPA
iv
ACKNOWLEDGEMENTS
I would like to acknowledge my mentor and advisor Dr Jay Kapat for all his
support and encouragement I would also like to thank my committee members Dr Ali
Gordon and Dr Weiwei Deng
I would also like to give a million thanks to Perry Johnson Lucky Tran Bryan
Bernier and William Clark for their help with the CFD portion of this study and for
letting me run on their computers Special thanks go to Mark Ricklick for helping me
throughout this project To everyone at CATER Mark Miller Michelle Valantino
Jimmy Kullberg Greg Natsui Michael Torrance Jeff Nguyen Nghia Tran Abhishek
Saha Kaylee Dorman Matt Golsen and everyone else that were once caterers a big thank
you for making these two years of work at the lab unforgettable
v
TABLE OF CONTENTS
ABSTRACT ii
ACKNOWLEDGEMENTS iv
LIST OF FIGURES vii
NOMENCLATURE ix
CHAPTER ONE INTRODUCTION 1
11 Gas Turbine as a Heat Engine 1
12 Cooling of Hot Components 2
CHAPTER TWO LITERATURE REVIEW 9
21 Impingement Literature Cornerstone 9
22 Relevant Impingement Channel Studies 11
23 Computational Studies on Impingement Channels 12
CHAPTER THREE EXPERIMENTAL SETUP AND TECHNIQUES 15
31 Temperature Measurements with TSP 15
32 Experimental Setup of Suction Channel 21
33 Data Processing and Reduction 24
34 Uncertainty Analysis 27
35 Lateral Conduction Analysis 28
CHAPTER FOUR HEAT TRANSFER RESULTS 32
vi
41 Heat Transfer Validation 32
42 Heat Transfer Results 33
43 XD Comparisons 40
44 3D Comparison of the Heat Transfer Profiles 45
45 Thermal Performance Calculations 48
CHAPTER FIVE COMPUTATIONAL FLUID DYNAMICS 52
51 Problem Setup 52
52 CFD Results 58
CHAPTER SIX CONCLUSIONS 63
APPENDICES 64
Appendix A 64
Appendix B 66
REFERENCES 108
vii
LIST OF FIGURES
Figure 1 Brayton Cycle Flow Path and T-s Diagram (Adapted from UPTB Website) 1
Figure 2 Thermal Loading Throughout a Turbine Blade (Daniels 1982) 3
Figure 3 Allowable Turbine Inlet Temperature vs Cooling Techniques over the Years
(Clifford 1985) 4
Figure 4 Turbine Inlet Temperature Increase with the help of TBC New Super Alloys
and Cooling Technologies (Kapat and Kiesow Lectures 2010) 4
Figure 5 Turbine Stator Cooled with Impingement Coupled with Film Cooling
(Florschuetz 1980) 5
Figure 6 Rotor Blade Cooling Configuration (Gladden 1988) 6
Figure 7 Cross-section of Turbine Airfoil with Cooling Channels (Han et al 1984) 6
Figure 8 Relative Temperatures for Hot Gas Metal Temperature and Coolant
Temperature (Cardwell 2005) 7
Figure 9 (a) The Development of the Wall Jet (b) Jet Diffusion to Surroundings (Liu
2006) 8
Figure 10 Simplified Jablonski Diagram (Adapted from ISSI Website) 17
Figure 11 Heater Strips Painted with TSP Too Closely 21
Figure 12 Flow Loop of Impingement Channel 22
Figure 13 Top View of Jet Plate 22
Figure 14 Front View of Impingement Channel 23
Figure 15 Target Wall Test Section with Heater Leads 23
Figure 16 Heat Transfer Coefficient Uncertainty Tree 27
viii
Figure 17 Temperature Profile of First Five Impingement Rows 29
Figure 18 Detailed View of First Heat Transfer Peak with a Polynomial Curve Fit 30
Figure 19 Control Volume Heat Transfer Analysis 30
Figure 20 Heat Loss through Convection and Lateral Conduction 31
Figure 21 Validation Spanwise Averaged Results 32
Figure 22 Target Wall Heat Transfer Coefficient Distributions 34
Figure 23 Span-averaged Target Wall Heat Transfer Distribution 35
Figure 24 Side Wall Heat Transfer Coefficient Distributions 36
Figure 25 Span-averaged Side wall Heat Transfer Distribution 37
Figure 26 XD=15 Target Wall Heat Transfer Profile 41
Figure 27 XD=15 Span-averaged Target Wall Heat Transfer Distribution 42
Figure 28 Target Wall Span-average Comparison of XD=5 and 15 at High Re 43
Figure 29 Side Wall Heat transfer Coefficient Profile 44
Figure 30 XD=15 Side Wall Span-averaged Heat Transfer Coefficients 45
Figure 31 3D Heat Transfer Profile for ZD=6 XD=5 46
Figure 32 3D Heat Transfer Profile for ZD=8 XD=5 47
Figure 33 3D Heat Transfer Profile for ZD=6 XD=15 48
Figure 34 Pressure Drop Ratio with Respect to Smooth Channel 49
Figure 35 Heat Transfer Enhancement 50
Figure 36 Thermal Performance at Constant Pressure Drop 50
Figure 37 Thermal Performance at Constant Pumping Power 51
Figure 38 Horizontal Plane of Impingement Channel Geometry 53
Figure 39 Target Side and Front End Wall y+ Values 54
ix
Figure 40 Finished Mesh with Boundary Conditions 55
Figure 41 Grid Independence Study 57
Figure 42 Residual Plots for the 26M Cell Run 57
Figure 43 Total Pressure Contours 58
Figure 44 Velocity Magnitude Contours 59
Figure 45 Turbulent Kinetic Energy Contours 60
Figure 46 Static Temperature Contours 60
Figure 47 Target and Side Wall Heat Transfer Coefficient Contours 61
Figure 48 Closer View of First few Rows of Impingement HTC Contours 61
Figure 49 Pathlines Generating from the First Row of Jets 62
NOMENCLATURE
Cross Sectional Area
Heater Surface Area (m2)
Specific Heat at Constant Pressure (kJkgK)
D Jet Diameter (m)
Channel Hydraulic Diameter (m)
Friction Factor
Heat Transfer Coefficient (HTC) (Wm2K)
Average Heat Transfer Coefficient (Wm2K)
Channel Length (m)
Mass Flow Rate (kgs)
Static Pressure (kPa)
x
Total Pressure (kPa)
Pr Prandtl Number
Heat Flux (Wm2)
Total Heat Input (W)
Heater Resistance (ohm)
Re Reynolds Number
SW Side Wall
Temperature (K)
TW Target Wall
Voltage Potential
Streamwise Location
y Spanwise Location
z Height from Target Wall
X Streamwise Distance (m)
Y Spanwise Distance (m)
Z Impingement Height (m)
Thermal Performance Parameter
Ratio of Specific Heats
Air Density (kgm3)
Subscripts
C Cold
H Hot
xi
Carnot Describing a Carnot cycle
Exit
Effective
Quantity Lost to the Environment
Reference Value
Wall Value
Base Line Value
1
CHAPTER ONE INTRODUCTION
11 Gas Turbine as a Heat Engine
Gas turbine is a form of heat engine where the hot reservoir is created by the
combustion of fuel and the cold reservoir is the open atmosphere It is well known that
the maximum efficiency of any heat engine is denoted as the Carnot efficiency
A more accurate cycle is used to describe the processes inside a gas turbine ndash the
Brayton Cycle The Brayton cycle as seen in Figure 1 is composed of four processes In
a gas turbine air is drawn in at state 1 it is compressed until it reaches state 2 The
compressed air is mixed with fuel and ignited as it passes through the combustor The hot
air then passes through the turbines where work is extracted The process from state 4 to
state 1 happens throughout the atmosphere therefore the Brayton cycle is an open loop
cycle as the same air is not continuously being fed through the motor
Figure 1 Brayton Cycle Flow Path and T-s Diagram (Adapted from UPTB Website)
The Brayton cycle has an isentropic efficiency similar to the carnot the Brayton
cycle efficiency is defined as
2
It can be seen that increasing the temperature at which air enters the first turbine
stage T3 increases the overall efficiency of the turbine Moreover increasing the
pressure ratio Pr also aids in the increase of the efficiency One of the hurdles of
increasing T3 is the fact that the post combustion gas is a few hundred degrees Celsius
above the melting point of the super alloys used to make the turbine stator vanes and
rotor blades For this reason it is important to cool the hot components of the gas turbine
in order to assure a reasonable life for the machine
12 Cooling of Hot Components
The transition duct that connects the combustor to the first stage turbine as well
as the first stage of the turbine are the parts that are subject to the harshest thermal
loadings and must therefore be cooled aggressively to maintain them in working
conditions for a long period of time Since the first stage guide vanes and rotor extrude
into the flow they are subject to the highest convection coefficients These heat transfer
coefficients can reach up to 4000 Wm2K (Downs 2009) Figure 2 shows the different
magnitudes of convection coefficient around the blade High heat transfer coefficients
occur where the air stagnates into the leading edge of the airfoil This high heat transfer
region is not only caused by the lack of a thermal boundary layer to protect the airfoil but
also because the effective heat transfer driving temperature is the recovery temperature
At the high Mach numbers that occur in turbines the ratio of total to static temperatures
is significant causing the leading edge to have the highest effective heat load Another
3
peak occurs on the suction side of the blade as the boundary layer created by the airfoil
switches from being a laminar boundary layer into a turbulent one Due to the nozzling
effect of the turbine rotor and stators the flow gathers speed toward the trailing edge of
the airfoil leading to higher convection coefficients on the pressure side of the airfoil
Figure 2 Thermal Loading Throughout a Turbine Blade (Daniels 1982)
Simple convection channels were implemented in the early nineteen sixties as
years passed the cooling techniques became more and more sophisticated allowing the
free stream temperature to increase to previously impossible levels Currently the use of
film cooling coupled with backside impingement leads the turbine cooling technology
The trend of allowable turbine inlet temperature is shown in Figure 3 from this figure it
can be seen that the allowable free stream temperature has increased around 600 degrees
in the past 50 years The addition of thermal barrier coatings also helps in the increase in
allowable combustion temperatures by creating an extra resistance that the heat needs to
move through as it moves from the combustion gasses into the coolant air It is impotatnt
to notice that as seen in Figure 4 the increase in turbine inlet temperatures is done with
the combined benefits of new alloys TBC and cooling technologies
4
Figure 3 Allowable Turbine Inlet Temperature vs Cooling Techniques over the Years (Clifford 1985)
Figure 4 Turbine Inlet Temperature Increase with the help of TBC New Super Alloys and Cooling
Technologies (Kapat and Kiesow Lectures 2010)
The cooling of inlet guide vanes can be done with the use of impingement inserts
inside the airfoils As air passes through the miniscule holes in the inserts a jet is formed
which then impinges on the wall of the airfoil producing one of the largest single phase
heat transfer coefficients This already impinged coolant air is then bled out as film
5
cooling as well as bled out through the trailing edge Figure 5 shows a stator vane with
the impingement insert in black the film cooling extraction as well as the trailing edge
bleed
Figure 5 Turbine Stator Cooled with Impingement Coupled with Film Cooling (Florschuetz 1980)
The cooling of turbine airfoils with the use of an impingement insert is only
possible in stationary components as the rotating ones are subject to centrifugal loadings
making it unfeasible to cool them with this setup Rotor blades are typically cooled with
serpentine passages that have heat transfer enhancing features such as ribs dimples and
other turbulators these serpentine passages are located in the mid chord of the blade On
the trailing edge a bank of pins are used to obtain high convective coefficients in the thin
region the coolant is the bled out to compensate for the boundary layer created around
the airfoil Rows of impingement holes cool the leading edge The spent air is then bled
out through showerhead cooling Figure 6 and Figure 7 show in detail the cooling
channels around two similar airfoils airfoils
6
Figure 6 Rotor Blade Cooling Configuration (Gladden 1988)
Figure 7 Cross-section of Turbine Airfoil with Cooling Channels (Han et al 1984)
7
The coolant air is bled out from the later stages of the compressor This air is
expensive as it has been compressed and not under gown the heat addition by
combustion It is imperative that the minimum amount of coolant is used in these cooling
configurations The cooling must also be as uniform as possible to reduce thermal
stresses within the blades leading to a higher component life Figure 8 shows freestream
metal and coolant temperatures of the flow blade and coolant air It can be seen that a
decrease of 25degrees in the surface temperature of the blade can provide an airfoil with
twice the working life Impingement cooling has great potential to provide high heat
transfer coefficients at a small flow rate Impingement of a jet onto a surface provides
high heat transfer coefficients due to a starting boundary layer as well as its high
turbulence When the jet is located around 3 diameters from the target surface the heat
transfer profile has two peaks one located at the stagnation region and the other located
between one and 3 diameters from the stagnation region As the jet is moved away from
the target wall the secondary peak diminishes leaving a profile with a maximum at the
stagnation region decreasing radialy
Figure 8 Relative Temperatures for Hot Gas Metal Temperature and Coolant Temperature (Cardwell 2005)
Cardwell N D 2005
8
Figure 9 shows a diagram of a jet impinging on a target surface The potential
core is the part of the jet that has not been affected by the surrounding stagnant fluid As
the jet moves towards the target wall its momentum diffuses into the surrounding fluid
decreasing the velocity at which it reaches the target wall and potentially decreasing the
corresponding heat transfer coefficient Studies have shown (Martin 1973 for example)
that the potential core may last anywhere between 7 to 10 diameters The successful
impingement of the potential core yields significantly higher heat transfer coefficients
than a fully diffused jet this comes however at a cost of higher pressure drop across the
jet plate as well as a highly non uniform heat transfer profile
Figure 9 (a) The Development of the Wall Jet (b) Jet Diffusion to Surroundings (Liu 2006)
9
CHAPTER TWO LITERATURE REVIEW
21 Impingement Literature Cornerstone
From the early days of simple convective cooling channels in turbine airfoils
studies have been done on modes of enhancing heat transfer coefficients while
maintaining a low pressure drop and minimum mass flow rate Heat transfer
characteristics of single round nozzle impingement were studied in the late 1960rsquos and
early 1970rsquos The collected works of many authors is combined into ldquoHeat and Mass
Transfer between Impinging Gas Jets and Solid Surfacesrdquo by Holger Martin 1977 The
paper collects works from multiple authors who studied single round nozzle impingement
effects on heat and mass transfer coefficients In this compilation non dimensional jet to
target spacing was studied they ranged from ZD=12-10 providing plots of Sherwood
number as a function of radius for four different jet to target spacings The local
Sherwood number was also given for a slot jet for HS ranging from 5 to 20 Studies on
impingement jet arrays were also gathered alongside an array of slot jets Correlations
were given for multiple setups present in the paper Circular jet arrays and slot arrays are
studied in detail with both analytical and experimental approaches The paper also
combines studies done on swirling jets turbulence enhancers on the target surface
impingement on concave surfaces and angle of attack variations Optimization studies
were also done to find the optimal spacing for round and slot jet arrays
Florschuetz studied the heat transfer characteristics of an array of jets impinging
on a flat surface This study was guided towards finding an optimal spacing for an array
for jets used to cool the midchord of turbine airfoils similar to that found in Figure 5 His
main contributions include a Nusselt number correlation as a function of jet to target
10
spacing jet Reynolds number and other flow and geometric parameters He found that an
increase in hole spacing and channel height resulted in a decrease of heat transfer He
also provided a one dimensional jet mass flux and channel mass flux correlations
His Nusselt number correlation takes the form of
Where A B and n are dependent by the two different types of arrays inline or staggered
Liu studied new techniques in temperature and pressure measurements of a single
slot jet with the use of temperature sensitive paint or TSP and pressure sensitive paint or
PSP In his work both measurement techniques are explained in detail Since TSP is the
only tool from that study currently used in this work it will be explained further in the
experimental setup section
11
22 Relevant Impingement Channel Studies
Al-Aqal 2003 studied three different types of impingement channels The use of
TLC was implemented in this work to obtain heat transfer distributions for the target
wall The three different configurations varied the number of holes in the streamwise and
spanwise directions The first channel had a single row of 6 streamwise jets the second
consisted of 2 rows of 12 streamwise holes summing up to a total of 24 holes The last
channel is a triple spanwise row with 18 streamwise jets This last geometry is the most
similar to the one present in the current study The third geometry will be used to
compare results There are differences however the total width of the channel is of 16
diameters as opposed to 8 in this study The streamwise jet spacing is also different Al-
Aqal used an XD of 65 compared to XD = 5 in this study The jet to target plate
spacings are similar on two occasions as he studied a ZD=4 6 and 8 while this work
uses a ZD = 6 8 and 10 Average jet Reynolds numbers also fall within the range of this
study as they range between 5000 and 33000 The author provides span averaged plots
for all cases and Reynolds numbers convenient when comparing the results
Ricklick 2009 studied a channel similar to the one found in this study His
channel was composed of a single row of 15 jets with a YcD = 4 XD = 5 and 15 and
ZD = 1 3 and 5 Two channels were tested one was pressure fed while the other was fed
by suction TSP was used to gather temperature data of all four wetted surfaces on the
pressure channel and two surfaces on the suction channel Since the maximum jet Mach
number was less than 03 the flow was assumed to be incompressible leading to the
conclusion that both channels contain identical flow patterns Thin foil heaters were used
to create the required heat flux for the channel Besides channel geometry Reynolds
12
numbers and heater geometry Ricklicksrsquo experimental setup is identical to the one
presented in this work The author also provided an ample comparison of his results to
literature He provided thermal performances of the entire channel at different Reynolds
numbers and channel heights
A small CFD study was also done A paved mesh was created on the target wall
with finer mesh near the impingement locations The resulting y+ at the wall was higher
than one yielding potentially faulty heat transfer values however this is acceptable since
the CFD was used as a tool to better understand the flow physics and help understand the
experimental heat transfer profiles
23 Computational Studies on Impingement Channels
El-Gabry did a numerical study of jet impingement with cross flow Two different
turbulence models were compared in their ability to predict surface Nusselt number The
Yang-Shih and standard k-ε models were used to compute the flow generated by jets
angled at 30 60 and 90 degrees with cross flow The computational results were
compared to previous experimental work by El-Gabry Comparisons to experimental
results at ZD = 1 and 2 90deg injection angle between Yang-Shih and standard k-ε The
error in the average Nu from the experimental results and both turbulence models were
calculated It was found that the Yang-Shih model behaved well at low Reynolds
numbers with the average Nusselt number being 5 off from the experimental value
while the standard k-ε was off my 94 As jet Reynolds number was increased the error
of the standard k-ε model dropped to as low as 39 while the error from the Yang-shih
model increased to -76 The span average plots show the experimental data Nusselt
number alongside the span averages of the results acquired by the Yang-Shih and
13
standard k-ε models High Nusselt numbers occur at the impingement location decreasing
thereafter after another impingement location is found The frequencies of these
variations are all the same for the experimental and the two numerical solutions The
amplitude of fluctuations between the impingement locations and the areas in between
are much larger for both of the numerical results however the Yang-Shih model over
predicts at the high Reynolds number for the ZD=2 case Since the amplitude of
fluctuations is greater for the CFD solutions it is important to note that even though the
error in average Nusselt number is not great the actual differences in the profile are much
greater upwards of 20 difference of heat transfer coefficients between the experimental
and numerical heat transfer peaks Other variations were studied (Injection angles for
example) but will not be discussed as their importance to the current study is minimal
Zuckerman compared a much wider set of turbulence models in their ability to
successfully predict Nusselt numbers caused by jet impingement The models tested were
k ndash ε k-ω Reynolds Stress Model algebraic stress models shear stress transport and
lastly the υ2f turbulence model DNS runs are extremely time consuming to run
therefore LES was run on its behalf to provide results for the unsteady turbulence
models The paper summarizes all the different models used their computational cost
impingement heat transfer coefficient and their ability to predict the second peak in heat
transfer As expected DNSLES provide the best prediction of both stagnation and
secondary peak heat transfer coefficient however this comes at a large computational
cost The k ndash ε and k-ω provide poor heat transfer results for the stagnation region where
they can have 30 error from the correct value The Realizable k ndash ε model provides
14
better heat transfer results while still maintaining a low computational cost The highest
accuracy to cost ratio was achieved by the υ2f model where it predicts the heat transfer
coefficient for the surface with a minimum of 2 error while not being as expensive as
the other unsteady models such as DNS and LES Ideally the CFD portion of this work
would be run with the υ2f model however since the code used to run the simulation
FLUENT does not have the υ2f model a realizable k ndash ε model will be used with
enhanced wall functions for both thermal and velocity gradients
15
CHAPTER THREE EXPERIMENTAL SETUP AND TECHNIQUES
31 Temperature Measurements with TSP
Temperature sensitive paint or TSP provides the capability of measuring
temperatures over the painted area This measurement technique supersedes the
advantages of other temperature measurement devices such as thermocouples because it
provides the user with data over a large area rather than point temperatures given by
thermocouples
Uni-Coat TSP is purchased from ISSI It is very robust to different working
conditions Calibration done on one batch of paint can be used for multiple cans as the
product is highly consistent The paint is calibrated in a dark booth a painted coupon is
placed on the hot side of a thermoelectric heat pump working on the Peltier effect
thermal paste is used to minimize contact resistance between the hot side and the TSP
coupon Calibrated thermocouples are placed in between the TSP and the thermoelectric
heat pump A reference temperature and picture are taken and the calibration commences
At least 5 or 6 data points should be taken to form the calibration Intensity ratios are
taken between the hot and cold pictures They are then plotted versus their corresponding
temperature
The paint consists of fluorescent molecules suspended in a binder These
molecules with a certain wavelength of light will be exited to a higher energy level The
molecules then can dissipate some of the energy by transferring it vibrationally to its
neighboring binder particles and dissipate the remainder of the energy by radiating it as a
photon as the molecule comes down to its original ground state Since the amount of
16
energy that the particle can transmit to others through vibration is directly proportional on
temperature and the total initial energy is fixed by measuring the ratio of the intensity at
a known temperature (reference picture) and intensity of the unknown temperature
feeding it through the correlation the unknown temperature can be found to an
uncertainty of 1 K Figure 10 shows a simplified Jablonski diagram adapted from the
suppliers website The blue arrows signify the blue light used to excite the luminescent
molecule Tris(22rsquo-bipyridyl) Ruthenium(II) Chloride Hexahydrate with a shellac binder
in our case The shellac binder is impermeable to oxygen opposite of that found in PSP
due to PSP relying on the presence of oxygen for it to function Once the particle is
excited it can give off the energy in two different ways one is by emitting it back out as
another photon of the same energy and therefore wavelength The second mode of the
particle to lose its energy is through vibrational relaxation This second process is directly
dependent on the temperature ie the higher the temperature the higher the probability
for it to lose energy to its surroundings Once it loses some energy to the surrounding
particles it releases the remainder of the energy as a photon of less energy of that which
excited it originally hence why a long pass filter is installed in the CCD camera For a
more descriptive explanation of the way TSP works refer to Liu 2006
17
Figure 10 Simplified Jablonski Diagram (Adapted from ISSI Website)
Throughout the past two years there have been numerous projects at CATER that
have used TSP Painting surfaces with TSP should be done carefully by someone who
has experience with spray painting since every single can costs $500 A single can should
be able to paint an area the size of an acrylic plate that is 36rdquo wide and 24rdquotallThe
sidewalls and the target wall of the impingement channel were painted with the use of
less than one can Painting on different surfaces is difficult for example when painting
Rohacell the paint canister can be held very close to the surface while spraying due to
the surface being somewhat porous and rough however when painting straight onto
metal heater strips the can should be placed as far back as possible for the first run
Ideally for the first pass through only a slight mist should be applied If the can is being
held too close to the surface the paint will run Figure 11 shows a set of heater strips that
has been painted too closely leading the paint to drip down Ideally the paint would be
applied to the surface in as many coats as possible Of course this would be time
18
demanding and impractical therefore with the knowledge that I have gained through the
multiple TSP paintings on different surfaces I have compiled a list of TSP dos and
donrsquots
Dos
Clean the surface to be painted with acetone or break parts cleaner Break
parts cleaner is preferable over acetone as it does not leave an oily residual
after cleaning
Paint the first coat as thin as possible Most of the surface should not be
covered There should be an even mist of miniscule TSP circles This will
give the later coats something to attach to
When positioning the test section to paint make sure to wipe it one last
time as small dust particles may have attached to the surface
Stop if you see small bumps in the paint This is caused by dust particles
collecting all the paint around it while it is still wet due to surface tension
Clean the surface and repaint This should be noticeable in the first few
coats If you see this pattern happening do not continue thinking it will be
covered by future coats What will happen is the problem will get worse
and worse ultimately the surface will have to be cleaned again and
repainted
When painting test sections try to paint the smallest section as possible
This will not only save paint but will make it very simple for the post
processing code to crop out the unpainted areas
19
Let the finished painted surface to sit at least for 90 minutes after the last
coat before baking There have been problems when baking steel and
acrylic test sections with the paint cracking while baking right after the
last coat Normally the finished surface is left to dry overnight and baked
first thing in the morning
For test sections that are too large to be baked in the oven the heat gun
may be used Carefully place a thermocouple in a central location with
blue painters tape The heating should be uniform and should not take
more than 20 minutes of continuous blowing When the thermocouple
reaches 80-90 C the plate can be assumed to be baked To introduce a
factor of safety in the baking it does not hurt to bake it longer than it
normally takes
Once the test section is mounted and ready to run cover it with cloth that
does not let any light through This will protect the paint for further uses
This is especially important on test sections that can be used multiple
times like the ones found in this study
When the test is running turn off the LED lights This light is the most
damaging to the TSP as it degrades the quality of the fluorescent
molecules
If there is a particular head of the TSP can that you prefer over others you
can remove it once the can is empty It is difficult to get used to a single
kind of nozzle being able to transfer it from can to can is a must if
painting consistency is to be kept
20
Donrsquots
Do not clean a test section that has already been used with too much
acetone The acetone is volatile evaporating quickly cooling the test
section rapidly If this test section has had heaters attached to it and run
previously the acrylic will crack due to uneven stresses inside of it
If paint is dripping stop painting immediately Clean the surface and start
over Hold the can far from the surface in order for it not to drip
Do not use TSP to teach new apprentices undergrads or graduate students
how to paint Regular spray paint is two orders of magnitude lower in cost
while the painting process is exactly the same
Do not paint with the doors closed The paint contains carcinogens that
can harm the lungs Always use a respirator and keep the room well
ventilated In-situ painting and baking has not been tried however it may
be a real option if the test section is difficult to disassemble and easily
accessible to painting and baking
If there is a can of paint that contains too little paint for the test section
that needs to be painted try to find a new can The mixing of two different
cans of TSP can be dangerous at times however it has been noticed over
the years that ISSI provides a very robust and dependable product that
does not vary significantly from batch to batch
21
Figure 11 Heater Strips Painted with TSP Too Closely
32 Experimental Setup of Suction Channel
The impingement channel is fed under suction As seen in Figure 12 air enters
through the plenum it crosses the jet plate as it gains speed to form the jets
which then impinge on the target wall The flow then passes through a venturi
flow meter and finally through the blower into the atmosphere A bypass valve is
used to control the flow rate of the impingement channel
22
Figure 12 Flow Loop of Impingement Channel
The impingement channel consists of 15 streamwise rows of 3 spanwise jets each The
total width of the channel YcD is of 8 diameters while the streamwise spacing between
the rows is XD=5 the spanwise distance between the holes is of YD=2 Figure 13shows
the top view of the jet plate The plate is counter bored to ensure that a nearly flat
velocity profile of the jet is achieved Figure 14 shows the front view of the channel Z is
denoted as the distance between the jet and target plates Side walls are interchangeable
to change the height of the channel to 6 8 and 10 diameters Two thirds of the
streamwise rows can be covered to change the XD from 5 to 15
Figure 13 Top View of Jet Plate
23
Figure 14 Front View of Impingement Channel
The target and sidewalls had heaters made specifically for them in a serpentine
style This was necessary to increase the resistance as the VARIACs used to power them
only had a maximum current output of 20 amps The heater strips are two diameters
wide at each end copper tape with conductive adhesive was used to connect the leads to
the power supply The heater consists of 50 micron thick steel sheet sandwiched between
two pieces of Kapton tape The heater is attached to the painted surface with the use of
double sided Kapton tape The target test section can be seen in Figure 15 also seen in
this figure are the two Teflon gaskets lined on the sides of the target plate With the target
wall bolted onto the sidewall the gasket is compressed generating a strong seal
Figure 15 Target Wall Test Section with Heater Leads
24
For this study the test matrix shown in Table 1 will be run Target and side wall
data will be taken at three different impingement heights at two different Reynolds
numbers of 7500 and 15000 denoted by A and B respectively A streamwise jet spacing
study is also done by testing the target and side wall heat transfer at an XD=15 for the
low impingement height channel
Table 1 Test Matrix
XD ZD Wall Re
5
10 TW
7500
15000
SW 7500
15000
8 TW
7500
15000
SW 7500
15000
6 TW
7500
15000
SW 7500
15000
15 6 TW
7500
15000
SW 7500
15000
33 Data Processing and Reduction
As described previously when taking temperature measurements with the use of TSP
reference temperatures are noted and a reference picture is taken The experiment is the
run once the experiment reaches steady state a new set of 4 pictures is taken Given the
calibration curve temperatures are backed out
25
Given the amount of heat generated inside the heater
Dividing by the heated area to get heat flux
Heat loss tests were run to consider how much of the heat flux generated by the heaters
goes through the backside instead of into the flow It was found that 25 of the heat flux
leaks out to the atmosphere through the acrylic In order to account for this heat leakage
it must be subtracted from the calculated value to become
Where Ah is the effective heated area given by
Where Aunheated is an estimate of how much unheated area is between the heater strips (~
3 of the total area)
To obtain heat transfer coefficient
Where Tref is the reference temperature Typically set in literature to be the jet
temperature
To obtain the average Reynolds number for the jets the total mass flow rate is used
Where Dj is the jet diameter and μ is dynamic viscosity (1983kgm s at 300K)
26
Pressure measurements were taken at the sidewall after the last jet entered the channel
These pressure measurements were used to determine the thermal performance of the
tallest two channels (ZD = 8 and 10)
The thermal performance at constant pumping power is found by using the equation
Where h is the average heat transfer coefficient for the target wall of them impingement
channel and ho is the heat transfer coefficient obtained by passing the same amount of
flow through a smooth duct ie the Dittus-Boelter correlation The friction factor f is
found with the use of
Where Ppl is the plenum static pressure assumed to be atmospheric and Plast jet is
the pressure read after the last jet V is the volumetric flow rate divided by the cross-
sectional area of the duct after the last impingement row The hydraulic diameter of the
channel is set to be
The baseline friction factor was calculated with the use of the Moody chart the hydraulic
diameter and the total mass flow rate though the channel Thermal performance at
constant pressure drop was also calculated with
27
34 Uncertainty Analysis
A simple uncertainty analysis was done to estimate the error in calculation of the
heat transfer coefficient from the given outputs of the test data From the bare basic
measurements for voltage area current temperature of thermocouples and temperature
profiles of paint a simple uncertainty analysis can be done to estimate the error for the
calculated heat transfer coefficient Figure 16 shows the different sources of error in the
calculation of heat transfer coefficient The effective uncertainty was calculated by taking
the root of the sum of the squares of all the individual percentage errors The
experimental uncertainty for heat transfer coefficient was of 703 This error may be
reduced by acquiring higher temperatures of the TSP reading current with a more
accurate ammeter or reading reference temperatures with the use of a thermopile instead
of a single thermocouple
Figure 16 Heat Transfer Coefficient Uncertainty Tree
28
35 Lateral Conduction Analysis
To take into account the lateral conduction occurring inside the heater foil while
the test is running two simple 1D conduction and convection equations were used to
quantify the amount of heat moving through the heater laterally and the amount of heat
convecting into the air The lateral conduction is expected to be at a maximum at the
places where there are large spatial variations of surface temperature which is why the
ZD = 6 XD = 5 case at high Re is chosen to be studied Figure 17 shows the
temperature distribution of the aforementioned case Four cold spots can be seen by their
distinct blue and yellow color located at the stagnation regions The maximum
temperature gradient occurs between the third jet impingement and the middle region
between jets The temperature difference was seen to be of 13degC The distance in between
these two temperatures is of 25D=01875m The corresponding heat flux between these
two points was calculated to be 13000Wm2 with ksteel~20Wm K A region of 1cm by
1cm was then created and the amount of heat calculated through conduction and
convection were compared To acquire the amount of heat removed through conduction
a heat flux of 13000Wm2 was imposed through an area of 01m by 00005m this
equaled to 00277 W The amount of heat moved through convection was calculated by
multiplying the heat flux used during the test by the area of the square 0001m2 the
resulting heat moving through the heater onto the air is 6 W Since the heat moving
through to the air is two orders of magnitudes larger than the heat moving laterally the
effective lateral conduction can be neglected
29
Figure 17 Temperature Profile of First Five Impingement Rows
A second order approach was also taken to quantify the amount of lateral
conduction in the heater The temperature gradient was taken from high peaks in heat
transfer caused by the second row of impingement of the same ZD=6 XD=5 channel at
high Re Figure 18 shows the high heat transfer coefficients created by the second row of
jets A quadratic curve fit was obtained by for this small region so that a continuous
equation of heat transfer coefficients as a function of streamwise distance was quantified
30
Figure 18 Detailed View of First Heat Transfer Peak with a Polynomial Curve Fit
The net heat gained by a differential volume from lateral conduction is the
difference in the temperature gradient at the entrance and the exit multiplied by the
thermal conductivity and cross sectional area Using this method shown in Figure 19 the
net change in convective heat transfer due to lateral conduction can be studied
Figure 19 Control Volume Heat Transfer Analysis
By taking the difference between the out flowing heat trough the right side and
the inflowing heat from the left side a net gain or loss can be found Figure 20 shows the
y = -470630x2 + 31244x - 14842Rsup2 = 09934
300
310
320
330
340
350
360
370
380
0 001 002 003 004 005
HTC
(W
m2K
)
x (m)
Heat Transfer Peak
Poly (Heat Transfer Peak)
31
difference in magnitude between the out flowing heat through convection seen in red and
the net inflow of heat from lateral conduction in blue From these calculations it was also
found that the amount of heat moving through lateral conduction is tow orders of
magnitude smaller than the amount of heat moving out through convection leading to the
belief that even at high temperature gradients lateral conduction does not play an
important role in the ongoing heat transfer processes in the impingement channel A more
detailed calculation of this work can be seen in appendix A
Figure 20 Heat Loss through Convection and Lateral Conduction
002 003 004 0051 10
5
1 104
1 103
001
qconv x( )
qnet x( )
x x
32
CHAPTER FOUR HEAT TRANSFER RESULTS
41 Heat Transfer Validation
In order to obtain confidence in our experimental setup an experiment was made
to test something that has already been published in literature A smooth channel was the
obvious choice as it was easy to setup by taking off the end cap and blocking all the holes
with smooth blue painters tape on the flow side and metal tape on the plenum side to
ensure no leaks into the channel from the jet plate The smooth channel has been studied
widely and multiple correlations exist one of these equations is the Dittus-Boelter
correlation (Incropera 2007) The test was run using the ZD=6 side wall so that the
hydraulic diameter was a minimum Figure 21 shows the span averaged results versus
non dimensional distance into the channel
Figure 21 Validation Spanwise Averaged Results
0
10
20
30
40
50
60
0 1 2 3 4 5 6 7 8 9
HTC
(W
m2K
)
XDc
Span Avg
Dittus Boelter
33
The plot shows decreasing heat transfer coefficient with increasing XDc due to
the developing thermal boundary layer The span average does not reach the Dittus-
Boelter due to it not being fully developed in the limited space it is given Typical flows
can take up to 60 diameters to achieve a fully developed profile with the current setup
the maximum length of the channel was of 9 diameters The profile however seems to
have an asymptote at the Dittus-Boelter correlation value leading to the belief that if the
channel was longer that value given by the correlation would be reached One important
factor to take into account in determining whether the experimental setup is validated is
the fact that the Dittus-Boelter correlation has an uncertainty near 30 Since the span
average at high XDc is well within 30 from the calculated value it is safe to assume
that the current experimental setup is validated
42 Heat Transfer Results
Heat transfer results are compared based on variations in channel height and
average jet Reynolds number As discussed earlier there are numerous other parameters
also affecting the heat transfer in these channels As these parameters are changed flow
structures within the channel are expected to be altered as well as discussed in the
literature Two of the major contributors to heat transfer in these channels are the
successful jet impingement and the resulting cross flow The same domain is captured in
both the local and averaged results
Figure 22 through Figure 25 highlights the heat transfer distribution for the cases
with a jet to jet spacing of 5 diameters in the streamwise direction and of 2 in the
spanwise direction It is evident that the smallest channel height (ZD=6) performs the
best at all Reynolds numbers on all surfaces It is also interesting to note the similarity
34
in the target wall profiles between case 528A and B where the curves are very similar
other than the obvious offset due to the change of the Reynolds number At this large
spacing we also see the degradation of the jets a few diameters downstream of each
impingement location The downstream shifts of the peaks are evident after the second
and third row of jets Also evident in these plots is the deflection of the impinging jet and
the wall jets from the cross flow The cross flow is forced to flow around the jet
deflecting the spread of the wall jet in the downstream direction Impingement locations
are also very evident at low XD however as XD and therefore the cross flow increase
the magnitude of the peaks start decreasing and eventually level out to pure internal flow
Figure 22 Target Wall Heat Transfer Coefficient Distributions
35
Figure 23 Span-averaged Target Wall Heat Transfer Distribution
36
Figure 24 Side Wall Heat Transfer Coefficient Distributions
37
Figure 25 Span-averaged Side wall Heat Transfer Distribution
Figure 23 and Figure 25 show similar details with impingement peaks clearly
diminishing and shifting in the downstream direction The cross flow clearly has some
negative influence on these geometries when compared to the more traditional
impingement highest on the order of 1 to 5 jet diameters The heat transfer profiles of the
target wall for all heights seen in Figure 22 and Figure 24 show the rapid decay in heat
transfer after the third jet This can be explained by understanding that the first jet does
not have any cross flow to deflect it the second jet only has the first jet worth of
momentum deflecting it downstream however since the channel is so tall the
momentum of the cross flow after the first and second jet are not enough to greatly
disturb the incoming jets After the third jet however the cross flow builds up enough
momentum to greatly affect the integrity of the jets downstream causing the span-
0
20
40
60
80
100
120
140
160
2 12 22 32 42 52 62 72
HTC
(W
m2K
)
XD
5210B_SW 528A_SW Jet Location
526A_TW 526B_TW
38
averaged heat transfer to rapidly drop The point at which the crossflow starts taking a
considerable effect occurs around XD =35 The target wall profile of the ZD=10
channel shows the outside jets on the second row of jet deflecting downstream It can be
conjectured that the bending of the outside jets downstream is caused by the wall jet
created by the first row of jets separating from the side wall and deflecting the outside
jets of the following rows of jets The heat transfer profile for the ZD case excludes the
first jet due to shadows being present when the data was taken
Also evident from this spanwise averaged data is the increase in heat transfer
with increases in Reynolds numbers and decreases in impingement height Results tend
to be the closest from case to case at the first impingement jet This is a reasonable
result as the effects of cross flow have little to no effect at the first few impingement
locations The impact of the jet would then be the driving force at these locations and
would be similar between cases except if the potential core is not reaching the target
surface The potential core of a jet tends to last between 6 and 10 diameters from its
origin It can be seen that the difference in heat transfer coefficient in the first two jets for
the ZD=8 and ZD=10 channel is much different than the corresponding difference
between the ZD=6 and ZD=8 heights This decreased difference between the heights of
the peaks may be attributed to the potential core reaching the target wall at the heights of
6 and 8 diameters leading to similar profiles and may not be reaching the surface at the
height of 10 diameters The heat transfer values of the peaks diminish in the downstream
direction The range of fluctuation also drops that is the profile becomes more uniform
at large XD This drop in fluctuation is more visible at the tallest channel height
(ZD=10) and less pronounced at the smallest channel This is due to the jet in the small
39
channel having to travel a shorter distance to impinge on the target plate leaving the
crossflow less time for it to deflect the jet as opposed to the tall channel where the jet has
to travel almost twice the distance as the ZD=6 channel for it to impinge on the target
wall This effect cannot be solely explained by the built up cross flow in the channel
Mixing loses also take part in the degradation of the stagnation size of the downstream
jets The mixing losses have much greater effect on the taller channels due to the same
reason that the cross flow has a higher impact on them too the jets have to travel a large
distance before hitting the target plate leading the stagnant or moving surrounding air to
be a sink of its downward momentum for a longer time and distance than the respective
smaller channels The heat transfer coefficient of the side wall was also analyzed
Similar effects are expected on the side wall due to the expected impact of the wall jet
As expected the strength of the cross flow is not enough to prevent wall jets from
successfully impacting the side wall at small XD jet locations however the crossflow
takes dominance at around XD=25 Also evident in these plots is the concentration of the
wall jet impact to the bottom of the channel on the order of 1-2 diameters in height It is
interesting to note that for the 5210B case in Figure 24 as the first jet diffuses outward
it impacts the sidewall at a height of ZD=6 The height at which the diffused jet affects
the sidewall heat transfer coefficient decreases as the crossflow increases The stagnation
regions are also deflected in the downstream direction similar to the target surface
results These effects are most evident in the 5210B Similar characteristics can be
explained from the spanwise-averaged plots shown in Figure 25 These results again
clearly show the effects of increasing the impingement height and increases in Reynolds
number As the height is increased the effect of the wall jet is significantly reduced
40
partially due to the increased surface area much of which is not affected by the wall jet
The diminishing effect of the cross flow accumulation is also evident in these plots as the
heat transfer peaks decrease in the downstream direction
43 XD Comparisons
The streamwise jet spacing was changed from XD=5 to 15 by covering two out
of three rows of jets This was done by covering the impingement holes inside the
channel with smooth blue painters tape and sealing the plenum side of the jet plate with
metal tape to ensure no leakage The profile is expected to be less uniform than the case
where XD=5 due to the large spreading of the high heat transfer peaks Due to the large
separation between the rows of jets there is a lower amount of downward momentum
than the equivalent XD=5 geometry for this reason it is expected to see a lower heat
transfer peak due to the jets momentum diffusing out faster to the stagnant air decreasing
the effective impingement velocity Figure 26 shows the target wall heat transfer
distribution Similar to the XD=5 profile it can be seen that the heat transfer due to the
jet impingement drastically reduces after the third jet This phenomenon leads us to
believe that at both Reynolds numbers the cross flow generated by the first three jets is
powerful enough to effectively deflect the fourth jet downstream diminishing its heat
transfer performance The similarity seen in Figure 26 between high and low Reynolds
number implies that the downstream deflection of the jets is not dependent on the jet
Reynolds numbers
41
Figure 26 XD=15 Target Wall Heat Transfer Profile
42
Figure 27 XD=15 Span-averaged Target Wall Heat Transfer Distribution
On the span averaged plots seen in Figure 27 the downstream deflection of the
jets is evident however as described previously the shifts in the peaks of heat transfer
occur at the same xD for both Reynolds numbers The amplitude of fluctuation of heat
transfer coefficients for the high Reynolds number case is larger than that of the low
Reynolds number Both profiles seem to start to level off at the end of the impingement
channel with the lowest span average being located just before the fourth jet at both
Reynolds numbers
A comparison of target wall heat transfer coefficients between XD =15 and 5 is
shown in Figure 28 At first glance it is clearly visible that the XD=15 average heat
transfer coefficient is smaller than its XD=5 counterpart This is also noticed by Ricklick
where he showed average HTC profiles for larger XD to be smaller than those at lower
XD (Ricklick 2009) This may occur due to there not being as high downward
0
50
100
150
200
250
300
350
0 20 40 60 80
HTC
(W
m2
K)
XD
Low Re
High Re
Impingement Location
43
momentum for the XD=15 case as compared to the XD=5 due to the lack of close jets
The stagnant air around the spaced out jets is taking away more of its momentum
decreasing the effective impingement Reynolds number Also important to notice is the
fact that since the XD=5 case has three times the flow impinged into it the cross flow
velocity and therefore Reynolds number will be three times as large increasing the heat
transfer coefficient
Figure 28 Target Wall Span-average Comparison of XD=5 and 15 at High Re
The side walls also show similar patterns to their XD=15 counterparts Strong
wall jet impingement can be seen on the side wall at low xD and zD Figure 29 shows
areas where the wall jet generated by the target wall impinges on the sidewall Similar to
the profile seen in Figure 24 the high heat transfer region reaches upward in the z
direction up to a height of 4-5 diameters for the first jet This high heat transfer stagnation
region decreases as xD increases to the point where the wall jet created by the last jet is
negligible when coupled with pure channel flow
0
50
100
150
200
250
300
350
400
0 10 20 30 40 50 60 70 80
HTC
(W
m2K
)
XD
XD = 5 XD = 15 Jet Location
- Blocked for XD =15
44
Figure 29 Side Wall Heat transfer Coefficient Profile
The span averaged plot seen in Figure 30 shows a nearly flat profile with peaks
located at the stagnation regions of the wall jets Thw downstream deflection for the
XD=15 case is much more pronounced than the one for the XD=5 case This is due to
the jet not being constrained by the wall jets generated by the previous and latter
impingement locations In the XD=15 case the wall jet is free to move downstream
more so than the XD=5 due to it not being disturbed by anything other than the cross
flow
45
Figure 30 XD=15 Side Wall Span-averaged Heat Transfer Coefficients
44 3D Comparison of the Heat Transfer Profiles
In order to further understand the targetsidewall interactions both heat transfer profiles
were positioned in an isometric view representative of the channel One important thing
to note is that both target and side wall profiles are not on the same scale This form of
data display is only qualitative way to describe the heat transfer profiles Figure 31 shows
the 3D profile of the XD=5 ZD=6 case The both stagnation regions of the jet onto the
target wall and the wall jet into the sidewall can be seen to occur at the same location for
the first three streamwise rows After the fourth and fifth row the wall jet diminishes in
magnitude Also visible in this view is the increasing heat transfer at low zD towards the
end of the channel of the side wall The constant input of mass and downward momentum
into the channel causes the cross flow generated by the previous jets to be squeezed into
the lower third of the channel increasing the velocity and the heat transfer of the target
wall
0
20
40
60
80
100
120
0 20 40 60 80
HTC
(W
m2K
)
XD
Low Re High Re Jet Locations
46
Figure 31 3D Heat Transfer Profile for ZD=6 XD=5
Similar patterns are seen in the taller ZD=8 channel seen in Figure 32 The wall jet
generate by the third streamwise row of jets is been deflected downward more than its
ZD=6 counterpart This can be attributed to the fact that the jet located at the ZD=8
channel has lost much of its momentum and is more easily bent downstream by the cross
flow generated by the first two jets The ZD=8 sidewall shows similar increasing heat
transfer at high xD however the increase is not as drastic as the one found in the ZD=6
channel This is caused due to the extra two diameters the jets have to cover to impinge
on the surface since the ZD=8 channel is one third larger than the ZD=6 one the flow
has to have more area to flow through The last few jets only deflect the cross flow
downward about 4 diameters this leaves two diameters for the flow to pass through on
the ZD=6 channel causing the velocity to increase rapidly and therefore increasing the
heat transfer coefficient at the low zD Since the ZD=8 channel has four remaining
47
diameters for the flow to move through it does not deflect it as much as the ZD=6
channel does only increasing the cross flow velocity and resulting heat transfer
coefficient slightly over the area at low zD and high xD
Figure 32 3D Heat Transfer Profile for ZD=8 XD=5
The 3D heat transfer profile for ZD=6 and xD=15 channel seen in Figure 33 shows
similar details to those seen in the XD=5 channels The stagnation regions of the jet and
wall jet occur at the same x location for the first three rows of jets the wall jet generated
by the fourth row of jets is deflected downstream only generating as small region of high
convective coefficients at the side wall The region located at the top right corner of the
side wall is colored red signifying high heat transfer however this area is generated by
the heaters providing non uniform heat flux at this location This region of high heat
transfer coefficients also occur at xD=0-4 of the target wall where the heater coil bends
48
Figure 33 3D Heat Transfer Profile for ZD=6 XD=15
45 Thermal Performance Calculations
Thermal performance calculations were done on the two tallest channels (ZD=8 and 10)
The pumping power was calculated for both channels at two Reynolds numbers Figure
34 shows the ratio of pressures required to pull the same amount of flow through as
smooth duct as opposed to through the jet plate The ZD=10 channel at high Reynolds
number requires the largest pressure as seen in the Figure however in order to pull the
same amount of flow rate through it requires a smaller pressure difference due to the
large cross section
49
Figure 34 Pressure Drop Ratio with Respect to Smooth Channel
Next the heat transfer enhancement was calculated A total area averaged heat
transfer coefficient was taken for the target wall and compared to the smooth channel
Dittus-Boelter value while using the same total mass flow rate Figure 35 shows an
average heat transfer enhancement of four times that of a smooth channel Similar trends
were noticed in the literature (Ricklick 2009) of decreasing heat transfer enhancement
with an increase of jet Reynolds number Ricklick also showed an increase in heat
transfer enhancement with an increase of jet to target spacing similar to the one seen in
Figure 35
0
10
20
30
40
50
60
528A_TW 528B_TW 5210A_TW 5210B_TW
PP
o
50
Figure 35 Heat Transfer Enhancement
Thermal performances at constant pressure drop were then calculated by dividing
the heat transfer enhancement by the pressure increase As seen in Figure 36 all the
values fall well below 1 making the impingement channel an unfeasible mode of heat
transfer enhancement when a constant pressure is supplied
Figure 36 Thermal Performance at Constant Pressure Drop
0
05
1
15
2
25
3
35
4
45
528A_TW 528B_TW 5210A_TW 5210B_TW
hh
o
0
002
004
006
008
01
012
014
528A_TW 528B_TW 5210A_TW 5210B_TW
(hh
o)
(PP
o)
51
The thermal performance at constant pumping drop was calculated in the same
way that the constant pressure drop was calculated the only difference being the pressure
ratio term was raised to the one third power As seen in Figure 37 the thermal
performances at constant pumping power are all higher than unity this signifies that if a
surface needs to be cooled with the supply of a constant pumping power the
impingement channel is a feasible option Similar to the figure literature (Ricklick 2009)
showed a decrease of thermal performance with an increase of channel height and
Reynolds number
Figure 37 Thermal Performance at Constant Pumping Power
0
02
04
06
08
1
12
14
528A_TW 528B_TW 5210A_TW 5210B_TW
(hh
o)
(PP
o)1
3
52
CHAPTER FIVE COMPUTATIONAL FLUID DYNAMICS
51 Problem Setup
In order to further enhance the understanding of the heat transfer profiles showed
previously a computational study was performed Even though CFD does not yield
accurate quantitative results it produces good qualitative data that can be used to explain
the flow physics in the channel and therefore increase the understanding of the patterns
seen previously The channel was meshed with the use of GAMBIT Due to the
symmetry the channel was split in half in the streamwise direction All horizontal
surfaces (parallel to the target wall) were divided into 6 different regions that are later on
going to be meshed individually The six regions are seen in Figure 38 section 1 is
located at the center of every jet also referred to as ldquojet centerrdquo This region was created
to reduce the squewness of the elements near the center of the jet by allowing the mesh to
be completely linear with a squewness of zero Section two complements section 1 to
complete the impingement hole The half impingement hole located at the symmetry wall
contains the same exact region 2 however it only has one half of the jet center Section 3
was made in order to bring the polar geometry of the holes to match the cartesian aspect
of the remainder of the channel With the addition of section 3 to the channel the only
remaining sections are square or rectangular regions Region 4 lies in between
streamwise rows of jets Section 5 is located at the entrance and the exit of the channel
These sections are not square in contrast with section 4 The last remaining section is
located near the side wall of the channel extending from the beginning to the exit of the
channel
53
Figure 38 Horizontal Plane of Impingement Channel Geometry
All the faces of sections 1 and 2 are linked throughout the channel and the
plenum however in order to have greater control of the mesh in the plenum and the
channel the remaining sections 3 4 5 and 6 are not linked to every single similar face
instead they are only linked to similar faces in either the plenum or the channel
Boundary layer spacing number of rows and growth factor are placed around the
channel In order to maintain a y+ of less than unity the first cell spacing of the boundary
layer inside the channel was set to be 000001 m (01mm) This first cell spacing yielded
y+
values varying between zero and 9 at the target side and front end wall Figure 39
shows a contour of y+ values on the heated walls The maximum values occur near the
impingement locations as expected due to large shear caused by the steep velocity
gradient normal to the wall On the downstream direction the y+ also increases due to the
increase of flow rate and therefore the increased skin friction on the wall At the
impingement location of the first jet the y+ is close to zero due to the velocity having its
direction mostly normal to the surface yielding no shear
54
Figure 39 Target Side and Front End Wall y+ Values
Once the faces were linked edge meshes were created on the sides of the jet center
Section 2rsquos inner edge was also meshed using a different parameter than the one used for
the jet center in order to allow for more freedom when trying to refine the mesh These
two edge meshes is followed by meshing all of section 2 faces alongside all the jet
centers Once these were complete section 3rsquos inner edge was meshed with different
parameters for the channel and plenum Sections 4 and 5 sides that connected with the
face made by section 6 were meshed so that their spacing was similar again the plenum
and channel were meshed separately for increased control of mesh density in both of
these areas The upstream-most edge of section 6 was meshed so that the spacing is
similar to the edge mesh in sections 4 and 5 this was done in order to have aspect ratios
of the wall be as close as possible to unity Sections 3 4 5 and 6 were meshed on both
the channel and the plenum With the entire target wall plane meshed these surface
meshes are coopered upwards to connect to the opposite wall The vertical spacing has
55
also been set up differently between the channel and the plenum The holes and the
plenum were also coopered The finished mesh was then exported as a msh file
Boundary conditions were set in GAMBIT once the mesh was imported into
Fluent values were set to every face depending on their location and purpose Figure 40
shows the four different boundary conditions Face 1 (blue) was set to be a mass flow
inlet The flow rate is half of the total flow rate at a given jet Reynolds number due to it
being only half of the entire domain Face 2 (yellow) is a symmetry plane face 3 (red) is
a pressure outlet at zero gauge pressure The rest of the faces in the channel denoted by
the number 4 (white) are set to walls The target side and front end wall had a heat flux
applied to them equal to 10000Wm2
Figure 40 Finished Mesh with Boundary Conditions
The model was imported into Fluent It was scaled down by a factor of 1000 due to it
being made in GAMBIT in millimeters The energy model was turned on The Realizable
k-ε model was used with enhanced wall functions on both the pressure and thermal
gradients The boundary conditions were set as discussed previously the mass flow inlet
was set to the specific flow rate normal to the surface the heat fluxes were set on the
56
heated walls the outflow gauge pressure was set to zero Two important reference values
characteristic length and reference temperature were set to be the diameter of the jet
(0075m) and 300K respectively The spatial discretization parameters were set to second
order upwind for momentum turbulent kinetic energy turbulent dissipation rate and
energy The under-relaxation factors were set to default Four monitors were created to
aid in the determination of convergence two of them read Nusselt numbers at the
stagnation region of the first and last jet the remaining two read the exit velocity at the
first and last jet The continuity x y and x velocities and energy equations residuals
were set to be 1E-6 while k and ε residuals were set to 1E-4 The solution was initialized
on the all zones at 1ms in the positive x direction The solution was set to autosave every
100 iterations while keeping only the two newest dat files The calculation was then run
for a maximum of 7000 iterations
A grid independence study was done on the domain to find the optimal size of
mesh that provides the correct solution while minimizing the compute time Two
monitors were set to check for grid independence both of them were vertex maximum
One of them read the Nusselt number at the impingement location of the first center jet
while the second one measures the velocity at the exit of the last jet Four different mesh
sizes were run to the convergence criterion explained before their sizes were 900000
15 million 28 million and 43 million cells
57
Figure 41 Grid Independence Study
It can be seen in Figure 41 that the difference between the 28 and 43 million cell
meshes are very small a difference of under 006 for velocity and 7 for Nusselt
number It can be safe to assume that the 28 million cell mesh is large enough to provide
a mesh independent solution The GAMBIT journal file used to create this mesh is
attached to the appendix The results shown hereafter are the ones obtained by the 28
million cell mesh
Figure 42 Residual Plots for the 26M Cell Run
67
69
71
73
75
77
79
81
83
85
485
4855
486
4865
487
4875
488
4885
489
0 1 2 3 4 5
Nu
sse
lt N
um
be
r
Cell Ammount (Millions)
Grid Independence Study
Velocity
Nusselt Number
58
For future reference Figure 42 shows the residuals of the 26M cell calculation
Up until around 4400 iterations the residuals were increasing shortly thereafter the
residuals started decreasing until it converged just after 5500 iterations All runs for the
differently sized meshes had the same residual patters with the peak of residuals and
point of convergence happening at different iterations
52 CFD Results
As describe previously all the results shown here are for the mesh containing 28 million
elements Figure 43 shows the total pressure contours It can be seen that the plenum
portion is at a constant total pressure Once the jets form since there are very small losses
in the jets due to the wall friction the total pressure still remains constant Only when the
jets enter the channel and start mixing with the cross flow is that they start losing the total
pressure head It is important to notice how the first two jets have the total pressure close
to the plenum arriving at the target wall This implies a successful impingement of the
undisturbed potential core As we move downstream the total pressure is lost quite
rapidly as the jets interact with the cross flow
Figure 43 Total Pressure Contours
59
Similar details can be drawn out from Figure 44 it can be seen that the first three
jets successfully impinge on the target wall while the rest of the downstream ones are
deflected by the cross flow As mentioned by Ricklick the velocity magnitude of the last
jet is larger than that of the first jet due to there being a lower static pressure at the end of
the channel providing it with a steeper pressure gradient hence higher velocity
Figure 44 Velocity Magnitude Contours
Turbulent kinetic energy was plotted in Figure 45 it is expected to have the
highest turbulent kinetic energy near the exit of the holes where the stagnant air is in
contact with the fast moving jet The mixing between the two regimes causes very
energetic eddies to form potentially enhancing the target and side wall heat transfer
coefficient As cross flow builds up towards the end of the channel the turbulent kinetic
energy increases due to larger overall velocities and fluctuations between the cross flow
and jets
60
Figure 45 Turbulent Kinetic Energy Contours
As Ricklick showed in his work the static temperature rise is quite small for such a small
channel It can be seen in Figure 46 that the driving temperature for heat transfer is that of
the plenum It is important to notice that a wall heat flux of 10000 Wm2 was used as the
boundary condition Not even in the most powerful tests would we ever use heat fluxes
that high they normally range between 2500 to a maximum of 7000 Wm2 A heat flux of
10000 Wm2 will increase the temperature at a faster rate than what it is normally used in
experimental testing
Figure 46 Static Temperature Contours
61
Figure 47 Target and Side Wall Heat Transfer Coefficient Contours
Figure 47 shows the target and sidewall heat transfer profiles Peaks can be seen at the
first three locations similar to that seen in Figure 22 The trend decreases rapidly to
eventually become a slowly increasing heat transfer profile due to the increase of mass
flow through the channel The sidewall provides the same results clear peaks in heat
transfer where the wall jets impinge on the sidewall seen in Figure 48 in more detail The
sidewall also shows a recirculation zone in between the first row of jets and the end wall
This is caused by the wall jet from the first row hitting the back wall moving upwards in
a circular pattern and coming back down when it encounters the first impingement row
Figure 48 Closer View of First few Rows of Impingement HTC Contours
62
Figure 49 Pathlines Generating from the First Row of Jets
Figure 49 helps explain the low heat transfer region between the first row of jets and
the end wall Pathlines are generated at the exit of each hole in the first row As the
air impinges on the surface half of it moves downstream and the other half movers
upstream to this recirculation zone where it circulates for a period of time before
reuniting with the remainder of the flow to move downstream The wall jet that
moves towards the second row of jets encounters the wall jet created by the second
row of jets causing the pathlines to drastically move upwards On the side of the
channel the pathlines behave erratically with no clear pattern clearly signifying the
highly turbulent and chaotic flow structure of this impingement channel
63
CHAPTER SIX CONCLUSIONS
It has been seen from this analysis that the side walls provide significant heat
transfer in an impingement channel especially at the relatively smaller channel
height This is primarily the result of successful impact of the wall jet with the side
walls It was shown that the tallest channel (ZD=10) has the most uniform profile with
low heat transfer coefficients when compared to the other channels The peaks of the
ZD=6 and 8 channels have a very similar profile which may indicate the successful
impingement of the potential core of the jet on the target surface As XD increases the
peaks diminish and a positive slope profile is attained by the increase of cross flow
velocity as more and more jets are introduced Tall impingement channels provide the
user with a heat transfer profile that is more uniform than those provided with the use of a
smaller channel while still maintaining higher convective coefficients when compared to
a smooth flow scenario The downstream shift of the wall jets is found to be independent
of Reynolds number and heavily dependent on streamwise position It was also found that
at XD=15 the wall jets decay faster than their XD=5 counterparts From the 3D heat
transfer profiles it was seen that the cross flow generated by multiple upstream jets is
deflected downward decreasing its effective flow area increasing its velocity hence
providing higher convective coefficients at the side wall at high xD and low zD
64
APPENDICES
Appendix A
Lateral Conduction Consideration
Thickness of foil heater Heat flux
Sample volume width
Volumetric heat generation
Volume of sample volume
Temperature profile from the first row of impingement ONLY valid for 02ltxlt045
t 50m k 20W
m K qflux 6000
W
m2
1mm
V 2
t qvol
qflux
t
T x( ) 298Kqflux
470630 x2
31244x 14842 W
m2K
N 15
x 02045 02
N 102 047
002 003 004 005314
315
316
317
318
319
320
T x( )
x
A t
qnet x( ) A kxT x
m
d
d xT x( )
d
d
1
m
002 003 004 0050
5 105
1 104
15 104
2 104
qnet x( )
x
65
Now comparing the net heat gained by lateral conduction to heat generated and convected out
It can be seen that the lateral conduction into the sample volume is two orders of magnitude smaller than the heat removed by convection
qgen qvol V 6 103
W
qconv x( ) 2
qflux qnet x( )
002 003 004 0051 10
5
1 104
1 103
001
qconv x( )
qnet x( )
x x
66
Appendix B
This is the journal file run on gambit to generate the geometry faces links
boundary layer face and volume meshes as well as the boundary conditions
set diameter
$d=75
$zc=6($d)
$xc=80($d)
$yc=4($d)
$y=2($d)
$x=5($d)
$zp=5($d)
$ztot=($zc)+($d)+($zp)
$jcf=(13)
$ocf=2
Boundary layer constants
$first=01
$growth=12
$rows=4
Meshing constants
$NumbNodes=5
$Numbtelnodes=6
$PLobnodes=5
$Chobnodes=5
$Plbenodes=($NumbNodes(4)+$rows)
$plsqnodes=($NumbNodes(3))
$Pllsnodes=($NumbNodes+$rows)
$Nojetcells=10
$Chzdnodes=($zc$Nojetcells)($d)
$Plzdnodes=($zp$Nojetcells)($d)
Boundary layer constants for channel
$firstch=001
$growthch=12
$rowsch=8
$CHbenodes=($NumbNodes(4)+$rowsch)
$CHlsnodes=($NumbNodes+$rowsch)
volume create body width ($xc) depth ($yc) height ($ztot) offset ($xc2) ($yc2) ($ztot2) brick
volume create cylinder height ($ztot) radius1 ($d2) radius3 ($d2) offset ($x) 0 ($ztot2) zaxis frustum
volume cmove cylinder multiple 1 offset 0 ($y) 0
volume cmove cylinder volume3 multiple 14 offset ($x) 0 0
volume create jetplate width ($xc) depth ($yc) height ($d)offset ($xc2) ($yc2) ($d2+$zc) brick
volume split body volumes jetplate connected
volume split jetplate volumes cylinder volume3 volume4 volume5
volume6 volume7 volume8 volume9 volume10 volume11
volume12 volume13 volume14 volume15 volume16 volume17
67
volume18 volume19 volume20 volume21 volume22 volume23
volume24 volume25 volume26 volume27 volume28 volume29
volume30 volume31 connected
face create jetcenter width ($jcf$d) height ($jcf$d) offset ($x) 0 0 xyplane rectangle
face create jetcircle radius ($d2) xyplane circle
face move jetcircle offset ($x) 0 0
face create outbox width ($ocf$d) height ($ocf$d) offset ($x) 0 0 xyplane rectangle
face split outbox connected faces jetcircle jetcenter
face split jetcircle connected faces face1
face split outbox connected faces face1
face cmove jetcenter outbox jetcircle face222 face223 multiple 1 offset 0 ($y) 0
face cmove jetcenter outbox jetcircle face222 face223 face224 face225 face226
face227 face228 multiple 14 offset ($x) 0 0
volume delete jetplate lowertopology
face split face1 connected keeptool faces jetcircle jetcenter outbox
face222 face223 face224 face225 face226 face227
face228 face229 face230 face231 face232 face233
face234 face235 face236 face237 face238 face239
face240 face241 face242 face243 face244 face245
face246 face247 face248 face249 face250 face251
face252 face253 face254 face255 face256 face257
face258 face259 face260 face261 face262 face263
face264 face265 face266 face267 face268 face269
face270 face271 face272 face273 face274 face275
face276 face277 face278 face279 face280 face281
face282 face283 face284 face285 face286 face287
face288 face289 face290 face291 face292 face293
face294 face295 face296 face297 face298 face299
face300 face301 face302 face303 face304 face305
face306 face307 face308 face309 face310 face311
face312 face313 face314 face315 face316 face317
face318 face319 face320 face321 face322 face323
face324 face325 face326 face327 face328 face329
face330 face331 face332 face333 face334 face335
face336 face337 face338 face339 face340 face341
face342 face343 face344 face345 face346 face347
face348 face349 face350 face351 face352 face353
face354 face355 face356 face357 face358 face359
face360 face361 face362 face363 face364 face365
face366 face367 face368
face move jetcircle jetcenter outbox face222 face223 face224
face225 face226 face227 face228 face229 face230
face231 face232 face233 face234 face235 face236
face237 face238 face239 face240 face241 face242
face243 face244 face245 face246 face247 face248
face249 face250 face251 face252 face253 face254
face255 face256 face257 face258 face259 face260
face261 face262 face263 face264 face265 face266
face267 face268 face269 face270 face271 face272
face273 face274 face275 face276 face277 face278
face279 face280 face281 face282 face283 face284
face285 face286 face287 face288 face289 face290
face291 face292 face293 face294 face295 face296
face297 face298 face299 face300 face301 face302
face303 face304 face305 face306 face307 face308
face309 face310 face311 face312 face313 face314
68
face315 face316 face317 face318 face319 face320
face321 face322 face323 face324 face325 face326
face327 face328 face329 face330 face331 face332
face333 face334 face335 face336 face337 face338
face339 face340 face341 face342 face343 face344
face345 face346 face347 face348 face349 face350
face351 face352 face353 face354 face355 face356
face357 face358 face359 face360 face361 face362
face363 face364 face365 face366 face367 face368 offset 0
0 $ztot
THIS SPLITS THE TOP PLENUM FACE WITH THE FACES CREATED IN THE BOTTOM
face split face6 connected keeptool faces jetcircle jetcenter outbox
face222 face223 face224 face225 face226 face227
face228 face229 face230 face231 face232 face233
face234 face235 face236 face237 face238 face239
face240 face241 face242 face243 face244 face245
face246 face247 face248 face249 face250 face251
face252 face253 face254 face255 face256 face257
face258 face259 face260 face261 face262 face263
face264 face265 face266 face267 face268 face269
face270 face271 face272 face273 face274 face275
face276 face277 face278 face279 face280 face281
face282 face283 face284 face285 face286 face287
face288 face289 face290 face291 face292 face293
face294 face295 face296 face297 face298 face299
face300 face301 face302 face303 face304 face305
face306 face307 face308 face309 face310 face311
face312 face313 face314 face315 face316 face317
face318 face319 face320 face321 face322 face323
face324 face325 face326 face327 face328 face329
face330 face331 face332 face333 face334 face335
face336 face337 face338 face339 face340 face341
face342 face343 face344 face345 face346 face347
face348 face349 face350 face351 face352 face353
face354 face355 face356 face357 face358 face359
face360 face361 face362 face363 face364 face365
face366 face367 face368
THIS MOVES THE FACES THAT WE ARE USING TO PLIT THE BOTTOM PLENUM SURFACE
face move jetcircle jetcenter outbox face222 face223 face224
face225 face226 face227 face228 face229 face230
face231 face232 face233 face234 face235 face236
face237 face238 face239 face240 face241 face242
face243 face244 face245 face246 face247 face248
face249 face250 face251 face252 face253 face254
face255 face256 face257 face258 face259 face260
face261 face262 face263 face264 face265 face266
face267 face268 face269 face270 face271 face272
face273 face274 face275 face276 face277 face278
face279 face280 face281 face282 face283 face284
face285 face286 face287 face288 face289 face290
face291 face292 face293 face294 face295 face296
face297 face298 face299 face300 face301 face302
69
face303 face304 face305 face306 face307 face308
face309 face310 face311 face312 face313 face314
face315 face316 face317 face318 face319 face320
face321 face322 face323 face324 face325 face326
face327 face328 face329 face330 face331 face332
face333 face334 face335 face336 face337 face338
face339 face340 face341 face342 face343 face344
face345 face346 face347 face348 face349 face350
face351 face352 face353 face354 face355 face356
face357 face358 face359 face360 face361 face362
face363 face364 face365 face366 face367 face368 offset 0
0 -$zp
SPLITS THE BOTTOM FACE OF THE PLENUM WITH THE FACES THAT ARE USED TO SPLIT
face split face114 connected keeptool faces jetcircle jetcenter
outbox face222 face223 face224 face225 face226 face227
face228 face229 face230 face231 face232 face233
face234 face235 face236 face237 face238 face239
face240 face241 face242 face243 face244 face245
face246 face247 face248 face249 face250 face251
face252 face253 face254 face255 face256 face257
face258 face259 face260 face261 face262 face263
face264 face265 face266 face267 face268 face269
face270 face271 face272 face273 face274 face275
face276 face277 face278 face279 face280 face281
face282 face283 face284 face285 face286 face287
face288 face289 face290 face291 face292 face293
face294 face295 face296 face297 face298 face299
face300 face301 face302 face303 face304 face305
face306 face307 face308 face309 face310 face311
face312 face313 face314 face315 face316 face317
face318 face319 face320 face321 face322 face323
face324 face325 face326 face327 face328 face329
face330 face331 face332 face333 face334 face335
face336 face337 face338 face339 face340 face341
face342 face343 face344 face345 face346 face347
face348 face349 face350 face351 face352 face353
face354 face355 face356 face357 face358 face359
face360 face361 face362 face363 face364 face365
face366 face367 face368
COPIES THE FACES THAT WE USED TO SPLIT TO BOTTOM OF THE PLENUM TO THE TOP OF
THE CHANNEL
face cmove jetcircle jetcenter outbox face222 face223 face224
face225 face226 face227 face228 face229 face230
face231 face232 face233 face234 face235 face236
face237 face238 face239 face240 face241 face242
face243 face244 face245 face246 face247 face248
face249 face250 face251 face252 face253 face254
face255 face256 face257 face258 face259 face260
face261 face262 face263 face264 face265 face266
face267 face268 face269 face270 face271 face272
face273 face274 face275 face276 face277 face278
face279 face280 face281 face282 face283 face284
70
face285 face286 face287 face288 face289 face290
face291 face292 face293 face294 face295 face296
face297 face298 face299 face300 face301 face302
face303 face304 face305 face306 face307 face308
face309 face310 face311 face312 face313 face314
face315 face316 face317 face318 face319 face320
face321 face322 face323 face324 face325 face326
face327 face328 face329 face330 face331 face332
face333 face334 face335 face336 face337 face338
face339 face340 face341 face342 face343 face344
face345 face346 face347 face348 face349 face350
face351 face352 face353 face354 face355 face356
face357 face358 face359 face360 face361 face362
face363 face364 face365 face366 face367 face368 multiple 1 offset 0
0 -$d
NAME OF COPIED NEW FACES
face1104 face1105 face1106 face1107 face1108 face1109 face1110 face1111
face1112 face1113 face1114 face1115 face1116 face1117 face1118 face1119
face1120 face1121 face1122 face1123 face1124 face1125 face1126 face1127
face1128 face1129 face1130 face1131 face1132 face1133 face1134 face1135
face1136 face1137 face1138 face1139 face1140 face1141 face1142 face1143
face1144 face1145 face1146 face1147 face1148 face1149 face1150 face1151
face1152 face1153 face1154 face1155 face1156 face1157 face1158 face1159
face1160 face1161 face1162 face1163 face1164 face1165 face1166 face1167
face1168 face1169 face1170 face1171 face1172 face1173 face1174 face1175
face1176 face1177 face1178 face1179 face1180 face1181 face1182 face1183
face1184 face1185 face1186 face1187 face1188 face1189 face1190 face1191
face1192 face1193 face1194 face1195 face1196 face1197 face1198 face1199
face1200 face1201 face1202 face1203 face1204 face1205 face1206 face1207
face1208 face1209 face1210 face1211 face1212 face1213 face1214 face1215
face1216 face1217 face1218 face1219 face1220 face1221 face1222 face1223
face1224 face1225 face1226 face1227 face1228 face1229 face1230 face1231
face1232 face1233 face1234 face1235 face1236 face1237 face1238 face1239
face1240 face1241 face1242 face1243 face1244 face1245 face1246 face1247
face1248 face1249 face1250 face1251 face1252 face1253
THIS SPLITS THE TOP OF THE CHANNEL WITH THE NEW COPIED FACES
face split face209 connected keeptool faces face1104 face1105 face1106 face1107
face1108 face1109 face1110 face1111 face1112 face1113 face1114 face1115
face1116 face1117 face1118 face1119 face1120 face1121 face1122 face1123
face1124 face1125 face1126 face1127 face1128 face1129 face1130 face1131
face1132 face1133 face1134 face1135 face1136 face1137 face1138 face1139
face1140 face1141 face1142 face1143 face1144 face1145 face1146 face1147
face1148 face1149 face1150 face1151 face1152 face1153 face1154 face1155
face1156 face1157 face1158 face1159 face1160 face1161 face1162 face1163
face1164 face1165 face1166 face1167 face1168 face1169 face1170 face1171
face1172 face1173 face1174 face1175 face1176 face1177 face1178 face1179
face1180 face1181 face1182 face1183 face1184 face1185 face1186 face1187
face1188 face1189 face1190 face1191 face1192 face1193 face1194 face1195
face1196 face1197 face1198 face1199 face1200 face1201 face1202 face1203
face1204 face1205 face1206 face1207 face1208 face1209 face1210 face1211
face1212 face1213 face1214 face1215 face1216 face1217 face1218 face1219
face1220 face1221 face1222 face1223 face1224 face1225 face1226 face1227
71
face1228 face1229 face1230 face1231 face1232 face1233 face1234 face1235
face1236 face1237 face1238 face1239 face1240 face1241 face1242 face1243
face1244 face1245 face1246 face1247 face1248 face1249 face1250 face1251
face1252 face1253
THIS UNITES THE RECTANGLE OUTSIDE FACES AND THE SEMICIRCLE SO THAT IT MAKES
A RECTANGLE WIHOUT THE CENTERJET
face unite faces jetcircle face223 real
face unite faces face222 outbox real
face unite faces face228 face226 real
face unite faces face225 face227 real
face unite faces face231 face233 real
face unite faces face232 face230 real
face unite faces face236 face238 real
face unite faces face237 face235 real
face unite faces face241 face243 real
face unite faces face242 face240 real
face unite faces face248 face246 real
face unite faces face245 face247 real
face unite faces face253 face251 real
face unite faces face252 face250 real
face unite faces face256 face258 real
face unite faces face257 face255 real
face unite faces face263 face261 real
face unite faces face260 face262 real
face unite faces face268 face266 real
face unite faces face265 face264 real
face unite faces face265 face267 real
face unite faces face273 face271 real
face unite faces face272 face270 real
face unite faces face276 face278 real
face unite faces face277 face275 real
face unite faces face281 face283 real
face unite faces face282 face280 real
face unite faces face286 face288 real
face unite faces face287 face285 real
face unite faces face291 face293 real
face unite faces face292 face290 real
face unite faces face296 face298 real
face unite faces face297 face295 real
face unite faces face301 face303 real
face unite faces face302 face300 real
face unite faces face306 face308 real
face unite faces face307 face305 real
face unite faces face316 face318 real
face unite faces face312 face310 real
face unite faces face311 face313 real
face unite faces face315 face317 real
face unite faces face321 face323 real
face unite faces face322 face320 real
face unite faces face326 face328 real
face unite faces face327 face325 real
face unite faces face331 face333 real
face unite faces face332 face330 real
face unite faces face336 face338 real
72
face unite faces face337 face335 real
face unite faces face347 face345 real
face unite faces face346 face348 real
face unite faces face342 face340 real
face unite faces face341 face343 real
face unite faces face356 face358 real
face unite faces face357 face355 real
face unite faces face352 face350 real
face unite faces face351 face353 real
face unite faces face361 face363 real
face unite faces face366 face368 real
face unite faces face360 face362 real
face unite faces face365 face367 real
SPLITTING ALL THE FACES OF THE CIRCLES IN THE BOTTOM OF THE PLENUM
face split face912 connected keeptool faces face222
face split face117 connected keeptool faces face228
face split face117 connected keeptool faces face225
face split face922 connected keeptool faces face232
face split face124 connected keeptool faces face236
face split face124 connected keeptool faces face237
face split face932 connected keeptool faces face242
face split face131 connected keeptool faces face248
face split face131 connected keeptool faces face245
face split face942 connected keeptool faces face252
face split face138 connected keeptool faces face256
face split face138 connected keeptool faces face257
face split face952 connected keeptool faces face260
face split face145 connected keeptool faces face268
face split face145 connected keeptool faces face265
face split face962 connected keeptool faces face272
face split face152 connected keeptool faces face276
face split face152 connected keeptool faces face277
face split face972 connected keeptool faces face282
face split face159 connected keeptool faces face286
face split face159 connected keeptool faces face287
face split face982 connected keeptool faces face292
face split face166 connected keeptool faces face296
face split face166 connected keeptool faces face297
face split face992 connected keeptool faces face302
face split face173 connected keeptool faces face306
face split face173 connected keeptool faces face307
face split face1002 connected keeptool faces face312
face split face180 connected keeptool faces face316
face split face180 connected keeptool faces face315
73
face split face1012 connected keeptool faces face322
face split face187 connected keeptool faces face326
face split face187 connected keeptool faces face327
face split face1022 connected keeptool faces face332
face split face194 connected keeptool faces face336
face split face194 connected keeptool faces face337
face split face1032 connected keeptool faces face342
face split face201 connected keeptool faces face346
face split face201 connected keeptool faces face347
face split face1042 connected keeptool faces face352
face split face208 connected keeptool faces face356
face split face208 connected keeptool faces face357
face split face1052 connected keeptool faces face360
face split face215 connected keeptool faces face366
face split face215 connected keeptool faces face365
THIS UNITES THE RECTANGLE OUTSIDE FACES AND THE SEMICIRCLE SO THAT IT MAKES
A RECTANGLE WIHOUT THE CENTERJET
face unite faces face1104 face1108 real
face unite faces face1107 face1106 real
face unite faces face1113 face1111 real
face unite faces face1112 face1110 real
face unite faces face1118 face1116 real
face unite faces face1117 face1115 real
face unite faces face1123 face1121 real
face unite faces face1122 face1120 real
face unite faces face1128 face1126 real
face unite faces face1127 face1125 real
face unite faces face1133 face1131 real
face unite faces face1132 face1130 real
face unite faces face1138 face1136 real
face unite faces face1137 face1135 real
face unite faces face1143 face1141 real
face unite faces face1142 face1140 real
face unite faces face1148 face1146 real
face unite faces face1147 face1145 real
face unite faces face1153 face1151 real
face unite faces face1152 face1150 real
face unite faces face1158 face1156 real
face unite faces face1157 face1155 real
face unite faces face1163 face1161 real
face unite faces face1162 face1160 real
face unite faces face1168 face1166 real
face unite faces face1167 face1165 real
face unite faces face1173 face1171 real
face unite faces face1172 face1170 real
face unite faces face1178 face1176 real
face unite faces face1177 face1175 real
face unite faces face1183 face1181 real
74
face unite faces face1182 face1180 real
face unite faces face1186 face1188 real
face unite faces face1187 face1185 real
face unite faces face1193 face1191 real
face unite faces face1192 face1190 real
face unite faces face1198 face1196 real
face unite faces face1197 face1195 real
face unite faces face1203 face1201 real
face unite faces face1202 face1200 real
face unite faces face1206 face1208 real
face unite faces face1207 face1205 real
face unite faces face1213 face1211 real
face unite faces face1212 face1210 real
face unite faces face1216 face1218 real
face unite faces face1217 face1215 real
face unite faces face1221 face1223 real
face unite faces face1222 face1220 real
face unite faces face1228 face1226 real
face unite faces face1227 face1225 real
face unite faces face1233 face1231 real
face unite faces face1232 face1230 real
face unite faces face1238 face1236 real
face unite faces face1237 face1235 real
face unite faces face1243 face1241 real
face unite faces face1242 face1240 real
face unite faces face1248 face1246 real
face unite faces face1247 face1245 real
face unite faces face1253 face1251 real
face unite faces face1252 face1250 real
SPLITTING ALL THE FACES OF THE CIRCLES IN THE TOP OF THE CHANNEL
face split face1257 connected keeptool faces face1107
face split face115 connected keeptool faces face1113
face split face115 connected keeptool faces face1112
face split face1267 connected keeptool faces face1117
face split face122 connected keeptool faces face1123
face split face122 connected keeptool faces face1122
face split face1277 connected keeptool faces face1127
face split face129 connected keeptool faces face1133
face split face129 connected keeptool faces face1132
face split face1287 connected keeptool faces face1137
face split face136 connected keeptool faces face1143
face split face136 connected keeptool faces face1142
face split face1297 connected keeptool faces face1147
face split face143 connected keeptool faces face1153
face split face143 connected keeptool faces face1152
face split face1307 connected keeptool faces face1157
face split face150 connected keeptool faces face1163
face split face150 connected keeptool faces face1162
75
face split face1317 connected keeptool faces face1167
face split face157 connected keeptool faces face1173
face split face157 connected keeptool faces face1172
face split face1327 connected keeptool faces face1177
face split face164 connected keeptool faces face1183
face split face164 connected keeptool faces face1182
face split face1337 connected keeptool faces face1187
face split face171 connected keeptool faces face1193
face split face171 connected keeptool faces face1192
face split face1347 connected keeptool faces face1197
face split face178 connected keeptool faces face1203
face split face178 connected keeptool faces face1202
face split face1357 connected keeptool faces face1207
face split face185 connected keeptool faces face1213
face split face185 connected keeptool faces face1212
face split face1367 connected keeptool faces face1217
face split face192 connected keeptool faces face1221
face split face192 connected keeptool faces face1222
face split face1377 connected keeptool faces face1227
face split face199 connected keeptool faces face1233
face split face199 connected keeptool faces face1232
face split face1387 connected keeptool faces face1237
face split face206 connected keeptool faces face1243
face split face206 connected keeptool faces face1242
face split face1397 connected keeptool faces face1247
face split face213 connected keeptool faces face1253
face split face213 connected keeptool faces face1252
face split face1452 connected keeptool faces face224
face split face1456 connected keeptool faces face234
face split face1460 connected keeptool faces face244
face split face1464 connected keeptool faces face254
face split face1468 connected keeptool faces face264
face split face1472 connected keeptool faces face274
face split face1476 connected keeptool faces face284
face split face1480 connected keeptool faces face294
face split face1484 connected keeptool faces face304
face split face1488 connected keeptool faces face314
face split face1492 connected keeptool faces face324
face split face1496 connected keeptool faces face334
face split face1500 connected keeptool faces face344
face split face1504 connected keeptool faces face354
face split face1508 connected keeptool faces face364
DELETING ALL THE FACES USED TO MAKE THE CUTS
face delete jetcircle face222 face228 face225 jetcenter
76
face224 face231 face232 face236 face237 face229
face1456 face241 face242 face239 face248 face244
face245 face253 face249 face252 face254 face256
face257 face263 face259 face260 face268 face264
face265 face273 face272 face269 face276 face277
face274 face281 face282 face286 face279 face287
face284 face291 face292 face296 face297 face289
face294 face301 face299 face302 face306 face307
face304 face311 face312 face316 face315 face309
face314 face321 face322 face326 face327 face319
face324 face331 face332 face329 face336 face334
face337 face341 face342 face339 face346 face344
face347 face351 face352 face349 face356 face354
face357 face361 face359 face360 face366 face364
face365 lowertopology
face delete face1104 face1105 face1107 face1113 face1112
face115 face234 face1118 face1114 face1117 face1123
face1122 face122 face1138 face1128 face1127 face1124
face1133 face1132 face129 face1134 face1137 face1143
face136 face1142 face1148 face1144 face1147 face1153
face143 face1152 face1158 face1154 face1157 face1163
face150 face1162 face1168 face1164 face1167 face1173
face157 face1172 face1178 face1174 face1177 face1183
face164 face1182 face1186 face1184 face1187 face1193
face171 face1192 face1198 face1194 face1197 face1203
face178 face1202 face1206 face1204 face1207 face1213
face185 face1212 face1216 face1214 face1217 face1221
face192 face1222 face1228 face1224 face1227 face1233
face199 face1232 face1238 face1234 face1237 face1243
face206 face1242 face1248 face1244 face1247 face1253
face213 face1252 lowertopology
face delete face1109 face1119 face1129 face1139 face1149 face1159
face1169 face1179 face1189 face1199 face1209 face1219
face1229 face1239 face1249 lowertopology
face create CP1 width 600 height 75 offset 300 (225+($d)2) 0 xyplane rectangle
face create CP2 width 600 height 75 offset 300 (225+($d)2) ($zc) xyplane rectangle
face create CP3 width 600 height 75 offset 300 (225+($d)2) ($zc+$d) xyplane rectangle
face create CP4 width 600 height 75 offset 300 (225+($d)2) ($zc+$d+$zp) xyplane rectangle
face split face6 connected faces CP4
face split face114 connected faces CP3
face split face209 connected faces CP2
face split face1 connected faces CP1
GEOMETRY IS FINISHED
face modify face912 side vertex6437 vertex6436
77
face modify face1600 side vertex7302 vertex7303
face modify face117 side vertex6446 vertex6447
face modify face646 side vertex3312
face modify face646 side vertex3313
face modify face647 side vertex3432 vertex3433
face modify face372 side vertex2040 vertex2041
face modify face376 side vertex2100 vertex2101
face modify face377 side vertex2221 vertex2220
LINKING ALL THE JET CENTERS
face link face1450 face640 edges edge6949 edge3518 vertices
vertex6437 vertex3253 reverse
face link face1450 face1257 edges edge6949 edge7340 vertices
vertex6437 vertex6797 reverse
face link face1257 face370 edges edge7340 edge2139 vertices
vertex6797 vertex2041 reverse
face link face1257 face1454 edges edge7340 edge6975 vertices
vertex6797 vertex6461 reverse
face link face1454 face649 edges edge6975 edge3519 vertices
vertex6461 vertex3255 reverse
face link face1454 face1267 edges edge6975 edge7377 vertices
vertex6461 vertex6831 reverse
face link face1267 face379 edges edge7377 edge2141 vertices
vertex6831 vertex2043 reverse
face link face1267 face1458 edges edge7377 edge7001 vertices
vertex6831 vertex6485 reverse
face link face1458 face659 edges edge7001 edge3520 vertices
vertex6485 vertex3257 reverse
face link face1458 face1277 edges edge7001 edge7414 vertices
vertex6485 vertex6865 reverse
face link face1277 face389 edges edge7414 edge2143 vertices
vertex6865 vertex2045 reverse
face link face1277 face1462 edges edge7414 edge7027 vertices
vertex6865 vertex6509 reverse
face link face1462 face669 edges edge7027 edge3521 vertices
vertex6509 vertex3259 reverse
face link face1462 face1287 edges edge7027 edge7451 vertices
vertex6509 vertex6899 reverse
face link face1287 face399 edges edge7451 edge2145 vertices
vertex6899 vertex2047 reverse
face link face1287 face1466 edges edge7451 edge7053 vertices
vertex6899 vertex6533 reverse
face link face1466 face679 edges edge7053 edge3522 vertices
vertex6533 vertex3261 reverse
face link face1466 face1297 edges edge7053 edge7488 vertices
vertex6533 vertex6933 reverse
face link face1297 face409 edges edge7488 edge2147 vertices
vertex6933 vertex2049 reverse
face link face1297 face1470 edges edge7488 edge7079 vertices
vertex6933 vertex6557 reverse
face link face1470 face689 edges edge7079 edge3523 vertices
vertex6557 vertex3263 reverse
face link face1470 face1307 edges edge7079 edge7525 vertices
vertex6557 vertex6967 reverse
face link face1307 face419 edges edge7525 edge2149 vertices
78
vertex6967 vertex2051 reverse
face link face1307 face1474 edges edge7525 edge7105 vertices
vertex6967 vertex6581 reverse
face link face1474 face1317 edges edge7105 edge7562 vertices
vertex6581 vertex7001 reverse
face link face1474 face699 edges edge7105 edge3524 vertices
vertex6581 vertex3265 reverse
face link face1317 face429 edges edge7562 edge2151 vertices
vertex7001 vertex2053 reverse
face link face1317 face1478 edges edge7562 edge7131 vertices
vertex7001 vertex6605 reverse
face link face1478 face1327 edges edge7131 edge7599 vertices
vertex6605 vertex7035 reverse
face link face1478 face709 edges edge7131 edge3525 vertices
vertex6605 vertex3267 reverse
face link face1327 face439 edges edge7599 edge2153 vertices
vertex7035 vertex2055 reverse
face link face1327 face1482 edges edge7599 edge7157 vertices
vertex7035 vertex6629 reverse
face link face1482 face719 edges edge7157 edge3526 vertices
vertex6629 vertex3269 reverse
face link face1482 face1337 edges edge7157 edge7636 vertices
vertex6629 vertex7069 reverse
face link face1337 face449 edges edge7636 edge2155 vertices
vertex7069 vertex2057 reverse
face link face1337 face1486 edges edge7636 edge7183 vertices
vertex7069 vertex6653 reverse
face link face1486 face1347 edges edge7183 edge7673 vertices
vertex6653 vertex7103 reverse
face link face1347 face459 edges edge7673 edge2157 vertices
vertex7103 vertex2059 reverse
face link face1486 face729 edges edge7183 edge3527 vertices
vertex6653 vertex3271 reverse
face link face1347 face1490 edges edge7673 edge7209 vertices
vertex7103 vertex6677 reverse
face link face1490 face1357 edges edge7209 edge7710 vertices
vertex6677 vertex7137 reverse
face link face1490 face739 edges edge7209 edge3528 vertices
vertex6677 vertex3273 reverse
face link face1357 face469 edges edge7710 edge2159 vertices
vertex7137 vertex2061 reverse
face link face1357 face1494 edges edge7710 edge7235 vertices
vertex7137 vertex6701 reverse
face link face1494 face1367 edges edge7235 edge7747 vertices
vertex6701 vertex7171 reverse
face link face1494 face749 edges edge7235 edge3529 vertices
vertex6701 vertex3275 reverse
face link face1367 face479 edges edge7747 edge2161 vertices
vertex7171 vertex2063 reverse
face link face1367 face1498 edges edge7747 edge7261 vertices
vertex7171 vertex6725 reverse
face link face1498 face1377 edges edge7261 edge7784 vertices
vertex6725 vertex7205 reverse
face link face1377 face489 edges edge7784 edge2163 vertices
vertex7205 vertex2065 reverse
face link face1498 face759 edges edge7261 edge3530 vertices
79
vertex6725 vertex3277 reverse
face link face1377 face1502 edges edge7784 edge7287 vertices
vertex7205 vertex6749 reverse
face link face1502 face1387 edges edge7287 edge7821 vertices
vertex6749 vertex7239 reverse
face link face1387 face499 edges edge7821 edge2165 vertices
vertex7239 vertex2067 reverse
face link face1387 face1506 edges edge7821 edge7313 vertices
vertex7239 vertex6773 reverse
face link face1502 face769 edges edge7287 edge3531 vertices
vertex6749 vertex3279 reverse
face link face1506 face1397 edges edge7313 edge7858 vertices
vertex6773 vertex7273 reverse
face link face1506 face779 edges edge7313 edge3532 vertices
vertex6773 vertex3281 reverse
face link face1397 face509 edges edge7858 edge2167 vertices
vertex7273 vertex2069 reverse
LINKING ALL THE COMPLETE JETCENTERS
face link face1452 face644 edges edge7891 edge3773 vertices
vertex7303 vertex3433
face link face1452 face115 edges edge7891 edge7364 vertices
vertex7303 vertex6819
face link face1452 face1456 edges edge7891 edge7900 vertices
vertex7303 vertex7311
face link face1456 face654 edges edge7900 edge3774 vertices
vertex7311 vertex3435
face link face1456 face122 edges edge7900 edge7401 vertices
vertex7311 vertex6853
face link face1456 face1460 edges edge7900 edge7909 vertices
vertex7311 vertex7319
face link face1460 face1464 edges edge7909 edge7918 vertices
vertex7319 vertex7327
face link face1460 face129 edges edge7909 edge7438 vertices
vertex7319 vertex6887
face link face1460 face664 edges edge7909 edge3775 vertices
vertex7319 vertex3437
face link face1464 face674 edges edge7918 edge3776 vertices
vertex7327 vertex3439
face link face1464 face136 edges edge7918 edge7475 vertices
vertex7327 vertex6921
face link face1464 face1468 edges edge7918 edge7927 vertices
vertex7327 vertex7335
face link face1472 face1468 edges edge7936 edge7927 vertices
vertex7343 vertex7335
face link face1468 face143 edges edge7927 edge7512 vertices
vertex7335 vertex6955
face link face1468 face684 edges edge7927 edge3777 vertices
vertex7335 vertex3441
face link face1472 face694 edges edge7936 edge3778 vertices
vertex7343 vertex3443
face link face1472 face150 edges edge7936 edge7549 vertices
vertex7343 vertex6989
face link face1472 face1476 edges edge7936 edge7945 vertices
80
vertex7343 vertex7351
face link face1476 face1480 edges edge7945 edge7954 vertices
vertex7351 vertex7359
face link face1476 face157 edges edge7945 edge7586 vertices
vertex7351 vertex7023
face link face1476 face704 edges edge7945 edge3779 vertices
vertex7351 vertex3445
face link face1480 face714 edges edge7954 edge3780 vertices
vertex7359 vertex3447
face link face1480 face164 edges edge7954 edge7623 vertices
vertex7359 vertex7057
face link face1480 face1484 edges edge7954 edge7963 vertices
vertex7359 vertex7367
face link face1484 face171 edges edge7963 edge7660 vertices
vertex7367 vertex7091
face link face1484 face724 edges edge7963 edge3781 vertices
vertex7367 vertex3449
face link face1480 face1488 edges edge7954 edge7972 vertices
vertex7359 vertex7375
face link face1488 face178 edges edge7972 edge7697 vertices
vertex7375 vertex7125
face link face1488 face734 edges edge7972 edge3782 vertices
vertex7375 vertex3451
face link face1488 face1492 edges edge7972 edge7981 vertices
vertex7375 vertex7383
face link face1492 face744 edges edge7981 edge3783 vertices
vertex7383 vertex3453
face link face1492 face185 edges edge7981 edge7734 vertices
vertex7383 vertex7159
face link face1492 face1496 edges edge7981 edge7990 vertices
vertex7383 vertex7391
face link face1496 face754 edges edge7990 edge3784 vertices
vertex7391 vertex3455
face link face1496 face192 edges edge7990 edge7771 vertices
vertex7391 vertex7193
face link face1496 face1500 edges edge7990 edge7999 vertices
vertex7391 vertex7399
face link face1500 face1504 edges edge7999 edge8008 vertices
vertex7399 vertex7407
face link face1504 face1508 edges edge8008 edge8017 vertices
vertex7407 vertex7415
face link face1500 face199 edges edge7999 edge7808 vertices
vertex7399 vertex7227
face link face1500 face764 edges edge7999 edge3785 vertices
vertex7399 vertex3457
face link face1504 face774 edges edge8008 edge3786 vertices
vertex7407 vertex3459
face link face1508 face784 edges edge8017 edge3787 vertices
vertex7415 vertex3461
face link face1504 face206 edges edge8008 edge7845 vertices
vertex7407 vertex7261
face link face1508 face213 edges edge8017 edge7882 vertices
vertex7415 vertex7295
linking the jetcenters of the bottom of the channel one of them has to be reversed but the otherones are not
81
face link face115 face374 edges edge7364 edge2394 vertices
vertex6819 vertex2221 reverse
face link face374 face384 edges edge2394 edge2396 vertices
vertex2221 vertex2223
face link face384 face394 edges edge2396 edge2398 vertices
vertex2223 vertex2225
face link face394 face404 edges edge2398 edge2400 vertices
vertex2225 vertex2227
face link face404 face414 edges edge2400 edge2402 vertices
vertex2227 vertex2229
face link face414 face424 edges edge2402 edge2404 vertices
vertex2229 vertex2231
face link face424 face434 edges edge2404 edge2406 vertices
vertex2231 vertex2233
face link face434 face444 edges edge2406 edge2408 vertices
vertex2233 vertex2235
face link face444 face454 edges edge2408 edge2410 vertices
vertex2235 vertex2237
face link face454 face464 edges edge2410 edge2412 vertices
vertex2237 vertex2239
face link face464 face474 edges edge2412 edge2414 vertices
vertex2239 vertex2241
face link face474 face484 edges edge2414 edge2416 vertices
vertex2241 vertex2243
face link face484 face494 edges edge2416 edge2418 vertices
vertex2243 vertex2245
face link face494 face504 edges edge2418 edge2420 vertices
vertex2245 vertex2247
face link face504 face514 edges edge2420 edge2422 vertices
vertex2247 vertex2249
UP TO THIS POINT ALL THE FACES ARE CONNCTED SUCCESSFULLY
LINKING THE FIRST THREE JET TELEPHONES
face link face912 face117 edges edge6950 edge6960 vertices
vertex6437 vertex6446 reverse
face link face912 face1600 edges edge6950 edge7890 vertices
vertex6437 vertex7303 reverse
face link face912 face372 edges edge6950 edge2168 vertices
vertex6437 vertex2041
face link face117 face376 edges edge6959 edge2304 vertices
vertex6447 vertex2101 reverse
face link face1600 face377 edges edge7890 edge2423 vertices
vertex7303 vertex2221 reverse
face link face372 face382 edges edge2168 edge2169 vertices
vertex2041 vertex2043
face link face377 face387 edges edge2423 edge2424 vertices
vertex2221 vertex2223
face link face376 face386 edges edge2304 edge2306 vertices
vertex2101 vertex2103
face link face387 face397 edges edge2424 edge2425 vertices
vertex2223 vertex2225
face link face386 face396 edges edge2306 edge2308 vertices
82
vertex2103 vertex2105
face link face382 face392 edges edge2169 edge2170 vertices
vertex2043 vertex2045
face link face382 face392 edges edge2169 edge2170 vertices
vertex2043 vertex2045
face link face382 face392 edges edge2169 edge2170 vertices
vertex2043 vertex2045
face link face382 face392 edges edge2169 edge2170 vertices
vertex2043 vertex2045
face link face397 face407 edges edge2425 edge2426 vertices
vertex2225 vertex2227
face link face392 face402 edges edge2170 edge2171 vertices
vertex2045 vertex2047
face link face396 face406 edges edge2290 edge2291 vertices
vertex2104 vertex2106
face link face407 face417 edges edge2426 edge2427 vertices
vertex2227 vertex2229
face link face417 face427 edges edge2427 edge2428 vertices
vertex2229 vertex2231
face link face427 face437 edges edge2428 edge2429 vertices
vertex2231 vertex2233
face link face437 face447 edges edge2429 edge2430 vertices
vertex2233 vertex2235
face link face447 face457 edges edge2430 edge2431 vertices
vertex2235 vertex2237
face link face457 face467 edges edge2431 edge2432 vertices
vertex2237 vertex2239
face link face467 face477 edges edge2432 edge2433 vertices
vertex2239 vertex2241
face link face477 face487 edges edge2433 edge2434 vertices
vertex2241 vertex2243
face link face487 face487 edges edge2434 edge2434 vertices
vertex2243 vertex2243
face link face487 face487 edges edge2434 edge2434 vertices
vertex2243 vertex2243
face link face487 face487 edges edge2434 edge2434 vertices
vertex2243 vertex2243
face link face487 face497 edges edge2434 edge2435 vertices
vertex2243 vertex2245
face link face497 face507 edges edge2435 edge2436 vertices
vertex2245 vertex2247
face link face507 face517 edges edge2436 edge2437 vertices
vertex2247 vertex2249
face link face406 face416 edges edge2291 edge2292 vertices
vertex2106 vertex2108
face link face416 face426 edges edge2292 edge2293 vertices
vertex2108 vertex2110
face link face426 face436 edges edge2293 edge2294 vertices
vertex2110 vertex2112
face link face436 face446 edges edge2294 edge2295 vertices
vertex2112 vertex2114
face link face446 face456 edges edge2295 edge2296 vertices
vertex2114 vertex2116
face link face456 face466 edges edge2296 edge2297 vertices
vertex2116 vertex2118
face link face466 face476 edges edge2297 edge2298 vertices
83
vertex2118 vertex2120
face link face486 face496 edges edge2299 edge2300 vertices
vertex2122 vertex2124
face link face476 face486 edges edge2298 edge2299 vertices
vertex2120 vertex2122
face link face496 face506 edges edge2300 edge2301 vertices
vertex2124 vertex2126
face link face506 face516 edges edge2301 edge2302 vertices
vertex2126 vertex2128
face link face392 face402 edges edge2142 edge2144 vertices
vertex2044 vertex2046
face link face402 face412 edges edge2171 edge2172 vertices
vertex2047 vertex2049
face link face412 face422 edges edge2172 edge2173 vertices
vertex2049 vertex2051
face link face422 face432 edges edge2173 edge2174 vertices
vertex2051 vertex2053
face link face432 face442 edges edge2174 edge2175 vertices
vertex2053 vertex2055
face link face442 face452 edges edge2175 edge2176 vertices
vertex2055 vertex2057
face link face452 face462 edges edge2176 edge2177 vertices
vertex2057 vertex2059
face link face462 face472 edges edge2177 edge2178 vertices
vertex2059 vertex2061
face link face472 face482 edges edge2178 edge2179 vertices
vertex2061 vertex2063
face link face482 face492 edges edge2179 edge2180 vertices
vertex2063 vertex2065
face link face492 face502 edges edge2180 edge2181 vertices
vertex2065 vertex2067
face link face502 face512 edges edge2181 edge2182 vertices
vertex2067 vertex2069
LINKING THE TELEPHONES OF THE BOTTOM OF THE PLENUM
face link face912 face922 edges edge6950 edge6976 vertices
vertex6437 vertex6461
face link face922 face932 edges edge6976 edge7002 vertices
vertex6461 vertex6485
face link face932 face942 edges edge7002 edge7028 vertices
vertex6485 vertex6509
face link face942 face952 edges edge7028 edge7054 vertices
vertex6509 vertex6533
face link face952 face962 edges edge7054 edge7080 vertices
vertex6533 vertex6557
face link face962 face972 edges edge7080 edge7106 vertices
vertex6557 vertex6581
face link face972 face982 edges edge7106 edge7132 vertices
vertex6581 vertex6605
face link face982 face992 edges edge7132 edge7158 vertices
vertex6605 vertex6629
face link face992 face1002 edges edge7158 edge7184 vertices
vertex6629 vertex6653
face link face1002 face1012 edges edge7184 edge7210 vertices
vertex6653 vertex6677
84
face link face1012 face1022 edges edge7210 edge7236 vertices
vertex6677 vertex6701
face link face1032 face1042 edges edge7262 edge7288 vertices
vertex6725 vertex6749
face link face1042 face1052 edges edge7288 edge7314 vertices
vertex6749 vertex6773
face link face117 face124 edges edge6960 edge6986 vertices
vertex6446 vertex6470
face link face124 face131 edges edge6986 edge7012 vertices
vertex6470 vertex6494
face link face131 face138 edges edge7012 edge7038 vertices
vertex6494 vertex6518
face link face138 face145 edges edge7038 edge7064 vertices
vertex6518 vertex6542
face link face145 face152 edges edge7064 edge7090 vertices
vertex6542 vertex6566
face link face152 face159 edges edge7090 edge7116 vertices
vertex6566 vertex6590
face link face159 face166 edges edge7116 edge7142 vertices
vertex6590 vertex6614
face link face166 face173 edges edge7142 edge7168 vertices
vertex6614 vertex6638
face link face173 face180 edges edge7168 edge7194 vertices
vertex6638 vertex6662
face link face180 face187 edges edge7194 edge7220 vertices
vertex6662 vertex6686
face link face187 face194 edges edge7220 edge7246 vertices
vertex6686 vertex6710
face link face194 face201 edges edge7246 edge7272 vertices
vertex6710 vertex6734
face link face1022 face1032 edges edge7236 edge7262 vertices
vertex6701 vertex6725
face link face1032 face1042 edges edge7262 edge7288 vertices
vertex6725 vertex6749
face link face201 face208 edges edge7271 edge7297 vertices
vertex6735 vertex6759
face link face208 face215 edges edge7297 edge7323 vertices
vertex6759 vertex6783
face link face1600 face1602 edges edge7890 edge7899 vertices
vertex7303 vertex7311
face link face1602 face1604 edges edge7899 edge7908 vertices
vertex7311 vertex7319
face link face1604 face1606 edges edge7908 edge7917 vertices
vertex7319 vertex7327
face link face1606 face1608 edges edge7917 edge7926 vertices
vertex7327 vertex7335
face link face1608 face1610 edges edge7926 edge7935 vertices
vertex7335 vertex7343
face link face1610 face1612 edges edge7935 edge7944 vertices
vertex7343 vertex7351
face link face1612 face1614 edges edge7944 edge7953 vertices
vertex7351 vertex7359
face link face1614 face1616 edges edge7953 edge7962 vertices
vertex7359 vertex7367
face link face1616 face1618 edges edge7962 edge7971 vertices
vertex7367 vertex7375
85
face link face1618 face1620 edges edge7971 edge7980 vertices
vertex7375 vertex7383
face link face1620 face1622 edges edge7980 edge7989 vertices
vertex7383 vertex7391
face link face1622 face1624 edges edge7989 edge7998 vertices
vertex7391 vertex7399
face link face1624 face1626 edges edge7998 edge8007 vertices
vertex7399 vertex7407
face link face1626 face1628 edges edge8007 edge8016 vertices
vertex7407 vertex7415
LINKING ALL THE TELEPHONES OF THE TOP OF THE CHANNEL
face link face912 face1510 edges edge6950 edge7339 vertices
vertex6437 vertex6797 reverse
face link face117 face1512 edges edge6959 edge7349 vertices
vertex6447 vertex6807
face link face1600 face1514 edges edge7890 edge7363 vertices
vertex7303 vertex6819
face link face1510 face1516 edges edge7339 edge7376 vertices
vertex6797 vertex6831
face link face1516 face1522 edges edge7376 edge7413 vertices
vertex6831 vertex6865
face link face1522 face1528 edges edge7413 edge7450 vertices
vertex6865 vertex6899
face link face1528 face1534 edges edge7450 edge7487 vertices
vertex6899 vertex6933
face link face1534 face1540 edges edge7487 edge7524 vertices
vertex6933 vertex6967
face link face1540 face1546 edges edge7524 edge7561 vertices
vertex6967 vertex7001
face link face1546 face1552 edges edge7561 edge7598 vertices
vertex7001 vertex7035
face link face1552 face1558 edges edge7598 edge7635 vertices
vertex7035 vertex7069
face link face1558 face1564 edges edge7635 edge7672 vertices
vertex7069 vertex7103
face link face1564 face1570 edges edge7672 edge7709 vertices
vertex7103 vertex7137
face link face1570 face1576 edges edge7709 edge7746 vertices
vertex7137 vertex7171
face link face1576 face1582 edges edge7746 edge7783 vertices
vertex7171 vertex7205
face link face1582 face1588 edges edge7783 edge7820 vertices
vertex7205 vertex7239
face link face1588 face1594 edges edge7820 edge7857 vertices
vertex7239 vertex7273
face link face1512 face1518 edges edge7350 edge7387 vertices
vertex6806 vertex6840
face link face1518 face1524 edges edge7387 edge7424 vertices
vertex6840 vertex6874
face link face1524 face1530 edges edge7424 edge7461 vertices
vertex6874 vertex6908
face link face1530 face1536 edges edge7461 edge7498 vertices
vertex6908 vertex6942
face link face1536 face1542 edges edge7498 edge7535 vertices
86
vertex6942 vertex6976
face link face1542 face1548 edges edge7535 edge7572 vertices
vertex6976 vertex7010
face link face1548 face1554 edges edge7572 edge7609 vertices
vertex7010 vertex7044
face link face1554 face1560 edges edge7609 edge7646 vertices
vertex7044 vertex7078
face link face1560 face1566 edges edge7646 edge7683 vertices
vertex7078 vertex7112
face link face1566 face1572 edges edge7683 edge7720 vertices
vertex7112 vertex7146
face link face1572 face1578 edges edge7720 edge7757 vertices
vertex7146 vertex7180
face link face1578 face1584 edges edge7757 edge7794 vertices
vertex7180 vertex7214
face link face1584 face1590 edges edge7794 edge7831 vertices
vertex7214 vertex7248
face link face1590 face1596 edges edge7831 edge7868 vertices
vertex7248 vertex7282
face link face1514 face1520 edges edge7363 edge7400 vertices
vertex6819 vertex6853
face link face1520 face1526 edges edge7400 edge7437 vertices
vertex6853 vertex6887
face link face1526 face1532 edges edge7437 edge7474 vertices
vertex6887 vertex6921
face link face1532 face1538 edges edge7474 edge7511 vertices
vertex6921 vertex6955
face link face1538 face1544 edges edge7511 edge7548 vertices
vertex6955 vertex6989
face link face1544 face1550 edges edge7548 edge7585 vertices
vertex6989 vertex7023
face link face1550 face1556 edges edge7585 edge7622 vertices
vertex7023 vertex7057
face link face1556 face1562 edges edge7622 edge7659 vertices
vertex7057 vertex7091
face link face1562 face1568 edges edge7659 edge7696 vertices
vertex7091 vertex7125
face link face1568 face1574 edges edge7696 edge7733 vertices
vertex7125 vertex7159
face link face1574 face1580 edges edge7733 edge7770 vertices
vertex7159 vertex7193
face link face1580 face1586 edges edge7770 edge7807 vertices
vertex7193 vertex7227
face link face1586 face1592 edges edge7807 edge7844 vertices
vertex7227 vertex7261
face link face1592 face1598 edges edge7844 edge7881 vertices
vertex7261 vertex7295
LINKING ALL THE TELEPHONES OF THE TOP OF THE PLENUM
face link face912 face642 edges edge6950 edge3489 vertices
vertex6437 vertex3253 reverse
face link face642 face647 edges edge3489 edge3744 vertices
vertex3253 vertex3433
face link face117 face646 edges edge6959 edge3638 vertices
vertex6447 vertex3313
87
face link face642 face652 edges edge3489 edge3491 vertices
vertex3253 vertex3255
face link face652 face662 edges edge3491 edge3493 vertices
vertex3255 vertex3257
face link face662 face672 edges edge3493 edge3495 vertices
vertex3257 vertex3259
face link face672 face682 edges edge3495 edge3497 vertices
vertex3259 vertex3261
face link face682 face692 edges edge3497 edge3499 vertices
vertex3261 vertex3263
face link face692 face702 edges edge3499 edge3501 vertices
vertex3263 vertex3265
face link face702 face712 edges edge3501 edge3503 vertices
vertex3265 vertex3267
face link face712 face722 edges edge3503 edge3505 vertices
vertex3267 vertex3269
face link face722 face732 edges edge3505 edge3507 vertices
vertex3269 vertex3271
face link face732 face742 edges edge3507 edge3509 vertices
vertex3271 vertex3273
face link face742 face752 edges edge3509 edge3511 vertices
vertex3273 vertex3275
face link face752 face762 edges edge3511 edge3513 vertices
vertex3275 vertex3277
face link face762 face772 edges edge3513 edge3515 vertices
vertex3277 vertex3279
face link face772 face782 edges edge3515 edge3517 vertices
vertex3279 vertex3281
face link face646 face656 edges edge3653 edge3655 vertices
vertex3312 vertex3314
face link face656 face666 edges edge3655 edge3657 vertices
vertex3314 vertex3316
face link face666 face676 edges edge3657 edge3659 vertices
vertex3316 vertex3318
face link face676 face686 edges edge3659 edge3661 vertices
vertex3318 vertex3320
face link face686 face696 edges edge3661 edge3663 vertices
vertex3320 vertex3322
face link face696 face706 edges edge3663 edge3665 vertices
vertex3322 vertex3324
face link face706 face716 edges edge3665 edge3667 vertices
vertex3324 vertex3326
face link face716 face726 edges edge3667 edge3669 vertices
vertex3326 vertex3328
face link face726 face736 edges edge3669 edge3671 vertices
vertex3328 vertex3330
face link face736 face746 edges edge3671 edge3673 vertices
vertex3330 vertex3332
face link face746 face756 edges edge3673 edge3675 vertices
vertex3332 vertex3334
face link face756 face766 edges edge3675 edge3677 vertices
vertex3334 vertex3336
face link face766 face776 edges edge3677 edge3679 vertices
vertex3336 vertex3338
face link face776 face786 edges edge3679 edge3681 vertices
88
vertex3338 vertex3340
face link face647 face657 edges edge3744 edge3746 vertices
vertex3433 vertex3435
face link face657 face667 edges edge3746 edge3748 vertices
vertex3435 vertex3437
face link face667 face677 edges edge3748 edge3750 vertices
vertex3437 vertex3439
face link face677 face687 edges edge3750 edge3752 vertices
vertex3439 vertex3441
face link face687 face697 edges edge3752 edge3754 vertices
vertex3441 vertex3443
face link face697 face707 edges edge3754 edge3756 vertices
vertex3443 vertex3445
face link face707 face717 edges edge3756 edge3758 vertices
vertex3445 vertex3447
face link face717 face727 edges edge3758 edge3760 vertices
vertex3447 vertex3449
face link face727 face737 edges edge3760 edge3762 vertices
vertex3449 vertex3451
face link face737 face747 edges edge3762 edge3764 vertices
vertex3451 vertex3453
face link face747 face757 edges edge3764 edge3766 vertices
vertex3453 vertex3455
face link face757 face767 edges edge3766 edge3768 vertices
vertex3455 vertex3457
face link face767 face777 edges edge3768 edge3770 vertices
vertex3457 vertex3459
face link face777 face787 edges edge3770 edge3772 vertices
vertex3459 vertex3461
face link face647 face1600 edges edge3685 edge6963 vertices
vertex3345 vertex6449
LINKING OUTBOXES ON THE PLENUM
face modify face911 side vertex4404 vertex4405
face modify face918 side vertex4405 vertex4404
face link face911 face915 edges edge4778 edge4898 vertices
vertex4374 vertex4434
face link face915 face645 edges edge4899 edge3833 vertices
vertex4480 vertex3463 reverse
face link face911 face641 edges edge4779 edge3578 vertices
vertex4405 vertex3283 reverse
face link face918 face648 edges edge4825 edge3686 vertices
vertex4436 vertex3347 reverse
face link face645 face655 edges edge3833 edge3834 vertices
vertex3463 vertex3465
face link face655 face665 edges edge3834 edge3835 vertices
vertex3465 vertex3467
face link face665 face675 edges edge3835 edge3836 vertices
vertex3467 vertex3469
face link face675 face685 edges edge3836 edge3837 vertices
vertex3469 vertex3471
face link face685 face695 edges edge3837 edge3838 vertices
89
vertex3471 vertex3473
face link face695 face705 edges edge3838 edge3839 vertices
vertex3473 vertex3475
face link face705 face715 edges edge3839 edge3840 vertices
vertex3475 vertex3477
face link face715 face725 edges edge3840 edge3841 vertices
vertex3477 vertex3479
face link face725 face735 edges edge3841 edge3842 vertices
vertex3479 vertex3481
face link face735 face745 edges edge3842 edge3843 vertices
vertex3481 vertex3483
face link face745 face755 edges edge3843 edge3844 vertices
vertex3483 vertex3485
face link face755 face765 edges edge3844 edge3845 vertices
vertex3485 vertex3487
face link face765 face775 edges edge3845 edge3846 vertices
vertex3487 vertex3489
face link face775 face785 edges edge3846 edge3847 vertices
vertex3489 vertex3491
face link face648 face658 edges edge3686 edge3690 vertices
vertex3347 vertex3353
face link face658 face668 edges edge3690 edge3694 vertices
vertex3353 vertex3359
face link face668 face678 edges edge3694 edge3698 vertices
vertex3359 vertex3365
face link face678 face688 edges edge3698 edge3702 vertices
vertex3365 vertex3371
face link face688 face698 edges edge3702 edge3706 vertices
vertex3371 vertex3377
face link face698 face708 edges edge3706 edge3710 vertices
vertex3377 vertex3383
face link face708 face718 edges edge3710 edge3714 vertices
vertex3383 vertex3389
face link face718 face728 edges edge3714 edge3718 vertices
vertex3389 vertex3395
face link face728 face738 edges edge3718 edge3722 vertices
vertex3395 vertex3401
face link face738 face748 edges edge3722 edge3726 vertices
vertex3401 vertex3407
face link face748 face758 edges edge3726 edge3730 vertices
vertex3407 vertex3413
face link face758 face768 edges edge3730 edge3734 vertices
vertex3413 vertex3419
face link face768 face778 edges edge3734 edge3738 vertices
vertex3419 vertex3425
face link face778 face788 edges edge3738 edge3742 vertices
vertex3425 vertex3431
face link face641 face650 edges edge3578 edge3579 vertices
vertex3283 vertex3285
face link face650 face660 edges edge3579 edge3580 vertices
vertex3285 vertex3287
face link face660 face670 edges edge3580 edge3581 vertices
vertex3287 vertex3289
face link face670 face680 edges edge3581 edge3582 vertices
vertex3289 vertex3291
face link face680 face690 edges edge3582 edge3583 vertices
90
vertex3291 vertex3293
face link face690 face700 edges edge3583 edge3584 vertices
vertex3293 vertex3295
face link face700 face710 edges edge3584 edge3585 vertices
vertex3295 vertex3297
face link face710 face720 edges edge3585 edge3586 vertices
vertex3297 vertex3299
face link face720 face730 edges edge3586 edge3587 vertices
vertex3299 vertex3301
face link face730 face740 edges edge3587 edge3588 vertices
vertex3301 vertex3303
face link face740 face750 edges edge3588 edge3589 vertices
vertex3303 vertex3305
face link face750 face760 edges edge3589 edge3590 vertices
vertex3305 vertex3307
face link face760 face770 edges edge3590 edge3591 vertices
vertex3307 vertex3309
face link face770 face780 edges edge3591 edge3592 vertices
vertex3309 vertex3311
face link face915 face925 edges edge4899 edge4901 vertices
vertex4480 vertex4482
face link face925 face935 edges edge4901 edge4903 vertices
vertex4482 vertex4484
face link face935 face945 edges edge4903 edge4905 vertices
vertex4484 vertex4486
face link face945 face955 edges edge4905 edge4907 vertices
vertex4486 vertex4488
face link face955 face965 edges edge4907 edge4909 vertices
vertex4488 vertex4490
face link face965 face975 edges edge4909 edge4911 vertices
vertex4490 vertex4492
face link face975 face985 edges edge4911 edge4913 vertices
vertex4492 vertex4494
face link face985 face995 edges edge4913 edge4915 vertices
vertex4494 vertex4496
face link face995 face1005 edges edge4915 edge4917 vertices
vertex4496 vertex4498
face link face1005 face1015 edges edge4917 edge4919 vertices
vertex4498 vertex4500
face link face1015 face1025 edges edge4919 edge4921 vertices
vertex4500 vertex4502
face link face1025 face1035 edges edge4921 edge4923 vertices
vertex4502 vertex4504
face link face1035 face1045 edges edge4923 edge4925 vertices
vertex4504 vertex4506
face link face1045 face1055 edges edge4925 edge4927 vertices
vertex4506 vertex4508
face link face918 face928 edges edge4825 edge4828 vertices
vertex4436 vertex4439
face link face928 face938 edges edge4828 edge4831 vertices
vertex4439 vertex4442
face link face938 face948 edges edge4831 edge4834 vertices
vertex4442 vertex4445
face link face948 face958 edges edge4834 edge4837 vertices
vertex4445 vertex4448
face link face958 face968 edges edge4837 edge4840 vertices
91
vertex4448 vertex4451
face link face968 face978 edges edge4840 edge4843 vertices
vertex4451 vertex4454
face link face978 face988 edges edge4843 edge4846 vertices
vertex4454 vertex4457
face link face988 face998 edges edge4846 edge4849 vertices
vertex4457 vertex4460
face link face998 face1008 edges edge4849 edge4852 vertices
vertex4460 vertex4463
face link face1008 face1018 edges edge4852 edge4855 vertices
vertex4463 vertex4466
face link face1018 face1028 edges edge4855 edge4858 vertices
vertex4466 vertex4469
face link face1028 face1038 edges edge4858 edge4861 vertices
vertex4469 vertex4472
face link face1038 face1048 edges edge4861 edge4864 vertices
vertex4472 vertex4475
face link face1048 face1058 edges edge4864 edge4867 vertices
vertex4475 vertex4478
face link face911 face920 edges edge108 edge118 vertices
vertex88 vertex94
face link face920 face930 edges edge118 edge128 vertices
vertex94 vertex100
face link face930 face940 edges edge4783 edge4785 vertices
vertex4409 vertex4411
face link face940 face950 edges edge4785 edge4787 vertices
vertex4411 vertex4413
face link face950 face960 edges edge4787 edge4789 vertices
vertex4413 vertex4415
face link face960 face970 edges edge4789 edge4791 vertices
vertex4415 vertex4417
face link face970 face980 edges edge4791 edge4793 vertices
vertex4417 vertex4419
face link face980 face990 edges edge4793 edge4795 vertices
vertex4419 vertex4421
face link face990 face1000 edges edge4795 edge4797 vertices
vertex4421 vertex4423
face link face1000 face1010 edges edge4797 edge4799 vertices
vertex4423 vertex4425
face link face1010 face1020 edges edge4799 edge4801 vertices
vertex4425 vertex4427
face link face1020 face1030 edges edge4801 edge4803 vertices
vertex4427 vertex4429
face link face1030 face1040 edges edge4803 edge4805 vertices
vertex4429 vertex4431
face link face1040 face1050 edges edge4805 edge4807 vertices
vertex4431 vertex4433
LINKING THE TOP OF THE CHANEL OUTBOXES
face modify face1256 side vertex6322 vertex6321
face modify face1263 side vertex6322 vertex6321
face modify face1260 side vertex6397 vertex6396
92
face link face1256 face1260 edges edge6803 edge6923 vertices
vertex6322 vertex6397
face link face1256 face371 edges edge6774 edge2053 vertices
vertex6292 vertex1955 reverse
face link face371 face375 edges edge2053 edge2336 vertices
vertex1955 vertex2135
face link face1263 face378 edges edge6820 edge2228 vertices
vertex6322 vertex2071 reverse
face link face1263 face1273 edges edge6820 edge6823 vertices
vertex6322 vertex6324
face link face1273 face1283 edges edge6823 edge6826 vertices
vertex6324 vertex6326
face link face1283 face1293 edges edge6826 edge6829 vertices
vertex6326 vertex6328
face link face1293 face1303 edges edge6829 edge6832 vertices
vertex6328 vertex6330
face link face1303 face1313 edges edge6832 edge6835 vertices
vertex6330 vertex6332
face link face1313 face1323 edges edge6835 edge6838 vertices
vertex6332 vertex6334
face link face1323 face1333 edges edge6838 edge6841 vertices
vertex6334 vertex6336
face link face1333 face1343 edges edge6841 edge6844 vertices
vertex6336 vertex6338
face link face1343 face1353 edges edge6844 edge6847 vertices
vertex6338 vertex6340
face link face1353 face1363 edges edge6847 edge6850 vertices
vertex6340 vertex6342
face link face1363 face1373 edges edge6850 edge6853 vertices
vertex6342 vertex6344
face link face1373 face1383 edges edge6853 edge6856 vertices
vertex6344 vertex6346
face link face1383 face1393 edges edge6856 edge6859 vertices
vertex6346 vertex6348
face link face1393 face1403 edges edge6859 edge6862 vertices
vertex6348 vertex6350
face link face1256 face1265 edges edge6774 edge6776 vertices
vertex6292 vertex6294
face link face1265 face1275 edges edge6776 edge6778 vertices
vertex6294 vertex6296
face link face1275 face1285 edges edge6778 edge6780 vertices
vertex6296 vertex6298
face link face1285 face1295 edges edge6780 edge6782 vertices
vertex6298 vertex6300
face link face1295 face1305 edges edge6782 edge6784 vertices
vertex6300 vertex6302
face link face1305 face1315 edges edge6784 edge6786 vertices
vertex6302 vertex6304
face link face1315 face1325 edges edge6786 edge6788 vertices
vertex6304 vertex6306
face link face1325 face1335 edges edge6788 edge6790 vertices
vertex6306 vertex6308
face link face1335 face1345 edges edge6790 edge6792 vertices
vertex6308 vertex6310
face link face1345 face1355 edges edge6792 edge6794 vertices
vertex6310 vertex6312
93
face link face1355 face1365 edges edge6794 edge6796 vertices
vertex6312 vertex6314
face link face1365 face1375 edges edge6796 edge6798 vertices
vertex6314 vertex6316
face link face1375 face1385 edges edge6798 edge6800 vertices
vertex6316 vertex6318
face link face1385 face1395 edges edge6800 edge6802 vertices
vertex6318 vertex6320
face link face1260 face1270 edges edge6894 edge6896 vertices
vertex6353 vertex6356
face link face1270 face1280 edges edge6896 edge6898 vertices
vertex6356 vertex6359
face link face1280 face1290 edges edge6898 edge6900 vertices
vertex6359 vertex6362
face link face1290 face1300 edges edge6900 edge6902 vertices
vertex6362 vertex6365
face link face1300 face1310 edges edge6902 edge6904 vertices
vertex6365 vertex6368
face link face1310 face1320 edges edge6904 edge6906 vertices
vertex6368 vertex6371
face link face1320 face1330 edges edge6906 edge6908 vertices
vertex6371 vertex6374
face link face1330 face1340 edges edge6908 edge6910 vertices
vertex6374 vertex6377
face link face1340 face1350 edges edge6910 edge6912 vertices
vertex6377 vertex6380
face link face1350 face1360 edges edge6912 edge6914 vertices
vertex6380 vertex6383
face link face1360 face1370 edges edge6914 edge6916 vertices
vertex6383 vertex6386
face link face1370 face1380 edges edge6916 edge6918 vertices
vertex6386 vertex6389
face link face1380 face1390 edges edge6918 edge6920 vertices
vertex6389 vertex6392
face link face1390 face1400 edges edge6920 edge6922 vertices
vertex6392 vertex6395
LINKING THE BOTTOM OF THE CHANEL OUTBOXES
face link face375 face385 edges edge2440 edge2443 vertices
vertex2251 vertex2253
face link face385 face395 edges edge2443 edge2446 vertices
vertex2253 vertex2255
face link face395 face405 edges edge2446 edge2449 vertices
vertex2255 vertex2257
face link face405 face415 edges edge2449 edge2452 vertices
vertex2257 vertex2259
face link face415 face425 edges edge2452 edge2455 vertices
vertex2259 vertex2261
face link face425 face435 edges edge2455 edge2458 vertices
vertex2261 vertex2263
face link face435 face445 edges edge2458 edge2461 vertices
vertex2263 vertex2265
face link face445 face455 edges edge2461 edge2464 vertices
vertex2265 vertex2267
face link face455 face465 edges edge2464 edge2467 vertices
94
vertex2267 vertex2269
face link face465 face475 edges edge2467 edge2470 vertices
vertex2269 vertex2271
face link face475 face485 edges edge2470 edge2473 vertices
vertex2271 vertex2273
face link face485 face495 edges edge2473 edge2476 vertices
vertex2273 vertex2275
face link face495 face505 edges edge2476 edge2479 vertices
vertex2275 vertex2277
face link face505 face515 edges edge2479 edge2482 vertices
vertex2277 vertex2279
face link face378 face388 edges edge2245 edge2248 vertices
vertex2135 vertex2141
face link face388 face398 edges edge2248 edge2251 vertices
vertex2141 vertex2147
face link face398 face408 edges edge2251 edge2254 vertices
vertex2147 vertex2153
face link face408 face418 edges edge2254 edge2257 vertices
vertex2153 vertex2159
face link face418 face428 edges edge2257 edge2260 vertices
vertex2159 vertex2165
face link face428 face438 edges edge2260 edge2263 vertices
vertex2165 vertex2171
face link face438 face448 edges edge2263 edge2266 vertices
vertex2171 vertex2177
face link face448 face458 edges edge2266 edge2269 vertices
vertex2177 vertex2183
face link face458 face468 edges edge2269 edge2272 vertices
vertex2183 vertex2189
face link face468 face478 edges edge2272 edge2275 vertices
vertex2189 vertex2195
face link face478 face488 edges edge2275 edge2278 vertices
vertex2195 vertex2201
face link face488 face498 edges edge2278 edge2281 vertices
vertex2201 vertex2207
face link face498 face508 edges edge2281 edge2284 vertices
vertex2207 vertex2213
face link face508 face518 edges edge2284 edge2287 vertices
vertex2213 vertex2219
face link face371 face380 edges edge2185 edge2188 vertices
vertex2071 vertex2073
face link face380 face390 edges edge2188 edge2191 vertices
vertex2073 vertex2075
face link face390 face400 edges edge2191 edge2194 vertices
vertex2075 vertex2077
face link face400 face410 edges edge2194 edge2197 vertices
vertex2077 vertex2079
face link face410 face420 edges edge2197 edge2200 vertices
vertex2079 vertex2081
face link face420 face430 edges edge2200 edge2203 vertices
vertex2081 vertex2083
face link face430 face440 edges edge2203 edge2206 vertices
vertex2083 vertex2085
face link face440 face450 edges edge2206 edge2209 vertices
vertex2085 vertex2087
face link face450 face460 edges edge2209 edge2212 vertices
95
vertex2087 vertex2089
face link face460 face470 edges edge2212 edge2215 vertices
vertex2089 vertex2091
face link face470 face480 edges edge2215 edge2218 vertices
vertex2091 vertex2093
face link face480 face490 edges edge2218 edge2221 vertices
vertex2093 vertex2095
face link face490 face500 edges edge2221 edge2224 vertices
vertex2095 vertex2097
face link face500 face510 edges edge2224 edge2227 vertices
vertex2097 vertex2099
TOP SIDE BOX beginning of channel
face link face1649 face1633 edges edge97 edge3533 vertices
vertex4374 vertex3162 reverse
TOP SIDE BOXES
face link face1650 face1651 edges edge4749 edge4751 vertices
vertex4376 vertex4378
face link face1652 face1653 edges edge4753 edge4755 vertices
vertex4380 vertex4382
face link face1653 face1654 edges edge4755 edge4757 vertices
vertex4382 vertex4384
face link face1654 face1655 edges edge4757 edge4759 vertices
vertex4384 vertex4386
face link face1655 face1656 edges edge4759 edge4761 vertices
vertex4386 vertex4388
face link face1656 face114 edges edge4761 edge4763 vertices
vertex4388 vertex4390
face link face114 face1657 edges edge4763 edge4765 vertices
vertex4390 vertex4392
face link face1657 face1658 edges edge4765 edge4767 vertices
vertex4392 vertex4394
face link face1658 face1659 edges edge4767 edge4769 vertices
vertex4394 vertex4396
face link face1659 face1660 edges edge4769 edge4771 vertices
vertex4396 vertex4398
face link face1660 face1661 edges edge4771 edge4773 vertices
vertex4398 vertex4400
face link face1661 face1662 edges edge4773 edge4775 vertices
vertex4400 vertex4402
face link face1650 face1634 edges edge4900 edge8036 vertices
vertex4481 vertex3464 reverse
face link face1634 face1635 edges edge8036 edge8037 vertices
vertex3464 vertex3466
face link face1635 face1636 edges edge8037 edge8038 vertices
vertex3466 vertex3468
face link face1636 face1637 edges edge8038 edge8039 vertices
vertex3468 vertex3470
face link face1637 face1638 edges edge8039 edge8040 vertices
vertex3470 vertex3472
face link face1638 face1639 edges edge8040 edge8041 vertices
vertex3472 vertex3474
face link face1639 face6 edges edge8041 edge8042 vertices
96
vertex3474 vertex3476
face link face6 face1640 edges edge8042 edge8043 vertices
vertex3476 vertex3478
face link face1640 face1641 edges edge8043 edge8044 vertices
vertex3478 vertex3480
face link face1641 face1642 edges edge8044 edge8045 vertices
vertex3480 vertex3482
face link face1642 face1643 edges edge8045 edge8046 vertices
vertex3482 vertex3484
face link face1643 face1644 edges edge8046 edge8047 vertices
vertex3484 vertex3486
face link face1644 face1645 edges edge8047 edge8048 vertices
vertex3486 vertex3488
face link face1645 face1646 edges edge8048 edge8049 vertices
vertex3488 vertex3490
face link face1651 face1652 edges edge4751 edge4753 vertices
vertex4378 vertex4380
TOP SIDE BOX END OF CHANNEL
face link face1647 face1663 edges edge8050 edge99 vertices
vertex7433 vertex7435 reverse
TOP SIDE BOX BACK OF CHANNEL
face link face1648 face1664 edges edge12 edge8069 vertices
vertex8 vertex84 reverse
BOTTOM SIDE BOX
face link face1665 face1681 edges edge6773 edge2048 vertices
vertex6291 vertex1950 reverse
face link face1680 face1696 edges edge8071 edge8105 vertices
vertex7436 vertex7438 reverse
face link face1666 face1667 edges edge6894 edge6896 vertices
vertex6397 vertex6399
face link face1667 face1668 edges edge6896 edge6898 vertices
vertex6399 vertex6401
face link face1668 face1669 edges edge6898 edge6900 vertices
vertex6401 vertex6403
face link face1669 face1670 edges edge6900 edge6902 vertices
vertex6403 vertex6405
face link face1670 face1671 edges edge6902 edge6904 vertices
vertex6405 vertex6407
face link face1671 face209 edges edge6904 edge6906 vertices
vertex6407 vertex6409
face link face209 face1672 edges edge6906 edge6908 vertices
vertex6409 vertex6411
face link face1672 face1673 edges edge6908 edge6910 vertices
vertex6411 vertex6413
face link face1673 face1674 edges edge6910 edge6912 vertices
vertex6413 vertex6415
face link face1674 face1675 edges edge6912 edge6914 vertices
vertex6415 vertex6417
face link face1675 face1676 edges edge6914 edge6916 vertices
vertex6417 vertex6419
97
face link face1676 face1677 edges edge6916 edge6918 vertices
vertex6419 vertex6421
face link face1677 face1678 edges edge6918 edge6920 vertices
vertex6421 vertex6423
face link face1666 face1682 edges edge6894 edge8090 vertices
vertex6397 vertex2251 reverse
face link face1682 face1683 edges edge8090 edge8091 vertices
vertex2251 vertex2253
face link face1683 face1684 edges edge8091 edge8092 vertices
vertex2253 vertex2255
face link face1684 face1685 edges edge8092 edge8093 vertices
vertex2255 vertex2257
face link face1685 face1686 edges edge8093 edge8094 vertices
vertex2257 vertex2259
face link face1686 face1687 edges edge8094 edge8095 vertices
vertex2259 vertex2261
face link face1687 face1688 edges edge8095 edge8096 vertices
vertex2261 vertex2263
face link face1688 face1 edges edge8096 edge8097 vertices
vertex2263 vertex2265
face link face1 face1689 edges edge8097 edge8098 vertices
vertex2265 vertex2267
face link face1689 face1690 edges edge8098 edge8099 vertices
vertex2267 vertex2269
face link face1690 face1691 edges edge8099 edge8100 vertices
vertex2269 vertex2271
face link face1691 face1692 edges edge8100 edge8101 vertices
vertex2271 vertex2273
face link face1692 face1693 edges edge8101 edge8102 vertices
vertex2273 vertex2275
face link face1693 face1694 edges edge8102 edge8103 vertices
vertex2275 vertex2277
face link face1679 face1695 edges edge89 edge2227 vertices
vertex6320 vertex2039 reverse
MESHING BEGINS HERE
BOUNDARY LAYERS BEGINS HERE
BOUNDARY LAYER FOR THE bottom of plenum
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer1 face face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
98
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 edge edge97
edge4748 edge106 edge6946 edge6947 edge107 edge4749
edge4750 edge116 edge6972 edge6973 edge117 edge4751
edge4752 edge126 edge6998 edge6999 edge127 edge4753
edge4754 edge136 edge7024 edge7025 edge137 edge4755
edge4756 edge146 edge7050 edge7051 edge147 edge4757
edge4758 edge156 edge7076 edge7077 edge157 edge4759
edge4760 edge166 edge7102 edge7103 edge167 edge4761
edge4762 edge176 edge7128 edge7129 edge177 edge4763
edge4764 edge186 edge7154 edge7155 edge187 edge4765
edge4766 edge196 edge7180 edge7181 edge197 edge4767
edge4768 edge206 edge7206 edge7207 edge207 edge4769
edge4770 edge216 edge7232 edge7233 edge217 edge4771
edge4772 edge226 edge7258 edge7259 edge227 edge4773
edge4774 edge236 edge7284 edge7285 edge237 edge4775
edge4776 edge246 edge7310 edge7311 edge247 edge4777 add
MESHING THE PLENUM
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer2 face face4 face4 face5 face110
face110 edge edge99 edge8069 edge100 edge8052 edge98 add
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer4 face face1649 face1664 face1664
face1664 face1663 edge edge8052 edge98 edge100 edge8069
edge99 add
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer4 face face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face4 face2 face2 face2 face2 face2 face4
face5 face110 face110 edge edge9 edge3398 edge3399
edge3400 edge3401 edge3402 edge3403 edge3404 edge3406
edge3405 edge3407 edge3408 edge3409 edge3415 edge3410
edge3411 edge3412 edge3413 edge3414 edge3416 edge3417
edge3418 edge3419 edge3420 edge3421 edge3422 edge3423
edge3424 edge3425 edge3426 edge3427 edge3428 edge3429
edge3430 edge3431 edge3432 edge3433 edge3434 edge3435
edge3436 edge3437 edge3438 edge3439 edge3440 edge3441
edge3442 edge3443 edge3444 edge3445 edge3446 edge3447
99
edge3448 edge3449 edge3450 edge3451 edge3457 edge3452
edge3453 edge3454 edge3455 edge3456 edge3458 edge3459
edge3460 edge3461 edge3462 edge3463 edge3464 edge3465
edge3466 edge3467 edge3468 edge3469 edge3475 edge3481
edge3470 edge3471 edge3472 edge3473 edge3474 edge3476
edge3477 edge3478 edge3479 edge3480 edge3487 edge11
edge3482 edge3483 edge3484 edge3485 edge3486 edge8051
edge12 edge10 edge8034 add
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer5 face face1663 face1664 face1664
face1664 face1649 edge edge99 edge8069 edge100 edge98
edge8052 add
BOUNDARY LAYER OF THE HOLES
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer1 face face642 edge edge3534 add
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer7 face face117 face1600 edge edge4824
edge110 add
BONDARY LAYER OF THE CHANNEL
TARGET WALL BOUNDARY LAYER
BBBL
BBL
BBL
BBBL
BBL
BBL
BBBLLLLL
blayer create first $firstch growth $growthch rows $rowsch transition 1 trows 0
uniform
blayer attach b_layer8 face face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
100
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face105 face105 face106
face104 face104 edge edge2048 edge2049 edge2050 edge2051
edge2052 edge2053 edge2054 edge2055 edge2056 edge2057
edge2058 edge2059 edge2060 edge2061 edge2062 edge2063
edge2064 edge2065 edge2066 edge2072 edge2067 edge2068
edge2069 edge2070 edge2071 edge2084 edge2078 edge2073
edge2074 edge2075 edge2076 edge2077 edge2079 edge2080
edge2081 edge2082 edge2083 edge2090 edge2096 edge2085
edge2086 edge2087 edge2088 edge2089 edge2091 edge2092
edge2093 edge2094 edge2095 edge2102 edge2108 edge2097
edge2098 edge2099 edge2100 edge2101 edge2103 edge2104
edge2105 edge2106 edge2107 edge2114 edge2120 edge2109
edge2110 edge2111 edge2112 edge2113 edge2115 edge2116
edge2117 edge2118 edge2119 edge2126 edge2132 edge2121
edge2122 edge2123 edge2124 edge2125 edge2127 edge2128
edge2129 edge2130 edge2131 edge2133 edge2134 edge2136
edge2137 edge1 edge2135 edge8088 edge3 edge4 edge8105
edge2 add
blayer create first $firstch growth $growthch rows $rowsch transition 1 trows 0
uniform
blayer attach b_layer9 face face1681 face1696 face1696
face1696 face1695 edge edge2 edge8105 edge4 edge3
edge8088 add
blayer create first $firstch growth $growthch rows $rowsch transition 1 trows 0
uniform
blayer attach b_layer10 face face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face105 face105
face106 face104 face104 edge edge6743 edge101
edge7336 edge7337 edge102 edge6744 edge6745 edge111
edge7373 edge7374 edge112 edge6746 edge6747 edge121
edge7410 edge7411 edge122 edge6748 edge6749 edge131
edge7447 edge7448 edge132 edge6750 edge6751 edge141
edge7484 edge7485 edge142 edge6752 edge6755 edge6753
edge151 edge6754 edge7521 edge7522 edge152 edge161
101
edge6756 edge6757 edge7558 edge7559 edge162 edge171
edge7595 edge7596 edge172 edge6758 edge6759 edge181
edge7632 edge7633 edge182 edge6760 edge6761 edge191
edge7669 edge7670 edge192 edge6762 edge6763 edge6767
edge6765 edge201 edge7706 edge7707 edge202 edge6764
edge211 edge6766 edge7743 edge7744 edge212 edge6769
edge221 edge6768 edge7780 edge7781 edge222 edge6771
edge231 edge6770 edge7817 edge7818 edge232 edge241
edge7854 edge7855 edge242 edge6772 edge89 edge8070
edge91 edge92 edge8087 edge90 add
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer11 face face4 face5 face2 face5
face110 face2 edge edge8 edge8 edge6 edge7 edge7
edge5 add
blayer create first $firstch growth $growthch rows $rowsch transition 1 trows 0
uniform
blayer attach b_layer12 face face106 face104 face103 face105
edge edge87 edge87 edge85 edge88 add
BOUNDARY LAYERS ENDS HERE
edge picklink edge6948 edge6949
edge mesh edge6949 edge6948 successive ratio1 1 intervals $NumbNodes
edge picklink edge6950
edge mesh edge6950 successive ratio1 1 intervals ($NumbNodes2)
face mesh face1450 map
edge picklink edge6963 edge6947
edge mesh edge6947 edge6963 successive ratio1 1 intervals ($Numbtelnodes+$rows)
face mesh face912 map
edge picklink edge6961 edge6960 edge7889 edge7890
edge mesh edge7890 edge7889 edge6960 edge6961 successive ratio1 1
intervals ($NumbNodes)
edge picklink edge6959 edge7891
edge mesh edge7891 edge6959 successive ratio1 1 intervals ($NumbNodes2)
face mesh face1452 map
face mesh face1600 face117 map
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer12 face face2 face110 face5 face110
face2 face4 face5 face4 edge edge5 edge5 edge7
edge7 edge6 edge6 edge8 edge8 add
Meshing constants
$NumbNodes=5
$Numbtelnodes=6
$PLobnodes=5
$Chobnodes=5
$Plbenodes=($NumbNodes(4)+$rows)
$plsqnodes=($NumbNodes(3))
102
$Pllsnodes=($NumbNodes+$rows)
$Nojetcells=10
edge picklink edge3686 edge3402
edge mesh edge3686 edge3402 successive ratio1 1 intervals ($PLobnodes)
edge picklink edge6744 edge6864
edge mesh edge6864 edge6744 successive ratio1 1 intervals 5
face link face1260 face375 edges edge6923 edge2440 vertices
vertex6397 vertex2251 reverse
face modify face915 side vertex4479 vertex4480
face mesh face915 face918 face911 map size 1
face mesh face1260 face1263 face1256 map size 1
edge picklink edge8068 edge8053
edge mesh edge8068 edge8053 successive ratio1 1 intervals ($Plbenodes)
edge picklink edge8086 edge8071
edge mesh edge8071 edge8086 successive ratio1 1 intervals ($CHbenodes)
edge delete edge8053 edge8068 keepsettings onlymesh
edge mesh edge8053 edge8068 successive ratio1 1 intervals ($Plbenodes)
edge delete edge8090 keepsettings onlymesh
edge picklink edge8090
edge mesh edge8090 successive ratio1 1 intervals ($plsqnodes)
edge delete edge8054 keepsettings onlymesh
edge picklink edge8054
edge mesh edge8054 successive ratio1 1 intervals ($plsqnodes)
face mesh face1647 face1679 face1678 face1646 face1633
face1665 map
edge delete edge98 edge8087 keepsettings onlymesh
edge picklink edge8087 edge98
edge mesh edge98 successive ratio1 1 intervals ($Pllsnodes)
edge mesh edge8087 successive ratio1 1 intervals ($CHlsnodes)
face mesh face1648 face1680 map
COOPERING ALL THE JETS
volume mesh volume3 cooper source face1600 face1452 face117
face1514 face1512 face115 intervals ($Nojetcells)
volume mesh volume5 cooper source face1456 face1602 face124
face1518 face1520 face122 intervals ($Nojetcells)
volume mesh volume7 cooper source face1460 face1604 face131
face1526 face1524 face129 intervals ($Nojetcells)
volume mesh volume9 cooper source face1464 face1606 face138
face1532 face1530 face136 intervals ($Nojetcells)
volume mesh volume11 cooper source face1468 face1608 face145
face1538 face143 face1536 intervals ($Nojetcells)
volume mesh volume13 cooper source face1472 face1610 face152
face1544 face1542 face150 intervals ($Nojetcells)
volume mesh volume15 cooper source face1476 face1612 face159
face1550 face1548 face157 intervals ($Nojetcells)
volume mesh volume17 cooper source face1480 face1614 face166
face1556 face1554 face164 intervals ($Nojetcells)
volume mesh volume19 cooper source face1484 face1616 face173
face1562 face171 face1560 intervals ($Nojetcells)
volume mesh volume21 cooper source face1488 face1618 face180
face1568 face1566 face178 intervals ($Nojetcells)
103
volume mesh volume23 cooper source face1492 face1620 face187
face1574 face1572 face185 intervals ($Nojetcells)
volume mesh volume25 cooper source face1496 face1622 face194
face1578 face1580 face192 intervals ($Nojetcells)
volume mesh volume27 cooper source face1624 face1500 face201
face1586 face1584 face199 intervals ($Nojetcells)
volume mesh volume29 cooper source face1504 face1626 face208
face1592 face1590 face206 intervals ($Nojetcells)
volume mesh volume31 cooper source face1628 face1508 face215
face1596 face1598 face213 intervals ($Nojetcells)
volume mesh volume30 cooper source face1506 face1052 face1594
face1397 intervals ($Nojetcells)
volume mesh volume28 cooper source face1502 face1042 face1588
face1387 intervals ($Nojetcells)
volume mesh volume26 cooper source face1498 face1032 face1582
face1377 intervals ($Nojetcells)
volume mesh volume24 cooper source face1494 face1022 face1576
face1367 intervals ($Nojetcells)
volume mesh volume22 cooper source face1490 face1012 face1570
face1357 intervals ($Nojetcells)
volume mesh volume20 cooper source face1486 face1002 face1564
face1347 intervals ($Nojetcells)
volume mesh volume18 cooper source face1482 face992 face1558
face1337 intervals ($Nojetcells)
volume mesh volume16 cooper source face1478 face982 face1552
face1327 intervals ($Nojetcells)
volume mesh volume14 cooper source face1474 face972 face1546
face1317 intervals ($Nojetcells)
volume mesh volume12 cooper source face1470 face962 face1540
face1307 intervals ($Nojetcells)
volume mesh volume10 cooper source face1466 face952 face1534
face1297 intervals ($Nojetcells)
volume mesh volume8 cooper source face1462 face942 face1528
face1287 intervals ($Nojetcells)
volume mesh volume6 cooper source face1458 face932 face1522
face1277 intervals ($Nojetcells)
volume mesh volume4 cooper source face1454 face922 face1516
face1267 intervals ($Nojetcells)
volume mesh cylinder cooper source face1450 face912 face1510
face1257 intervals ($Nojetcells)
window modify invisible mesh
volume mesh volume34 cooper source face1649 face1650 face1651
face1652 face1653 face1654 face1655 face1664 face1639
face1638 face1637 face1636 face1635 face1634 face1633
face1648 face1610 face1608 face1606 face1604 face1602
face1600 face1472 face962 face1468 face952 face1464
face942 face1460 face932 face1456 face922 face1452
face912 face915 face918 face911 face925 face928
face920 face935 face938 face930 face945 face948
face940 face955 face958 face950 face965 face968
face960 face694 face689 face684 face679 face674
face669 face664 face659 face654 face649 face644
face640 face697 face696 face692 face687 face686
face682 face677 face676 face672 face667 face666
104
face662 face657 face656 face652 face647 face646
face642 face695 face698 face690 face685 face688
face680 face675 face678 face670 face665 face668
face660 face655 face658 face650 face645 face648
face641 face152 face1470 face145 face1466 face138
face1462 face131 face1458 face124 face1454 face117
face1450 face1657 face1658 face1659 face1660 face1661
face1662 face1663 face788 face1656 face1474 face159
face1647 face1646 face1645 face1644 face1643 face1642
face1641 face1640 face1478 face1628 face1626 face1624
face1622 face1620 face1618 face1616 face1614 face1612
face1508 face1052 face1504 face1042 face1500 face1032
face1496 face1022 face1492 face1012 face1488 face1002
face1484 face992 face1480 face982 face1476 face972
face975 face978 face970 face985 face988 face980
face995 face998 face990 face1005 face1008 face1000
face1015 face1018 face1010 face1025 face1028 face1020
face1035 face1038 face1030 face1045 face1048 face1040
face1050 face114 face1058 face774 face769 face764
face759 face754 face749 face744 face739 face734
face729 face724 face719 face714 face709 face704
face699 face777 face776 face772 face767 face766
face762 face757 face756 face752 face747 face746
face742 face737 face736 face732 face727 face726
face722 face717 face716 face712 face707 face706
face702 face779 face784 face787 face775 face778
face770 face765 face768 face760 face755 face758
face750 face745 face748 face740 face735 face738
face730 face725 face728 face720 face715 face718
face710 face705 face708 face700 face782 face786
face785 face6 face780 face1055 face215 face1506
face208 face1502 face201 face1498 face194 face1494
face187 face1490 face180 face1486 face173 face1482
face166 intervals ($Plzdnodes)
volume delete body onlymesh
volume mesh body cooper source face1689 face1690 face1691
face1692 face1693 face1681 face1682 face1683 face1684
face1685 face1686 face1687 face1688 face1696 face1671
face1670 face1669 face1668 face1667 face1666 face1665
face1677 face1676 face1675 face1674 face1673 face1672
face1680 face199 face1584 face1377 face192 face1578
face1367 face185 face1572 face1357 face178 face1566
face1347 face171 face1560 face1337 face164 face1554
face1327 face157 face1548 face1317 face150 face1542
face1307 face143 face1536 face1297 face136 face1530
face1287 face129 face1524 face1277 face122 face1518
face1267 face115 face1512 face1257 face1380 face1383
face1375 face1370 face1373 face1365 face1360 face1363
face1355 face1350 face1353 face1345 face1340 face1343
face1335 face1330 face1333 face1325 face1320 face1323
face1315 face1310 face1313 face1305 face1300 face1303
face1295 face1290 face1293 face1285 face1280 face1283
face1275 face1270 face1273 face1265 face1260 face1263
face1256 face209 face374 face370 face384 face379
face394 face389 face404 face399 face414 face409
105
face424 face419 face434 face429 face444 face439
face454 face449 face464 face459 face474 face469
face484 face479 face494 face489 face377 face376
face372 face387 face386 face382 face397 face396
face392 face407 face406 face402 face417 face416
face412 face427 face426 face422 face437 face436
face432 face447 face446 face442 face457 face456
face452 face467 face466 face462 face477 face476
face472 face487 face486 face482 face497 face496
face492 face375 face378 face371 face385 face388
face380 face395 face398 face390 face405 face408
face400 face415 face418 face410 face425 face428
face420 face435 face438 face430 face445 face448
face440 face455 face458 face450 face465 face468
face460 face475 face478 face470 face485 face488
face480 face495 face498 face490 face1 face1586
face1582 face1580 face1576 face1574 face1570 face1568
face1564 face1562 face1558 face1556 face1552 face1550
face1546 face1544 face1540 face1538 face1534 face1532
face1528 face1526 face1522 face1520 face1516 face1514
face1510 face1403 face518 face1588 face1592 face1594
face1694 face1695 face1598 face1679 face1678 face515
face516 face510 face500 face508 face505 face213
face1596 face1397 face206 face1590 face1387 face517
face514 face512 face502 face506 face507 face509
face499 face504 face1400 face1395 face1385 face1390
face1393 intervals ($Chzdnodes)
BOUNDARY CONDITIONS
physics create Symmetry btype SYMMETRY face face2 face103
face211 face204 face197 face190 face183 face176
face169 face162 face155 face148 face141 face134
face127 face120 face112
physics create Wall btype SYMMETRY face face110 face5 face1649
face1664 face918 face915 face911 face925 face1650
face928 face920 face935 face938 face930 face1652
face1651 face948 face945 face940 face1653 face1654
face958 face955 face950 face1655 face965 face968
face960 face978 face975 face970 face1656 face114
face985 face988 face980 face995 face998 face990
face1657 face1005 face1008 face1000 face1658 face1015
face1018 face1010 face1659 face1028 face1025 face1020
face1035 face1660 face1038 face1030 face1045 face1661
face1048 face1040 face1055 face1662 face1058 face1050
face1663 face4 face1395 face1679 face1403 face1400
face1680 face1385 face1678 face1393 face1390 face1375
face1677 face1383 face1380 face1676 face1365 face1373
face1370 face1675 face1355 face1363 face1360 face1674
face1345 face1353 face1350 face1673 face1335 face1343
face1340 face1672 face1325 face1333 face1330 face209
face1315 face1323 face1320 face1671 face1305 face1313
face1310 face1670 face1295 face1303 face1300 face1669
106
face1285 face1293 face1290 face1668 face1275 face1283
face1280 face1667 face1265 face1273 face1270 face1666
face1256 face1263 face1260 face1665 face214 face91
face207 face85 face200 face79 face193 face73 face186
face67 face179 face61 face172 face55 face165 face49
face158 face43 face151 face37 face144 face31 face137
face25 face130 face19 face123 face13 face116 face8
physics modify Wall btype WALL face face110 face5 face1649
face1664 face918 face915 face911 face925 face1650
face928 face920 face935 face938 face930 face1652
face1651 face948 face945 face940 face1653 face1654
face958 face955 face950 face1655 face965 face968
face960 face978 face975 face970 face1656 face114
face985 face988 face980 face995 face998 face990
face1657 face1005 face1008 face1000 face1658 face1015
face1018 face1010 face1659 face1028 face1025 face1020
face1035 face1660 face1038 face1030 face1045 face1661
face1048 face1040 face1055 face1662 face1058 face1050
face1663 face4 face1395 face1679 face1403 face1400
face1680 face1385 face1678 face1393 face1390 face1375
face1677 face1383 face1380 face1676 face1365 face1373
face1370 face1675 face1355 face1363 face1360 face1674
face1345 face1353 face1350 face1673 face1335 face1343
face1340 face1672 face1325 face1333 face1330 face209
face1315 face1323 face1320 face1671 face1305 face1313
face1310 face1670 face1295 face1303 face1300 face1669
face1285 face1293 face1290 face1668 face1275 face1283
face1280 face1667 face1265 face1273 face1270 face1666
face1256 face1263 face1260 face1665 face214 face91
face207 face85 face200 face79 face193 face73 face186
face67 face179 face61 face172 face55 face165 face49
face158 face43 face151 face37 face144 face31 face137
face25 face130 face19 face123 face13 face116 face8
physics create Heat Fluxes btype WALL face face104 face106
face370 face379 face389 face372 face382 face392
face371 face380 face390 face378 face388 face398
face376 face386 face396 face374 face384 face394
face377 face387 face397 face375 face385 face395
face1681 face1682 face1683 face1684 face1696 face402
face412 face422 face432 face442 face400 face410
face420 face430 face440 face408 face418 face428
face438 face448 face406 face416 face426 face436
face446 face404 face414 face424 face434 face444
face407 face417 face427 face437 face447 face405
face415 face425 face435 face445 face1688 face1685
face1686 face1687 face452 face462 face472 face482
face492 face1693 face450 face460 face470 face480
face490 face1692 face458 face468 face478 face488
face498 face1 face456 face466 face476 face486 face496
face454 face464 face474 face484 face494 face457
face467 face477 face487 face497 face1691 face455
face465 face475 face485 face495 face1689 face1690
face518 face502 face512 face1695 face500 face510
face1694 face508 face506 face516 face504 face514
face507 face517 face515 face505
physics create Mass flow inlet btype SYMMETRY face face640 face649
107
face659 face642 face652 face662 face672 face641
face650 face660 face670 face648 face658 face668
face678 face646 face656 face666 face676 face644
face654 face664 face674 face647 face657 face667
face677 face645 face655 face665 face675 face1633
face1634 face1635 face1636 face1637 face1648 face679
face689 face699 face682 face692 face702 face712
face680 face690 face700 face710 face688 face698
face708 face718 face6 face686 face696 face706 face716
face684 face694 face704 face714 face687 face697
face707 face717 face685 face695 face705 face715
face1640 face1638 face1639 face719 face729 face739
face749 face722 face732 face742 face752 face762
face720 face730 face740 face750 face760 face728
face738 face748 face758 face768 face726 face736
face746 face756 face766 face724 face734 face744
face754 face764 face727 face737 face747 face757
face767 face725 face735 face745 face755 face765
face1645 face1641 face1642 face1643 face1644 face788
face769 face779 face772 face782 face770 face780
face778 face776 face786 face774 face784 face777
face787 face775 face785 face1647 face1646
physics create Outflow btype OUTFLOW face face105
108
REFERENCES
Al-Aqal O M A 2003 ldquoHeat transfer distributions on the walls of a narrow channel
with jet impingement and cross flowrdquo PhD Thesis University of Pittsburgh
Bunker Ronald S 2007 Gas Turbine Heat Transfer Ten Remaining Hot Gas Path
Challengesrdquo Journal of Turbomachinery April Vol 129 pp 193-201
Downs James P Landis Kenneth K 2009 ldquoTurbine Cooling Systems Design- Past
Present and Futurerdquo Proceedings of ASME Turbo Expo 2009 June 8-12 2009
GT2009-59991
Florschuetz LW Berry R A Metzger D E 1980 ldquoPeriodic streamswise variations of
heat transfer coefficients for inline and staggered arrays of circular jets with cross
flow of spent airrdquo ASME J of Heat Transfer 102 p 132-137
Florschuetz L W Truman C R Metzger D E 1981 ldquoStreamwise Flow and Heat
Transfer Distributions for Jet Array Impingement with Cross flowrdquo Journal of
Heat Transfer Vol 103 pp 337
Florschuetz L W Isoda Y 1983 ldquoFlow Distributions and Discharge Coefficient for
Jet Array Impingement With Initial Cross flowrdquo Journal of Engineering for
Power Vol 105 pp 296
Incropera Frank P DeWitt D P 2002 Fundamentals of Heat and Mass Transfer John
Wiley amp Sons Inc New Jersey pp 491-493
Liu Quan Kapat J May 2006 ldquoStudy of Heat Transfer Characteristics of Impinging
Air Jet Using Pressure and Temperature Sensitive Luminescent Paintrdquo UCF
Dissertation
109
Martin H 1977 ldquoImpinging jet flow heat and mass transferrdquo Advances in heat transfer
Vol 13
Ricklick Mark Kapat J December 2009 ldquoCharacterization of an Inline Row
Impingement Channel for Turbine Blade Cooling Applicationsrdquo UCF
Dissertation
Zuckerman N Lior N 2005 ldquoImpingement Heat transfer Correlations and Numerical
Modelingrdquo Journal of Heat Transfer Vol 127 pp 544
ii
ABSTRACT
Advanced cooling techniques are required to increase the Brayton cycle
temperature ratio necessary for the increase of the overall cyclersquos efficiency Current
turbine components are cooled with an array of internal cooling channels in the midchord
section of the blade pin fin arrays at the trailing edge and impingement channels in the
leading edge Impingement channels provide the designer with high convective
coefficients on the target surface Increasing the heat transfer coefficient of these
channels has been a subject of research for the past 20 years In the current study a triple
row impingement channel is studied with a jet to target spacing of 6 8 and 10 The
effects of sidewalls are also analyzed Temperature sensitive paint alongside thin foil
heaters are used to obtain heat transfer distributions throughout the target and side walls
of the three different channels Thermal performances were also calculated for the two
largest channels It was found that the side walls provide a significant amount of cooling
especially when the channels are mounted side by side so that their sidewalls behave as
fins Similar to literature it was found that an increase in ZD decreases heat transfer
coefficient and provides a more uniform profile It was also found that the ZD = 6 and 8
target wall heat transfer profiles are very similar hinting to the fact that successful
potential core impingement may have occurred at height of eight diameters A
Computational Fluid Dynamics or CFD study was also performed to provide better
insight into the flow field that creates such characteristic heat transfer profiles The
Realizable k-ε solution with enhanced wall functions gave surface heat transfer
coefficients 30 off from the experimental data
iii
DEDICATED TO ENNIO MAMA Y PAPA
iv
ACKNOWLEDGEMENTS
I would like to acknowledge my mentor and advisor Dr Jay Kapat for all his
support and encouragement I would also like to thank my committee members Dr Ali
Gordon and Dr Weiwei Deng
I would also like to give a million thanks to Perry Johnson Lucky Tran Bryan
Bernier and William Clark for their help with the CFD portion of this study and for
letting me run on their computers Special thanks go to Mark Ricklick for helping me
throughout this project To everyone at CATER Mark Miller Michelle Valantino
Jimmy Kullberg Greg Natsui Michael Torrance Jeff Nguyen Nghia Tran Abhishek
Saha Kaylee Dorman Matt Golsen and everyone else that were once caterers a big thank
you for making these two years of work at the lab unforgettable
v
TABLE OF CONTENTS
ABSTRACT ii
ACKNOWLEDGEMENTS iv
LIST OF FIGURES vii
NOMENCLATURE ix
CHAPTER ONE INTRODUCTION 1
11 Gas Turbine as a Heat Engine 1
12 Cooling of Hot Components 2
CHAPTER TWO LITERATURE REVIEW 9
21 Impingement Literature Cornerstone 9
22 Relevant Impingement Channel Studies 11
23 Computational Studies on Impingement Channels 12
CHAPTER THREE EXPERIMENTAL SETUP AND TECHNIQUES 15
31 Temperature Measurements with TSP 15
32 Experimental Setup of Suction Channel 21
33 Data Processing and Reduction 24
34 Uncertainty Analysis 27
35 Lateral Conduction Analysis 28
CHAPTER FOUR HEAT TRANSFER RESULTS 32
vi
41 Heat Transfer Validation 32
42 Heat Transfer Results 33
43 XD Comparisons 40
44 3D Comparison of the Heat Transfer Profiles 45
45 Thermal Performance Calculations 48
CHAPTER FIVE COMPUTATIONAL FLUID DYNAMICS 52
51 Problem Setup 52
52 CFD Results 58
CHAPTER SIX CONCLUSIONS 63
APPENDICES 64
Appendix A 64
Appendix B 66
REFERENCES 108
vii
LIST OF FIGURES
Figure 1 Brayton Cycle Flow Path and T-s Diagram (Adapted from UPTB Website) 1
Figure 2 Thermal Loading Throughout a Turbine Blade (Daniels 1982) 3
Figure 3 Allowable Turbine Inlet Temperature vs Cooling Techniques over the Years
(Clifford 1985) 4
Figure 4 Turbine Inlet Temperature Increase with the help of TBC New Super Alloys
and Cooling Technologies (Kapat and Kiesow Lectures 2010) 4
Figure 5 Turbine Stator Cooled with Impingement Coupled with Film Cooling
(Florschuetz 1980) 5
Figure 6 Rotor Blade Cooling Configuration (Gladden 1988) 6
Figure 7 Cross-section of Turbine Airfoil with Cooling Channels (Han et al 1984) 6
Figure 8 Relative Temperatures for Hot Gas Metal Temperature and Coolant
Temperature (Cardwell 2005) 7
Figure 9 (a) The Development of the Wall Jet (b) Jet Diffusion to Surroundings (Liu
2006) 8
Figure 10 Simplified Jablonski Diagram (Adapted from ISSI Website) 17
Figure 11 Heater Strips Painted with TSP Too Closely 21
Figure 12 Flow Loop of Impingement Channel 22
Figure 13 Top View of Jet Plate 22
Figure 14 Front View of Impingement Channel 23
Figure 15 Target Wall Test Section with Heater Leads 23
Figure 16 Heat Transfer Coefficient Uncertainty Tree 27
viii
Figure 17 Temperature Profile of First Five Impingement Rows 29
Figure 18 Detailed View of First Heat Transfer Peak with a Polynomial Curve Fit 30
Figure 19 Control Volume Heat Transfer Analysis 30
Figure 20 Heat Loss through Convection and Lateral Conduction 31
Figure 21 Validation Spanwise Averaged Results 32
Figure 22 Target Wall Heat Transfer Coefficient Distributions 34
Figure 23 Span-averaged Target Wall Heat Transfer Distribution 35
Figure 24 Side Wall Heat Transfer Coefficient Distributions 36
Figure 25 Span-averaged Side wall Heat Transfer Distribution 37
Figure 26 XD=15 Target Wall Heat Transfer Profile 41
Figure 27 XD=15 Span-averaged Target Wall Heat Transfer Distribution 42
Figure 28 Target Wall Span-average Comparison of XD=5 and 15 at High Re 43
Figure 29 Side Wall Heat transfer Coefficient Profile 44
Figure 30 XD=15 Side Wall Span-averaged Heat Transfer Coefficients 45
Figure 31 3D Heat Transfer Profile for ZD=6 XD=5 46
Figure 32 3D Heat Transfer Profile for ZD=8 XD=5 47
Figure 33 3D Heat Transfer Profile for ZD=6 XD=15 48
Figure 34 Pressure Drop Ratio with Respect to Smooth Channel 49
Figure 35 Heat Transfer Enhancement 50
Figure 36 Thermal Performance at Constant Pressure Drop 50
Figure 37 Thermal Performance at Constant Pumping Power 51
Figure 38 Horizontal Plane of Impingement Channel Geometry 53
Figure 39 Target Side and Front End Wall y+ Values 54
ix
Figure 40 Finished Mesh with Boundary Conditions 55
Figure 41 Grid Independence Study 57
Figure 42 Residual Plots for the 26M Cell Run 57
Figure 43 Total Pressure Contours 58
Figure 44 Velocity Magnitude Contours 59
Figure 45 Turbulent Kinetic Energy Contours 60
Figure 46 Static Temperature Contours 60
Figure 47 Target and Side Wall Heat Transfer Coefficient Contours 61
Figure 48 Closer View of First few Rows of Impingement HTC Contours 61
Figure 49 Pathlines Generating from the First Row of Jets 62
NOMENCLATURE
Cross Sectional Area
Heater Surface Area (m2)
Specific Heat at Constant Pressure (kJkgK)
D Jet Diameter (m)
Channel Hydraulic Diameter (m)
Friction Factor
Heat Transfer Coefficient (HTC) (Wm2K)
Average Heat Transfer Coefficient (Wm2K)
Channel Length (m)
Mass Flow Rate (kgs)
Static Pressure (kPa)
x
Total Pressure (kPa)
Pr Prandtl Number
Heat Flux (Wm2)
Total Heat Input (W)
Heater Resistance (ohm)
Re Reynolds Number
SW Side Wall
Temperature (K)
TW Target Wall
Voltage Potential
Streamwise Location
y Spanwise Location
z Height from Target Wall
X Streamwise Distance (m)
Y Spanwise Distance (m)
Z Impingement Height (m)
Thermal Performance Parameter
Ratio of Specific Heats
Air Density (kgm3)
Subscripts
C Cold
H Hot
xi
Carnot Describing a Carnot cycle
Exit
Effective
Quantity Lost to the Environment
Reference Value
Wall Value
Base Line Value
1
CHAPTER ONE INTRODUCTION
11 Gas Turbine as a Heat Engine
Gas turbine is a form of heat engine where the hot reservoir is created by the
combustion of fuel and the cold reservoir is the open atmosphere It is well known that
the maximum efficiency of any heat engine is denoted as the Carnot efficiency
A more accurate cycle is used to describe the processes inside a gas turbine ndash the
Brayton Cycle The Brayton cycle as seen in Figure 1 is composed of four processes In
a gas turbine air is drawn in at state 1 it is compressed until it reaches state 2 The
compressed air is mixed with fuel and ignited as it passes through the combustor The hot
air then passes through the turbines where work is extracted The process from state 4 to
state 1 happens throughout the atmosphere therefore the Brayton cycle is an open loop
cycle as the same air is not continuously being fed through the motor
Figure 1 Brayton Cycle Flow Path and T-s Diagram (Adapted from UPTB Website)
The Brayton cycle has an isentropic efficiency similar to the carnot the Brayton
cycle efficiency is defined as
2
It can be seen that increasing the temperature at which air enters the first turbine
stage T3 increases the overall efficiency of the turbine Moreover increasing the
pressure ratio Pr also aids in the increase of the efficiency One of the hurdles of
increasing T3 is the fact that the post combustion gas is a few hundred degrees Celsius
above the melting point of the super alloys used to make the turbine stator vanes and
rotor blades For this reason it is important to cool the hot components of the gas turbine
in order to assure a reasonable life for the machine
12 Cooling of Hot Components
The transition duct that connects the combustor to the first stage turbine as well
as the first stage of the turbine are the parts that are subject to the harshest thermal
loadings and must therefore be cooled aggressively to maintain them in working
conditions for a long period of time Since the first stage guide vanes and rotor extrude
into the flow they are subject to the highest convection coefficients These heat transfer
coefficients can reach up to 4000 Wm2K (Downs 2009) Figure 2 shows the different
magnitudes of convection coefficient around the blade High heat transfer coefficients
occur where the air stagnates into the leading edge of the airfoil This high heat transfer
region is not only caused by the lack of a thermal boundary layer to protect the airfoil but
also because the effective heat transfer driving temperature is the recovery temperature
At the high Mach numbers that occur in turbines the ratio of total to static temperatures
is significant causing the leading edge to have the highest effective heat load Another
3
peak occurs on the suction side of the blade as the boundary layer created by the airfoil
switches from being a laminar boundary layer into a turbulent one Due to the nozzling
effect of the turbine rotor and stators the flow gathers speed toward the trailing edge of
the airfoil leading to higher convection coefficients on the pressure side of the airfoil
Figure 2 Thermal Loading Throughout a Turbine Blade (Daniels 1982)
Simple convection channels were implemented in the early nineteen sixties as
years passed the cooling techniques became more and more sophisticated allowing the
free stream temperature to increase to previously impossible levels Currently the use of
film cooling coupled with backside impingement leads the turbine cooling technology
The trend of allowable turbine inlet temperature is shown in Figure 3 from this figure it
can be seen that the allowable free stream temperature has increased around 600 degrees
in the past 50 years The addition of thermal barrier coatings also helps in the increase in
allowable combustion temperatures by creating an extra resistance that the heat needs to
move through as it moves from the combustion gasses into the coolant air It is impotatnt
to notice that as seen in Figure 4 the increase in turbine inlet temperatures is done with
the combined benefits of new alloys TBC and cooling technologies
4
Figure 3 Allowable Turbine Inlet Temperature vs Cooling Techniques over the Years (Clifford 1985)
Figure 4 Turbine Inlet Temperature Increase with the help of TBC New Super Alloys and Cooling
Technologies (Kapat and Kiesow Lectures 2010)
The cooling of inlet guide vanes can be done with the use of impingement inserts
inside the airfoils As air passes through the miniscule holes in the inserts a jet is formed
which then impinges on the wall of the airfoil producing one of the largest single phase
heat transfer coefficients This already impinged coolant air is then bled out as film
5
cooling as well as bled out through the trailing edge Figure 5 shows a stator vane with
the impingement insert in black the film cooling extraction as well as the trailing edge
bleed
Figure 5 Turbine Stator Cooled with Impingement Coupled with Film Cooling (Florschuetz 1980)
The cooling of turbine airfoils with the use of an impingement insert is only
possible in stationary components as the rotating ones are subject to centrifugal loadings
making it unfeasible to cool them with this setup Rotor blades are typically cooled with
serpentine passages that have heat transfer enhancing features such as ribs dimples and
other turbulators these serpentine passages are located in the mid chord of the blade On
the trailing edge a bank of pins are used to obtain high convective coefficients in the thin
region the coolant is the bled out to compensate for the boundary layer created around
the airfoil Rows of impingement holes cool the leading edge The spent air is then bled
out through showerhead cooling Figure 6 and Figure 7 show in detail the cooling
channels around two similar airfoils airfoils
6
Figure 6 Rotor Blade Cooling Configuration (Gladden 1988)
Figure 7 Cross-section of Turbine Airfoil with Cooling Channels (Han et al 1984)
7
The coolant air is bled out from the later stages of the compressor This air is
expensive as it has been compressed and not under gown the heat addition by
combustion It is imperative that the minimum amount of coolant is used in these cooling
configurations The cooling must also be as uniform as possible to reduce thermal
stresses within the blades leading to a higher component life Figure 8 shows freestream
metal and coolant temperatures of the flow blade and coolant air It can be seen that a
decrease of 25degrees in the surface temperature of the blade can provide an airfoil with
twice the working life Impingement cooling has great potential to provide high heat
transfer coefficients at a small flow rate Impingement of a jet onto a surface provides
high heat transfer coefficients due to a starting boundary layer as well as its high
turbulence When the jet is located around 3 diameters from the target surface the heat
transfer profile has two peaks one located at the stagnation region and the other located
between one and 3 diameters from the stagnation region As the jet is moved away from
the target wall the secondary peak diminishes leaving a profile with a maximum at the
stagnation region decreasing radialy
Figure 8 Relative Temperatures for Hot Gas Metal Temperature and Coolant Temperature (Cardwell 2005)
Cardwell N D 2005
8
Figure 9 shows a diagram of a jet impinging on a target surface The potential
core is the part of the jet that has not been affected by the surrounding stagnant fluid As
the jet moves towards the target wall its momentum diffuses into the surrounding fluid
decreasing the velocity at which it reaches the target wall and potentially decreasing the
corresponding heat transfer coefficient Studies have shown (Martin 1973 for example)
that the potential core may last anywhere between 7 to 10 diameters The successful
impingement of the potential core yields significantly higher heat transfer coefficients
than a fully diffused jet this comes however at a cost of higher pressure drop across the
jet plate as well as a highly non uniform heat transfer profile
Figure 9 (a) The Development of the Wall Jet (b) Jet Diffusion to Surroundings (Liu 2006)
9
CHAPTER TWO LITERATURE REVIEW
21 Impingement Literature Cornerstone
From the early days of simple convective cooling channels in turbine airfoils
studies have been done on modes of enhancing heat transfer coefficients while
maintaining a low pressure drop and minimum mass flow rate Heat transfer
characteristics of single round nozzle impingement were studied in the late 1960rsquos and
early 1970rsquos The collected works of many authors is combined into ldquoHeat and Mass
Transfer between Impinging Gas Jets and Solid Surfacesrdquo by Holger Martin 1977 The
paper collects works from multiple authors who studied single round nozzle impingement
effects on heat and mass transfer coefficients In this compilation non dimensional jet to
target spacing was studied they ranged from ZD=12-10 providing plots of Sherwood
number as a function of radius for four different jet to target spacings The local
Sherwood number was also given for a slot jet for HS ranging from 5 to 20 Studies on
impingement jet arrays were also gathered alongside an array of slot jets Correlations
were given for multiple setups present in the paper Circular jet arrays and slot arrays are
studied in detail with both analytical and experimental approaches The paper also
combines studies done on swirling jets turbulence enhancers on the target surface
impingement on concave surfaces and angle of attack variations Optimization studies
were also done to find the optimal spacing for round and slot jet arrays
Florschuetz studied the heat transfer characteristics of an array of jets impinging
on a flat surface This study was guided towards finding an optimal spacing for an array
for jets used to cool the midchord of turbine airfoils similar to that found in Figure 5 His
main contributions include a Nusselt number correlation as a function of jet to target
10
spacing jet Reynolds number and other flow and geometric parameters He found that an
increase in hole spacing and channel height resulted in a decrease of heat transfer He
also provided a one dimensional jet mass flux and channel mass flux correlations
His Nusselt number correlation takes the form of
Where A B and n are dependent by the two different types of arrays inline or staggered
Liu studied new techniques in temperature and pressure measurements of a single
slot jet with the use of temperature sensitive paint or TSP and pressure sensitive paint or
PSP In his work both measurement techniques are explained in detail Since TSP is the
only tool from that study currently used in this work it will be explained further in the
experimental setup section
11
22 Relevant Impingement Channel Studies
Al-Aqal 2003 studied three different types of impingement channels The use of
TLC was implemented in this work to obtain heat transfer distributions for the target
wall The three different configurations varied the number of holes in the streamwise and
spanwise directions The first channel had a single row of 6 streamwise jets the second
consisted of 2 rows of 12 streamwise holes summing up to a total of 24 holes The last
channel is a triple spanwise row with 18 streamwise jets This last geometry is the most
similar to the one present in the current study The third geometry will be used to
compare results There are differences however the total width of the channel is of 16
diameters as opposed to 8 in this study The streamwise jet spacing is also different Al-
Aqal used an XD of 65 compared to XD = 5 in this study The jet to target plate
spacings are similar on two occasions as he studied a ZD=4 6 and 8 while this work
uses a ZD = 6 8 and 10 Average jet Reynolds numbers also fall within the range of this
study as they range between 5000 and 33000 The author provides span averaged plots
for all cases and Reynolds numbers convenient when comparing the results
Ricklick 2009 studied a channel similar to the one found in this study His
channel was composed of a single row of 15 jets with a YcD = 4 XD = 5 and 15 and
ZD = 1 3 and 5 Two channels were tested one was pressure fed while the other was fed
by suction TSP was used to gather temperature data of all four wetted surfaces on the
pressure channel and two surfaces on the suction channel Since the maximum jet Mach
number was less than 03 the flow was assumed to be incompressible leading to the
conclusion that both channels contain identical flow patterns Thin foil heaters were used
to create the required heat flux for the channel Besides channel geometry Reynolds
12
numbers and heater geometry Ricklicksrsquo experimental setup is identical to the one
presented in this work The author also provided an ample comparison of his results to
literature He provided thermal performances of the entire channel at different Reynolds
numbers and channel heights
A small CFD study was also done A paved mesh was created on the target wall
with finer mesh near the impingement locations The resulting y+ at the wall was higher
than one yielding potentially faulty heat transfer values however this is acceptable since
the CFD was used as a tool to better understand the flow physics and help understand the
experimental heat transfer profiles
23 Computational Studies on Impingement Channels
El-Gabry did a numerical study of jet impingement with cross flow Two different
turbulence models were compared in their ability to predict surface Nusselt number The
Yang-Shih and standard k-ε models were used to compute the flow generated by jets
angled at 30 60 and 90 degrees with cross flow The computational results were
compared to previous experimental work by El-Gabry Comparisons to experimental
results at ZD = 1 and 2 90deg injection angle between Yang-Shih and standard k-ε The
error in the average Nu from the experimental results and both turbulence models were
calculated It was found that the Yang-Shih model behaved well at low Reynolds
numbers with the average Nusselt number being 5 off from the experimental value
while the standard k-ε was off my 94 As jet Reynolds number was increased the error
of the standard k-ε model dropped to as low as 39 while the error from the Yang-shih
model increased to -76 The span average plots show the experimental data Nusselt
number alongside the span averages of the results acquired by the Yang-Shih and
13
standard k-ε models High Nusselt numbers occur at the impingement location decreasing
thereafter after another impingement location is found The frequencies of these
variations are all the same for the experimental and the two numerical solutions The
amplitude of fluctuations between the impingement locations and the areas in between
are much larger for both of the numerical results however the Yang-Shih model over
predicts at the high Reynolds number for the ZD=2 case Since the amplitude of
fluctuations is greater for the CFD solutions it is important to note that even though the
error in average Nusselt number is not great the actual differences in the profile are much
greater upwards of 20 difference of heat transfer coefficients between the experimental
and numerical heat transfer peaks Other variations were studied (Injection angles for
example) but will not be discussed as their importance to the current study is minimal
Zuckerman compared a much wider set of turbulence models in their ability to
successfully predict Nusselt numbers caused by jet impingement The models tested were
k ndash ε k-ω Reynolds Stress Model algebraic stress models shear stress transport and
lastly the υ2f turbulence model DNS runs are extremely time consuming to run
therefore LES was run on its behalf to provide results for the unsteady turbulence
models The paper summarizes all the different models used their computational cost
impingement heat transfer coefficient and their ability to predict the second peak in heat
transfer As expected DNSLES provide the best prediction of both stagnation and
secondary peak heat transfer coefficient however this comes at a large computational
cost The k ndash ε and k-ω provide poor heat transfer results for the stagnation region where
they can have 30 error from the correct value The Realizable k ndash ε model provides
14
better heat transfer results while still maintaining a low computational cost The highest
accuracy to cost ratio was achieved by the υ2f model where it predicts the heat transfer
coefficient for the surface with a minimum of 2 error while not being as expensive as
the other unsteady models such as DNS and LES Ideally the CFD portion of this work
would be run with the υ2f model however since the code used to run the simulation
FLUENT does not have the υ2f model a realizable k ndash ε model will be used with
enhanced wall functions for both thermal and velocity gradients
15
CHAPTER THREE EXPERIMENTAL SETUP AND TECHNIQUES
31 Temperature Measurements with TSP
Temperature sensitive paint or TSP provides the capability of measuring
temperatures over the painted area This measurement technique supersedes the
advantages of other temperature measurement devices such as thermocouples because it
provides the user with data over a large area rather than point temperatures given by
thermocouples
Uni-Coat TSP is purchased from ISSI It is very robust to different working
conditions Calibration done on one batch of paint can be used for multiple cans as the
product is highly consistent The paint is calibrated in a dark booth a painted coupon is
placed on the hot side of a thermoelectric heat pump working on the Peltier effect
thermal paste is used to minimize contact resistance between the hot side and the TSP
coupon Calibrated thermocouples are placed in between the TSP and the thermoelectric
heat pump A reference temperature and picture are taken and the calibration commences
At least 5 or 6 data points should be taken to form the calibration Intensity ratios are
taken between the hot and cold pictures They are then plotted versus their corresponding
temperature
The paint consists of fluorescent molecules suspended in a binder These
molecules with a certain wavelength of light will be exited to a higher energy level The
molecules then can dissipate some of the energy by transferring it vibrationally to its
neighboring binder particles and dissipate the remainder of the energy by radiating it as a
photon as the molecule comes down to its original ground state Since the amount of
16
energy that the particle can transmit to others through vibration is directly proportional on
temperature and the total initial energy is fixed by measuring the ratio of the intensity at
a known temperature (reference picture) and intensity of the unknown temperature
feeding it through the correlation the unknown temperature can be found to an
uncertainty of 1 K Figure 10 shows a simplified Jablonski diagram adapted from the
suppliers website The blue arrows signify the blue light used to excite the luminescent
molecule Tris(22rsquo-bipyridyl) Ruthenium(II) Chloride Hexahydrate with a shellac binder
in our case The shellac binder is impermeable to oxygen opposite of that found in PSP
due to PSP relying on the presence of oxygen for it to function Once the particle is
excited it can give off the energy in two different ways one is by emitting it back out as
another photon of the same energy and therefore wavelength The second mode of the
particle to lose its energy is through vibrational relaxation This second process is directly
dependent on the temperature ie the higher the temperature the higher the probability
for it to lose energy to its surroundings Once it loses some energy to the surrounding
particles it releases the remainder of the energy as a photon of less energy of that which
excited it originally hence why a long pass filter is installed in the CCD camera For a
more descriptive explanation of the way TSP works refer to Liu 2006
17
Figure 10 Simplified Jablonski Diagram (Adapted from ISSI Website)
Throughout the past two years there have been numerous projects at CATER that
have used TSP Painting surfaces with TSP should be done carefully by someone who
has experience with spray painting since every single can costs $500 A single can should
be able to paint an area the size of an acrylic plate that is 36rdquo wide and 24rdquotallThe
sidewalls and the target wall of the impingement channel were painted with the use of
less than one can Painting on different surfaces is difficult for example when painting
Rohacell the paint canister can be held very close to the surface while spraying due to
the surface being somewhat porous and rough however when painting straight onto
metal heater strips the can should be placed as far back as possible for the first run
Ideally for the first pass through only a slight mist should be applied If the can is being
held too close to the surface the paint will run Figure 11 shows a set of heater strips that
has been painted too closely leading the paint to drip down Ideally the paint would be
applied to the surface in as many coats as possible Of course this would be time
18
demanding and impractical therefore with the knowledge that I have gained through the
multiple TSP paintings on different surfaces I have compiled a list of TSP dos and
donrsquots
Dos
Clean the surface to be painted with acetone or break parts cleaner Break
parts cleaner is preferable over acetone as it does not leave an oily residual
after cleaning
Paint the first coat as thin as possible Most of the surface should not be
covered There should be an even mist of miniscule TSP circles This will
give the later coats something to attach to
When positioning the test section to paint make sure to wipe it one last
time as small dust particles may have attached to the surface
Stop if you see small bumps in the paint This is caused by dust particles
collecting all the paint around it while it is still wet due to surface tension
Clean the surface and repaint This should be noticeable in the first few
coats If you see this pattern happening do not continue thinking it will be
covered by future coats What will happen is the problem will get worse
and worse ultimately the surface will have to be cleaned again and
repainted
When painting test sections try to paint the smallest section as possible
This will not only save paint but will make it very simple for the post
processing code to crop out the unpainted areas
19
Let the finished painted surface to sit at least for 90 minutes after the last
coat before baking There have been problems when baking steel and
acrylic test sections with the paint cracking while baking right after the
last coat Normally the finished surface is left to dry overnight and baked
first thing in the morning
For test sections that are too large to be baked in the oven the heat gun
may be used Carefully place a thermocouple in a central location with
blue painters tape The heating should be uniform and should not take
more than 20 minutes of continuous blowing When the thermocouple
reaches 80-90 C the plate can be assumed to be baked To introduce a
factor of safety in the baking it does not hurt to bake it longer than it
normally takes
Once the test section is mounted and ready to run cover it with cloth that
does not let any light through This will protect the paint for further uses
This is especially important on test sections that can be used multiple
times like the ones found in this study
When the test is running turn off the LED lights This light is the most
damaging to the TSP as it degrades the quality of the fluorescent
molecules
If there is a particular head of the TSP can that you prefer over others you
can remove it once the can is empty It is difficult to get used to a single
kind of nozzle being able to transfer it from can to can is a must if
painting consistency is to be kept
20
Donrsquots
Do not clean a test section that has already been used with too much
acetone The acetone is volatile evaporating quickly cooling the test
section rapidly If this test section has had heaters attached to it and run
previously the acrylic will crack due to uneven stresses inside of it
If paint is dripping stop painting immediately Clean the surface and start
over Hold the can far from the surface in order for it not to drip
Do not use TSP to teach new apprentices undergrads or graduate students
how to paint Regular spray paint is two orders of magnitude lower in cost
while the painting process is exactly the same
Do not paint with the doors closed The paint contains carcinogens that
can harm the lungs Always use a respirator and keep the room well
ventilated In-situ painting and baking has not been tried however it may
be a real option if the test section is difficult to disassemble and easily
accessible to painting and baking
If there is a can of paint that contains too little paint for the test section
that needs to be painted try to find a new can The mixing of two different
cans of TSP can be dangerous at times however it has been noticed over
the years that ISSI provides a very robust and dependable product that
does not vary significantly from batch to batch
21
Figure 11 Heater Strips Painted with TSP Too Closely
32 Experimental Setup of Suction Channel
The impingement channel is fed under suction As seen in Figure 12 air enters
through the plenum it crosses the jet plate as it gains speed to form the jets
which then impinge on the target wall The flow then passes through a venturi
flow meter and finally through the blower into the atmosphere A bypass valve is
used to control the flow rate of the impingement channel
22
Figure 12 Flow Loop of Impingement Channel
The impingement channel consists of 15 streamwise rows of 3 spanwise jets each The
total width of the channel YcD is of 8 diameters while the streamwise spacing between
the rows is XD=5 the spanwise distance between the holes is of YD=2 Figure 13shows
the top view of the jet plate The plate is counter bored to ensure that a nearly flat
velocity profile of the jet is achieved Figure 14 shows the front view of the channel Z is
denoted as the distance between the jet and target plates Side walls are interchangeable
to change the height of the channel to 6 8 and 10 diameters Two thirds of the
streamwise rows can be covered to change the XD from 5 to 15
Figure 13 Top View of Jet Plate
23
Figure 14 Front View of Impingement Channel
The target and sidewalls had heaters made specifically for them in a serpentine
style This was necessary to increase the resistance as the VARIACs used to power them
only had a maximum current output of 20 amps The heater strips are two diameters
wide at each end copper tape with conductive adhesive was used to connect the leads to
the power supply The heater consists of 50 micron thick steel sheet sandwiched between
two pieces of Kapton tape The heater is attached to the painted surface with the use of
double sided Kapton tape The target test section can be seen in Figure 15 also seen in
this figure are the two Teflon gaskets lined on the sides of the target plate With the target
wall bolted onto the sidewall the gasket is compressed generating a strong seal
Figure 15 Target Wall Test Section with Heater Leads
24
For this study the test matrix shown in Table 1 will be run Target and side wall
data will be taken at three different impingement heights at two different Reynolds
numbers of 7500 and 15000 denoted by A and B respectively A streamwise jet spacing
study is also done by testing the target and side wall heat transfer at an XD=15 for the
low impingement height channel
Table 1 Test Matrix
XD ZD Wall Re
5
10 TW
7500
15000
SW 7500
15000
8 TW
7500
15000
SW 7500
15000
6 TW
7500
15000
SW 7500
15000
15 6 TW
7500
15000
SW 7500
15000
33 Data Processing and Reduction
As described previously when taking temperature measurements with the use of TSP
reference temperatures are noted and a reference picture is taken The experiment is the
run once the experiment reaches steady state a new set of 4 pictures is taken Given the
calibration curve temperatures are backed out
25
Given the amount of heat generated inside the heater
Dividing by the heated area to get heat flux
Heat loss tests were run to consider how much of the heat flux generated by the heaters
goes through the backside instead of into the flow It was found that 25 of the heat flux
leaks out to the atmosphere through the acrylic In order to account for this heat leakage
it must be subtracted from the calculated value to become
Where Ah is the effective heated area given by
Where Aunheated is an estimate of how much unheated area is between the heater strips (~
3 of the total area)
To obtain heat transfer coefficient
Where Tref is the reference temperature Typically set in literature to be the jet
temperature
To obtain the average Reynolds number for the jets the total mass flow rate is used
Where Dj is the jet diameter and μ is dynamic viscosity (1983kgm s at 300K)
26
Pressure measurements were taken at the sidewall after the last jet entered the channel
These pressure measurements were used to determine the thermal performance of the
tallest two channels (ZD = 8 and 10)
The thermal performance at constant pumping power is found by using the equation
Where h is the average heat transfer coefficient for the target wall of them impingement
channel and ho is the heat transfer coefficient obtained by passing the same amount of
flow through a smooth duct ie the Dittus-Boelter correlation The friction factor f is
found with the use of
Where Ppl is the plenum static pressure assumed to be atmospheric and Plast jet is
the pressure read after the last jet V is the volumetric flow rate divided by the cross-
sectional area of the duct after the last impingement row The hydraulic diameter of the
channel is set to be
The baseline friction factor was calculated with the use of the Moody chart the hydraulic
diameter and the total mass flow rate though the channel Thermal performance at
constant pressure drop was also calculated with
27
34 Uncertainty Analysis
A simple uncertainty analysis was done to estimate the error in calculation of the
heat transfer coefficient from the given outputs of the test data From the bare basic
measurements for voltage area current temperature of thermocouples and temperature
profiles of paint a simple uncertainty analysis can be done to estimate the error for the
calculated heat transfer coefficient Figure 16 shows the different sources of error in the
calculation of heat transfer coefficient The effective uncertainty was calculated by taking
the root of the sum of the squares of all the individual percentage errors The
experimental uncertainty for heat transfer coefficient was of 703 This error may be
reduced by acquiring higher temperatures of the TSP reading current with a more
accurate ammeter or reading reference temperatures with the use of a thermopile instead
of a single thermocouple
Figure 16 Heat Transfer Coefficient Uncertainty Tree
28
35 Lateral Conduction Analysis
To take into account the lateral conduction occurring inside the heater foil while
the test is running two simple 1D conduction and convection equations were used to
quantify the amount of heat moving through the heater laterally and the amount of heat
convecting into the air The lateral conduction is expected to be at a maximum at the
places where there are large spatial variations of surface temperature which is why the
ZD = 6 XD = 5 case at high Re is chosen to be studied Figure 17 shows the
temperature distribution of the aforementioned case Four cold spots can be seen by their
distinct blue and yellow color located at the stagnation regions The maximum
temperature gradient occurs between the third jet impingement and the middle region
between jets The temperature difference was seen to be of 13degC The distance in between
these two temperatures is of 25D=01875m The corresponding heat flux between these
two points was calculated to be 13000Wm2 with ksteel~20Wm K A region of 1cm by
1cm was then created and the amount of heat calculated through conduction and
convection were compared To acquire the amount of heat removed through conduction
a heat flux of 13000Wm2 was imposed through an area of 01m by 00005m this
equaled to 00277 W The amount of heat moved through convection was calculated by
multiplying the heat flux used during the test by the area of the square 0001m2 the
resulting heat moving through the heater onto the air is 6 W Since the heat moving
through to the air is two orders of magnitudes larger than the heat moving laterally the
effective lateral conduction can be neglected
29
Figure 17 Temperature Profile of First Five Impingement Rows
A second order approach was also taken to quantify the amount of lateral
conduction in the heater The temperature gradient was taken from high peaks in heat
transfer caused by the second row of impingement of the same ZD=6 XD=5 channel at
high Re Figure 18 shows the high heat transfer coefficients created by the second row of
jets A quadratic curve fit was obtained by for this small region so that a continuous
equation of heat transfer coefficients as a function of streamwise distance was quantified
30
Figure 18 Detailed View of First Heat Transfer Peak with a Polynomial Curve Fit
The net heat gained by a differential volume from lateral conduction is the
difference in the temperature gradient at the entrance and the exit multiplied by the
thermal conductivity and cross sectional area Using this method shown in Figure 19 the
net change in convective heat transfer due to lateral conduction can be studied
Figure 19 Control Volume Heat Transfer Analysis
By taking the difference between the out flowing heat trough the right side and
the inflowing heat from the left side a net gain or loss can be found Figure 20 shows the
y = -470630x2 + 31244x - 14842Rsup2 = 09934
300
310
320
330
340
350
360
370
380
0 001 002 003 004 005
HTC
(W
m2K
)
x (m)
Heat Transfer Peak
Poly (Heat Transfer Peak)
31
difference in magnitude between the out flowing heat through convection seen in red and
the net inflow of heat from lateral conduction in blue From these calculations it was also
found that the amount of heat moving through lateral conduction is tow orders of
magnitude smaller than the amount of heat moving out through convection leading to the
belief that even at high temperature gradients lateral conduction does not play an
important role in the ongoing heat transfer processes in the impingement channel A more
detailed calculation of this work can be seen in appendix A
Figure 20 Heat Loss through Convection and Lateral Conduction
002 003 004 0051 10
5
1 104
1 103
001
qconv x( )
qnet x( )
x x
32
CHAPTER FOUR HEAT TRANSFER RESULTS
41 Heat Transfer Validation
In order to obtain confidence in our experimental setup an experiment was made
to test something that has already been published in literature A smooth channel was the
obvious choice as it was easy to setup by taking off the end cap and blocking all the holes
with smooth blue painters tape on the flow side and metal tape on the plenum side to
ensure no leaks into the channel from the jet plate The smooth channel has been studied
widely and multiple correlations exist one of these equations is the Dittus-Boelter
correlation (Incropera 2007) The test was run using the ZD=6 side wall so that the
hydraulic diameter was a minimum Figure 21 shows the span averaged results versus
non dimensional distance into the channel
Figure 21 Validation Spanwise Averaged Results
0
10
20
30
40
50
60
0 1 2 3 4 5 6 7 8 9
HTC
(W
m2K
)
XDc
Span Avg
Dittus Boelter
33
The plot shows decreasing heat transfer coefficient with increasing XDc due to
the developing thermal boundary layer The span average does not reach the Dittus-
Boelter due to it not being fully developed in the limited space it is given Typical flows
can take up to 60 diameters to achieve a fully developed profile with the current setup
the maximum length of the channel was of 9 diameters The profile however seems to
have an asymptote at the Dittus-Boelter correlation value leading to the belief that if the
channel was longer that value given by the correlation would be reached One important
factor to take into account in determining whether the experimental setup is validated is
the fact that the Dittus-Boelter correlation has an uncertainty near 30 Since the span
average at high XDc is well within 30 from the calculated value it is safe to assume
that the current experimental setup is validated
42 Heat Transfer Results
Heat transfer results are compared based on variations in channel height and
average jet Reynolds number As discussed earlier there are numerous other parameters
also affecting the heat transfer in these channels As these parameters are changed flow
structures within the channel are expected to be altered as well as discussed in the
literature Two of the major contributors to heat transfer in these channels are the
successful jet impingement and the resulting cross flow The same domain is captured in
both the local and averaged results
Figure 22 through Figure 25 highlights the heat transfer distribution for the cases
with a jet to jet spacing of 5 diameters in the streamwise direction and of 2 in the
spanwise direction It is evident that the smallest channel height (ZD=6) performs the
best at all Reynolds numbers on all surfaces It is also interesting to note the similarity
34
in the target wall profiles between case 528A and B where the curves are very similar
other than the obvious offset due to the change of the Reynolds number At this large
spacing we also see the degradation of the jets a few diameters downstream of each
impingement location The downstream shifts of the peaks are evident after the second
and third row of jets Also evident in these plots is the deflection of the impinging jet and
the wall jets from the cross flow The cross flow is forced to flow around the jet
deflecting the spread of the wall jet in the downstream direction Impingement locations
are also very evident at low XD however as XD and therefore the cross flow increase
the magnitude of the peaks start decreasing and eventually level out to pure internal flow
Figure 22 Target Wall Heat Transfer Coefficient Distributions
35
Figure 23 Span-averaged Target Wall Heat Transfer Distribution
36
Figure 24 Side Wall Heat Transfer Coefficient Distributions
37
Figure 25 Span-averaged Side wall Heat Transfer Distribution
Figure 23 and Figure 25 show similar details with impingement peaks clearly
diminishing and shifting in the downstream direction The cross flow clearly has some
negative influence on these geometries when compared to the more traditional
impingement highest on the order of 1 to 5 jet diameters The heat transfer profiles of the
target wall for all heights seen in Figure 22 and Figure 24 show the rapid decay in heat
transfer after the third jet This can be explained by understanding that the first jet does
not have any cross flow to deflect it the second jet only has the first jet worth of
momentum deflecting it downstream however since the channel is so tall the
momentum of the cross flow after the first and second jet are not enough to greatly
disturb the incoming jets After the third jet however the cross flow builds up enough
momentum to greatly affect the integrity of the jets downstream causing the span-
0
20
40
60
80
100
120
140
160
2 12 22 32 42 52 62 72
HTC
(W
m2K
)
XD
5210B_SW 528A_SW Jet Location
526A_TW 526B_TW
38
averaged heat transfer to rapidly drop The point at which the crossflow starts taking a
considerable effect occurs around XD =35 The target wall profile of the ZD=10
channel shows the outside jets on the second row of jet deflecting downstream It can be
conjectured that the bending of the outside jets downstream is caused by the wall jet
created by the first row of jets separating from the side wall and deflecting the outside
jets of the following rows of jets The heat transfer profile for the ZD case excludes the
first jet due to shadows being present when the data was taken
Also evident from this spanwise averaged data is the increase in heat transfer
with increases in Reynolds numbers and decreases in impingement height Results tend
to be the closest from case to case at the first impingement jet This is a reasonable
result as the effects of cross flow have little to no effect at the first few impingement
locations The impact of the jet would then be the driving force at these locations and
would be similar between cases except if the potential core is not reaching the target
surface The potential core of a jet tends to last between 6 and 10 diameters from its
origin It can be seen that the difference in heat transfer coefficient in the first two jets for
the ZD=8 and ZD=10 channel is much different than the corresponding difference
between the ZD=6 and ZD=8 heights This decreased difference between the heights of
the peaks may be attributed to the potential core reaching the target wall at the heights of
6 and 8 diameters leading to similar profiles and may not be reaching the surface at the
height of 10 diameters The heat transfer values of the peaks diminish in the downstream
direction The range of fluctuation also drops that is the profile becomes more uniform
at large XD This drop in fluctuation is more visible at the tallest channel height
(ZD=10) and less pronounced at the smallest channel This is due to the jet in the small
39
channel having to travel a shorter distance to impinge on the target plate leaving the
crossflow less time for it to deflect the jet as opposed to the tall channel where the jet has
to travel almost twice the distance as the ZD=6 channel for it to impinge on the target
wall This effect cannot be solely explained by the built up cross flow in the channel
Mixing loses also take part in the degradation of the stagnation size of the downstream
jets The mixing losses have much greater effect on the taller channels due to the same
reason that the cross flow has a higher impact on them too the jets have to travel a large
distance before hitting the target plate leading the stagnant or moving surrounding air to
be a sink of its downward momentum for a longer time and distance than the respective
smaller channels The heat transfer coefficient of the side wall was also analyzed
Similar effects are expected on the side wall due to the expected impact of the wall jet
As expected the strength of the cross flow is not enough to prevent wall jets from
successfully impacting the side wall at small XD jet locations however the crossflow
takes dominance at around XD=25 Also evident in these plots is the concentration of the
wall jet impact to the bottom of the channel on the order of 1-2 diameters in height It is
interesting to note that for the 5210B case in Figure 24 as the first jet diffuses outward
it impacts the sidewall at a height of ZD=6 The height at which the diffused jet affects
the sidewall heat transfer coefficient decreases as the crossflow increases The stagnation
regions are also deflected in the downstream direction similar to the target surface
results These effects are most evident in the 5210B Similar characteristics can be
explained from the spanwise-averaged plots shown in Figure 25 These results again
clearly show the effects of increasing the impingement height and increases in Reynolds
number As the height is increased the effect of the wall jet is significantly reduced
40
partially due to the increased surface area much of which is not affected by the wall jet
The diminishing effect of the cross flow accumulation is also evident in these plots as the
heat transfer peaks decrease in the downstream direction
43 XD Comparisons
The streamwise jet spacing was changed from XD=5 to 15 by covering two out
of three rows of jets This was done by covering the impingement holes inside the
channel with smooth blue painters tape and sealing the plenum side of the jet plate with
metal tape to ensure no leakage The profile is expected to be less uniform than the case
where XD=5 due to the large spreading of the high heat transfer peaks Due to the large
separation between the rows of jets there is a lower amount of downward momentum
than the equivalent XD=5 geometry for this reason it is expected to see a lower heat
transfer peak due to the jets momentum diffusing out faster to the stagnant air decreasing
the effective impingement velocity Figure 26 shows the target wall heat transfer
distribution Similar to the XD=5 profile it can be seen that the heat transfer due to the
jet impingement drastically reduces after the third jet This phenomenon leads us to
believe that at both Reynolds numbers the cross flow generated by the first three jets is
powerful enough to effectively deflect the fourth jet downstream diminishing its heat
transfer performance The similarity seen in Figure 26 between high and low Reynolds
number implies that the downstream deflection of the jets is not dependent on the jet
Reynolds numbers
41
Figure 26 XD=15 Target Wall Heat Transfer Profile
42
Figure 27 XD=15 Span-averaged Target Wall Heat Transfer Distribution
On the span averaged plots seen in Figure 27 the downstream deflection of the
jets is evident however as described previously the shifts in the peaks of heat transfer
occur at the same xD for both Reynolds numbers The amplitude of fluctuation of heat
transfer coefficients for the high Reynolds number case is larger than that of the low
Reynolds number Both profiles seem to start to level off at the end of the impingement
channel with the lowest span average being located just before the fourth jet at both
Reynolds numbers
A comparison of target wall heat transfer coefficients between XD =15 and 5 is
shown in Figure 28 At first glance it is clearly visible that the XD=15 average heat
transfer coefficient is smaller than its XD=5 counterpart This is also noticed by Ricklick
where he showed average HTC profiles for larger XD to be smaller than those at lower
XD (Ricklick 2009) This may occur due to there not being as high downward
0
50
100
150
200
250
300
350
0 20 40 60 80
HTC
(W
m2
K)
XD
Low Re
High Re
Impingement Location
43
momentum for the XD=15 case as compared to the XD=5 due to the lack of close jets
The stagnant air around the spaced out jets is taking away more of its momentum
decreasing the effective impingement Reynolds number Also important to notice is the
fact that since the XD=5 case has three times the flow impinged into it the cross flow
velocity and therefore Reynolds number will be three times as large increasing the heat
transfer coefficient
Figure 28 Target Wall Span-average Comparison of XD=5 and 15 at High Re
The side walls also show similar patterns to their XD=15 counterparts Strong
wall jet impingement can be seen on the side wall at low xD and zD Figure 29 shows
areas where the wall jet generated by the target wall impinges on the sidewall Similar to
the profile seen in Figure 24 the high heat transfer region reaches upward in the z
direction up to a height of 4-5 diameters for the first jet This high heat transfer stagnation
region decreases as xD increases to the point where the wall jet created by the last jet is
negligible when coupled with pure channel flow
0
50
100
150
200
250
300
350
400
0 10 20 30 40 50 60 70 80
HTC
(W
m2K
)
XD
XD = 5 XD = 15 Jet Location
- Blocked for XD =15
44
Figure 29 Side Wall Heat transfer Coefficient Profile
The span averaged plot seen in Figure 30 shows a nearly flat profile with peaks
located at the stagnation regions of the wall jets Thw downstream deflection for the
XD=15 case is much more pronounced than the one for the XD=5 case This is due to
the jet not being constrained by the wall jets generated by the previous and latter
impingement locations In the XD=15 case the wall jet is free to move downstream
more so than the XD=5 due to it not being disturbed by anything other than the cross
flow
45
Figure 30 XD=15 Side Wall Span-averaged Heat Transfer Coefficients
44 3D Comparison of the Heat Transfer Profiles
In order to further understand the targetsidewall interactions both heat transfer profiles
were positioned in an isometric view representative of the channel One important thing
to note is that both target and side wall profiles are not on the same scale This form of
data display is only qualitative way to describe the heat transfer profiles Figure 31 shows
the 3D profile of the XD=5 ZD=6 case The both stagnation regions of the jet onto the
target wall and the wall jet into the sidewall can be seen to occur at the same location for
the first three streamwise rows After the fourth and fifth row the wall jet diminishes in
magnitude Also visible in this view is the increasing heat transfer at low zD towards the
end of the channel of the side wall The constant input of mass and downward momentum
into the channel causes the cross flow generated by the previous jets to be squeezed into
the lower third of the channel increasing the velocity and the heat transfer of the target
wall
0
20
40
60
80
100
120
0 20 40 60 80
HTC
(W
m2K
)
XD
Low Re High Re Jet Locations
46
Figure 31 3D Heat Transfer Profile for ZD=6 XD=5
Similar patterns are seen in the taller ZD=8 channel seen in Figure 32 The wall jet
generate by the third streamwise row of jets is been deflected downward more than its
ZD=6 counterpart This can be attributed to the fact that the jet located at the ZD=8
channel has lost much of its momentum and is more easily bent downstream by the cross
flow generated by the first two jets The ZD=8 sidewall shows similar increasing heat
transfer at high xD however the increase is not as drastic as the one found in the ZD=6
channel This is caused due to the extra two diameters the jets have to cover to impinge
on the surface since the ZD=8 channel is one third larger than the ZD=6 one the flow
has to have more area to flow through The last few jets only deflect the cross flow
downward about 4 diameters this leaves two diameters for the flow to pass through on
the ZD=6 channel causing the velocity to increase rapidly and therefore increasing the
heat transfer coefficient at the low zD Since the ZD=8 channel has four remaining
47
diameters for the flow to move through it does not deflect it as much as the ZD=6
channel does only increasing the cross flow velocity and resulting heat transfer
coefficient slightly over the area at low zD and high xD
Figure 32 3D Heat Transfer Profile for ZD=8 XD=5
The 3D heat transfer profile for ZD=6 and xD=15 channel seen in Figure 33 shows
similar details to those seen in the XD=5 channels The stagnation regions of the jet and
wall jet occur at the same x location for the first three rows of jets the wall jet generated
by the fourth row of jets is deflected downstream only generating as small region of high
convective coefficients at the side wall The region located at the top right corner of the
side wall is colored red signifying high heat transfer however this area is generated by
the heaters providing non uniform heat flux at this location This region of high heat
transfer coefficients also occur at xD=0-4 of the target wall where the heater coil bends
48
Figure 33 3D Heat Transfer Profile for ZD=6 XD=15
45 Thermal Performance Calculations
Thermal performance calculations were done on the two tallest channels (ZD=8 and 10)
The pumping power was calculated for both channels at two Reynolds numbers Figure
34 shows the ratio of pressures required to pull the same amount of flow through as
smooth duct as opposed to through the jet plate The ZD=10 channel at high Reynolds
number requires the largest pressure as seen in the Figure however in order to pull the
same amount of flow rate through it requires a smaller pressure difference due to the
large cross section
49
Figure 34 Pressure Drop Ratio with Respect to Smooth Channel
Next the heat transfer enhancement was calculated A total area averaged heat
transfer coefficient was taken for the target wall and compared to the smooth channel
Dittus-Boelter value while using the same total mass flow rate Figure 35 shows an
average heat transfer enhancement of four times that of a smooth channel Similar trends
were noticed in the literature (Ricklick 2009) of decreasing heat transfer enhancement
with an increase of jet Reynolds number Ricklick also showed an increase in heat
transfer enhancement with an increase of jet to target spacing similar to the one seen in
Figure 35
0
10
20
30
40
50
60
528A_TW 528B_TW 5210A_TW 5210B_TW
PP
o
50
Figure 35 Heat Transfer Enhancement
Thermal performances at constant pressure drop were then calculated by dividing
the heat transfer enhancement by the pressure increase As seen in Figure 36 all the
values fall well below 1 making the impingement channel an unfeasible mode of heat
transfer enhancement when a constant pressure is supplied
Figure 36 Thermal Performance at Constant Pressure Drop
0
05
1
15
2
25
3
35
4
45
528A_TW 528B_TW 5210A_TW 5210B_TW
hh
o
0
002
004
006
008
01
012
014
528A_TW 528B_TW 5210A_TW 5210B_TW
(hh
o)
(PP
o)
51
The thermal performance at constant pumping drop was calculated in the same
way that the constant pressure drop was calculated the only difference being the pressure
ratio term was raised to the one third power As seen in Figure 37 the thermal
performances at constant pumping power are all higher than unity this signifies that if a
surface needs to be cooled with the supply of a constant pumping power the
impingement channel is a feasible option Similar to the figure literature (Ricklick 2009)
showed a decrease of thermal performance with an increase of channel height and
Reynolds number
Figure 37 Thermal Performance at Constant Pumping Power
0
02
04
06
08
1
12
14
528A_TW 528B_TW 5210A_TW 5210B_TW
(hh
o)
(PP
o)1
3
52
CHAPTER FIVE COMPUTATIONAL FLUID DYNAMICS
51 Problem Setup
In order to further enhance the understanding of the heat transfer profiles showed
previously a computational study was performed Even though CFD does not yield
accurate quantitative results it produces good qualitative data that can be used to explain
the flow physics in the channel and therefore increase the understanding of the patterns
seen previously The channel was meshed with the use of GAMBIT Due to the
symmetry the channel was split in half in the streamwise direction All horizontal
surfaces (parallel to the target wall) were divided into 6 different regions that are later on
going to be meshed individually The six regions are seen in Figure 38 section 1 is
located at the center of every jet also referred to as ldquojet centerrdquo This region was created
to reduce the squewness of the elements near the center of the jet by allowing the mesh to
be completely linear with a squewness of zero Section two complements section 1 to
complete the impingement hole The half impingement hole located at the symmetry wall
contains the same exact region 2 however it only has one half of the jet center Section 3
was made in order to bring the polar geometry of the holes to match the cartesian aspect
of the remainder of the channel With the addition of section 3 to the channel the only
remaining sections are square or rectangular regions Region 4 lies in between
streamwise rows of jets Section 5 is located at the entrance and the exit of the channel
These sections are not square in contrast with section 4 The last remaining section is
located near the side wall of the channel extending from the beginning to the exit of the
channel
53
Figure 38 Horizontal Plane of Impingement Channel Geometry
All the faces of sections 1 and 2 are linked throughout the channel and the
plenum however in order to have greater control of the mesh in the plenum and the
channel the remaining sections 3 4 5 and 6 are not linked to every single similar face
instead they are only linked to similar faces in either the plenum or the channel
Boundary layer spacing number of rows and growth factor are placed around the
channel In order to maintain a y+ of less than unity the first cell spacing of the boundary
layer inside the channel was set to be 000001 m (01mm) This first cell spacing yielded
y+
values varying between zero and 9 at the target side and front end wall Figure 39
shows a contour of y+ values on the heated walls The maximum values occur near the
impingement locations as expected due to large shear caused by the steep velocity
gradient normal to the wall On the downstream direction the y+ also increases due to the
increase of flow rate and therefore the increased skin friction on the wall At the
impingement location of the first jet the y+ is close to zero due to the velocity having its
direction mostly normal to the surface yielding no shear
54
Figure 39 Target Side and Front End Wall y+ Values
Once the faces were linked edge meshes were created on the sides of the jet center
Section 2rsquos inner edge was also meshed using a different parameter than the one used for
the jet center in order to allow for more freedom when trying to refine the mesh These
two edge meshes is followed by meshing all of section 2 faces alongside all the jet
centers Once these were complete section 3rsquos inner edge was meshed with different
parameters for the channel and plenum Sections 4 and 5 sides that connected with the
face made by section 6 were meshed so that their spacing was similar again the plenum
and channel were meshed separately for increased control of mesh density in both of
these areas The upstream-most edge of section 6 was meshed so that the spacing is
similar to the edge mesh in sections 4 and 5 this was done in order to have aspect ratios
of the wall be as close as possible to unity Sections 3 4 5 and 6 were meshed on both
the channel and the plenum With the entire target wall plane meshed these surface
meshes are coopered upwards to connect to the opposite wall The vertical spacing has
55
also been set up differently between the channel and the plenum The holes and the
plenum were also coopered The finished mesh was then exported as a msh file
Boundary conditions were set in GAMBIT once the mesh was imported into
Fluent values were set to every face depending on their location and purpose Figure 40
shows the four different boundary conditions Face 1 (blue) was set to be a mass flow
inlet The flow rate is half of the total flow rate at a given jet Reynolds number due to it
being only half of the entire domain Face 2 (yellow) is a symmetry plane face 3 (red) is
a pressure outlet at zero gauge pressure The rest of the faces in the channel denoted by
the number 4 (white) are set to walls The target side and front end wall had a heat flux
applied to them equal to 10000Wm2
Figure 40 Finished Mesh with Boundary Conditions
The model was imported into Fluent It was scaled down by a factor of 1000 due to it
being made in GAMBIT in millimeters The energy model was turned on The Realizable
k-ε model was used with enhanced wall functions on both the pressure and thermal
gradients The boundary conditions were set as discussed previously the mass flow inlet
was set to the specific flow rate normal to the surface the heat fluxes were set on the
56
heated walls the outflow gauge pressure was set to zero Two important reference values
characteristic length and reference temperature were set to be the diameter of the jet
(0075m) and 300K respectively The spatial discretization parameters were set to second
order upwind for momentum turbulent kinetic energy turbulent dissipation rate and
energy The under-relaxation factors were set to default Four monitors were created to
aid in the determination of convergence two of them read Nusselt numbers at the
stagnation region of the first and last jet the remaining two read the exit velocity at the
first and last jet The continuity x y and x velocities and energy equations residuals
were set to be 1E-6 while k and ε residuals were set to 1E-4 The solution was initialized
on the all zones at 1ms in the positive x direction The solution was set to autosave every
100 iterations while keeping only the two newest dat files The calculation was then run
for a maximum of 7000 iterations
A grid independence study was done on the domain to find the optimal size of
mesh that provides the correct solution while minimizing the compute time Two
monitors were set to check for grid independence both of them were vertex maximum
One of them read the Nusselt number at the impingement location of the first center jet
while the second one measures the velocity at the exit of the last jet Four different mesh
sizes were run to the convergence criterion explained before their sizes were 900000
15 million 28 million and 43 million cells
57
Figure 41 Grid Independence Study
It can be seen in Figure 41 that the difference between the 28 and 43 million cell
meshes are very small a difference of under 006 for velocity and 7 for Nusselt
number It can be safe to assume that the 28 million cell mesh is large enough to provide
a mesh independent solution The GAMBIT journal file used to create this mesh is
attached to the appendix The results shown hereafter are the ones obtained by the 28
million cell mesh
Figure 42 Residual Plots for the 26M Cell Run
67
69
71
73
75
77
79
81
83
85
485
4855
486
4865
487
4875
488
4885
489
0 1 2 3 4 5
Nu
sse
lt N
um
be
r
Cell Ammount (Millions)
Grid Independence Study
Velocity
Nusselt Number
58
For future reference Figure 42 shows the residuals of the 26M cell calculation
Up until around 4400 iterations the residuals were increasing shortly thereafter the
residuals started decreasing until it converged just after 5500 iterations All runs for the
differently sized meshes had the same residual patters with the peak of residuals and
point of convergence happening at different iterations
52 CFD Results
As describe previously all the results shown here are for the mesh containing 28 million
elements Figure 43 shows the total pressure contours It can be seen that the plenum
portion is at a constant total pressure Once the jets form since there are very small losses
in the jets due to the wall friction the total pressure still remains constant Only when the
jets enter the channel and start mixing with the cross flow is that they start losing the total
pressure head It is important to notice how the first two jets have the total pressure close
to the plenum arriving at the target wall This implies a successful impingement of the
undisturbed potential core As we move downstream the total pressure is lost quite
rapidly as the jets interact with the cross flow
Figure 43 Total Pressure Contours
59
Similar details can be drawn out from Figure 44 it can be seen that the first three
jets successfully impinge on the target wall while the rest of the downstream ones are
deflected by the cross flow As mentioned by Ricklick the velocity magnitude of the last
jet is larger than that of the first jet due to there being a lower static pressure at the end of
the channel providing it with a steeper pressure gradient hence higher velocity
Figure 44 Velocity Magnitude Contours
Turbulent kinetic energy was plotted in Figure 45 it is expected to have the
highest turbulent kinetic energy near the exit of the holes where the stagnant air is in
contact with the fast moving jet The mixing between the two regimes causes very
energetic eddies to form potentially enhancing the target and side wall heat transfer
coefficient As cross flow builds up towards the end of the channel the turbulent kinetic
energy increases due to larger overall velocities and fluctuations between the cross flow
and jets
60
Figure 45 Turbulent Kinetic Energy Contours
As Ricklick showed in his work the static temperature rise is quite small for such a small
channel It can be seen in Figure 46 that the driving temperature for heat transfer is that of
the plenum It is important to notice that a wall heat flux of 10000 Wm2 was used as the
boundary condition Not even in the most powerful tests would we ever use heat fluxes
that high they normally range between 2500 to a maximum of 7000 Wm2 A heat flux of
10000 Wm2 will increase the temperature at a faster rate than what it is normally used in
experimental testing
Figure 46 Static Temperature Contours
61
Figure 47 Target and Side Wall Heat Transfer Coefficient Contours
Figure 47 shows the target and sidewall heat transfer profiles Peaks can be seen at the
first three locations similar to that seen in Figure 22 The trend decreases rapidly to
eventually become a slowly increasing heat transfer profile due to the increase of mass
flow through the channel The sidewall provides the same results clear peaks in heat
transfer where the wall jets impinge on the sidewall seen in Figure 48 in more detail The
sidewall also shows a recirculation zone in between the first row of jets and the end wall
This is caused by the wall jet from the first row hitting the back wall moving upwards in
a circular pattern and coming back down when it encounters the first impingement row
Figure 48 Closer View of First few Rows of Impingement HTC Contours
62
Figure 49 Pathlines Generating from the First Row of Jets
Figure 49 helps explain the low heat transfer region between the first row of jets and
the end wall Pathlines are generated at the exit of each hole in the first row As the
air impinges on the surface half of it moves downstream and the other half movers
upstream to this recirculation zone where it circulates for a period of time before
reuniting with the remainder of the flow to move downstream The wall jet that
moves towards the second row of jets encounters the wall jet created by the second
row of jets causing the pathlines to drastically move upwards On the side of the
channel the pathlines behave erratically with no clear pattern clearly signifying the
highly turbulent and chaotic flow structure of this impingement channel
63
CHAPTER SIX CONCLUSIONS
It has been seen from this analysis that the side walls provide significant heat
transfer in an impingement channel especially at the relatively smaller channel
height This is primarily the result of successful impact of the wall jet with the side
walls It was shown that the tallest channel (ZD=10) has the most uniform profile with
low heat transfer coefficients when compared to the other channels The peaks of the
ZD=6 and 8 channels have a very similar profile which may indicate the successful
impingement of the potential core of the jet on the target surface As XD increases the
peaks diminish and a positive slope profile is attained by the increase of cross flow
velocity as more and more jets are introduced Tall impingement channels provide the
user with a heat transfer profile that is more uniform than those provided with the use of a
smaller channel while still maintaining higher convective coefficients when compared to
a smooth flow scenario The downstream shift of the wall jets is found to be independent
of Reynolds number and heavily dependent on streamwise position It was also found that
at XD=15 the wall jets decay faster than their XD=5 counterparts From the 3D heat
transfer profiles it was seen that the cross flow generated by multiple upstream jets is
deflected downward decreasing its effective flow area increasing its velocity hence
providing higher convective coefficients at the side wall at high xD and low zD
64
APPENDICES
Appendix A
Lateral Conduction Consideration
Thickness of foil heater Heat flux
Sample volume width
Volumetric heat generation
Volume of sample volume
Temperature profile from the first row of impingement ONLY valid for 02ltxlt045
t 50m k 20W
m K qflux 6000
W
m2
1mm
V 2
t qvol
qflux
t
T x( ) 298Kqflux
470630 x2
31244x 14842 W
m2K
N 15
x 02045 02
N 102 047
002 003 004 005314
315
316
317
318
319
320
T x( )
x
A t
qnet x( ) A kxT x
m
d
d xT x( )
d
d
1
m
002 003 004 0050
5 105
1 104
15 104
2 104
qnet x( )
x
65
Now comparing the net heat gained by lateral conduction to heat generated and convected out
It can be seen that the lateral conduction into the sample volume is two orders of magnitude smaller than the heat removed by convection
qgen qvol V 6 103
W
qconv x( ) 2
qflux qnet x( )
002 003 004 0051 10
5
1 104
1 103
001
qconv x( )
qnet x( )
x x
66
Appendix B
This is the journal file run on gambit to generate the geometry faces links
boundary layer face and volume meshes as well as the boundary conditions
set diameter
$d=75
$zc=6($d)
$xc=80($d)
$yc=4($d)
$y=2($d)
$x=5($d)
$zp=5($d)
$ztot=($zc)+($d)+($zp)
$jcf=(13)
$ocf=2
Boundary layer constants
$first=01
$growth=12
$rows=4
Meshing constants
$NumbNodes=5
$Numbtelnodes=6
$PLobnodes=5
$Chobnodes=5
$Plbenodes=($NumbNodes(4)+$rows)
$plsqnodes=($NumbNodes(3))
$Pllsnodes=($NumbNodes+$rows)
$Nojetcells=10
$Chzdnodes=($zc$Nojetcells)($d)
$Plzdnodes=($zp$Nojetcells)($d)
Boundary layer constants for channel
$firstch=001
$growthch=12
$rowsch=8
$CHbenodes=($NumbNodes(4)+$rowsch)
$CHlsnodes=($NumbNodes+$rowsch)
volume create body width ($xc) depth ($yc) height ($ztot) offset ($xc2) ($yc2) ($ztot2) brick
volume create cylinder height ($ztot) radius1 ($d2) radius3 ($d2) offset ($x) 0 ($ztot2) zaxis frustum
volume cmove cylinder multiple 1 offset 0 ($y) 0
volume cmove cylinder volume3 multiple 14 offset ($x) 0 0
volume create jetplate width ($xc) depth ($yc) height ($d)offset ($xc2) ($yc2) ($d2+$zc) brick
volume split body volumes jetplate connected
volume split jetplate volumes cylinder volume3 volume4 volume5
volume6 volume7 volume8 volume9 volume10 volume11
volume12 volume13 volume14 volume15 volume16 volume17
67
volume18 volume19 volume20 volume21 volume22 volume23
volume24 volume25 volume26 volume27 volume28 volume29
volume30 volume31 connected
face create jetcenter width ($jcf$d) height ($jcf$d) offset ($x) 0 0 xyplane rectangle
face create jetcircle radius ($d2) xyplane circle
face move jetcircle offset ($x) 0 0
face create outbox width ($ocf$d) height ($ocf$d) offset ($x) 0 0 xyplane rectangle
face split outbox connected faces jetcircle jetcenter
face split jetcircle connected faces face1
face split outbox connected faces face1
face cmove jetcenter outbox jetcircle face222 face223 multiple 1 offset 0 ($y) 0
face cmove jetcenter outbox jetcircle face222 face223 face224 face225 face226
face227 face228 multiple 14 offset ($x) 0 0
volume delete jetplate lowertopology
face split face1 connected keeptool faces jetcircle jetcenter outbox
face222 face223 face224 face225 face226 face227
face228 face229 face230 face231 face232 face233
face234 face235 face236 face237 face238 face239
face240 face241 face242 face243 face244 face245
face246 face247 face248 face249 face250 face251
face252 face253 face254 face255 face256 face257
face258 face259 face260 face261 face262 face263
face264 face265 face266 face267 face268 face269
face270 face271 face272 face273 face274 face275
face276 face277 face278 face279 face280 face281
face282 face283 face284 face285 face286 face287
face288 face289 face290 face291 face292 face293
face294 face295 face296 face297 face298 face299
face300 face301 face302 face303 face304 face305
face306 face307 face308 face309 face310 face311
face312 face313 face314 face315 face316 face317
face318 face319 face320 face321 face322 face323
face324 face325 face326 face327 face328 face329
face330 face331 face332 face333 face334 face335
face336 face337 face338 face339 face340 face341
face342 face343 face344 face345 face346 face347
face348 face349 face350 face351 face352 face353
face354 face355 face356 face357 face358 face359
face360 face361 face362 face363 face364 face365
face366 face367 face368
face move jetcircle jetcenter outbox face222 face223 face224
face225 face226 face227 face228 face229 face230
face231 face232 face233 face234 face235 face236
face237 face238 face239 face240 face241 face242
face243 face244 face245 face246 face247 face248
face249 face250 face251 face252 face253 face254
face255 face256 face257 face258 face259 face260
face261 face262 face263 face264 face265 face266
face267 face268 face269 face270 face271 face272
face273 face274 face275 face276 face277 face278
face279 face280 face281 face282 face283 face284
face285 face286 face287 face288 face289 face290
face291 face292 face293 face294 face295 face296
face297 face298 face299 face300 face301 face302
face303 face304 face305 face306 face307 face308
face309 face310 face311 face312 face313 face314
68
face315 face316 face317 face318 face319 face320
face321 face322 face323 face324 face325 face326
face327 face328 face329 face330 face331 face332
face333 face334 face335 face336 face337 face338
face339 face340 face341 face342 face343 face344
face345 face346 face347 face348 face349 face350
face351 face352 face353 face354 face355 face356
face357 face358 face359 face360 face361 face362
face363 face364 face365 face366 face367 face368 offset 0
0 $ztot
THIS SPLITS THE TOP PLENUM FACE WITH THE FACES CREATED IN THE BOTTOM
face split face6 connected keeptool faces jetcircle jetcenter outbox
face222 face223 face224 face225 face226 face227
face228 face229 face230 face231 face232 face233
face234 face235 face236 face237 face238 face239
face240 face241 face242 face243 face244 face245
face246 face247 face248 face249 face250 face251
face252 face253 face254 face255 face256 face257
face258 face259 face260 face261 face262 face263
face264 face265 face266 face267 face268 face269
face270 face271 face272 face273 face274 face275
face276 face277 face278 face279 face280 face281
face282 face283 face284 face285 face286 face287
face288 face289 face290 face291 face292 face293
face294 face295 face296 face297 face298 face299
face300 face301 face302 face303 face304 face305
face306 face307 face308 face309 face310 face311
face312 face313 face314 face315 face316 face317
face318 face319 face320 face321 face322 face323
face324 face325 face326 face327 face328 face329
face330 face331 face332 face333 face334 face335
face336 face337 face338 face339 face340 face341
face342 face343 face344 face345 face346 face347
face348 face349 face350 face351 face352 face353
face354 face355 face356 face357 face358 face359
face360 face361 face362 face363 face364 face365
face366 face367 face368
THIS MOVES THE FACES THAT WE ARE USING TO PLIT THE BOTTOM PLENUM SURFACE
face move jetcircle jetcenter outbox face222 face223 face224
face225 face226 face227 face228 face229 face230
face231 face232 face233 face234 face235 face236
face237 face238 face239 face240 face241 face242
face243 face244 face245 face246 face247 face248
face249 face250 face251 face252 face253 face254
face255 face256 face257 face258 face259 face260
face261 face262 face263 face264 face265 face266
face267 face268 face269 face270 face271 face272
face273 face274 face275 face276 face277 face278
face279 face280 face281 face282 face283 face284
face285 face286 face287 face288 face289 face290
face291 face292 face293 face294 face295 face296
face297 face298 face299 face300 face301 face302
69
face303 face304 face305 face306 face307 face308
face309 face310 face311 face312 face313 face314
face315 face316 face317 face318 face319 face320
face321 face322 face323 face324 face325 face326
face327 face328 face329 face330 face331 face332
face333 face334 face335 face336 face337 face338
face339 face340 face341 face342 face343 face344
face345 face346 face347 face348 face349 face350
face351 face352 face353 face354 face355 face356
face357 face358 face359 face360 face361 face362
face363 face364 face365 face366 face367 face368 offset 0
0 -$zp
SPLITS THE BOTTOM FACE OF THE PLENUM WITH THE FACES THAT ARE USED TO SPLIT
face split face114 connected keeptool faces jetcircle jetcenter
outbox face222 face223 face224 face225 face226 face227
face228 face229 face230 face231 face232 face233
face234 face235 face236 face237 face238 face239
face240 face241 face242 face243 face244 face245
face246 face247 face248 face249 face250 face251
face252 face253 face254 face255 face256 face257
face258 face259 face260 face261 face262 face263
face264 face265 face266 face267 face268 face269
face270 face271 face272 face273 face274 face275
face276 face277 face278 face279 face280 face281
face282 face283 face284 face285 face286 face287
face288 face289 face290 face291 face292 face293
face294 face295 face296 face297 face298 face299
face300 face301 face302 face303 face304 face305
face306 face307 face308 face309 face310 face311
face312 face313 face314 face315 face316 face317
face318 face319 face320 face321 face322 face323
face324 face325 face326 face327 face328 face329
face330 face331 face332 face333 face334 face335
face336 face337 face338 face339 face340 face341
face342 face343 face344 face345 face346 face347
face348 face349 face350 face351 face352 face353
face354 face355 face356 face357 face358 face359
face360 face361 face362 face363 face364 face365
face366 face367 face368
COPIES THE FACES THAT WE USED TO SPLIT TO BOTTOM OF THE PLENUM TO THE TOP OF
THE CHANNEL
face cmove jetcircle jetcenter outbox face222 face223 face224
face225 face226 face227 face228 face229 face230
face231 face232 face233 face234 face235 face236
face237 face238 face239 face240 face241 face242
face243 face244 face245 face246 face247 face248
face249 face250 face251 face252 face253 face254
face255 face256 face257 face258 face259 face260
face261 face262 face263 face264 face265 face266
face267 face268 face269 face270 face271 face272
face273 face274 face275 face276 face277 face278
face279 face280 face281 face282 face283 face284
70
face285 face286 face287 face288 face289 face290
face291 face292 face293 face294 face295 face296
face297 face298 face299 face300 face301 face302
face303 face304 face305 face306 face307 face308
face309 face310 face311 face312 face313 face314
face315 face316 face317 face318 face319 face320
face321 face322 face323 face324 face325 face326
face327 face328 face329 face330 face331 face332
face333 face334 face335 face336 face337 face338
face339 face340 face341 face342 face343 face344
face345 face346 face347 face348 face349 face350
face351 face352 face353 face354 face355 face356
face357 face358 face359 face360 face361 face362
face363 face364 face365 face366 face367 face368 multiple 1 offset 0
0 -$d
NAME OF COPIED NEW FACES
face1104 face1105 face1106 face1107 face1108 face1109 face1110 face1111
face1112 face1113 face1114 face1115 face1116 face1117 face1118 face1119
face1120 face1121 face1122 face1123 face1124 face1125 face1126 face1127
face1128 face1129 face1130 face1131 face1132 face1133 face1134 face1135
face1136 face1137 face1138 face1139 face1140 face1141 face1142 face1143
face1144 face1145 face1146 face1147 face1148 face1149 face1150 face1151
face1152 face1153 face1154 face1155 face1156 face1157 face1158 face1159
face1160 face1161 face1162 face1163 face1164 face1165 face1166 face1167
face1168 face1169 face1170 face1171 face1172 face1173 face1174 face1175
face1176 face1177 face1178 face1179 face1180 face1181 face1182 face1183
face1184 face1185 face1186 face1187 face1188 face1189 face1190 face1191
face1192 face1193 face1194 face1195 face1196 face1197 face1198 face1199
face1200 face1201 face1202 face1203 face1204 face1205 face1206 face1207
face1208 face1209 face1210 face1211 face1212 face1213 face1214 face1215
face1216 face1217 face1218 face1219 face1220 face1221 face1222 face1223
face1224 face1225 face1226 face1227 face1228 face1229 face1230 face1231
face1232 face1233 face1234 face1235 face1236 face1237 face1238 face1239
face1240 face1241 face1242 face1243 face1244 face1245 face1246 face1247
face1248 face1249 face1250 face1251 face1252 face1253
THIS SPLITS THE TOP OF THE CHANNEL WITH THE NEW COPIED FACES
face split face209 connected keeptool faces face1104 face1105 face1106 face1107
face1108 face1109 face1110 face1111 face1112 face1113 face1114 face1115
face1116 face1117 face1118 face1119 face1120 face1121 face1122 face1123
face1124 face1125 face1126 face1127 face1128 face1129 face1130 face1131
face1132 face1133 face1134 face1135 face1136 face1137 face1138 face1139
face1140 face1141 face1142 face1143 face1144 face1145 face1146 face1147
face1148 face1149 face1150 face1151 face1152 face1153 face1154 face1155
face1156 face1157 face1158 face1159 face1160 face1161 face1162 face1163
face1164 face1165 face1166 face1167 face1168 face1169 face1170 face1171
face1172 face1173 face1174 face1175 face1176 face1177 face1178 face1179
face1180 face1181 face1182 face1183 face1184 face1185 face1186 face1187
face1188 face1189 face1190 face1191 face1192 face1193 face1194 face1195
face1196 face1197 face1198 face1199 face1200 face1201 face1202 face1203
face1204 face1205 face1206 face1207 face1208 face1209 face1210 face1211
face1212 face1213 face1214 face1215 face1216 face1217 face1218 face1219
face1220 face1221 face1222 face1223 face1224 face1225 face1226 face1227
71
face1228 face1229 face1230 face1231 face1232 face1233 face1234 face1235
face1236 face1237 face1238 face1239 face1240 face1241 face1242 face1243
face1244 face1245 face1246 face1247 face1248 face1249 face1250 face1251
face1252 face1253
THIS UNITES THE RECTANGLE OUTSIDE FACES AND THE SEMICIRCLE SO THAT IT MAKES
A RECTANGLE WIHOUT THE CENTERJET
face unite faces jetcircle face223 real
face unite faces face222 outbox real
face unite faces face228 face226 real
face unite faces face225 face227 real
face unite faces face231 face233 real
face unite faces face232 face230 real
face unite faces face236 face238 real
face unite faces face237 face235 real
face unite faces face241 face243 real
face unite faces face242 face240 real
face unite faces face248 face246 real
face unite faces face245 face247 real
face unite faces face253 face251 real
face unite faces face252 face250 real
face unite faces face256 face258 real
face unite faces face257 face255 real
face unite faces face263 face261 real
face unite faces face260 face262 real
face unite faces face268 face266 real
face unite faces face265 face264 real
face unite faces face265 face267 real
face unite faces face273 face271 real
face unite faces face272 face270 real
face unite faces face276 face278 real
face unite faces face277 face275 real
face unite faces face281 face283 real
face unite faces face282 face280 real
face unite faces face286 face288 real
face unite faces face287 face285 real
face unite faces face291 face293 real
face unite faces face292 face290 real
face unite faces face296 face298 real
face unite faces face297 face295 real
face unite faces face301 face303 real
face unite faces face302 face300 real
face unite faces face306 face308 real
face unite faces face307 face305 real
face unite faces face316 face318 real
face unite faces face312 face310 real
face unite faces face311 face313 real
face unite faces face315 face317 real
face unite faces face321 face323 real
face unite faces face322 face320 real
face unite faces face326 face328 real
face unite faces face327 face325 real
face unite faces face331 face333 real
face unite faces face332 face330 real
face unite faces face336 face338 real
72
face unite faces face337 face335 real
face unite faces face347 face345 real
face unite faces face346 face348 real
face unite faces face342 face340 real
face unite faces face341 face343 real
face unite faces face356 face358 real
face unite faces face357 face355 real
face unite faces face352 face350 real
face unite faces face351 face353 real
face unite faces face361 face363 real
face unite faces face366 face368 real
face unite faces face360 face362 real
face unite faces face365 face367 real
SPLITTING ALL THE FACES OF THE CIRCLES IN THE BOTTOM OF THE PLENUM
face split face912 connected keeptool faces face222
face split face117 connected keeptool faces face228
face split face117 connected keeptool faces face225
face split face922 connected keeptool faces face232
face split face124 connected keeptool faces face236
face split face124 connected keeptool faces face237
face split face932 connected keeptool faces face242
face split face131 connected keeptool faces face248
face split face131 connected keeptool faces face245
face split face942 connected keeptool faces face252
face split face138 connected keeptool faces face256
face split face138 connected keeptool faces face257
face split face952 connected keeptool faces face260
face split face145 connected keeptool faces face268
face split face145 connected keeptool faces face265
face split face962 connected keeptool faces face272
face split face152 connected keeptool faces face276
face split face152 connected keeptool faces face277
face split face972 connected keeptool faces face282
face split face159 connected keeptool faces face286
face split face159 connected keeptool faces face287
face split face982 connected keeptool faces face292
face split face166 connected keeptool faces face296
face split face166 connected keeptool faces face297
face split face992 connected keeptool faces face302
face split face173 connected keeptool faces face306
face split face173 connected keeptool faces face307
face split face1002 connected keeptool faces face312
face split face180 connected keeptool faces face316
face split face180 connected keeptool faces face315
73
face split face1012 connected keeptool faces face322
face split face187 connected keeptool faces face326
face split face187 connected keeptool faces face327
face split face1022 connected keeptool faces face332
face split face194 connected keeptool faces face336
face split face194 connected keeptool faces face337
face split face1032 connected keeptool faces face342
face split face201 connected keeptool faces face346
face split face201 connected keeptool faces face347
face split face1042 connected keeptool faces face352
face split face208 connected keeptool faces face356
face split face208 connected keeptool faces face357
face split face1052 connected keeptool faces face360
face split face215 connected keeptool faces face366
face split face215 connected keeptool faces face365
THIS UNITES THE RECTANGLE OUTSIDE FACES AND THE SEMICIRCLE SO THAT IT MAKES
A RECTANGLE WIHOUT THE CENTERJET
face unite faces face1104 face1108 real
face unite faces face1107 face1106 real
face unite faces face1113 face1111 real
face unite faces face1112 face1110 real
face unite faces face1118 face1116 real
face unite faces face1117 face1115 real
face unite faces face1123 face1121 real
face unite faces face1122 face1120 real
face unite faces face1128 face1126 real
face unite faces face1127 face1125 real
face unite faces face1133 face1131 real
face unite faces face1132 face1130 real
face unite faces face1138 face1136 real
face unite faces face1137 face1135 real
face unite faces face1143 face1141 real
face unite faces face1142 face1140 real
face unite faces face1148 face1146 real
face unite faces face1147 face1145 real
face unite faces face1153 face1151 real
face unite faces face1152 face1150 real
face unite faces face1158 face1156 real
face unite faces face1157 face1155 real
face unite faces face1163 face1161 real
face unite faces face1162 face1160 real
face unite faces face1168 face1166 real
face unite faces face1167 face1165 real
face unite faces face1173 face1171 real
face unite faces face1172 face1170 real
face unite faces face1178 face1176 real
face unite faces face1177 face1175 real
face unite faces face1183 face1181 real
74
face unite faces face1182 face1180 real
face unite faces face1186 face1188 real
face unite faces face1187 face1185 real
face unite faces face1193 face1191 real
face unite faces face1192 face1190 real
face unite faces face1198 face1196 real
face unite faces face1197 face1195 real
face unite faces face1203 face1201 real
face unite faces face1202 face1200 real
face unite faces face1206 face1208 real
face unite faces face1207 face1205 real
face unite faces face1213 face1211 real
face unite faces face1212 face1210 real
face unite faces face1216 face1218 real
face unite faces face1217 face1215 real
face unite faces face1221 face1223 real
face unite faces face1222 face1220 real
face unite faces face1228 face1226 real
face unite faces face1227 face1225 real
face unite faces face1233 face1231 real
face unite faces face1232 face1230 real
face unite faces face1238 face1236 real
face unite faces face1237 face1235 real
face unite faces face1243 face1241 real
face unite faces face1242 face1240 real
face unite faces face1248 face1246 real
face unite faces face1247 face1245 real
face unite faces face1253 face1251 real
face unite faces face1252 face1250 real
SPLITTING ALL THE FACES OF THE CIRCLES IN THE TOP OF THE CHANNEL
face split face1257 connected keeptool faces face1107
face split face115 connected keeptool faces face1113
face split face115 connected keeptool faces face1112
face split face1267 connected keeptool faces face1117
face split face122 connected keeptool faces face1123
face split face122 connected keeptool faces face1122
face split face1277 connected keeptool faces face1127
face split face129 connected keeptool faces face1133
face split face129 connected keeptool faces face1132
face split face1287 connected keeptool faces face1137
face split face136 connected keeptool faces face1143
face split face136 connected keeptool faces face1142
face split face1297 connected keeptool faces face1147
face split face143 connected keeptool faces face1153
face split face143 connected keeptool faces face1152
face split face1307 connected keeptool faces face1157
face split face150 connected keeptool faces face1163
face split face150 connected keeptool faces face1162
75
face split face1317 connected keeptool faces face1167
face split face157 connected keeptool faces face1173
face split face157 connected keeptool faces face1172
face split face1327 connected keeptool faces face1177
face split face164 connected keeptool faces face1183
face split face164 connected keeptool faces face1182
face split face1337 connected keeptool faces face1187
face split face171 connected keeptool faces face1193
face split face171 connected keeptool faces face1192
face split face1347 connected keeptool faces face1197
face split face178 connected keeptool faces face1203
face split face178 connected keeptool faces face1202
face split face1357 connected keeptool faces face1207
face split face185 connected keeptool faces face1213
face split face185 connected keeptool faces face1212
face split face1367 connected keeptool faces face1217
face split face192 connected keeptool faces face1221
face split face192 connected keeptool faces face1222
face split face1377 connected keeptool faces face1227
face split face199 connected keeptool faces face1233
face split face199 connected keeptool faces face1232
face split face1387 connected keeptool faces face1237
face split face206 connected keeptool faces face1243
face split face206 connected keeptool faces face1242
face split face1397 connected keeptool faces face1247
face split face213 connected keeptool faces face1253
face split face213 connected keeptool faces face1252
face split face1452 connected keeptool faces face224
face split face1456 connected keeptool faces face234
face split face1460 connected keeptool faces face244
face split face1464 connected keeptool faces face254
face split face1468 connected keeptool faces face264
face split face1472 connected keeptool faces face274
face split face1476 connected keeptool faces face284
face split face1480 connected keeptool faces face294
face split face1484 connected keeptool faces face304
face split face1488 connected keeptool faces face314
face split face1492 connected keeptool faces face324
face split face1496 connected keeptool faces face334
face split face1500 connected keeptool faces face344
face split face1504 connected keeptool faces face354
face split face1508 connected keeptool faces face364
DELETING ALL THE FACES USED TO MAKE THE CUTS
face delete jetcircle face222 face228 face225 jetcenter
76
face224 face231 face232 face236 face237 face229
face1456 face241 face242 face239 face248 face244
face245 face253 face249 face252 face254 face256
face257 face263 face259 face260 face268 face264
face265 face273 face272 face269 face276 face277
face274 face281 face282 face286 face279 face287
face284 face291 face292 face296 face297 face289
face294 face301 face299 face302 face306 face307
face304 face311 face312 face316 face315 face309
face314 face321 face322 face326 face327 face319
face324 face331 face332 face329 face336 face334
face337 face341 face342 face339 face346 face344
face347 face351 face352 face349 face356 face354
face357 face361 face359 face360 face366 face364
face365 lowertopology
face delete face1104 face1105 face1107 face1113 face1112
face115 face234 face1118 face1114 face1117 face1123
face1122 face122 face1138 face1128 face1127 face1124
face1133 face1132 face129 face1134 face1137 face1143
face136 face1142 face1148 face1144 face1147 face1153
face143 face1152 face1158 face1154 face1157 face1163
face150 face1162 face1168 face1164 face1167 face1173
face157 face1172 face1178 face1174 face1177 face1183
face164 face1182 face1186 face1184 face1187 face1193
face171 face1192 face1198 face1194 face1197 face1203
face178 face1202 face1206 face1204 face1207 face1213
face185 face1212 face1216 face1214 face1217 face1221
face192 face1222 face1228 face1224 face1227 face1233
face199 face1232 face1238 face1234 face1237 face1243
face206 face1242 face1248 face1244 face1247 face1253
face213 face1252 lowertopology
face delete face1109 face1119 face1129 face1139 face1149 face1159
face1169 face1179 face1189 face1199 face1209 face1219
face1229 face1239 face1249 lowertopology
face create CP1 width 600 height 75 offset 300 (225+($d)2) 0 xyplane rectangle
face create CP2 width 600 height 75 offset 300 (225+($d)2) ($zc) xyplane rectangle
face create CP3 width 600 height 75 offset 300 (225+($d)2) ($zc+$d) xyplane rectangle
face create CP4 width 600 height 75 offset 300 (225+($d)2) ($zc+$d+$zp) xyplane rectangle
face split face6 connected faces CP4
face split face114 connected faces CP3
face split face209 connected faces CP2
face split face1 connected faces CP1
GEOMETRY IS FINISHED
face modify face912 side vertex6437 vertex6436
77
face modify face1600 side vertex7302 vertex7303
face modify face117 side vertex6446 vertex6447
face modify face646 side vertex3312
face modify face646 side vertex3313
face modify face647 side vertex3432 vertex3433
face modify face372 side vertex2040 vertex2041
face modify face376 side vertex2100 vertex2101
face modify face377 side vertex2221 vertex2220
LINKING ALL THE JET CENTERS
face link face1450 face640 edges edge6949 edge3518 vertices
vertex6437 vertex3253 reverse
face link face1450 face1257 edges edge6949 edge7340 vertices
vertex6437 vertex6797 reverse
face link face1257 face370 edges edge7340 edge2139 vertices
vertex6797 vertex2041 reverse
face link face1257 face1454 edges edge7340 edge6975 vertices
vertex6797 vertex6461 reverse
face link face1454 face649 edges edge6975 edge3519 vertices
vertex6461 vertex3255 reverse
face link face1454 face1267 edges edge6975 edge7377 vertices
vertex6461 vertex6831 reverse
face link face1267 face379 edges edge7377 edge2141 vertices
vertex6831 vertex2043 reverse
face link face1267 face1458 edges edge7377 edge7001 vertices
vertex6831 vertex6485 reverse
face link face1458 face659 edges edge7001 edge3520 vertices
vertex6485 vertex3257 reverse
face link face1458 face1277 edges edge7001 edge7414 vertices
vertex6485 vertex6865 reverse
face link face1277 face389 edges edge7414 edge2143 vertices
vertex6865 vertex2045 reverse
face link face1277 face1462 edges edge7414 edge7027 vertices
vertex6865 vertex6509 reverse
face link face1462 face669 edges edge7027 edge3521 vertices
vertex6509 vertex3259 reverse
face link face1462 face1287 edges edge7027 edge7451 vertices
vertex6509 vertex6899 reverse
face link face1287 face399 edges edge7451 edge2145 vertices
vertex6899 vertex2047 reverse
face link face1287 face1466 edges edge7451 edge7053 vertices
vertex6899 vertex6533 reverse
face link face1466 face679 edges edge7053 edge3522 vertices
vertex6533 vertex3261 reverse
face link face1466 face1297 edges edge7053 edge7488 vertices
vertex6533 vertex6933 reverse
face link face1297 face409 edges edge7488 edge2147 vertices
vertex6933 vertex2049 reverse
face link face1297 face1470 edges edge7488 edge7079 vertices
vertex6933 vertex6557 reverse
face link face1470 face689 edges edge7079 edge3523 vertices
vertex6557 vertex3263 reverse
face link face1470 face1307 edges edge7079 edge7525 vertices
vertex6557 vertex6967 reverse
face link face1307 face419 edges edge7525 edge2149 vertices
78
vertex6967 vertex2051 reverse
face link face1307 face1474 edges edge7525 edge7105 vertices
vertex6967 vertex6581 reverse
face link face1474 face1317 edges edge7105 edge7562 vertices
vertex6581 vertex7001 reverse
face link face1474 face699 edges edge7105 edge3524 vertices
vertex6581 vertex3265 reverse
face link face1317 face429 edges edge7562 edge2151 vertices
vertex7001 vertex2053 reverse
face link face1317 face1478 edges edge7562 edge7131 vertices
vertex7001 vertex6605 reverse
face link face1478 face1327 edges edge7131 edge7599 vertices
vertex6605 vertex7035 reverse
face link face1478 face709 edges edge7131 edge3525 vertices
vertex6605 vertex3267 reverse
face link face1327 face439 edges edge7599 edge2153 vertices
vertex7035 vertex2055 reverse
face link face1327 face1482 edges edge7599 edge7157 vertices
vertex7035 vertex6629 reverse
face link face1482 face719 edges edge7157 edge3526 vertices
vertex6629 vertex3269 reverse
face link face1482 face1337 edges edge7157 edge7636 vertices
vertex6629 vertex7069 reverse
face link face1337 face449 edges edge7636 edge2155 vertices
vertex7069 vertex2057 reverse
face link face1337 face1486 edges edge7636 edge7183 vertices
vertex7069 vertex6653 reverse
face link face1486 face1347 edges edge7183 edge7673 vertices
vertex6653 vertex7103 reverse
face link face1347 face459 edges edge7673 edge2157 vertices
vertex7103 vertex2059 reverse
face link face1486 face729 edges edge7183 edge3527 vertices
vertex6653 vertex3271 reverse
face link face1347 face1490 edges edge7673 edge7209 vertices
vertex7103 vertex6677 reverse
face link face1490 face1357 edges edge7209 edge7710 vertices
vertex6677 vertex7137 reverse
face link face1490 face739 edges edge7209 edge3528 vertices
vertex6677 vertex3273 reverse
face link face1357 face469 edges edge7710 edge2159 vertices
vertex7137 vertex2061 reverse
face link face1357 face1494 edges edge7710 edge7235 vertices
vertex7137 vertex6701 reverse
face link face1494 face1367 edges edge7235 edge7747 vertices
vertex6701 vertex7171 reverse
face link face1494 face749 edges edge7235 edge3529 vertices
vertex6701 vertex3275 reverse
face link face1367 face479 edges edge7747 edge2161 vertices
vertex7171 vertex2063 reverse
face link face1367 face1498 edges edge7747 edge7261 vertices
vertex7171 vertex6725 reverse
face link face1498 face1377 edges edge7261 edge7784 vertices
vertex6725 vertex7205 reverse
face link face1377 face489 edges edge7784 edge2163 vertices
vertex7205 vertex2065 reverse
face link face1498 face759 edges edge7261 edge3530 vertices
79
vertex6725 vertex3277 reverse
face link face1377 face1502 edges edge7784 edge7287 vertices
vertex7205 vertex6749 reverse
face link face1502 face1387 edges edge7287 edge7821 vertices
vertex6749 vertex7239 reverse
face link face1387 face499 edges edge7821 edge2165 vertices
vertex7239 vertex2067 reverse
face link face1387 face1506 edges edge7821 edge7313 vertices
vertex7239 vertex6773 reverse
face link face1502 face769 edges edge7287 edge3531 vertices
vertex6749 vertex3279 reverse
face link face1506 face1397 edges edge7313 edge7858 vertices
vertex6773 vertex7273 reverse
face link face1506 face779 edges edge7313 edge3532 vertices
vertex6773 vertex3281 reverse
face link face1397 face509 edges edge7858 edge2167 vertices
vertex7273 vertex2069 reverse
LINKING ALL THE COMPLETE JETCENTERS
face link face1452 face644 edges edge7891 edge3773 vertices
vertex7303 vertex3433
face link face1452 face115 edges edge7891 edge7364 vertices
vertex7303 vertex6819
face link face1452 face1456 edges edge7891 edge7900 vertices
vertex7303 vertex7311
face link face1456 face654 edges edge7900 edge3774 vertices
vertex7311 vertex3435
face link face1456 face122 edges edge7900 edge7401 vertices
vertex7311 vertex6853
face link face1456 face1460 edges edge7900 edge7909 vertices
vertex7311 vertex7319
face link face1460 face1464 edges edge7909 edge7918 vertices
vertex7319 vertex7327
face link face1460 face129 edges edge7909 edge7438 vertices
vertex7319 vertex6887
face link face1460 face664 edges edge7909 edge3775 vertices
vertex7319 vertex3437
face link face1464 face674 edges edge7918 edge3776 vertices
vertex7327 vertex3439
face link face1464 face136 edges edge7918 edge7475 vertices
vertex7327 vertex6921
face link face1464 face1468 edges edge7918 edge7927 vertices
vertex7327 vertex7335
face link face1472 face1468 edges edge7936 edge7927 vertices
vertex7343 vertex7335
face link face1468 face143 edges edge7927 edge7512 vertices
vertex7335 vertex6955
face link face1468 face684 edges edge7927 edge3777 vertices
vertex7335 vertex3441
face link face1472 face694 edges edge7936 edge3778 vertices
vertex7343 vertex3443
face link face1472 face150 edges edge7936 edge7549 vertices
vertex7343 vertex6989
face link face1472 face1476 edges edge7936 edge7945 vertices
80
vertex7343 vertex7351
face link face1476 face1480 edges edge7945 edge7954 vertices
vertex7351 vertex7359
face link face1476 face157 edges edge7945 edge7586 vertices
vertex7351 vertex7023
face link face1476 face704 edges edge7945 edge3779 vertices
vertex7351 vertex3445
face link face1480 face714 edges edge7954 edge3780 vertices
vertex7359 vertex3447
face link face1480 face164 edges edge7954 edge7623 vertices
vertex7359 vertex7057
face link face1480 face1484 edges edge7954 edge7963 vertices
vertex7359 vertex7367
face link face1484 face171 edges edge7963 edge7660 vertices
vertex7367 vertex7091
face link face1484 face724 edges edge7963 edge3781 vertices
vertex7367 vertex3449
face link face1480 face1488 edges edge7954 edge7972 vertices
vertex7359 vertex7375
face link face1488 face178 edges edge7972 edge7697 vertices
vertex7375 vertex7125
face link face1488 face734 edges edge7972 edge3782 vertices
vertex7375 vertex3451
face link face1488 face1492 edges edge7972 edge7981 vertices
vertex7375 vertex7383
face link face1492 face744 edges edge7981 edge3783 vertices
vertex7383 vertex3453
face link face1492 face185 edges edge7981 edge7734 vertices
vertex7383 vertex7159
face link face1492 face1496 edges edge7981 edge7990 vertices
vertex7383 vertex7391
face link face1496 face754 edges edge7990 edge3784 vertices
vertex7391 vertex3455
face link face1496 face192 edges edge7990 edge7771 vertices
vertex7391 vertex7193
face link face1496 face1500 edges edge7990 edge7999 vertices
vertex7391 vertex7399
face link face1500 face1504 edges edge7999 edge8008 vertices
vertex7399 vertex7407
face link face1504 face1508 edges edge8008 edge8017 vertices
vertex7407 vertex7415
face link face1500 face199 edges edge7999 edge7808 vertices
vertex7399 vertex7227
face link face1500 face764 edges edge7999 edge3785 vertices
vertex7399 vertex3457
face link face1504 face774 edges edge8008 edge3786 vertices
vertex7407 vertex3459
face link face1508 face784 edges edge8017 edge3787 vertices
vertex7415 vertex3461
face link face1504 face206 edges edge8008 edge7845 vertices
vertex7407 vertex7261
face link face1508 face213 edges edge8017 edge7882 vertices
vertex7415 vertex7295
linking the jetcenters of the bottom of the channel one of them has to be reversed but the otherones are not
81
face link face115 face374 edges edge7364 edge2394 vertices
vertex6819 vertex2221 reverse
face link face374 face384 edges edge2394 edge2396 vertices
vertex2221 vertex2223
face link face384 face394 edges edge2396 edge2398 vertices
vertex2223 vertex2225
face link face394 face404 edges edge2398 edge2400 vertices
vertex2225 vertex2227
face link face404 face414 edges edge2400 edge2402 vertices
vertex2227 vertex2229
face link face414 face424 edges edge2402 edge2404 vertices
vertex2229 vertex2231
face link face424 face434 edges edge2404 edge2406 vertices
vertex2231 vertex2233
face link face434 face444 edges edge2406 edge2408 vertices
vertex2233 vertex2235
face link face444 face454 edges edge2408 edge2410 vertices
vertex2235 vertex2237
face link face454 face464 edges edge2410 edge2412 vertices
vertex2237 vertex2239
face link face464 face474 edges edge2412 edge2414 vertices
vertex2239 vertex2241
face link face474 face484 edges edge2414 edge2416 vertices
vertex2241 vertex2243
face link face484 face494 edges edge2416 edge2418 vertices
vertex2243 vertex2245
face link face494 face504 edges edge2418 edge2420 vertices
vertex2245 vertex2247
face link face504 face514 edges edge2420 edge2422 vertices
vertex2247 vertex2249
UP TO THIS POINT ALL THE FACES ARE CONNCTED SUCCESSFULLY
LINKING THE FIRST THREE JET TELEPHONES
face link face912 face117 edges edge6950 edge6960 vertices
vertex6437 vertex6446 reverse
face link face912 face1600 edges edge6950 edge7890 vertices
vertex6437 vertex7303 reverse
face link face912 face372 edges edge6950 edge2168 vertices
vertex6437 vertex2041
face link face117 face376 edges edge6959 edge2304 vertices
vertex6447 vertex2101 reverse
face link face1600 face377 edges edge7890 edge2423 vertices
vertex7303 vertex2221 reverse
face link face372 face382 edges edge2168 edge2169 vertices
vertex2041 vertex2043
face link face377 face387 edges edge2423 edge2424 vertices
vertex2221 vertex2223
face link face376 face386 edges edge2304 edge2306 vertices
vertex2101 vertex2103
face link face387 face397 edges edge2424 edge2425 vertices
vertex2223 vertex2225
face link face386 face396 edges edge2306 edge2308 vertices
82
vertex2103 vertex2105
face link face382 face392 edges edge2169 edge2170 vertices
vertex2043 vertex2045
face link face382 face392 edges edge2169 edge2170 vertices
vertex2043 vertex2045
face link face382 face392 edges edge2169 edge2170 vertices
vertex2043 vertex2045
face link face382 face392 edges edge2169 edge2170 vertices
vertex2043 vertex2045
face link face397 face407 edges edge2425 edge2426 vertices
vertex2225 vertex2227
face link face392 face402 edges edge2170 edge2171 vertices
vertex2045 vertex2047
face link face396 face406 edges edge2290 edge2291 vertices
vertex2104 vertex2106
face link face407 face417 edges edge2426 edge2427 vertices
vertex2227 vertex2229
face link face417 face427 edges edge2427 edge2428 vertices
vertex2229 vertex2231
face link face427 face437 edges edge2428 edge2429 vertices
vertex2231 vertex2233
face link face437 face447 edges edge2429 edge2430 vertices
vertex2233 vertex2235
face link face447 face457 edges edge2430 edge2431 vertices
vertex2235 vertex2237
face link face457 face467 edges edge2431 edge2432 vertices
vertex2237 vertex2239
face link face467 face477 edges edge2432 edge2433 vertices
vertex2239 vertex2241
face link face477 face487 edges edge2433 edge2434 vertices
vertex2241 vertex2243
face link face487 face487 edges edge2434 edge2434 vertices
vertex2243 vertex2243
face link face487 face487 edges edge2434 edge2434 vertices
vertex2243 vertex2243
face link face487 face487 edges edge2434 edge2434 vertices
vertex2243 vertex2243
face link face487 face497 edges edge2434 edge2435 vertices
vertex2243 vertex2245
face link face497 face507 edges edge2435 edge2436 vertices
vertex2245 vertex2247
face link face507 face517 edges edge2436 edge2437 vertices
vertex2247 vertex2249
face link face406 face416 edges edge2291 edge2292 vertices
vertex2106 vertex2108
face link face416 face426 edges edge2292 edge2293 vertices
vertex2108 vertex2110
face link face426 face436 edges edge2293 edge2294 vertices
vertex2110 vertex2112
face link face436 face446 edges edge2294 edge2295 vertices
vertex2112 vertex2114
face link face446 face456 edges edge2295 edge2296 vertices
vertex2114 vertex2116
face link face456 face466 edges edge2296 edge2297 vertices
vertex2116 vertex2118
face link face466 face476 edges edge2297 edge2298 vertices
83
vertex2118 vertex2120
face link face486 face496 edges edge2299 edge2300 vertices
vertex2122 vertex2124
face link face476 face486 edges edge2298 edge2299 vertices
vertex2120 vertex2122
face link face496 face506 edges edge2300 edge2301 vertices
vertex2124 vertex2126
face link face506 face516 edges edge2301 edge2302 vertices
vertex2126 vertex2128
face link face392 face402 edges edge2142 edge2144 vertices
vertex2044 vertex2046
face link face402 face412 edges edge2171 edge2172 vertices
vertex2047 vertex2049
face link face412 face422 edges edge2172 edge2173 vertices
vertex2049 vertex2051
face link face422 face432 edges edge2173 edge2174 vertices
vertex2051 vertex2053
face link face432 face442 edges edge2174 edge2175 vertices
vertex2053 vertex2055
face link face442 face452 edges edge2175 edge2176 vertices
vertex2055 vertex2057
face link face452 face462 edges edge2176 edge2177 vertices
vertex2057 vertex2059
face link face462 face472 edges edge2177 edge2178 vertices
vertex2059 vertex2061
face link face472 face482 edges edge2178 edge2179 vertices
vertex2061 vertex2063
face link face482 face492 edges edge2179 edge2180 vertices
vertex2063 vertex2065
face link face492 face502 edges edge2180 edge2181 vertices
vertex2065 vertex2067
face link face502 face512 edges edge2181 edge2182 vertices
vertex2067 vertex2069
LINKING THE TELEPHONES OF THE BOTTOM OF THE PLENUM
face link face912 face922 edges edge6950 edge6976 vertices
vertex6437 vertex6461
face link face922 face932 edges edge6976 edge7002 vertices
vertex6461 vertex6485
face link face932 face942 edges edge7002 edge7028 vertices
vertex6485 vertex6509
face link face942 face952 edges edge7028 edge7054 vertices
vertex6509 vertex6533
face link face952 face962 edges edge7054 edge7080 vertices
vertex6533 vertex6557
face link face962 face972 edges edge7080 edge7106 vertices
vertex6557 vertex6581
face link face972 face982 edges edge7106 edge7132 vertices
vertex6581 vertex6605
face link face982 face992 edges edge7132 edge7158 vertices
vertex6605 vertex6629
face link face992 face1002 edges edge7158 edge7184 vertices
vertex6629 vertex6653
face link face1002 face1012 edges edge7184 edge7210 vertices
vertex6653 vertex6677
84
face link face1012 face1022 edges edge7210 edge7236 vertices
vertex6677 vertex6701
face link face1032 face1042 edges edge7262 edge7288 vertices
vertex6725 vertex6749
face link face1042 face1052 edges edge7288 edge7314 vertices
vertex6749 vertex6773
face link face117 face124 edges edge6960 edge6986 vertices
vertex6446 vertex6470
face link face124 face131 edges edge6986 edge7012 vertices
vertex6470 vertex6494
face link face131 face138 edges edge7012 edge7038 vertices
vertex6494 vertex6518
face link face138 face145 edges edge7038 edge7064 vertices
vertex6518 vertex6542
face link face145 face152 edges edge7064 edge7090 vertices
vertex6542 vertex6566
face link face152 face159 edges edge7090 edge7116 vertices
vertex6566 vertex6590
face link face159 face166 edges edge7116 edge7142 vertices
vertex6590 vertex6614
face link face166 face173 edges edge7142 edge7168 vertices
vertex6614 vertex6638
face link face173 face180 edges edge7168 edge7194 vertices
vertex6638 vertex6662
face link face180 face187 edges edge7194 edge7220 vertices
vertex6662 vertex6686
face link face187 face194 edges edge7220 edge7246 vertices
vertex6686 vertex6710
face link face194 face201 edges edge7246 edge7272 vertices
vertex6710 vertex6734
face link face1022 face1032 edges edge7236 edge7262 vertices
vertex6701 vertex6725
face link face1032 face1042 edges edge7262 edge7288 vertices
vertex6725 vertex6749
face link face201 face208 edges edge7271 edge7297 vertices
vertex6735 vertex6759
face link face208 face215 edges edge7297 edge7323 vertices
vertex6759 vertex6783
face link face1600 face1602 edges edge7890 edge7899 vertices
vertex7303 vertex7311
face link face1602 face1604 edges edge7899 edge7908 vertices
vertex7311 vertex7319
face link face1604 face1606 edges edge7908 edge7917 vertices
vertex7319 vertex7327
face link face1606 face1608 edges edge7917 edge7926 vertices
vertex7327 vertex7335
face link face1608 face1610 edges edge7926 edge7935 vertices
vertex7335 vertex7343
face link face1610 face1612 edges edge7935 edge7944 vertices
vertex7343 vertex7351
face link face1612 face1614 edges edge7944 edge7953 vertices
vertex7351 vertex7359
face link face1614 face1616 edges edge7953 edge7962 vertices
vertex7359 vertex7367
face link face1616 face1618 edges edge7962 edge7971 vertices
vertex7367 vertex7375
85
face link face1618 face1620 edges edge7971 edge7980 vertices
vertex7375 vertex7383
face link face1620 face1622 edges edge7980 edge7989 vertices
vertex7383 vertex7391
face link face1622 face1624 edges edge7989 edge7998 vertices
vertex7391 vertex7399
face link face1624 face1626 edges edge7998 edge8007 vertices
vertex7399 vertex7407
face link face1626 face1628 edges edge8007 edge8016 vertices
vertex7407 vertex7415
LINKING ALL THE TELEPHONES OF THE TOP OF THE CHANNEL
face link face912 face1510 edges edge6950 edge7339 vertices
vertex6437 vertex6797 reverse
face link face117 face1512 edges edge6959 edge7349 vertices
vertex6447 vertex6807
face link face1600 face1514 edges edge7890 edge7363 vertices
vertex7303 vertex6819
face link face1510 face1516 edges edge7339 edge7376 vertices
vertex6797 vertex6831
face link face1516 face1522 edges edge7376 edge7413 vertices
vertex6831 vertex6865
face link face1522 face1528 edges edge7413 edge7450 vertices
vertex6865 vertex6899
face link face1528 face1534 edges edge7450 edge7487 vertices
vertex6899 vertex6933
face link face1534 face1540 edges edge7487 edge7524 vertices
vertex6933 vertex6967
face link face1540 face1546 edges edge7524 edge7561 vertices
vertex6967 vertex7001
face link face1546 face1552 edges edge7561 edge7598 vertices
vertex7001 vertex7035
face link face1552 face1558 edges edge7598 edge7635 vertices
vertex7035 vertex7069
face link face1558 face1564 edges edge7635 edge7672 vertices
vertex7069 vertex7103
face link face1564 face1570 edges edge7672 edge7709 vertices
vertex7103 vertex7137
face link face1570 face1576 edges edge7709 edge7746 vertices
vertex7137 vertex7171
face link face1576 face1582 edges edge7746 edge7783 vertices
vertex7171 vertex7205
face link face1582 face1588 edges edge7783 edge7820 vertices
vertex7205 vertex7239
face link face1588 face1594 edges edge7820 edge7857 vertices
vertex7239 vertex7273
face link face1512 face1518 edges edge7350 edge7387 vertices
vertex6806 vertex6840
face link face1518 face1524 edges edge7387 edge7424 vertices
vertex6840 vertex6874
face link face1524 face1530 edges edge7424 edge7461 vertices
vertex6874 vertex6908
face link face1530 face1536 edges edge7461 edge7498 vertices
vertex6908 vertex6942
face link face1536 face1542 edges edge7498 edge7535 vertices
86
vertex6942 vertex6976
face link face1542 face1548 edges edge7535 edge7572 vertices
vertex6976 vertex7010
face link face1548 face1554 edges edge7572 edge7609 vertices
vertex7010 vertex7044
face link face1554 face1560 edges edge7609 edge7646 vertices
vertex7044 vertex7078
face link face1560 face1566 edges edge7646 edge7683 vertices
vertex7078 vertex7112
face link face1566 face1572 edges edge7683 edge7720 vertices
vertex7112 vertex7146
face link face1572 face1578 edges edge7720 edge7757 vertices
vertex7146 vertex7180
face link face1578 face1584 edges edge7757 edge7794 vertices
vertex7180 vertex7214
face link face1584 face1590 edges edge7794 edge7831 vertices
vertex7214 vertex7248
face link face1590 face1596 edges edge7831 edge7868 vertices
vertex7248 vertex7282
face link face1514 face1520 edges edge7363 edge7400 vertices
vertex6819 vertex6853
face link face1520 face1526 edges edge7400 edge7437 vertices
vertex6853 vertex6887
face link face1526 face1532 edges edge7437 edge7474 vertices
vertex6887 vertex6921
face link face1532 face1538 edges edge7474 edge7511 vertices
vertex6921 vertex6955
face link face1538 face1544 edges edge7511 edge7548 vertices
vertex6955 vertex6989
face link face1544 face1550 edges edge7548 edge7585 vertices
vertex6989 vertex7023
face link face1550 face1556 edges edge7585 edge7622 vertices
vertex7023 vertex7057
face link face1556 face1562 edges edge7622 edge7659 vertices
vertex7057 vertex7091
face link face1562 face1568 edges edge7659 edge7696 vertices
vertex7091 vertex7125
face link face1568 face1574 edges edge7696 edge7733 vertices
vertex7125 vertex7159
face link face1574 face1580 edges edge7733 edge7770 vertices
vertex7159 vertex7193
face link face1580 face1586 edges edge7770 edge7807 vertices
vertex7193 vertex7227
face link face1586 face1592 edges edge7807 edge7844 vertices
vertex7227 vertex7261
face link face1592 face1598 edges edge7844 edge7881 vertices
vertex7261 vertex7295
LINKING ALL THE TELEPHONES OF THE TOP OF THE PLENUM
face link face912 face642 edges edge6950 edge3489 vertices
vertex6437 vertex3253 reverse
face link face642 face647 edges edge3489 edge3744 vertices
vertex3253 vertex3433
face link face117 face646 edges edge6959 edge3638 vertices
vertex6447 vertex3313
87
face link face642 face652 edges edge3489 edge3491 vertices
vertex3253 vertex3255
face link face652 face662 edges edge3491 edge3493 vertices
vertex3255 vertex3257
face link face662 face672 edges edge3493 edge3495 vertices
vertex3257 vertex3259
face link face672 face682 edges edge3495 edge3497 vertices
vertex3259 vertex3261
face link face682 face692 edges edge3497 edge3499 vertices
vertex3261 vertex3263
face link face692 face702 edges edge3499 edge3501 vertices
vertex3263 vertex3265
face link face702 face712 edges edge3501 edge3503 vertices
vertex3265 vertex3267
face link face712 face722 edges edge3503 edge3505 vertices
vertex3267 vertex3269
face link face722 face732 edges edge3505 edge3507 vertices
vertex3269 vertex3271
face link face732 face742 edges edge3507 edge3509 vertices
vertex3271 vertex3273
face link face742 face752 edges edge3509 edge3511 vertices
vertex3273 vertex3275
face link face752 face762 edges edge3511 edge3513 vertices
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face link face762 face772 edges edge3513 edge3515 vertices
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vertex3314 vertex3316
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face link face676 face686 edges edge3659 edge3661 vertices
vertex3318 vertex3320
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face link face696 face706 edges edge3663 edge3665 vertices
vertex3322 vertex3324
face link face706 face716 edges edge3665 edge3667 vertices
vertex3324 vertex3326
face link face716 face726 edges edge3667 edge3669 vertices
vertex3326 vertex3328
face link face726 face736 edges edge3669 edge3671 vertices
vertex3328 vertex3330
face link face736 face746 edges edge3671 edge3673 vertices
vertex3330 vertex3332
face link face746 face756 edges edge3673 edge3675 vertices
vertex3332 vertex3334
face link face756 face766 edges edge3675 edge3677 vertices
vertex3334 vertex3336
face link face766 face776 edges edge3677 edge3679 vertices
vertex3336 vertex3338
face link face776 face786 edges edge3679 edge3681 vertices
88
vertex3338 vertex3340
face link face647 face657 edges edge3744 edge3746 vertices
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face link face657 face667 edges edge3746 edge3748 vertices
vertex3435 vertex3437
face link face667 face677 edges edge3748 edge3750 vertices
vertex3437 vertex3439
face link face677 face687 edges edge3750 edge3752 vertices
vertex3439 vertex3441
face link face687 face697 edges edge3752 edge3754 vertices
vertex3441 vertex3443
face link face697 face707 edges edge3754 edge3756 vertices
vertex3443 vertex3445
face link face707 face717 edges edge3756 edge3758 vertices
vertex3445 vertex3447
face link face717 face727 edges edge3758 edge3760 vertices
vertex3447 vertex3449
face link face727 face737 edges edge3760 edge3762 vertices
vertex3449 vertex3451
face link face737 face747 edges edge3762 edge3764 vertices
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vertex3457 vertex3459
face link face777 face787 edges edge3770 edge3772 vertices
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face link face647 face1600 edges edge3685 edge6963 vertices
vertex3345 vertex6449
LINKING OUTBOXES ON THE PLENUM
face modify face911 side vertex4404 vertex4405
face modify face918 side vertex4405 vertex4404
face link face911 face915 edges edge4778 edge4898 vertices
vertex4374 vertex4434
face link face915 face645 edges edge4899 edge3833 vertices
vertex4480 vertex3463 reverse
face link face911 face641 edges edge4779 edge3578 vertices
vertex4405 vertex3283 reverse
face link face918 face648 edges edge4825 edge3686 vertices
vertex4436 vertex3347 reverse
face link face645 face655 edges edge3833 edge3834 vertices
vertex3463 vertex3465
face link face655 face665 edges edge3834 edge3835 vertices
vertex3465 vertex3467
face link face665 face675 edges edge3835 edge3836 vertices
vertex3467 vertex3469
face link face675 face685 edges edge3836 edge3837 vertices
vertex3469 vertex3471
face link face685 face695 edges edge3837 edge3838 vertices
89
vertex3471 vertex3473
face link face695 face705 edges edge3838 edge3839 vertices
vertex3473 vertex3475
face link face705 face715 edges edge3839 edge3840 vertices
vertex3475 vertex3477
face link face715 face725 edges edge3840 edge3841 vertices
vertex3477 vertex3479
face link face725 face735 edges edge3841 edge3842 vertices
vertex3479 vertex3481
face link face735 face745 edges edge3842 edge3843 vertices
vertex3481 vertex3483
face link face745 face755 edges edge3843 edge3844 vertices
vertex3483 vertex3485
face link face755 face765 edges edge3844 edge3845 vertices
vertex3485 vertex3487
face link face765 face775 edges edge3845 edge3846 vertices
vertex3487 vertex3489
face link face775 face785 edges edge3846 edge3847 vertices
vertex3489 vertex3491
face link face648 face658 edges edge3686 edge3690 vertices
vertex3347 vertex3353
face link face658 face668 edges edge3690 edge3694 vertices
vertex3353 vertex3359
face link face668 face678 edges edge3694 edge3698 vertices
vertex3359 vertex3365
face link face678 face688 edges edge3698 edge3702 vertices
vertex3365 vertex3371
face link face688 face698 edges edge3702 edge3706 vertices
vertex3371 vertex3377
face link face698 face708 edges edge3706 edge3710 vertices
vertex3377 vertex3383
face link face708 face718 edges edge3710 edge3714 vertices
vertex3383 vertex3389
face link face718 face728 edges edge3714 edge3718 vertices
vertex3389 vertex3395
face link face728 face738 edges edge3718 edge3722 vertices
vertex3395 vertex3401
face link face738 face748 edges edge3722 edge3726 vertices
vertex3401 vertex3407
face link face748 face758 edges edge3726 edge3730 vertices
vertex3407 vertex3413
face link face758 face768 edges edge3730 edge3734 vertices
vertex3413 vertex3419
face link face768 face778 edges edge3734 edge3738 vertices
vertex3419 vertex3425
face link face778 face788 edges edge3738 edge3742 vertices
vertex3425 vertex3431
face link face641 face650 edges edge3578 edge3579 vertices
vertex3283 vertex3285
face link face650 face660 edges edge3579 edge3580 vertices
vertex3285 vertex3287
face link face660 face670 edges edge3580 edge3581 vertices
vertex3287 vertex3289
face link face670 face680 edges edge3581 edge3582 vertices
vertex3289 vertex3291
face link face680 face690 edges edge3582 edge3583 vertices
90
vertex3291 vertex3293
face link face690 face700 edges edge3583 edge3584 vertices
vertex3293 vertex3295
face link face700 face710 edges edge3584 edge3585 vertices
vertex3295 vertex3297
face link face710 face720 edges edge3585 edge3586 vertices
vertex3297 vertex3299
face link face720 face730 edges edge3586 edge3587 vertices
vertex3299 vertex3301
face link face730 face740 edges edge3587 edge3588 vertices
vertex3301 vertex3303
face link face740 face750 edges edge3588 edge3589 vertices
vertex3303 vertex3305
face link face750 face760 edges edge3589 edge3590 vertices
vertex3305 vertex3307
face link face760 face770 edges edge3590 edge3591 vertices
vertex3307 vertex3309
face link face770 face780 edges edge3591 edge3592 vertices
vertex3309 vertex3311
face link face915 face925 edges edge4899 edge4901 vertices
vertex4480 vertex4482
face link face925 face935 edges edge4901 edge4903 vertices
vertex4482 vertex4484
face link face935 face945 edges edge4903 edge4905 vertices
vertex4484 vertex4486
face link face945 face955 edges edge4905 edge4907 vertices
vertex4486 vertex4488
face link face955 face965 edges edge4907 edge4909 vertices
vertex4488 vertex4490
face link face965 face975 edges edge4909 edge4911 vertices
vertex4490 vertex4492
face link face975 face985 edges edge4911 edge4913 vertices
vertex4492 vertex4494
face link face985 face995 edges edge4913 edge4915 vertices
vertex4494 vertex4496
face link face995 face1005 edges edge4915 edge4917 vertices
vertex4496 vertex4498
face link face1005 face1015 edges edge4917 edge4919 vertices
vertex4498 vertex4500
face link face1015 face1025 edges edge4919 edge4921 vertices
vertex4500 vertex4502
face link face1025 face1035 edges edge4921 edge4923 vertices
vertex4502 vertex4504
face link face1035 face1045 edges edge4923 edge4925 vertices
vertex4504 vertex4506
face link face1045 face1055 edges edge4925 edge4927 vertices
vertex4506 vertex4508
face link face918 face928 edges edge4825 edge4828 vertices
vertex4436 vertex4439
face link face928 face938 edges edge4828 edge4831 vertices
vertex4439 vertex4442
face link face938 face948 edges edge4831 edge4834 vertices
vertex4442 vertex4445
face link face948 face958 edges edge4834 edge4837 vertices
vertex4445 vertex4448
face link face958 face968 edges edge4837 edge4840 vertices
91
vertex4448 vertex4451
face link face968 face978 edges edge4840 edge4843 vertices
vertex4451 vertex4454
face link face978 face988 edges edge4843 edge4846 vertices
vertex4454 vertex4457
face link face988 face998 edges edge4846 edge4849 vertices
vertex4457 vertex4460
face link face998 face1008 edges edge4849 edge4852 vertices
vertex4460 vertex4463
face link face1008 face1018 edges edge4852 edge4855 vertices
vertex4463 vertex4466
face link face1018 face1028 edges edge4855 edge4858 vertices
vertex4466 vertex4469
face link face1028 face1038 edges edge4858 edge4861 vertices
vertex4469 vertex4472
face link face1038 face1048 edges edge4861 edge4864 vertices
vertex4472 vertex4475
face link face1048 face1058 edges edge4864 edge4867 vertices
vertex4475 vertex4478
face link face911 face920 edges edge108 edge118 vertices
vertex88 vertex94
face link face920 face930 edges edge118 edge128 vertices
vertex94 vertex100
face link face930 face940 edges edge4783 edge4785 vertices
vertex4409 vertex4411
face link face940 face950 edges edge4785 edge4787 vertices
vertex4411 vertex4413
face link face950 face960 edges edge4787 edge4789 vertices
vertex4413 vertex4415
face link face960 face970 edges edge4789 edge4791 vertices
vertex4415 vertex4417
face link face970 face980 edges edge4791 edge4793 vertices
vertex4417 vertex4419
face link face980 face990 edges edge4793 edge4795 vertices
vertex4419 vertex4421
face link face990 face1000 edges edge4795 edge4797 vertices
vertex4421 vertex4423
face link face1000 face1010 edges edge4797 edge4799 vertices
vertex4423 vertex4425
face link face1010 face1020 edges edge4799 edge4801 vertices
vertex4425 vertex4427
face link face1020 face1030 edges edge4801 edge4803 vertices
vertex4427 vertex4429
face link face1030 face1040 edges edge4803 edge4805 vertices
vertex4429 vertex4431
face link face1040 face1050 edges edge4805 edge4807 vertices
vertex4431 vertex4433
LINKING THE TOP OF THE CHANEL OUTBOXES
face modify face1256 side vertex6322 vertex6321
face modify face1263 side vertex6322 vertex6321
face modify face1260 side vertex6397 vertex6396
92
face link face1256 face1260 edges edge6803 edge6923 vertices
vertex6322 vertex6397
face link face1256 face371 edges edge6774 edge2053 vertices
vertex6292 vertex1955 reverse
face link face371 face375 edges edge2053 edge2336 vertices
vertex1955 vertex2135
face link face1263 face378 edges edge6820 edge2228 vertices
vertex6322 vertex2071 reverse
face link face1263 face1273 edges edge6820 edge6823 vertices
vertex6322 vertex6324
face link face1273 face1283 edges edge6823 edge6826 vertices
vertex6324 vertex6326
face link face1283 face1293 edges edge6826 edge6829 vertices
vertex6326 vertex6328
face link face1293 face1303 edges edge6829 edge6832 vertices
vertex6328 vertex6330
face link face1303 face1313 edges edge6832 edge6835 vertices
vertex6330 vertex6332
face link face1313 face1323 edges edge6835 edge6838 vertices
vertex6332 vertex6334
face link face1323 face1333 edges edge6838 edge6841 vertices
vertex6334 vertex6336
face link face1333 face1343 edges edge6841 edge6844 vertices
vertex6336 vertex6338
face link face1343 face1353 edges edge6844 edge6847 vertices
vertex6338 vertex6340
face link face1353 face1363 edges edge6847 edge6850 vertices
vertex6340 vertex6342
face link face1363 face1373 edges edge6850 edge6853 vertices
vertex6342 vertex6344
face link face1373 face1383 edges edge6853 edge6856 vertices
vertex6344 vertex6346
face link face1383 face1393 edges edge6856 edge6859 vertices
vertex6346 vertex6348
face link face1393 face1403 edges edge6859 edge6862 vertices
vertex6348 vertex6350
face link face1256 face1265 edges edge6774 edge6776 vertices
vertex6292 vertex6294
face link face1265 face1275 edges edge6776 edge6778 vertices
vertex6294 vertex6296
face link face1275 face1285 edges edge6778 edge6780 vertices
vertex6296 vertex6298
face link face1285 face1295 edges edge6780 edge6782 vertices
vertex6298 vertex6300
face link face1295 face1305 edges edge6782 edge6784 vertices
vertex6300 vertex6302
face link face1305 face1315 edges edge6784 edge6786 vertices
vertex6302 vertex6304
face link face1315 face1325 edges edge6786 edge6788 vertices
vertex6304 vertex6306
face link face1325 face1335 edges edge6788 edge6790 vertices
vertex6306 vertex6308
face link face1335 face1345 edges edge6790 edge6792 vertices
vertex6308 vertex6310
face link face1345 face1355 edges edge6792 edge6794 vertices
vertex6310 vertex6312
93
face link face1355 face1365 edges edge6794 edge6796 vertices
vertex6312 vertex6314
face link face1365 face1375 edges edge6796 edge6798 vertices
vertex6314 vertex6316
face link face1375 face1385 edges edge6798 edge6800 vertices
vertex6316 vertex6318
face link face1385 face1395 edges edge6800 edge6802 vertices
vertex6318 vertex6320
face link face1260 face1270 edges edge6894 edge6896 vertices
vertex6353 vertex6356
face link face1270 face1280 edges edge6896 edge6898 vertices
vertex6356 vertex6359
face link face1280 face1290 edges edge6898 edge6900 vertices
vertex6359 vertex6362
face link face1290 face1300 edges edge6900 edge6902 vertices
vertex6362 vertex6365
face link face1300 face1310 edges edge6902 edge6904 vertices
vertex6365 vertex6368
face link face1310 face1320 edges edge6904 edge6906 vertices
vertex6368 vertex6371
face link face1320 face1330 edges edge6906 edge6908 vertices
vertex6371 vertex6374
face link face1330 face1340 edges edge6908 edge6910 vertices
vertex6374 vertex6377
face link face1340 face1350 edges edge6910 edge6912 vertices
vertex6377 vertex6380
face link face1350 face1360 edges edge6912 edge6914 vertices
vertex6380 vertex6383
face link face1360 face1370 edges edge6914 edge6916 vertices
vertex6383 vertex6386
face link face1370 face1380 edges edge6916 edge6918 vertices
vertex6386 vertex6389
face link face1380 face1390 edges edge6918 edge6920 vertices
vertex6389 vertex6392
face link face1390 face1400 edges edge6920 edge6922 vertices
vertex6392 vertex6395
LINKING THE BOTTOM OF THE CHANEL OUTBOXES
face link face375 face385 edges edge2440 edge2443 vertices
vertex2251 vertex2253
face link face385 face395 edges edge2443 edge2446 vertices
vertex2253 vertex2255
face link face395 face405 edges edge2446 edge2449 vertices
vertex2255 vertex2257
face link face405 face415 edges edge2449 edge2452 vertices
vertex2257 vertex2259
face link face415 face425 edges edge2452 edge2455 vertices
vertex2259 vertex2261
face link face425 face435 edges edge2455 edge2458 vertices
vertex2261 vertex2263
face link face435 face445 edges edge2458 edge2461 vertices
vertex2263 vertex2265
face link face445 face455 edges edge2461 edge2464 vertices
vertex2265 vertex2267
face link face455 face465 edges edge2464 edge2467 vertices
94
vertex2267 vertex2269
face link face465 face475 edges edge2467 edge2470 vertices
vertex2269 vertex2271
face link face475 face485 edges edge2470 edge2473 vertices
vertex2271 vertex2273
face link face485 face495 edges edge2473 edge2476 vertices
vertex2273 vertex2275
face link face495 face505 edges edge2476 edge2479 vertices
vertex2275 vertex2277
face link face505 face515 edges edge2479 edge2482 vertices
vertex2277 vertex2279
face link face378 face388 edges edge2245 edge2248 vertices
vertex2135 vertex2141
face link face388 face398 edges edge2248 edge2251 vertices
vertex2141 vertex2147
face link face398 face408 edges edge2251 edge2254 vertices
vertex2147 vertex2153
face link face408 face418 edges edge2254 edge2257 vertices
vertex2153 vertex2159
face link face418 face428 edges edge2257 edge2260 vertices
vertex2159 vertex2165
face link face428 face438 edges edge2260 edge2263 vertices
vertex2165 vertex2171
face link face438 face448 edges edge2263 edge2266 vertices
vertex2171 vertex2177
face link face448 face458 edges edge2266 edge2269 vertices
vertex2177 vertex2183
face link face458 face468 edges edge2269 edge2272 vertices
vertex2183 vertex2189
face link face468 face478 edges edge2272 edge2275 vertices
vertex2189 vertex2195
face link face478 face488 edges edge2275 edge2278 vertices
vertex2195 vertex2201
face link face488 face498 edges edge2278 edge2281 vertices
vertex2201 vertex2207
face link face498 face508 edges edge2281 edge2284 vertices
vertex2207 vertex2213
face link face508 face518 edges edge2284 edge2287 vertices
vertex2213 vertex2219
face link face371 face380 edges edge2185 edge2188 vertices
vertex2071 vertex2073
face link face380 face390 edges edge2188 edge2191 vertices
vertex2073 vertex2075
face link face390 face400 edges edge2191 edge2194 vertices
vertex2075 vertex2077
face link face400 face410 edges edge2194 edge2197 vertices
vertex2077 vertex2079
face link face410 face420 edges edge2197 edge2200 vertices
vertex2079 vertex2081
face link face420 face430 edges edge2200 edge2203 vertices
vertex2081 vertex2083
face link face430 face440 edges edge2203 edge2206 vertices
vertex2083 vertex2085
face link face440 face450 edges edge2206 edge2209 vertices
vertex2085 vertex2087
face link face450 face460 edges edge2209 edge2212 vertices
95
vertex2087 vertex2089
face link face460 face470 edges edge2212 edge2215 vertices
vertex2089 vertex2091
face link face470 face480 edges edge2215 edge2218 vertices
vertex2091 vertex2093
face link face480 face490 edges edge2218 edge2221 vertices
vertex2093 vertex2095
face link face490 face500 edges edge2221 edge2224 vertices
vertex2095 vertex2097
face link face500 face510 edges edge2224 edge2227 vertices
vertex2097 vertex2099
TOP SIDE BOX beginning of channel
face link face1649 face1633 edges edge97 edge3533 vertices
vertex4374 vertex3162 reverse
TOP SIDE BOXES
face link face1650 face1651 edges edge4749 edge4751 vertices
vertex4376 vertex4378
face link face1652 face1653 edges edge4753 edge4755 vertices
vertex4380 vertex4382
face link face1653 face1654 edges edge4755 edge4757 vertices
vertex4382 vertex4384
face link face1654 face1655 edges edge4757 edge4759 vertices
vertex4384 vertex4386
face link face1655 face1656 edges edge4759 edge4761 vertices
vertex4386 vertex4388
face link face1656 face114 edges edge4761 edge4763 vertices
vertex4388 vertex4390
face link face114 face1657 edges edge4763 edge4765 vertices
vertex4390 vertex4392
face link face1657 face1658 edges edge4765 edge4767 vertices
vertex4392 vertex4394
face link face1658 face1659 edges edge4767 edge4769 vertices
vertex4394 vertex4396
face link face1659 face1660 edges edge4769 edge4771 vertices
vertex4396 vertex4398
face link face1660 face1661 edges edge4771 edge4773 vertices
vertex4398 vertex4400
face link face1661 face1662 edges edge4773 edge4775 vertices
vertex4400 vertex4402
face link face1650 face1634 edges edge4900 edge8036 vertices
vertex4481 vertex3464 reverse
face link face1634 face1635 edges edge8036 edge8037 vertices
vertex3464 vertex3466
face link face1635 face1636 edges edge8037 edge8038 vertices
vertex3466 vertex3468
face link face1636 face1637 edges edge8038 edge8039 vertices
vertex3468 vertex3470
face link face1637 face1638 edges edge8039 edge8040 vertices
vertex3470 vertex3472
face link face1638 face1639 edges edge8040 edge8041 vertices
vertex3472 vertex3474
face link face1639 face6 edges edge8041 edge8042 vertices
96
vertex3474 vertex3476
face link face6 face1640 edges edge8042 edge8043 vertices
vertex3476 vertex3478
face link face1640 face1641 edges edge8043 edge8044 vertices
vertex3478 vertex3480
face link face1641 face1642 edges edge8044 edge8045 vertices
vertex3480 vertex3482
face link face1642 face1643 edges edge8045 edge8046 vertices
vertex3482 vertex3484
face link face1643 face1644 edges edge8046 edge8047 vertices
vertex3484 vertex3486
face link face1644 face1645 edges edge8047 edge8048 vertices
vertex3486 vertex3488
face link face1645 face1646 edges edge8048 edge8049 vertices
vertex3488 vertex3490
face link face1651 face1652 edges edge4751 edge4753 vertices
vertex4378 vertex4380
TOP SIDE BOX END OF CHANNEL
face link face1647 face1663 edges edge8050 edge99 vertices
vertex7433 vertex7435 reverse
TOP SIDE BOX BACK OF CHANNEL
face link face1648 face1664 edges edge12 edge8069 vertices
vertex8 vertex84 reverse
BOTTOM SIDE BOX
face link face1665 face1681 edges edge6773 edge2048 vertices
vertex6291 vertex1950 reverse
face link face1680 face1696 edges edge8071 edge8105 vertices
vertex7436 vertex7438 reverse
face link face1666 face1667 edges edge6894 edge6896 vertices
vertex6397 vertex6399
face link face1667 face1668 edges edge6896 edge6898 vertices
vertex6399 vertex6401
face link face1668 face1669 edges edge6898 edge6900 vertices
vertex6401 vertex6403
face link face1669 face1670 edges edge6900 edge6902 vertices
vertex6403 vertex6405
face link face1670 face1671 edges edge6902 edge6904 vertices
vertex6405 vertex6407
face link face1671 face209 edges edge6904 edge6906 vertices
vertex6407 vertex6409
face link face209 face1672 edges edge6906 edge6908 vertices
vertex6409 vertex6411
face link face1672 face1673 edges edge6908 edge6910 vertices
vertex6411 vertex6413
face link face1673 face1674 edges edge6910 edge6912 vertices
vertex6413 vertex6415
face link face1674 face1675 edges edge6912 edge6914 vertices
vertex6415 vertex6417
face link face1675 face1676 edges edge6914 edge6916 vertices
vertex6417 vertex6419
97
face link face1676 face1677 edges edge6916 edge6918 vertices
vertex6419 vertex6421
face link face1677 face1678 edges edge6918 edge6920 vertices
vertex6421 vertex6423
face link face1666 face1682 edges edge6894 edge8090 vertices
vertex6397 vertex2251 reverse
face link face1682 face1683 edges edge8090 edge8091 vertices
vertex2251 vertex2253
face link face1683 face1684 edges edge8091 edge8092 vertices
vertex2253 vertex2255
face link face1684 face1685 edges edge8092 edge8093 vertices
vertex2255 vertex2257
face link face1685 face1686 edges edge8093 edge8094 vertices
vertex2257 vertex2259
face link face1686 face1687 edges edge8094 edge8095 vertices
vertex2259 vertex2261
face link face1687 face1688 edges edge8095 edge8096 vertices
vertex2261 vertex2263
face link face1688 face1 edges edge8096 edge8097 vertices
vertex2263 vertex2265
face link face1 face1689 edges edge8097 edge8098 vertices
vertex2265 vertex2267
face link face1689 face1690 edges edge8098 edge8099 vertices
vertex2267 vertex2269
face link face1690 face1691 edges edge8099 edge8100 vertices
vertex2269 vertex2271
face link face1691 face1692 edges edge8100 edge8101 vertices
vertex2271 vertex2273
face link face1692 face1693 edges edge8101 edge8102 vertices
vertex2273 vertex2275
face link face1693 face1694 edges edge8102 edge8103 vertices
vertex2275 vertex2277
face link face1679 face1695 edges edge89 edge2227 vertices
vertex6320 vertex2039 reverse
MESHING BEGINS HERE
BOUNDARY LAYERS BEGINS HERE
BOUNDARY LAYER FOR THE bottom of plenum
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer1 face face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
98
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 edge edge97
edge4748 edge106 edge6946 edge6947 edge107 edge4749
edge4750 edge116 edge6972 edge6973 edge117 edge4751
edge4752 edge126 edge6998 edge6999 edge127 edge4753
edge4754 edge136 edge7024 edge7025 edge137 edge4755
edge4756 edge146 edge7050 edge7051 edge147 edge4757
edge4758 edge156 edge7076 edge7077 edge157 edge4759
edge4760 edge166 edge7102 edge7103 edge167 edge4761
edge4762 edge176 edge7128 edge7129 edge177 edge4763
edge4764 edge186 edge7154 edge7155 edge187 edge4765
edge4766 edge196 edge7180 edge7181 edge197 edge4767
edge4768 edge206 edge7206 edge7207 edge207 edge4769
edge4770 edge216 edge7232 edge7233 edge217 edge4771
edge4772 edge226 edge7258 edge7259 edge227 edge4773
edge4774 edge236 edge7284 edge7285 edge237 edge4775
edge4776 edge246 edge7310 edge7311 edge247 edge4777 add
MESHING THE PLENUM
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer2 face face4 face4 face5 face110
face110 edge edge99 edge8069 edge100 edge8052 edge98 add
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer4 face face1649 face1664 face1664
face1664 face1663 edge edge8052 edge98 edge100 edge8069
edge99 add
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer4 face face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face4 face2 face2 face2 face2 face2 face4
face5 face110 face110 edge edge9 edge3398 edge3399
edge3400 edge3401 edge3402 edge3403 edge3404 edge3406
edge3405 edge3407 edge3408 edge3409 edge3415 edge3410
edge3411 edge3412 edge3413 edge3414 edge3416 edge3417
edge3418 edge3419 edge3420 edge3421 edge3422 edge3423
edge3424 edge3425 edge3426 edge3427 edge3428 edge3429
edge3430 edge3431 edge3432 edge3433 edge3434 edge3435
edge3436 edge3437 edge3438 edge3439 edge3440 edge3441
edge3442 edge3443 edge3444 edge3445 edge3446 edge3447
99
edge3448 edge3449 edge3450 edge3451 edge3457 edge3452
edge3453 edge3454 edge3455 edge3456 edge3458 edge3459
edge3460 edge3461 edge3462 edge3463 edge3464 edge3465
edge3466 edge3467 edge3468 edge3469 edge3475 edge3481
edge3470 edge3471 edge3472 edge3473 edge3474 edge3476
edge3477 edge3478 edge3479 edge3480 edge3487 edge11
edge3482 edge3483 edge3484 edge3485 edge3486 edge8051
edge12 edge10 edge8034 add
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer5 face face1663 face1664 face1664
face1664 face1649 edge edge99 edge8069 edge100 edge98
edge8052 add
BOUNDARY LAYER OF THE HOLES
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer1 face face642 edge edge3534 add
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer7 face face117 face1600 edge edge4824
edge110 add
BONDARY LAYER OF THE CHANNEL
TARGET WALL BOUNDARY LAYER
BBBL
BBL
BBL
BBBL
BBL
BBL
BBBLLLLL
blayer create first $firstch growth $growthch rows $rowsch transition 1 trows 0
uniform
blayer attach b_layer8 face face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
100
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face105 face105 face106
face104 face104 edge edge2048 edge2049 edge2050 edge2051
edge2052 edge2053 edge2054 edge2055 edge2056 edge2057
edge2058 edge2059 edge2060 edge2061 edge2062 edge2063
edge2064 edge2065 edge2066 edge2072 edge2067 edge2068
edge2069 edge2070 edge2071 edge2084 edge2078 edge2073
edge2074 edge2075 edge2076 edge2077 edge2079 edge2080
edge2081 edge2082 edge2083 edge2090 edge2096 edge2085
edge2086 edge2087 edge2088 edge2089 edge2091 edge2092
edge2093 edge2094 edge2095 edge2102 edge2108 edge2097
edge2098 edge2099 edge2100 edge2101 edge2103 edge2104
edge2105 edge2106 edge2107 edge2114 edge2120 edge2109
edge2110 edge2111 edge2112 edge2113 edge2115 edge2116
edge2117 edge2118 edge2119 edge2126 edge2132 edge2121
edge2122 edge2123 edge2124 edge2125 edge2127 edge2128
edge2129 edge2130 edge2131 edge2133 edge2134 edge2136
edge2137 edge1 edge2135 edge8088 edge3 edge4 edge8105
edge2 add
blayer create first $firstch growth $growthch rows $rowsch transition 1 trows 0
uniform
blayer attach b_layer9 face face1681 face1696 face1696
face1696 face1695 edge edge2 edge8105 edge4 edge3
edge8088 add
blayer create first $firstch growth $growthch rows $rowsch transition 1 trows 0
uniform
blayer attach b_layer10 face face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face105 face105
face106 face104 face104 edge edge6743 edge101
edge7336 edge7337 edge102 edge6744 edge6745 edge111
edge7373 edge7374 edge112 edge6746 edge6747 edge121
edge7410 edge7411 edge122 edge6748 edge6749 edge131
edge7447 edge7448 edge132 edge6750 edge6751 edge141
edge7484 edge7485 edge142 edge6752 edge6755 edge6753
edge151 edge6754 edge7521 edge7522 edge152 edge161
101
edge6756 edge6757 edge7558 edge7559 edge162 edge171
edge7595 edge7596 edge172 edge6758 edge6759 edge181
edge7632 edge7633 edge182 edge6760 edge6761 edge191
edge7669 edge7670 edge192 edge6762 edge6763 edge6767
edge6765 edge201 edge7706 edge7707 edge202 edge6764
edge211 edge6766 edge7743 edge7744 edge212 edge6769
edge221 edge6768 edge7780 edge7781 edge222 edge6771
edge231 edge6770 edge7817 edge7818 edge232 edge241
edge7854 edge7855 edge242 edge6772 edge89 edge8070
edge91 edge92 edge8087 edge90 add
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer11 face face4 face5 face2 face5
face110 face2 edge edge8 edge8 edge6 edge7 edge7
edge5 add
blayer create first $firstch growth $growthch rows $rowsch transition 1 trows 0
uniform
blayer attach b_layer12 face face106 face104 face103 face105
edge edge87 edge87 edge85 edge88 add
BOUNDARY LAYERS ENDS HERE
edge picklink edge6948 edge6949
edge mesh edge6949 edge6948 successive ratio1 1 intervals $NumbNodes
edge picklink edge6950
edge mesh edge6950 successive ratio1 1 intervals ($NumbNodes2)
face mesh face1450 map
edge picklink edge6963 edge6947
edge mesh edge6947 edge6963 successive ratio1 1 intervals ($Numbtelnodes+$rows)
face mesh face912 map
edge picklink edge6961 edge6960 edge7889 edge7890
edge mesh edge7890 edge7889 edge6960 edge6961 successive ratio1 1
intervals ($NumbNodes)
edge picklink edge6959 edge7891
edge mesh edge7891 edge6959 successive ratio1 1 intervals ($NumbNodes2)
face mesh face1452 map
face mesh face1600 face117 map
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer12 face face2 face110 face5 face110
face2 face4 face5 face4 edge edge5 edge5 edge7
edge7 edge6 edge6 edge8 edge8 add
Meshing constants
$NumbNodes=5
$Numbtelnodes=6
$PLobnodes=5
$Chobnodes=5
$Plbenodes=($NumbNodes(4)+$rows)
$plsqnodes=($NumbNodes(3))
102
$Pllsnodes=($NumbNodes+$rows)
$Nojetcells=10
edge picklink edge3686 edge3402
edge mesh edge3686 edge3402 successive ratio1 1 intervals ($PLobnodes)
edge picklink edge6744 edge6864
edge mesh edge6864 edge6744 successive ratio1 1 intervals 5
face link face1260 face375 edges edge6923 edge2440 vertices
vertex6397 vertex2251 reverse
face modify face915 side vertex4479 vertex4480
face mesh face915 face918 face911 map size 1
face mesh face1260 face1263 face1256 map size 1
edge picklink edge8068 edge8053
edge mesh edge8068 edge8053 successive ratio1 1 intervals ($Plbenodes)
edge picklink edge8086 edge8071
edge mesh edge8071 edge8086 successive ratio1 1 intervals ($CHbenodes)
edge delete edge8053 edge8068 keepsettings onlymesh
edge mesh edge8053 edge8068 successive ratio1 1 intervals ($Plbenodes)
edge delete edge8090 keepsettings onlymesh
edge picklink edge8090
edge mesh edge8090 successive ratio1 1 intervals ($plsqnodes)
edge delete edge8054 keepsettings onlymesh
edge picklink edge8054
edge mesh edge8054 successive ratio1 1 intervals ($plsqnodes)
face mesh face1647 face1679 face1678 face1646 face1633
face1665 map
edge delete edge98 edge8087 keepsettings onlymesh
edge picklink edge8087 edge98
edge mesh edge98 successive ratio1 1 intervals ($Pllsnodes)
edge mesh edge8087 successive ratio1 1 intervals ($CHlsnodes)
face mesh face1648 face1680 map
COOPERING ALL THE JETS
volume mesh volume3 cooper source face1600 face1452 face117
face1514 face1512 face115 intervals ($Nojetcells)
volume mesh volume5 cooper source face1456 face1602 face124
face1518 face1520 face122 intervals ($Nojetcells)
volume mesh volume7 cooper source face1460 face1604 face131
face1526 face1524 face129 intervals ($Nojetcells)
volume mesh volume9 cooper source face1464 face1606 face138
face1532 face1530 face136 intervals ($Nojetcells)
volume mesh volume11 cooper source face1468 face1608 face145
face1538 face143 face1536 intervals ($Nojetcells)
volume mesh volume13 cooper source face1472 face1610 face152
face1544 face1542 face150 intervals ($Nojetcells)
volume mesh volume15 cooper source face1476 face1612 face159
face1550 face1548 face157 intervals ($Nojetcells)
volume mesh volume17 cooper source face1480 face1614 face166
face1556 face1554 face164 intervals ($Nojetcells)
volume mesh volume19 cooper source face1484 face1616 face173
face1562 face171 face1560 intervals ($Nojetcells)
volume mesh volume21 cooper source face1488 face1618 face180
face1568 face1566 face178 intervals ($Nojetcells)
103
volume mesh volume23 cooper source face1492 face1620 face187
face1574 face1572 face185 intervals ($Nojetcells)
volume mesh volume25 cooper source face1496 face1622 face194
face1578 face1580 face192 intervals ($Nojetcells)
volume mesh volume27 cooper source face1624 face1500 face201
face1586 face1584 face199 intervals ($Nojetcells)
volume mesh volume29 cooper source face1504 face1626 face208
face1592 face1590 face206 intervals ($Nojetcells)
volume mesh volume31 cooper source face1628 face1508 face215
face1596 face1598 face213 intervals ($Nojetcells)
volume mesh volume30 cooper source face1506 face1052 face1594
face1397 intervals ($Nojetcells)
volume mesh volume28 cooper source face1502 face1042 face1588
face1387 intervals ($Nojetcells)
volume mesh volume26 cooper source face1498 face1032 face1582
face1377 intervals ($Nojetcells)
volume mesh volume24 cooper source face1494 face1022 face1576
face1367 intervals ($Nojetcells)
volume mesh volume22 cooper source face1490 face1012 face1570
face1357 intervals ($Nojetcells)
volume mesh volume20 cooper source face1486 face1002 face1564
face1347 intervals ($Nojetcells)
volume mesh volume18 cooper source face1482 face992 face1558
face1337 intervals ($Nojetcells)
volume mesh volume16 cooper source face1478 face982 face1552
face1327 intervals ($Nojetcells)
volume mesh volume14 cooper source face1474 face972 face1546
face1317 intervals ($Nojetcells)
volume mesh volume12 cooper source face1470 face962 face1540
face1307 intervals ($Nojetcells)
volume mesh volume10 cooper source face1466 face952 face1534
face1297 intervals ($Nojetcells)
volume mesh volume8 cooper source face1462 face942 face1528
face1287 intervals ($Nojetcells)
volume mesh volume6 cooper source face1458 face932 face1522
face1277 intervals ($Nojetcells)
volume mesh volume4 cooper source face1454 face922 face1516
face1267 intervals ($Nojetcells)
volume mesh cylinder cooper source face1450 face912 face1510
face1257 intervals ($Nojetcells)
window modify invisible mesh
volume mesh volume34 cooper source face1649 face1650 face1651
face1652 face1653 face1654 face1655 face1664 face1639
face1638 face1637 face1636 face1635 face1634 face1633
face1648 face1610 face1608 face1606 face1604 face1602
face1600 face1472 face962 face1468 face952 face1464
face942 face1460 face932 face1456 face922 face1452
face912 face915 face918 face911 face925 face928
face920 face935 face938 face930 face945 face948
face940 face955 face958 face950 face965 face968
face960 face694 face689 face684 face679 face674
face669 face664 face659 face654 face649 face644
face640 face697 face696 face692 face687 face686
face682 face677 face676 face672 face667 face666
104
face662 face657 face656 face652 face647 face646
face642 face695 face698 face690 face685 face688
face680 face675 face678 face670 face665 face668
face660 face655 face658 face650 face645 face648
face641 face152 face1470 face145 face1466 face138
face1462 face131 face1458 face124 face1454 face117
face1450 face1657 face1658 face1659 face1660 face1661
face1662 face1663 face788 face1656 face1474 face159
face1647 face1646 face1645 face1644 face1643 face1642
face1641 face1640 face1478 face1628 face1626 face1624
face1622 face1620 face1618 face1616 face1614 face1612
face1508 face1052 face1504 face1042 face1500 face1032
face1496 face1022 face1492 face1012 face1488 face1002
face1484 face992 face1480 face982 face1476 face972
face975 face978 face970 face985 face988 face980
face995 face998 face990 face1005 face1008 face1000
face1015 face1018 face1010 face1025 face1028 face1020
face1035 face1038 face1030 face1045 face1048 face1040
face1050 face114 face1058 face774 face769 face764
face759 face754 face749 face744 face739 face734
face729 face724 face719 face714 face709 face704
face699 face777 face776 face772 face767 face766
face762 face757 face756 face752 face747 face746
face742 face737 face736 face732 face727 face726
face722 face717 face716 face712 face707 face706
face702 face779 face784 face787 face775 face778
face770 face765 face768 face760 face755 face758
face750 face745 face748 face740 face735 face738
face730 face725 face728 face720 face715 face718
face710 face705 face708 face700 face782 face786
face785 face6 face780 face1055 face215 face1506
face208 face1502 face201 face1498 face194 face1494
face187 face1490 face180 face1486 face173 face1482
face166 intervals ($Plzdnodes)
volume delete body onlymesh
volume mesh body cooper source face1689 face1690 face1691
face1692 face1693 face1681 face1682 face1683 face1684
face1685 face1686 face1687 face1688 face1696 face1671
face1670 face1669 face1668 face1667 face1666 face1665
face1677 face1676 face1675 face1674 face1673 face1672
face1680 face199 face1584 face1377 face192 face1578
face1367 face185 face1572 face1357 face178 face1566
face1347 face171 face1560 face1337 face164 face1554
face1327 face157 face1548 face1317 face150 face1542
face1307 face143 face1536 face1297 face136 face1530
face1287 face129 face1524 face1277 face122 face1518
face1267 face115 face1512 face1257 face1380 face1383
face1375 face1370 face1373 face1365 face1360 face1363
face1355 face1350 face1353 face1345 face1340 face1343
face1335 face1330 face1333 face1325 face1320 face1323
face1315 face1310 face1313 face1305 face1300 face1303
face1295 face1290 face1293 face1285 face1280 face1283
face1275 face1270 face1273 face1265 face1260 face1263
face1256 face209 face374 face370 face384 face379
face394 face389 face404 face399 face414 face409
105
face424 face419 face434 face429 face444 face439
face454 face449 face464 face459 face474 face469
face484 face479 face494 face489 face377 face376
face372 face387 face386 face382 face397 face396
face392 face407 face406 face402 face417 face416
face412 face427 face426 face422 face437 face436
face432 face447 face446 face442 face457 face456
face452 face467 face466 face462 face477 face476
face472 face487 face486 face482 face497 face496
face492 face375 face378 face371 face385 face388
face380 face395 face398 face390 face405 face408
face400 face415 face418 face410 face425 face428
face420 face435 face438 face430 face445 face448
face440 face455 face458 face450 face465 face468
face460 face475 face478 face470 face485 face488
face480 face495 face498 face490 face1 face1586
face1582 face1580 face1576 face1574 face1570 face1568
face1564 face1562 face1558 face1556 face1552 face1550
face1546 face1544 face1540 face1538 face1534 face1532
face1528 face1526 face1522 face1520 face1516 face1514
face1510 face1403 face518 face1588 face1592 face1594
face1694 face1695 face1598 face1679 face1678 face515
face516 face510 face500 face508 face505 face213
face1596 face1397 face206 face1590 face1387 face517
face514 face512 face502 face506 face507 face509
face499 face504 face1400 face1395 face1385 face1390
face1393 intervals ($Chzdnodes)
BOUNDARY CONDITIONS
physics create Symmetry btype SYMMETRY face face2 face103
face211 face204 face197 face190 face183 face176
face169 face162 face155 face148 face141 face134
face127 face120 face112
physics create Wall btype SYMMETRY face face110 face5 face1649
face1664 face918 face915 face911 face925 face1650
face928 face920 face935 face938 face930 face1652
face1651 face948 face945 face940 face1653 face1654
face958 face955 face950 face1655 face965 face968
face960 face978 face975 face970 face1656 face114
face985 face988 face980 face995 face998 face990
face1657 face1005 face1008 face1000 face1658 face1015
face1018 face1010 face1659 face1028 face1025 face1020
face1035 face1660 face1038 face1030 face1045 face1661
face1048 face1040 face1055 face1662 face1058 face1050
face1663 face4 face1395 face1679 face1403 face1400
face1680 face1385 face1678 face1393 face1390 face1375
face1677 face1383 face1380 face1676 face1365 face1373
face1370 face1675 face1355 face1363 face1360 face1674
face1345 face1353 face1350 face1673 face1335 face1343
face1340 face1672 face1325 face1333 face1330 face209
face1315 face1323 face1320 face1671 face1305 face1313
face1310 face1670 face1295 face1303 face1300 face1669
106
face1285 face1293 face1290 face1668 face1275 face1283
face1280 face1667 face1265 face1273 face1270 face1666
face1256 face1263 face1260 face1665 face214 face91
face207 face85 face200 face79 face193 face73 face186
face67 face179 face61 face172 face55 face165 face49
face158 face43 face151 face37 face144 face31 face137
face25 face130 face19 face123 face13 face116 face8
physics modify Wall btype WALL face face110 face5 face1649
face1664 face918 face915 face911 face925 face1650
face928 face920 face935 face938 face930 face1652
face1651 face948 face945 face940 face1653 face1654
face958 face955 face950 face1655 face965 face968
face960 face978 face975 face970 face1656 face114
face985 face988 face980 face995 face998 face990
face1657 face1005 face1008 face1000 face1658 face1015
face1018 face1010 face1659 face1028 face1025 face1020
face1035 face1660 face1038 face1030 face1045 face1661
face1048 face1040 face1055 face1662 face1058 face1050
face1663 face4 face1395 face1679 face1403 face1400
face1680 face1385 face1678 face1393 face1390 face1375
face1677 face1383 face1380 face1676 face1365 face1373
face1370 face1675 face1355 face1363 face1360 face1674
face1345 face1353 face1350 face1673 face1335 face1343
face1340 face1672 face1325 face1333 face1330 face209
face1315 face1323 face1320 face1671 face1305 face1313
face1310 face1670 face1295 face1303 face1300 face1669
face1285 face1293 face1290 face1668 face1275 face1283
face1280 face1667 face1265 face1273 face1270 face1666
face1256 face1263 face1260 face1665 face214 face91
face207 face85 face200 face79 face193 face73 face186
face67 face179 face61 face172 face55 face165 face49
face158 face43 face151 face37 face144 face31 face137
face25 face130 face19 face123 face13 face116 face8
physics create Heat Fluxes btype WALL face face104 face106
face370 face379 face389 face372 face382 face392
face371 face380 face390 face378 face388 face398
face376 face386 face396 face374 face384 face394
face377 face387 face397 face375 face385 face395
face1681 face1682 face1683 face1684 face1696 face402
face412 face422 face432 face442 face400 face410
face420 face430 face440 face408 face418 face428
face438 face448 face406 face416 face426 face436
face446 face404 face414 face424 face434 face444
face407 face417 face427 face437 face447 face405
face415 face425 face435 face445 face1688 face1685
face1686 face1687 face452 face462 face472 face482
face492 face1693 face450 face460 face470 face480
face490 face1692 face458 face468 face478 face488
face498 face1 face456 face466 face476 face486 face496
face454 face464 face474 face484 face494 face457
face467 face477 face487 face497 face1691 face455
face465 face475 face485 face495 face1689 face1690
face518 face502 face512 face1695 face500 face510
face1694 face508 face506 face516 face504 face514
face507 face517 face515 face505
physics create Mass flow inlet btype SYMMETRY face face640 face649
107
face659 face642 face652 face662 face672 face641
face650 face660 face670 face648 face658 face668
face678 face646 face656 face666 face676 face644
face654 face664 face674 face647 face657 face667
face677 face645 face655 face665 face675 face1633
face1634 face1635 face1636 face1637 face1648 face679
face689 face699 face682 face692 face702 face712
face680 face690 face700 face710 face688 face698
face708 face718 face6 face686 face696 face706 face716
face684 face694 face704 face714 face687 face697
face707 face717 face685 face695 face705 face715
face1640 face1638 face1639 face719 face729 face739
face749 face722 face732 face742 face752 face762
face720 face730 face740 face750 face760 face728
face738 face748 face758 face768 face726 face736
face746 face756 face766 face724 face734 face744
face754 face764 face727 face737 face747 face757
face767 face725 face735 face745 face755 face765
face1645 face1641 face1642 face1643 face1644 face788
face769 face779 face772 face782 face770 face780
face778 face776 face786 face774 face784 face777
face787 face775 face785 face1647 face1646
physics create Outflow btype OUTFLOW face face105
108
REFERENCES
Al-Aqal O M A 2003 ldquoHeat transfer distributions on the walls of a narrow channel
with jet impingement and cross flowrdquo PhD Thesis University of Pittsburgh
Bunker Ronald S 2007 Gas Turbine Heat Transfer Ten Remaining Hot Gas Path
Challengesrdquo Journal of Turbomachinery April Vol 129 pp 193-201
Downs James P Landis Kenneth K 2009 ldquoTurbine Cooling Systems Design- Past
Present and Futurerdquo Proceedings of ASME Turbo Expo 2009 June 8-12 2009
GT2009-59991
Florschuetz LW Berry R A Metzger D E 1980 ldquoPeriodic streamswise variations of
heat transfer coefficients for inline and staggered arrays of circular jets with cross
flow of spent airrdquo ASME J of Heat Transfer 102 p 132-137
Florschuetz L W Truman C R Metzger D E 1981 ldquoStreamwise Flow and Heat
Transfer Distributions for Jet Array Impingement with Cross flowrdquo Journal of
Heat Transfer Vol 103 pp 337
Florschuetz L W Isoda Y 1983 ldquoFlow Distributions and Discharge Coefficient for
Jet Array Impingement With Initial Cross flowrdquo Journal of Engineering for
Power Vol 105 pp 296
Incropera Frank P DeWitt D P 2002 Fundamentals of Heat and Mass Transfer John
Wiley amp Sons Inc New Jersey pp 491-493
Liu Quan Kapat J May 2006 ldquoStudy of Heat Transfer Characteristics of Impinging
Air Jet Using Pressure and Temperature Sensitive Luminescent Paintrdquo UCF
Dissertation
109
Martin H 1977 ldquoImpinging jet flow heat and mass transferrdquo Advances in heat transfer
Vol 13
Ricklick Mark Kapat J December 2009 ldquoCharacterization of an Inline Row
Impingement Channel for Turbine Blade Cooling Applicationsrdquo UCF
Dissertation
Zuckerman N Lior N 2005 ldquoImpingement Heat transfer Correlations and Numerical
Modelingrdquo Journal of Heat Transfer Vol 127 pp 544
iii
DEDICATED TO ENNIO MAMA Y PAPA
iv
ACKNOWLEDGEMENTS
I would like to acknowledge my mentor and advisor Dr Jay Kapat for all his
support and encouragement I would also like to thank my committee members Dr Ali
Gordon and Dr Weiwei Deng
I would also like to give a million thanks to Perry Johnson Lucky Tran Bryan
Bernier and William Clark for their help with the CFD portion of this study and for
letting me run on their computers Special thanks go to Mark Ricklick for helping me
throughout this project To everyone at CATER Mark Miller Michelle Valantino
Jimmy Kullberg Greg Natsui Michael Torrance Jeff Nguyen Nghia Tran Abhishek
Saha Kaylee Dorman Matt Golsen and everyone else that were once caterers a big thank
you for making these two years of work at the lab unforgettable
v
TABLE OF CONTENTS
ABSTRACT ii
ACKNOWLEDGEMENTS iv
LIST OF FIGURES vii
NOMENCLATURE ix
CHAPTER ONE INTRODUCTION 1
11 Gas Turbine as a Heat Engine 1
12 Cooling of Hot Components 2
CHAPTER TWO LITERATURE REVIEW 9
21 Impingement Literature Cornerstone 9
22 Relevant Impingement Channel Studies 11
23 Computational Studies on Impingement Channels 12
CHAPTER THREE EXPERIMENTAL SETUP AND TECHNIQUES 15
31 Temperature Measurements with TSP 15
32 Experimental Setup of Suction Channel 21
33 Data Processing and Reduction 24
34 Uncertainty Analysis 27
35 Lateral Conduction Analysis 28
CHAPTER FOUR HEAT TRANSFER RESULTS 32
vi
41 Heat Transfer Validation 32
42 Heat Transfer Results 33
43 XD Comparisons 40
44 3D Comparison of the Heat Transfer Profiles 45
45 Thermal Performance Calculations 48
CHAPTER FIVE COMPUTATIONAL FLUID DYNAMICS 52
51 Problem Setup 52
52 CFD Results 58
CHAPTER SIX CONCLUSIONS 63
APPENDICES 64
Appendix A 64
Appendix B 66
REFERENCES 108
vii
LIST OF FIGURES
Figure 1 Brayton Cycle Flow Path and T-s Diagram (Adapted from UPTB Website) 1
Figure 2 Thermal Loading Throughout a Turbine Blade (Daniels 1982) 3
Figure 3 Allowable Turbine Inlet Temperature vs Cooling Techniques over the Years
(Clifford 1985) 4
Figure 4 Turbine Inlet Temperature Increase with the help of TBC New Super Alloys
and Cooling Technologies (Kapat and Kiesow Lectures 2010) 4
Figure 5 Turbine Stator Cooled with Impingement Coupled with Film Cooling
(Florschuetz 1980) 5
Figure 6 Rotor Blade Cooling Configuration (Gladden 1988) 6
Figure 7 Cross-section of Turbine Airfoil with Cooling Channels (Han et al 1984) 6
Figure 8 Relative Temperatures for Hot Gas Metal Temperature and Coolant
Temperature (Cardwell 2005) 7
Figure 9 (a) The Development of the Wall Jet (b) Jet Diffusion to Surroundings (Liu
2006) 8
Figure 10 Simplified Jablonski Diagram (Adapted from ISSI Website) 17
Figure 11 Heater Strips Painted with TSP Too Closely 21
Figure 12 Flow Loop of Impingement Channel 22
Figure 13 Top View of Jet Plate 22
Figure 14 Front View of Impingement Channel 23
Figure 15 Target Wall Test Section with Heater Leads 23
Figure 16 Heat Transfer Coefficient Uncertainty Tree 27
viii
Figure 17 Temperature Profile of First Five Impingement Rows 29
Figure 18 Detailed View of First Heat Transfer Peak with a Polynomial Curve Fit 30
Figure 19 Control Volume Heat Transfer Analysis 30
Figure 20 Heat Loss through Convection and Lateral Conduction 31
Figure 21 Validation Spanwise Averaged Results 32
Figure 22 Target Wall Heat Transfer Coefficient Distributions 34
Figure 23 Span-averaged Target Wall Heat Transfer Distribution 35
Figure 24 Side Wall Heat Transfer Coefficient Distributions 36
Figure 25 Span-averaged Side wall Heat Transfer Distribution 37
Figure 26 XD=15 Target Wall Heat Transfer Profile 41
Figure 27 XD=15 Span-averaged Target Wall Heat Transfer Distribution 42
Figure 28 Target Wall Span-average Comparison of XD=5 and 15 at High Re 43
Figure 29 Side Wall Heat transfer Coefficient Profile 44
Figure 30 XD=15 Side Wall Span-averaged Heat Transfer Coefficients 45
Figure 31 3D Heat Transfer Profile for ZD=6 XD=5 46
Figure 32 3D Heat Transfer Profile for ZD=8 XD=5 47
Figure 33 3D Heat Transfer Profile for ZD=6 XD=15 48
Figure 34 Pressure Drop Ratio with Respect to Smooth Channel 49
Figure 35 Heat Transfer Enhancement 50
Figure 36 Thermal Performance at Constant Pressure Drop 50
Figure 37 Thermal Performance at Constant Pumping Power 51
Figure 38 Horizontal Plane of Impingement Channel Geometry 53
Figure 39 Target Side and Front End Wall y+ Values 54
ix
Figure 40 Finished Mesh with Boundary Conditions 55
Figure 41 Grid Independence Study 57
Figure 42 Residual Plots for the 26M Cell Run 57
Figure 43 Total Pressure Contours 58
Figure 44 Velocity Magnitude Contours 59
Figure 45 Turbulent Kinetic Energy Contours 60
Figure 46 Static Temperature Contours 60
Figure 47 Target and Side Wall Heat Transfer Coefficient Contours 61
Figure 48 Closer View of First few Rows of Impingement HTC Contours 61
Figure 49 Pathlines Generating from the First Row of Jets 62
NOMENCLATURE
Cross Sectional Area
Heater Surface Area (m2)
Specific Heat at Constant Pressure (kJkgK)
D Jet Diameter (m)
Channel Hydraulic Diameter (m)
Friction Factor
Heat Transfer Coefficient (HTC) (Wm2K)
Average Heat Transfer Coefficient (Wm2K)
Channel Length (m)
Mass Flow Rate (kgs)
Static Pressure (kPa)
x
Total Pressure (kPa)
Pr Prandtl Number
Heat Flux (Wm2)
Total Heat Input (W)
Heater Resistance (ohm)
Re Reynolds Number
SW Side Wall
Temperature (K)
TW Target Wall
Voltage Potential
Streamwise Location
y Spanwise Location
z Height from Target Wall
X Streamwise Distance (m)
Y Spanwise Distance (m)
Z Impingement Height (m)
Thermal Performance Parameter
Ratio of Specific Heats
Air Density (kgm3)
Subscripts
C Cold
H Hot
xi
Carnot Describing a Carnot cycle
Exit
Effective
Quantity Lost to the Environment
Reference Value
Wall Value
Base Line Value
1
CHAPTER ONE INTRODUCTION
11 Gas Turbine as a Heat Engine
Gas turbine is a form of heat engine where the hot reservoir is created by the
combustion of fuel and the cold reservoir is the open atmosphere It is well known that
the maximum efficiency of any heat engine is denoted as the Carnot efficiency
A more accurate cycle is used to describe the processes inside a gas turbine ndash the
Brayton Cycle The Brayton cycle as seen in Figure 1 is composed of four processes In
a gas turbine air is drawn in at state 1 it is compressed until it reaches state 2 The
compressed air is mixed with fuel and ignited as it passes through the combustor The hot
air then passes through the turbines where work is extracted The process from state 4 to
state 1 happens throughout the atmosphere therefore the Brayton cycle is an open loop
cycle as the same air is not continuously being fed through the motor
Figure 1 Brayton Cycle Flow Path and T-s Diagram (Adapted from UPTB Website)
The Brayton cycle has an isentropic efficiency similar to the carnot the Brayton
cycle efficiency is defined as
2
It can be seen that increasing the temperature at which air enters the first turbine
stage T3 increases the overall efficiency of the turbine Moreover increasing the
pressure ratio Pr also aids in the increase of the efficiency One of the hurdles of
increasing T3 is the fact that the post combustion gas is a few hundred degrees Celsius
above the melting point of the super alloys used to make the turbine stator vanes and
rotor blades For this reason it is important to cool the hot components of the gas turbine
in order to assure a reasonable life for the machine
12 Cooling of Hot Components
The transition duct that connects the combustor to the first stage turbine as well
as the first stage of the turbine are the parts that are subject to the harshest thermal
loadings and must therefore be cooled aggressively to maintain them in working
conditions for a long period of time Since the first stage guide vanes and rotor extrude
into the flow they are subject to the highest convection coefficients These heat transfer
coefficients can reach up to 4000 Wm2K (Downs 2009) Figure 2 shows the different
magnitudes of convection coefficient around the blade High heat transfer coefficients
occur where the air stagnates into the leading edge of the airfoil This high heat transfer
region is not only caused by the lack of a thermal boundary layer to protect the airfoil but
also because the effective heat transfer driving temperature is the recovery temperature
At the high Mach numbers that occur in turbines the ratio of total to static temperatures
is significant causing the leading edge to have the highest effective heat load Another
3
peak occurs on the suction side of the blade as the boundary layer created by the airfoil
switches from being a laminar boundary layer into a turbulent one Due to the nozzling
effect of the turbine rotor and stators the flow gathers speed toward the trailing edge of
the airfoil leading to higher convection coefficients on the pressure side of the airfoil
Figure 2 Thermal Loading Throughout a Turbine Blade (Daniels 1982)
Simple convection channels were implemented in the early nineteen sixties as
years passed the cooling techniques became more and more sophisticated allowing the
free stream temperature to increase to previously impossible levels Currently the use of
film cooling coupled with backside impingement leads the turbine cooling technology
The trend of allowable turbine inlet temperature is shown in Figure 3 from this figure it
can be seen that the allowable free stream temperature has increased around 600 degrees
in the past 50 years The addition of thermal barrier coatings also helps in the increase in
allowable combustion temperatures by creating an extra resistance that the heat needs to
move through as it moves from the combustion gasses into the coolant air It is impotatnt
to notice that as seen in Figure 4 the increase in turbine inlet temperatures is done with
the combined benefits of new alloys TBC and cooling technologies
4
Figure 3 Allowable Turbine Inlet Temperature vs Cooling Techniques over the Years (Clifford 1985)
Figure 4 Turbine Inlet Temperature Increase with the help of TBC New Super Alloys and Cooling
Technologies (Kapat and Kiesow Lectures 2010)
The cooling of inlet guide vanes can be done with the use of impingement inserts
inside the airfoils As air passes through the miniscule holes in the inserts a jet is formed
which then impinges on the wall of the airfoil producing one of the largest single phase
heat transfer coefficients This already impinged coolant air is then bled out as film
5
cooling as well as bled out through the trailing edge Figure 5 shows a stator vane with
the impingement insert in black the film cooling extraction as well as the trailing edge
bleed
Figure 5 Turbine Stator Cooled with Impingement Coupled with Film Cooling (Florschuetz 1980)
The cooling of turbine airfoils with the use of an impingement insert is only
possible in stationary components as the rotating ones are subject to centrifugal loadings
making it unfeasible to cool them with this setup Rotor blades are typically cooled with
serpentine passages that have heat transfer enhancing features such as ribs dimples and
other turbulators these serpentine passages are located in the mid chord of the blade On
the trailing edge a bank of pins are used to obtain high convective coefficients in the thin
region the coolant is the bled out to compensate for the boundary layer created around
the airfoil Rows of impingement holes cool the leading edge The spent air is then bled
out through showerhead cooling Figure 6 and Figure 7 show in detail the cooling
channels around two similar airfoils airfoils
6
Figure 6 Rotor Blade Cooling Configuration (Gladden 1988)
Figure 7 Cross-section of Turbine Airfoil with Cooling Channels (Han et al 1984)
7
The coolant air is bled out from the later stages of the compressor This air is
expensive as it has been compressed and not under gown the heat addition by
combustion It is imperative that the minimum amount of coolant is used in these cooling
configurations The cooling must also be as uniform as possible to reduce thermal
stresses within the blades leading to a higher component life Figure 8 shows freestream
metal and coolant temperatures of the flow blade and coolant air It can be seen that a
decrease of 25degrees in the surface temperature of the blade can provide an airfoil with
twice the working life Impingement cooling has great potential to provide high heat
transfer coefficients at a small flow rate Impingement of a jet onto a surface provides
high heat transfer coefficients due to a starting boundary layer as well as its high
turbulence When the jet is located around 3 diameters from the target surface the heat
transfer profile has two peaks one located at the stagnation region and the other located
between one and 3 diameters from the stagnation region As the jet is moved away from
the target wall the secondary peak diminishes leaving a profile with a maximum at the
stagnation region decreasing radialy
Figure 8 Relative Temperatures for Hot Gas Metal Temperature and Coolant Temperature (Cardwell 2005)
Cardwell N D 2005
8
Figure 9 shows a diagram of a jet impinging on a target surface The potential
core is the part of the jet that has not been affected by the surrounding stagnant fluid As
the jet moves towards the target wall its momentum diffuses into the surrounding fluid
decreasing the velocity at which it reaches the target wall and potentially decreasing the
corresponding heat transfer coefficient Studies have shown (Martin 1973 for example)
that the potential core may last anywhere between 7 to 10 diameters The successful
impingement of the potential core yields significantly higher heat transfer coefficients
than a fully diffused jet this comes however at a cost of higher pressure drop across the
jet plate as well as a highly non uniform heat transfer profile
Figure 9 (a) The Development of the Wall Jet (b) Jet Diffusion to Surroundings (Liu 2006)
9
CHAPTER TWO LITERATURE REVIEW
21 Impingement Literature Cornerstone
From the early days of simple convective cooling channels in turbine airfoils
studies have been done on modes of enhancing heat transfer coefficients while
maintaining a low pressure drop and minimum mass flow rate Heat transfer
characteristics of single round nozzle impingement were studied in the late 1960rsquos and
early 1970rsquos The collected works of many authors is combined into ldquoHeat and Mass
Transfer between Impinging Gas Jets and Solid Surfacesrdquo by Holger Martin 1977 The
paper collects works from multiple authors who studied single round nozzle impingement
effects on heat and mass transfer coefficients In this compilation non dimensional jet to
target spacing was studied they ranged from ZD=12-10 providing plots of Sherwood
number as a function of radius for four different jet to target spacings The local
Sherwood number was also given for a slot jet for HS ranging from 5 to 20 Studies on
impingement jet arrays were also gathered alongside an array of slot jets Correlations
were given for multiple setups present in the paper Circular jet arrays and slot arrays are
studied in detail with both analytical and experimental approaches The paper also
combines studies done on swirling jets turbulence enhancers on the target surface
impingement on concave surfaces and angle of attack variations Optimization studies
were also done to find the optimal spacing for round and slot jet arrays
Florschuetz studied the heat transfer characteristics of an array of jets impinging
on a flat surface This study was guided towards finding an optimal spacing for an array
for jets used to cool the midchord of turbine airfoils similar to that found in Figure 5 His
main contributions include a Nusselt number correlation as a function of jet to target
10
spacing jet Reynolds number and other flow and geometric parameters He found that an
increase in hole spacing and channel height resulted in a decrease of heat transfer He
also provided a one dimensional jet mass flux and channel mass flux correlations
His Nusselt number correlation takes the form of
Where A B and n are dependent by the two different types of arrays inline or staggered
Liu studied new techniques in temperature and pressure measurements of a single
slot jet with the use of temperature sensitive paint or TSP and pressure sensitive paint or
PSP In his work both measurement techniques are explained in detail Since TSP is the
only tool from that study currently used in this work it will be explained further in the
experimental setup section
11
22 Relevant Impingement Channel Studies
Al-Aqal 2003 studied three different types of impingement channels The use of
TLC was implemented in this work to obtain heat transfer distributions for the target
wall The three different configurations varied the number of holes in the streamwise and
spanwise directions The first channel had a single row of 6 streamwise jets the second
consisted of 2 rows of 12 streamwise holes summing up to a total of 24 holes The last
channel is a triple spanwise row with 18 streamwise jets This last geometry is the most
similar to the one present in the current study The third geometry will be used to
compare results There are differences however the total width of the channel is of 16
diameters as opposed to 8 in this study The streamwise jet spacing is also different Al-
Aqal used an XD of 65 compared to XD = 5 in this study The jet to target plate
spacings are similar on two occasions as he studied a ZD=4 6 and 8 while this work
uses a ZD = 6 8 and 10 Average jet Reynolds numbers also fall within the range of this
study as they range between 5000 and 33000 The author provides span averaged plots
for all cases and Reynolds numbers convenient when comparing the results
Ricklick 2009 studied a channel similar to the one found in this study His
channel was composed of a single row of 15 jets with a YcD = 4 XD = 5 and 15 and
ZD = 1 3 and 5 Two channels were tested one was pressure fed while the other was fed
by suction TSP was used to gather temperature data of all four wetted surfaces on the
pressure channel and two surfaces on the suction channel Since the maximum jet Mach
number was less than 03 the flow was assumed to be incompressible leading to the
conclusion that both channels contain identical flow patterns Thin foil heaters were used
to create the required heat flux for the channel Besides channel geometry Reynolds
12
numbers and heater geometry Ricklicksrsquo experimental setup is identical to the one
presented in this work The author also provided an ample comparison of his results to
literature He provided thermal performances of the entire channel at different Reynolds
numbers and channel heights
A small CFD study was also done A paved mesh was created on the target wall
with finer mesh near the impingement locations The resulting y+ at the wall was higher
than one yielding potentially faulty heat transfer values however this is acceptable since
the CFD was used as a tool to better understand the flow physics and help understand the
experimental heat transfer profiles
23 Computational Studies on Impingement Channels
El-Gabry did a numerical study of jet impingement with cross flow Two different
turbulence models were compared in their ability to predict surface Nusselt number The
Yang-Shih and standard k-ε models were used to compute the flow generated by jets
angled at 30 60 and 90 degrees with cross flow The computational results were
compared to previous experimental work by El-Gabry Comparisons to experimental
results at ZD = 1 and 2 90deg injection angle between Yang-Shih and standard k-ε The
error in the average Nu from the experimental results and both turbulence models were
calculated It was found that the Yang-Shih model behaved well at low Reynolds
numbers with the average Nusselt number being 5 off from the experimental value
while the standard k-ε was off my 94 As jet Reynolds number was increased the error
of the standard k-ε model dropped to as low as 39 while the error from the Yang-shih
model increased to -76 The span average plots show the experimental data Nusselt
number alongside the span averages of the results acquired by the Yang-Shih and
13
standard k-ε models High Nusselt numbers occur at the impingement location decreasing
thereafter after another impingement location is found The frequencies of these
variations are all the same for the experimental and the two numerical solutions The
amplitude of fluctuations between the impingement locations and the areas in between
are much larger for both of the numerical results however the Yang-Shih model over
predicts at the high Reynolds number for the ZD=2 case Since the amplitude of
fluctuations is greater for the CFD solutions it is important to note that even though the
error in average Nusselt number is not great the actual differences in the profile are much
greater upwards of 20 difference of heat transfer coefficients between the experimental
and numerical heat transfer peaks Other variations were studied (Injection angles for
example) but will not be discussed as their importance to the current study is minimal
Zuckerman compared a much wider set of turbulence models in their ability to
successfully predict Nusselt numbers caused by jet impingement The models tested were
k ndash ε k-ω Reynolds Stress Model algebraic stress models shear stress transport and
lastly the υ2f turbulence model DNS runs are extremely time consuming to run
therefore LES was run on its behalf to provide results for the unsteady turbulence
models The paper summarizes all the different models used their computational cost
impingement heat transfer coefficient and their ability to predict the second peak in heat
transfer As expected DNSLES provide the best prediction of both stagnation and
secondary peak heat transfer coefficient however this comes at a large computational
cost The k ndash ε and k-ω provide poor heat transfer results for the stagnation region where
they can have 30 error from the correct value The Realizable k ndash ε model provides
14
better heat transfer results while still maintaining a low computational cost The highest
accuracy to cost ratio was achieved by the υ2f model where it predicts the heat transfer
coefficient for the surface with a minimum of 2 error while not being as expensive as
the other unsteady models such as DNS and LES Ideally the CFD portion of this work
would be run with the υ2f model however since the code used to run the simulation
FLUENT does not have the υ2f model a realizable k ndash ε model will be used with
enhanced wall functions for both thermal and velocity gradients
15
CHAPTER THREE EXPERIMENTAL SETUP AND TECHNIQUES
31 Temperature Measurements with TSP
Temperature sensitive paint or TSP provides the capability of measuring
temperatures over the painted area This measurement technique supersedes the
advantages of other temperature measurement devices such as thermocouples because it
provides the user with data over a large area rather than point temperatures given by
thermocouples
Uni-Coat TSP is purchased from ISSI It is very robust to different working
conditions Calibration done on one batch of paint can be used for multiple cans as the
product is highly consistent The paint is calibrated in a dark booth a painted coupon is
placed on the hot side of a thermoelectric heat pump working on the Peltier effect
thermal paste is used to minimize contact resistance between the hot side and the TSP
coupon Calibrated thermocouples are placed in between the TSP and the thermoelectric
heat pump A reference temperature and picture are taken and the calibration commences
At least 5 or 6 data points should be taken to form the calibration Intensity ratios are
taken between the hot and cold pictures They are then plotted versus their corresponding
temperature
The paint consists of fluorescent molecules suspended in a binder These
molecules with a certain wavelength of light will be exited to a higher energy level The
molecules then can dissipate some of the energy by transferring it vibrationally to its
neighboring binder particles and dissipate the remainder of the energy by radiating it as a
photon as the molecule comes down to its original ground state Since the amount of
16
energy that the particle can transmit to others through vibration is directly proportional on
temperature and the total initial energy is fixed by measuring the ratio of the intensity at
a known temperature (reference picture) and intensity of the unknown temperature
feeding it through the correlation the unknown temperature can be found to an
uncertainty of 1 K Figure 10 shows a simplified Jablonski diagram adapted from the
suppliers website The blue arrows signify the blue light used to excite the luminescent
molecule Tris(22rsquo-bipyridyl) Ruthenium(II) Chloride Hexahydrate with a shellac binder
in our case The shellac binder is impermeable to oxygen opposite of that found in PSP
due to PSP relying on the presence of oxygen for it to function Once the particle is
excited it can give off the energy in two different ways one is by emitting it back out as
another photon of the same energy and therefore wavelength The second mode of the
particle to lose its energy is through vibrational relaxation This second process is directly
dependent on the temperature ie the higher the temperature the higher the probability
for it to lose energy to its surroundings Once it loses some energy to the surrounding
particles it releases the remainder of the energy as a photon of less energy of that which
excited it originally hence why a long pass filter is installed in the CCD camera For a
more descriptive explanation of the way TSP works refer to Liu 2006
17
Figure 10 Simplified Jablonski Diagram (Adapted from ISSI Website)
Throughout the past two years there have been numerous projects at CATER that
have used TSP Painting surfaces with TSP should be done carefully by someone who
has experience with spray painting since every single can costs $500 A single can should
be able to paint an area the size of an acrylic plate that is 36rdquo wide and 24rdquotallThe
sidewalls and the target wall of the impingement channel were painted with the use of
less than one can Painting on different surfaces is difficult for example when painting
Rohacell the paint canister can be held very close to the surface while spraying due to
the surface being somewhat porous and rough however when painting straight onto
metal heater strips the can should be placed as far back as possible for the first run
Ideally for the first pass through only a slight mist should be applied If the can is being
held too close to the surface the paint will run Figure 11 shows a set of heater strips that
has been painted too closely leading the paint to drip down Ideally the paint would be
applied to the surface in as many coats as possible Of course this would be time
18
demanding and impractical therefore with the knowledge that I have gained through the
multiple TSP paintings on different surfaces I have compiled a list of TSP dos and
donrsquots
Dos
Clean the surface to be painted with acetone or break parts cleaner Break
parts cleaner is preferable over acetone as it does not leave an oily residual
after cleaning
Paint the first coat as thin as possible Most of the surface should not be
covered There should be an even mist of miniscule TSP circles This will
give the later coats something to attach to
When positioning the test section to paint make sure to wipe it one last
time as small dust particles may have attached to the surface
Stop if you see small bumps in the paint This is caused by dust particles
collecting all the paint around it while it is still wet due to surface tension
Clean the surface and repaint This should be noticeable in the first few
coats If you see this pattern happening do not continue thinking it will be
covered by future coats What will happen is the problem will get worse
and worse ultimately the surface will have to be cleaned again and
repainted
When painting test sections try to paint the smallest section as possible
This will not only save paint but will make it very simple for the post
processing code to crop out the unpainted areas
19
Let the finished painted surface to sit at least for 90 minutes after the last
coat before baking There have been problems when baking steel and
acrylic test sections with the paint cracking while baking right after the
last coat Normally the finished surface is left to dry overnight and baked
first thing in the morning
For test sections that are too large to be baked in the oven the heat gun
may be used Carefully place a thermocouple in a central location with
blue painters tape The heating should be uniform and should not take
more than 20 minutes of continuous blowing When the thermocouple
reaches 80-90 C the plate can be assumed to be baked To introduce a
factor of safety in the baking it does not hurt to bake it longer than it
normally takes
Once the test section is mounted and ready to run cover it with cloth that
does not let any light through This will protect the paint for further uses
This is especially important on test sections that can be used multiple
times like the ones found in this study
When the test is running turn off the LED lights This light is the most
damaging to the TSP as it degrades the quality of the fluorescent
molecules
If there is a particular head of the TSP can that you prefer over others you
can remove it once the can is empty It is difficult to get used to a single
kind of nozzle being able to transfer it from can to can is a must if
painting consistency is to be kept
20
Donrsquots
Do not clean a test section that has already been used with too much
acetone The acetone is volatile evaporating quickly cooling the test
section rapidly If this test section has had heaters attached to it and run
previously the acrylic will crack due to uneven stresses inside of it
If paint is dripping stop painting immediately Clean the surface and start
over Hold the can far from the surface in order for it not to drip
Do not use TSP to teach new apprentices undergrads or graduate students
how to paint Regular spray paint is two orders of magnitude lower in cost
while the painting process is exactly the same
Do not paint with the doors closed The paint contains carcinogens that
can harm the lungs Always use a respirator and keep the room well
ventilated In-situ painting and baking has not been tried however it may
be a real option if the test section is difficult to disassemble and easily
accessible to painting and baking
If there is a can of paint that contains too little paint for the test section
that needs to be painted try to find a new can The mixing of two different
cans of TSP can be dangerous at times however it has been noticed over
the years that ISSI provides a very robust and dependable product that
does not vary significantly from batch to batch
21
Figure 11 Heater Strips Painted with TSP Too Closely
32 Experimental Setup of Suction Channel
The impingement channel is fed under suction As seen in Figure 12 air enters
through the plenum it crosses the jet plate as it gains speed to form the jets
which then impinge on the target wall The flow then passes through a venturi
flow meter and finally through the blower into the atmosphere A bypass valve is
used to control the flow rate of the impingement channel
22
Figure 12 Flow Loop of Impingement Channel
The impingement channel consists of 15 streamwise rows of 3 spanwise jets each The
total width of the channel YcD is of 8 diameters while the streamwise spacing between
the rows is XD=5 the spanwise distance between the holes is of YD=2 Figure 13shows
the top view of the jet plate The plate is counter bored to ensure that a nearly flat
velocity profile of the jet is achieved Figure 14 shows the front view of the channel Z is
denoted as the distance between the jet and target plates Side walls are interchangeable
to change the height of the channel to 6 8 and 10 diameters Two thirds of the
streamwise rows can be covered to change the XD from 5 to 15
Figure 13 Top View of Jet Plate
23
Figure 14 Front View of Impingement Channel
The target and sidewalls had heaters made specifically for them in a serpentine
style This was necessary to increase the resistance as the VARIACs used to power them
only had a maximum current output of 20 amps The heater strips are two diameters
wide at each end copper tape with conductive adhesive was used to connect the leads to
the power supply The heater consists of 50 micron thick steel sheet sandwiched between
two pieces of Kapton tape The heater is attached to the painted surface with the use of
double sided Kapton tape The target test section can be seen in Figure 15 also seen in
this figure are the two Teflon gaskets lined on the sides of the target plate With the target
wall bolted onto the sidewall the gasket is compressed generating a strong seal
Figure 15 Target Wall Test Section with Heater Leads
24
For this study the test matrix shown in Table 1 will be run Target and side wall
data will be taken at three different impingement heights at two different Reynolds
numbers of 7500 and 15000 denoted by A and B respectively A streamwise jet spacing
study is also done by testing the target and side wall heat transfer at an XD=15 for the
low impingement height channel
Table 1 Test Matrix
XD ZD Wall Re
5
10 TW
7500
15000
SW 7500
15000
8 TW
7500
15000
SW 7500
15000
6 TW
7500
15000
SW 7500
15000
15 6 TW
7500
15000
SW 7500
15000
33 Data Processing and Reduction
As described previously when taking temperature measurements with the use of TSP
reference temperatures are noted and a reference picture is taken The experiment is the
run once the experiment reaches steady state a new set of 4 pictures is taken Given the
calibration curve temperatures are backed out
25
Given the amount of heat generated inside the heater
Dividing by the heated area to get heat flux
Heat loss tests were run to consider how much of the heat flux generated by the heaters
goes through the backside instead of into the flow It was found that 25 of the heat flux
leaks out to the atmosphere through the acrylic In order to account for this heat leakage
it must be subtracted from the calculated value to become
Where Ah is the effective heated area given by
Where Aunheated is an estimate of how much unheated area is between the heater strips (~
3 of the total area)
To obtain heat transfer coefficient
Where Tref is the reference temperature Typically set in literature to be the jet
temperature
To obtain the average Reynolds number for the jets the total mass flow rate is used
Where Dj is the jet diameter and μ is dynamic viscosity (1983kgm s at 300K)
26
Pressure measurements were taken at the sidewall after the last jet entered the channel
These pressure measurements were used to determine the thermal performance of the
tallest two channels (ZD = 8 and 10)
The thermal performance at constant pumping power is found by using the equation
Where h is the average heat transfer coefficient for the target wall of them impingement
channel and ho is the heat transfer coefficient obtained by passing the same amount of
flow through a smooth duct ie the Dittus-Boelter correlation The friction factor f is
found with the use of
Where Ppl is the plenum static pressure assumed to be atmospheric and Plast jet is
the pressure read after the last jet V is the volumetric flow rate divided by the cross-
sectional area of the duct after the last impingement row The hydraulic diameter of the
channel is set to be
The baseline friction factor was calculated with the use of the Moody chart the hydraulic
diameter and the total mass flow rate though the channel Thermal performance at
constant pressure drop was also calculated with
27
34 Uncertainty Analysis
A simple uncertainty analysis was done to estimate the error in calculation of the
heat transfer coefficient from the given outputs of the test data From the bare basic
measurements for voltage area current temperature of thermocouples and temperature
profiles of paint a simple uncertainty analysis can be done to estimate the error for the
calculated heat transfer coefficient Figure 16 shows the different sources of error in the
calculation of heat transfer coefficient The effective uncertainty was calculated by taking
the root of the sum of the squares of all the individual percentage errors The
experimental uncertainty for heat transfer coefficient was of 703 This error may be
reduced by acquiring higher temperatures of the TSP reading current with a more
accurate ammeter or reading reference temperatures with the use of a thermopile instead
of a single thermocouple
Figure 16 Heat Transfer Coefficient Uncertainty Tree
28
35 Lateral Conduction Analysis
To take into account the lateral conduction occurring inside the heater foil while
the test is running two simple 1D conduction and convection equations were used to
quantify the amount of heat moving through the heater laterally and the amount of heat
convecting into the air The lateral conduction is expected to be at a maximum at the
places where there are large spatial variations of surface temperature which is why the
ZD = 6 XD = 5 case at high Re is chosen to be studied Figure 17 shows the
temperature distribution of the aforementioned case Four cold spots can be seen by their
distinct blue and yellow color located at the stagnation regions The maximum
temperature gradient occurs between the third jet impingement and the middle region
between jets The temperature difference was seen to be of 13degC The distance in between
these two temperatures is of 25D=01875m The corresponding heat flux between these
two points was calculated to be 13000Wm2 with ksteel~20Wm K A region of 1cm by
1cm was then created and the amount of heat calculated through conduction and
convection were compared To acquire the amount of heat removed through conduction
a heat flux of 13000Wm2 was imposed through an area of 01m by 00005m this
equaled to 00277 W The amount of heat moved through convection was calculated by
multiplying the heat flux used during the test by the area of the square 0001m2 the
resulting heat moving through the heater onto the air is 6 W Since the heat moving
through to the air is two orders of magnitudes larger than the heat moving laterally the
effective lateral conduction can be neglected
29
Figure 17 Temperature Profile of First Five Impingement Rows
A second order approach was also taken to quantify the amount of lateral
conduction in the heater The temperature gradient was taken from high peaks in heat
transfer caused by the second row of impingement of the same ZD=6 XD=5 channel at
high Re Figure 18 shows the high heat transfer coefficients created by the second row of
jets A quadratic curve fit was obtained by for this small region so that a continuous
equation of heat transfer coefficients as a function of streamwise distance was quantified
30
Figure 18 Detailed View of First Heat Transfer Peak with a Polynomial Curve Fit
The net heat gained by a differential volume from lateral conduction is the
difference in the temperature gradient at the entrance and the exit multiplied by the
thermal conductivity and cross sectional area Using this method shown in Figure 19 the
net change in convective heat transfer due to lateral conduction can be studied
Figure 19 Control Volume Heat Transfer Analysis
By taking the difference between the out flowing heat trough the right side and
the inflowing heat from the left side a net gain or loss can be found Figure 20 shows the
y = -470630x2 + 31244x - 14842Rsup2 = 09934
300
310
320
330
340
350
360
370
380
0 001 002 003 004 005
HTC
(W
m2K
)
x (m)
Heat Transfer Peak
Poly (Heat Transfer Peak)
31
difference in magnitude between the out flowing heat through convection seen in red and
the net inflow of heat from lateral conduction in blue From these calculations it was also
found that the amount of heat moving through lateral conduction is tow orders of
magnitude smaller than the amount of heat moving out through convection leading to the
belief that even at high temperature gradients lateral conduction does not play an
important role in the ongoing heat transfer processes in the impingement channel A more
detailed calculation of this work can be seen in appendix A
Figure 20 Heat Loss through Convection and Lateral Conduction
002 003 004 0051 10
5
1 104
1 103
001
qconv x( )
qnet x( )
x x
32
CHAPTER FOUR HEAT TRANSFER RESULTS
41 Heat Transfer Validation
In order to obtain confidence in our experimental setup an experiment was made
to test something that has already been published in literature A smooth channel was the
obvious choice as it was easy to setup by taking off the end cap and blocking all the holes
with smooth blue painters tape on the flow side and metal tape on the plenum side to
ensure no leaks into the channel from the jet plate The smooth channel has been studied
widely and multiple correlations exist one of these equations is the Dittus-Boelter
correlation (Incropera 2007) The test was run using the ZD=6 side wall so that the
hydraulic diameter was a minimum Figure 21 shows the span averaged results versus
non dimensional distance into the channel
Figure 21 Validation Spanwise Averaged Results
0
10
20
30
40
50
60
0 1 2 3 4 5 6 7 8 9
HTC
(W
m2K
)
XDc
Span Avg
Dittus Boelter
33
The plot shows decreasing heat transfer coefficient with increasing XDc due to
the developing thermal boundary layer The span average does not reach the Dittus-
Boelter due to it not being fully developed in the limited space it is given Typical flows
can take up to 60 diameters to achieve a fully developed profile with the current setup
the maximum length of the channel was of 9 diameters The profile however seems to
have an asymptote at the Dittus-Boelter correlation value leading to the belief that if the
channel was longer that value given by the correlation would be reached One important
factor to take into account in determining whether the experimental setup is validated is
the fact that the Dittus-Boelter correlation has an uncertainty near 30 Since the span
average at high XDc is well within 30 from the calculated value it is safe to assume
that the current experimental setup is validated
42 Heat Transfer Results
Heat transfer results are compared based on variations in channel height and
average jet Reynolds number As discussed earlier there are numerous other parameters
also affecting the heat transfer in these channels As these parameters are changed flow
structures within the channel are expected to be altered as well as discussed in the
literature Two of the major contributors to heat transfer in these channels are the
successful jet impingement and the resulting cross flow The same domain is captured in
both the local and averaged results
Figure 22 through Figure 25 highlights the heat transfer distribution for the cases
with a jet to jet spacing of 5 diameters in the streamwise direction and of 2 in the
spanwise direction It is evident that the smallest channel height (ZD=6) performs the
best at all Reynolds numbers on all surfaces It is also interesting to note the similarity
34
in the target wall profiles between case 528A and B where the curves are very similar
other than the obvious offset due to the change of the Reynolds number At this large
spacing we also see the degradation of the jets a few diameters downstream of each
impingement location The downstream shifts of the peaks are evident after the second
and third row of jets Also evident in these plots is the deflection of the impinging jet and
the wall jets from the cross flow The cross flow is forced to flow around the jet
deflecting the spread of the wall jet in the downstream direction Impingement locations
are also very evident at low XD however as XD and therefore the cross flow increase
the magnitude of the peaks start decreasing and eventually level out to pure internal flow
Figure 22 Target Wall Heat Transfer Coefficient Distributions
35
Figure 23 Span-averaged Target Wall Heat Transfer Distribution
36
Figure 24 Side Wall Heat Transfer Coefficient Distributions
37
Figure 25 Span-averaged Side wall Heat Transfer Distribution
Figure 23 and Figure 25 show similar details with impingement peaks clearly
diminishing and shifting in the downstream direction The cross flow clearly has some
negative influence on these geometries when compared to the more traditional
impingement highest on the order of 1 to 5 jet diameters The heat transfer profiles of the
target wall for all heights seen in Figure 22 and Figure 24 show the rapid decay in heat
transfer after the third jet This can be explained by understanding that the first jet does
not have any cross flow to deflect it the second jet only has the first jet worth of
momentum deflecting it downstream however since the channel is so tall the
momentum of the cross flow after the first and second jet are not enough to greatly
disturb the incoming jets After the third jet however the cross flow builds up enough
momentum to greatly affect the integrity of the jets downstream causing the span-
0
20
40
60
80
100
120
140
160
2 12 22 32 42 52 62 72
HTC
(W
m2K
)
XD
5210B_SW 528A_SW Jet Location
526A_TW 526B_TW
38
averaged heat transfer to rapidly drop The point at which the crossflow starts taking a
considerable effect occurs around XD =35 The target wall profile of the ZD=10
channel shows the outside jets on the second row of jet deflecting downstream It can be
conjectured that the bending of the outside jets downstream is caused by the wall jet
created by the first row of jets separating from the side wall and deflecting the outside
jets of the following rows of jets The heat transfer profile for the ZD case excludes the
first jet due to shadows being present when the data was taken
Also evident from this spanwise averaged data is the increase in heat transfer
with increases in Reynolds numbers and decreases in impingement height Results tend
to be the closest from case to case at the first impingement jet This is a reasonable
result as the effects of cross flow have little to no effect at the first few impingement
locations The impact of the jet would then be the driving force at these locations and
would be similar between cases except if the potential core is not reaching the target
surface The potential core of a jet tends to last between 6 and 10 diameters from its
origin It can be seen that the difference in heat transfer coefficient in the first two jets for
the ZD=8 and ZD=10 channel is much different than the corresponding difference
between the ZD=6 and ZD=8 heights This decreased difference between the heights of
the peaks may be attributed to the potential core reaching the target wall at the heights of
6 and 8 diameters leading to similar profiles and may not be reaching the surface at the
height of 10 diameters The heat transfer values of the peaks diminish in the downstream
direction The range of fluctuation also drops that is the profile becomes more uniform
at large XD This drop in fluctuation is more visible at the tallest channel height
(ZD=10) and less pronounced at the smallest channel This is due to the jet in the small
39
channel having to travel a shorter distance to impinge on the target plate leaving the
crossflow less time for it to deflect the jet as opposed to the tall channel where the jet has
to travel almost twice the distance as the ZD=6 channel for it to impinge on the target
wall This effect cannot be solely explained by the built up cross flow in the channel
Mixing loses also take part in the degradation of the stagnation size of the downstream
jets The mixing losses have much greater effect on the taller channels due to the same
reason that the cross flow has a higher impact on them too the jets have to travel a large
distance before hitting the target plate leading the stagnant or moving surrounding air to
be a sink of its downward momentum for a longer time and distance than the respective
smaller channels The heat transfer coefficient of the side wall was also analyzed
Similar effects are expected on the side wall due to the expected impact of the wall jet
As expected the strength of the cross flow is not enough to prevent wall jets from
successfully impacting the side wall at small XD jet locations however the crossflow
takes dominance at around XD=25 Also evident in these plots is the concentration of the
wall jet impact to the bottom of the channel on the order of 1-2 diameters in height It is
interesting to note that for the 5210B case in Figure 24 as the first jet diffuses outward
it impacts the sidewall at a height of ZD=6 The height at which the diffused jet affects
the sidewall heat transfer coefficient decreases as the crossflow increases The stagnation
regions are also deflected in the downstream direction similar to the target surface
results These effects are most evident in the 5210B Similar characteristics can be
explained from the spanwise-averaged plots shown in Figure 25 These results again
clearly show the effects of increasing the impingement height and increases in Reynolds
number As the height is increased the effect of the wall jet is significantly reduced
40
partially due to the increased surface area much of which is not affected by the wall jet
The diminishing effect of the cross flow accumulation is also evident in these plots as the
heat transfer peaks decrease in the downstream direction
43 XD Comparisons
The streamwise jet spacing was changed from XD=5 to 15 by covering two out
of three rows of jets This was done by covering the impingement holes inside the
channel with smooth blue painters tape and sealing the plenum side of the jet plate with
metal tape to ensure no leakage The profile is expected to be less uniform than the case
where XD=5 due to the large spreading of the high heat transfer peaks Due to the large
separation between the rows of jets there is a lower amount of downward momentum
than the equivalent XD=5 geometry for this reason it is expected to see a lower heat
transfer peak due to the jets momentum diffusing out faster to the stagnant air decreasing
the effective impingement velocity Figure 26 shows the target wall heat transfer
distribution Similar to the XD=5 profile it can be seen that the heat transfer due to the
jet impingement drastically reduces after the third jet This phenomenon leads us to
believe that at both Reynolds numbers the cross flow generated by the first three jets is
powerful enough to effectively deflect the fourth jet downstream diminishing its heat
transfer performance The similarity seen in Figure 26 between high and low Reynolds
number implies that the downstream deflection of the jets is not dependent on the jet
Reynolds numbers
41
Figure 26 XD=15 Target Wall Heat Transfer Profile
42
Figure 27 XD=15 Span-averaged Target Wall Heat Transfer Distribution
On the span averaged plots seen in Figure 27 the downstream deflection of the
jets is evident however as described previously the shifts in the peaks of heat transfer
occur at the same xD for both Reynolds numbers The amplitude of fluctuation of heat
transfer coefficients for the high Reynolds number case is larger than that of the low
Reynolds number Both profiles seem to start to level off at the end of the impingement
channel with the lowest span average being located just before the fourth jet at both
Reynolds numbers
A comparison of target wall heat transfer coefficients between XD =15 and 5 is
shown in Figure 28 At first glance it is clearly visible that the XD=15 average heat
transfer coefficient is smaller than its XD=5 counterpart This is also noticed by Ricklick
where he showed average HTC profiles for larger XD to be smaller than those at lower
XD (Ricklick 2009) This may occur due to there not being as high downward
0
50
100
150
200
250
300
350
0 20 40 60 80
HTC
(W
m2
K)
XD
Low Re
High Re
Impingement Location
43
momentum for the XD=15 case as compared to the XD=5 due to the lack of close jets
The stagnant air around the spaced out jets is taking away more of its momentum
decreasing the effective impingement Reynolds number Also important to notice is the
fact that since the XD=5 case has three times the flow impinged into it the cross flow
velocity and therefore Reynolds number will be three times as large increasing the heat
transfer coefficient
Figure 28 Target Wall Span-average Comparison of XD=5 and 15 at High Re
The side walls also show similar patterns to their XD=15 counterparts Strong
wall jet impingement can be seen on the side wall at low xD and zD Figure 29 shows
areas where the wall jet generated by the target wall impinges on the sidewall Similar to
the profile seen in Figure 24 the high heat transfer region reaches upward in the z
direction up to a height of 4-5 diameters for the first jet This high heat transfer stagnation
region decreases as xD increases to the point where the wall jet created by the last jet is
negligible when coupled with pure channel flow
0
50
100
150
200
250
300
350
400
0 10 20 30 40 50 60 70 80
HTC
(W
m2K
)
XD
XD = 5 XD = 15 Jet Location
- Blocked for XD =15
44
Figure 29 Side Wall Heat transfer Coefficient Profile
The span averaged plot seen in Figure 30 shows a nearly flat profile with peaks
located at the stagnation regions of the wall jets Thw downstream deflection for the
XD=15 case is much more pronounced than the one for the XD=5 case This is due to
the jet not being constrained by the wall jets generated by the previous and latter
impingement locations In the XD=15 case the wall jet is free to move downstream
more so than the XD=5 due to it not being disturbed by anything other than the cross
flow
45
Figure 30 XD=15 Side Wall Span-averaged Heat Transfer Coefficients
44 3D Comparison of the Heat Transfer Profiles
In order to further understand the targetsidewall interactions both heat transfer profiles
were positioned in an isometric view representative of the channel One important thing
to note is that both target and side wall profiles are not on the same scale This form of
data display is only qualitative way to describe the heat transfer profiles Figure 31 shows
the 3D profile of the XD=5 ZD=6 case The both stagnation regions of the jet onto the
target wall and the wall jet into the sidewall can be seen to occur at the same location for
the first three streamwise rows After the fourth and fifth row the wall jet diminishes in
magnitude Also visible in this view is the increasing heat transfer at low zD towards the
end of the channel of the side wall The constant input of mass and downward momentum
into the channel causes the cross flow generated by the previous jets to be squeezed into
the lower third of the channel increasing the velocity and the heat transfer of the target
wall
0
20
40
60
80
100
120
0 20 40 60 80
HTC
(W
m2K
)
XD
Low Re High Re Jet Locations
46
Figure 31 3D Heat Transfer Profile for ZD=6 XD=5
Similar patterns are seen in the taller ZD=8 channel seen in Figure 32 The wall jet
generate by the third streamwise row of jets is been deflected downward more than its
ZD=6 counterpart This can be attributed to the fact that the jet located at the ZD=8
channel has lost much of its momentum and is more easily bent downstream by the cross
flow generated by the first two jets The ZD=8 sidewall shows similar increasing heat
transfer at high xD however the increase is not as drastic as the one found in the ZD=6
channel This is caused due to the extra two diameters the jets have to cover to impinge
on the surface since the ZD=8 channel is one third larger than the ZD=6 one the flow
has to have more area to flow through The last few jets only deflect the cross flow
downward about 4 diameters this leaves two diameters for the flow to pass through on
the ZD=6 channel causing the velocity to increase rapidly and therefore increasing the
heat transfer coefficient at the low zD Since the ZD=8 channel has four remaining
47
diameters for the flow to move through it does not deflect it as much as the ZD=6
channel does only increasing the cross flow velocity and resulting heat transfer
coefficient slightly over the area at low zD and high xD
Figure 32 3D Heat Transfer Profile for ZD=8 XD=5
The 3D heat transfer profile for ZD=6 and xD=15 channel seen in Figure 33 shows
similar details to those seen in the XD=5 channels The stagnation regions of the jet and
wall jet occur at the same x location for the first three rows of jets the wall jet generated
by the fourth row of jets is deflected downstream only generating as small region of high
convective coefficients at the side wall The region located at the top right corner of the
side wall is colored red signifying high heat transfer however this area is generated by
the heaters providing non uniform heat flux at this location This region of high heat
transfer coefficients also occur at xD=0-4 of the target wall where the heater coil bends
48
Figure 33 3D Heat Transfer Profile for ZD=6 XD=15
45 Thermal Performance Calculations
Thermal performance calculations were done on the two tallest channels (ZD=8 and 10)
The pumping power was calculated for both channels at two Reynolds numbers Figure
34 shows the ratio of pressures required to pull the same amount of flow through as
smooth duct as opposed to through the jet plate The ZD=10 channel at high Reynolds
number requires the largest pressure as seen in the Figure however in order to pull the
same amount of flow rate through it requires a smaller pressure difference due to the
large cross section
49
Figure 34 Pressure Drop Ratio with Respect to Smooth Channel
Next the heat transfer enhancement was calculated A total area averaged heat
transfer coefficient was taken for the target wall and compared to the smooth channel
Dittus-Boelter value while using the same total mass flow rate Figure 35 shows an
average heat transfer enhancement of four times that of a smooth channel Similar trends
were noticed in the literature (Ricklick 2009) of decreasing heat transfer enhancement
with an increase of jet Reynolds number Ricklick also showed an increase in heat
transfer enhancement with an increase of jet to target spacing similar to the one seen in
Figure 35
0
10
20
30
40
50
60
528A_TW 528B_TW 5210A_TW 5210B_TW
PP
o
50
Figure 35 Heat Transfer Enhancement
Thermal performances at constant pressure drop were then calculated by dividing
the heat transfer enhancement by the pressure increase As seen in Figure 36 all the
values fall well below 1 making the impingement channel an unfeasible mode of heat
transfer enhancement when a constant pressure is supplied
Figure 36 Thermal Performance at Constant Pressure Drop
0
05
1
15
2
25
3
35
4
45
528A_TW 528B_TW 5210A_TW 5210B_TW
hh
o
0
002
004
006
008
01
012
014
528A_TW 528B_TW 5210A_TW 5210B_TW
(hh
o)
(PP
o)
51
The thermal performance at constant pumping drop was calculated in the same
way that the constant pressure drop was calculated the only difference being the pressure
ratio term was raised to the one third power As seen in Figure 37 the thermal
performances at constant pumping power are all higher than unity this signifies that if a
surface needs to be cooled with the supply of a constant pumping power the
impingement channel is a feasible option Similar to the figure literature (Ricklick 2009)
showed a decrease of thermal performance with an increase of channel height and
Reynolds number
Figure 37 Thermal Performance at Constant Pumping Power
0
02
04
06
08
1
12
14
528A_TW 528B_TW 5210A_TW 5210B_TW
(hh
o)
(PP
o)1
3
52
CHAPTER FIVE COMPUTATIONAL FLUID DYNAMICS
51 Problem Setup
In order to further enhance the understanding of the heat transfer profiles showed
previously a computational study was performed Even though CFD does not yield
accurate quantitative results it produces good qualitative data that can be used to explain
the flow physics in the channel and therefore increase the understanding of the patterns
seen previously The channel was meshed with the use of GAMBIT Due to the
symmetry the channel was split in half in the streamwise direction All horizontal
surfaces (parallel to the target wall) were divided into 6 different regions that are later on
going to be meshed individually The six regions are seen in Figure 38 section 1 is
located at the center of every jet also referred to as ldquojet centerrdquo This region was created
to reduce the squewness of the elements near the center of the jet by allowing the mesh to
be completely linear with a squewness of zero Section two complements section 1 to
complete the impingement hole The half impingement hole located at the symmetry wall
contains the same exact region 2 however it only has one half of the jet center Section 3
was made in order to bring the polar geometry of the holes to match the cartesian aspect
of the remainder of the channel With the addition of section 3 to the channel the only
remaining sections are square or rectangular regions Region 4 lies in between
streamwise rows of jets Section 5 is located at the entrance and the exit of the channel
These sections are not square in contrast with section 4 The last remaining section is
located near the side wall of the channel extending from the beginning to the exit of the
channel
53
Figure 38 Horizontal Plane of Impingement Channel Geometry
All the faces of sections 1 and 2 are linked throughout the channel and the
plenum however in order to have greater control of the mesh in the plenum and the
channel the remaining sections 3 4 5 and 6 are not linked to every single similar face
instead they are only linked to similar faces in either the plenum or the channel
Boundary layer spacing number of rows and growth factor are placed around the
channel In order to maintain a y+ of less than unity the first cell spacing of the boundary
layer inside the channel was set to be 000001 m (01mm) This first cell spacing yielded
y+
values varying between zero and 9 at the target side and front end wall Figure 39
shows a contour of y+ values on the heated walls The maximum values occur near the
impingement locations as expected due to large shear caused by the steep velocity
gradient normal to the wall On the downstream direction the y+ also increases due to the
increase of flow rate and therefore the increased skin friction on the wall At the
impingement location of the first jet the y+ is close to zero due to the velocity having its
direction mostly normal to the surface yielding no shear
54
Figure 39 Target Side and Front End Wall y+ Values
Once the faces were linked edge meshes were created on the sides of the jet center
Section 2rsquos inner edge was also meshed using a different parameter than the one used for
the jet center in order to allow for more freedom when trying to refine the mesh These
two edge meshes is followed by meshing all of section 2 faces alongside all the jet
centers Once these were complete section 3rsquos inner edge was meshed with different
parameters for the channel and plenum Sections 4 and 5 sides that connected with the
face made by section 6 were meshed so that their spacing was similar again the plenum
and channel were meshed separately for increased control of mesh density in both of
these areas The upstream-most edge of section 6 was meshed so that the spacing is
similar to the edge mesh in sections 4 and 5 this was done in order to have aspect ratios
of the wall be as close as possible to unity Sections 3 4 5 and 6 were meshed on both
the channel and the plenum With the entire target wall plane meshed these surface
meshes are coopered upwards to connect to the opposite wall The vertical spacing has
55
also been set up differently between the channel and the plenum The holes and the
plenum were also coopered The finished mesh was then exported as a msh file
Boundary conditions were set in GAMBIT once the mesh was imported into
Fluent values were set to every face depending on their location and purpose Figure 40
shows the four different boundary conditions Face 1 (blue) was set to be a mass flow
inlet The flow rate is half of the total flow rate at a given jet Reynolds number due to it
being only half of the entire domain Face 2 (yellow) is a symmetry plane face 3 (red) is
a pressure outlet at zero gauge pressure The rest of the faces in the channel denoted by
the number 4 (white) are set to walls The target side and front end wall had a heat flux
applied to them equal to 10000Wm2
Figure 40 Finished Mesh with Boundary Conditions
The model was imported into Fluent It was scaled down by a factor of 1000 due to it
being made in GAMBIT in millimeters The energy model was turned on The Realizable
k-ε model was used with enhanced wall functions on both the pressure and thermal
gradients The boundary conditions were set as discussed previously the mass flow inlet
was set to the specific flow rate normal to the surface the heat fluxes were set on the
56
heated walls the outflow gauge pressure was set to zero Two important reference values
characteristic length and reference temperature were set to be the diameter of the jet
(0075m) and 300K respectively The spatial discretization parameters were set to second
order upwind for momentum turbulent kinetic energy turbulent dissipation rate and
energy The under-relaxation factors were set to default Four monitors were created to
aid in the determination of convergence two of them read Nusselt numbers at the
stagnation region of the first and last jet the remaining two read the exit velocity at the
first and last jet The continuity x y and x velocities and energy equations residuals
were set to be 1E-6 while k and ε residuals were set to 1E-4 The solution was initialized
on the all zones at 1ms in the positive x direction The solution was set to autosave every
100 iterations while keeping only the two newest dat files The calculation was then run
for a maximum of 7000 iterations
A grid independence study was done on the domain to find the optimal size of
mesh that provides the correct solution while minimizing the compute time Two
monitors were set to check for grid independence both of them were vertex maximum
One of them read the Nusselt number at the impingement location of the first center jet
while the second one measures the velocity at the exit of the last jet Four different mesh
sizes were run to the convergence criterion explained before their sizes were 900000
15 million 28 million and 43 million cells
57
Figure 41 Grid Independence Study
It can be seen in Figure 41 that the difference between the 28 and 43 million cell
meshes are very small a difference of under 006 for velocity and 7 for Nusselt
number It can be safe to assume that the 28 million cell mesh is large enough to provide
a mesh independent solution The GAMBIT journal file used to create this mesh is
attached to the appendix The results shown hereafter are the ones obtained by the 28
million cell mesh
Figure 42 Residual Plots for the 26M Cell Run
67
69
71
73
75
77
79
81
83
85
485
4855
486
4865
487
4875
488
4885
489
0 1 2 3 4 5
Nu
sse
lt N
um
be
r
Cell Ammount (Millions)
Grid Independence Study
Velocity
Nusselt Number
58
For future reference Figure 42 shows the residuals of the 26M cell calculation
Up until around 4400 iterations the residuals were increasing shortly thereafter the
residuals started decreasing until it converged just after 5500 iterations All runs for the
differently sized meshes had the same residual patters with the peak of residuals and
point of convergence happening at different iterations
52 CFD Results
As describe previously all the results shown here are for the mesh containing 28 million
elements Figure 43 shows the total pressure contours It can be seen that the plenum
portion is at a constant total pressure Once the jets form since there are very small losses
in the jets due to the wall friction the total pressure still remains constant Only when the
jets enter the channel and start mixing with the cross flow is that they start losing the total
pressure head It is important to notice how the first two jets have the total pressure close
to the plenum arriving at the target wall This implies a successful impingement of the
undisturbed potential core As we move downstream the total pressure is lost quite
rapidly as the jets interact with the cross flow
Figure 43 Total Pressure Contours
59
Similar details can be drawn out from Figure 44 it can be seen that the first three
jets successfully impinge on the target wall while the rest of the downstream ones are
deflected by the cross flow As mentioned by Ricklick the velocity magnitude of the last
jet is larger than that of the first jet due to there being a lower static pressure at the end of
the channel providing it with a steeper pressure gradient hence higher velocity
Figure 44 Velocity Magnitude Contours
Turbulent kinetic energy was plotted in Figure 45 it is expected to have the
highest turbulent kinetic energy near the exit of the holes where the stagnant air is in
contact with the fast moving jet The mixing between the two regimes causes very
energetic eddies to form potentially enhancing the target and side wall heat transfer
coefficient As cross flow builds up towards the end of the channel the turbulent kinetic
energy increases due to larger overall velocities and fluctuations between the cross flow
and jets
60
Figure 45 Turbulent Kinetic Energy Contours
As Ricklick showed in his work the static temperature rise is quite small for such a small
channel It can be seen in Figure 46 that the driving temperature for heat transfer is that of
the plenum It is important to notice that a wall heat flux of 10000 Wm2 was used as the
boundary condition Not even in the most powerful tests would we ever use heat fluxes
that high they normally range between 2500 to a maximum of 7000 Wm2 A heat flux of
10000 Wm2 will increase the temperature at a faster rate than what it is normally used in
experimental testing
Figure 46 Static Temperature Contours
61
Figure 47 Target and Side Wall Heat Transfer Coefficient Contours
Figure 47 shows the target and sidewall heat transfer profiles Peaks can be seen at the
first three locations similar to that seen in Figure 22 The trend decreases rapidly to
eventually become a slowly increasing heat transfer profile due to the increase of mass
flow through the channel The sidewall provides the same results clear peaks in heat
transfer where the wall jets impinge on the sidewall seen in Figure 48 in more detail The
sidewall also shows a recirculation zone in between the first row of jets and the end wall
This is caused by the wall jet from the first row hitting the back wall moving upwards in
a circular pattern and coming back down when it encounters the first impingement row
Figure 48 Closer View of First few Rows of Impingement HTC Contours
62
Figure 49 Pathlines Generating from the First Row of Jets
Figure 49 helps explain the low heat transfer region between the first row of jets and
the end wall Pathlines are generated at the exit of each hole in the first row As the
air impinges on the surface half of it moves downstream and the other half movers
upstream to this recirculation zone where it circulates for a period of time before
reuniting with the remainder of the flow to move downstream The wall jet that
moves towards the second row of jets encounters the wall jet created by the second
row of jets causing the pathlines to drastically move upwards On the side of the
channel the pathlines behave erratically with no clear pattern clearly signifying the
highly turbulent and chaotic flow structure of this impingement channel
63
CHAPTER SIX CONCLUSIONS
It has been seen from this analysis that the side walls provide significant heat
transfer in an impingement channel especially at the relatively smaller channel
height This is primarily the result of successful impact of the wall jet with the side
walls It was shown that the tallest channel (ZD=10) has the most uniform profile with
low heat transfer coefficients when compared to the other channels The peaks of the
ZD=6 and 8 channels have a very similar profile which may indicate the successful
impingement of the potential core of the jet on the target surface As XD increases the
peaks diminish and a positive slope profile is attained by the increase of cross flow
velocity as more and more jets are introduced Tall impingement channels provide the
user with a heat transfer profile that is more uniform than those provided with the use of a
smaller channel while still maintaining higher convective coefficients when compared to
a smooth flow scenario The downstream shift of the wall jets is found to be independent
of Reynolds number and heavily dependent on streamwise position It was also found that
at XD=15 the wall jets decay faster than their XD=5 counterparts From the 3D heat
transfer profiles it was seen that the cross flow generated by multiple upstream jets is
deflected downward decreasing its effective flow area increasing its velocity hence
providing higher convective coefficients at the side wall at high xD and low zD
64
APPENDICES
Appendix A
Lateral Conduction Consideration
Thickness of foil heater Heat flux
Sample volume width
Volumetric heat generation
Volume of sample volume
Temperature profile from the first row of impingement ONLY valid for 02ltxlt045
t 50m k 20W
m K qflux 6000
W
m2
1mm
V 2
t qvol
qflux
t
T x( ) 298Kqflux
470630 x2
31244x 14842 W
m2K
N 15
x 02045 02
N 102 047
002 003 004 005314
315
316
317
318
319
320
T x( )
x
A t
qnet x( ) A kxT x
m
d
d xT x( )
d
d
1
m
002 003 004 0050
5 105
1 104
15 104
2 104
qnet x( )
x
65
Now comparing the net heat gained by lateral conduction to heat generated and convected out
It can be seen that the lateral conduction into the sample volume is two orders of magnitude smaller than the heat removed by convection
qgen qvol V 6 103
W
qconv x( ) 2
qflux qnet x( )
002 003 004 0051 10
5
1 104
1 103
001
qconv x( )
qnet x( )
x x
66
Appendix B
This is the journal file run on gambit to generate the geometry faces links
boundary layer face and volume meshes as well as the boundary conditions
set diameter
$d=75
$zc=6($d)
$xc=80($d)
$yc=4($d)
$y=2($d)
$x=5($d)
$zp=5($d)
$ztot=($zc)+($d)+($zp)
$jcf=(13)
$ocf=2
Boundary layer constants
$first=01
$growth=12
$rows=4
Meshing constants
$NumbNodes=5
$Numbtelnodes=6
$PLobnodes=5
$Chobnodes=5
$Plbenodes=($NumbNodes(4)+$rows)
$plsqnodes=($NumbNodes(3))
$Pllsnodes=($NumbNodes+$rows)
$Nojetcells=10
$Chzdnodes=($zc$Nojetcells)($d)
$Plzdnodes=($zp$Nojetcells)($d)
Boundary layer constants for channel
$firstch=001
$growthch=12
$rowsch=8
$CHbenodes=($NumbNodes(4)+$rowsch)
$CHlsnodes=($NumbNodes+$rowsch)
volume create body width ($xc) depth ($yc) height ($ztot) offset ($xc2) ($yc2) ($ztot2) brick
volume create cylinder height ($ztot) radius1 ($d2) radius3 ($d2) offset ($x) 0 ($ztot2) zaxis frustum
volume cmove cylinder multiple 1 offset 0 ($y) 0
volume cmove cylinder volume3 multiple 14 offset ($x) 0 0
volume create jetplate width ($xc) depth ($yc) height ($d)offset ($xc2) ($yc2) ($d2+$zc) brick
volume split body volumes jetplate connected
volume split jetplate volumes cylinder volume3 volume4 volume5
volume6 volume7 volume8 volume9 volume10 volume11
volume12 volume13 volume14 volume15 volume16 volume17
67
volume18 volume19 volume20 volume21 volume22 volume23
volume24 volume25 volume26 volume27 volume28 volume29
volume30 volume31 connected
face create jetcenter width ($jcf$d) height ($jcf$d) offset ($x) 0 0 xyplane rectangle
face create jetcircle radius ($d2) xyplane circle
face move jetcircle offset ($x) 0 0
face create outbox width ($ocf$d) height ($ocf$d) offset ($x) 0 0 xyplane rectangle
face split outbox connected faces jetcircle jetcenter
face split jetcircle connected faces face1
face split outbox connected faces face1
face cmove jetcenter outbox jetcircle face222 face223 multiple 1 offset 0 ($y) 0
face cmove jetcenter outbox jetcircle face222 face223 face224 face225 face226
face227 face228 multiple 14 offset ($x) 0 0
volume delete jetplate lowertopology
face split face1 connected keeptool faces jetcircle jetcenter outbox
face222 face223 face224 face225 face226 face227
face228 face229 face230 face231 face232 face233
face234 face235 face236 face237 face238 face239
face240 face241 face242 face243 face244 face245
face246 face247 face248 face249 face250 face251
face252 face253 face254 face255 face256 face257
face258 face259 face260 face261 face262 face263
face264 face265 face266 face267 face268 face269
face270 face271 face272 face273 face274 face275
face276 face277 face278 face279 face280 face281
face282 face283 face284 face285 face286 face287
face288 face289 face290 face291 face292 face293
face294 face295 face296 face297 face298 face299
face300 face301 face302 face303 face304 face305
face306 face307 face308 face309 face310 face311
face312 face313 face314 face315 face316 face317
face318 face319 face320 face321 face322 face323
face324 face325 face326 face327 face328 face329
face330 face331 face332 face333 face334 face335
face336 face337 face338 face339 face340 face341
face342 face343 face344 face345 face346 face347
face348 face349 face350 face351 face352 face353
face354 face355 face356 face357 face358 face359
face360 face361 face362 face363 face364 face365
face366 face367 face368
face move jetcircle jetcenter outbox face222 face223 face224
face225 face226 face227 face228 face229 face230
face231 face232 face233 face234 face235 face236
face237 face238 face239 face240 face241 face242
face243 face244 face245 face246 face247 face248
face249 face250 face251 face252 face253 face254
face255 face256 face257 face258 face259 face260
face261 face262 face263 face264 face265 face266
face267 face268 face269 face270 face271 face272
face273 face274 face275 face276 face277 face278
face279 face280 face281 face282 face283 face284
face285 face286 face287 face288 face289 face290
face291 face292 face293 face294 face295 face296
face297 face298 face299 face300 face301 face302
face303 face304 face305 face306 face307 face308
face309 face310 face311 face312 face313 face314
68
face315 face316 face317 face318 face319 face320
face321 face322 face323 face324 face325 face326
face327 face328 face329 face330 face331 face332
face333 face334 face335 face336 face337 face338
face339 face340 face341 face342 face343 face344
face345 face346 face347 face348 face349 face350
face351 face352 face353 face354 face355 face356
face357 face358 face359 face360 face361 face362
face363 face364 face365 face366 face367 face368 offset 0
0 $ztot
THIS SPLITS THE TOP PLENUM FACE WITH THE FACES CREATED IN THE BOTTOM
face split face6 connected keeptool faces jetcircle jetcenter outbox
face222 face223 face224 face225 face226 face227
face228 face229 face230 face231 face232 face233
face234 face235 face236 face237 face238 face239
face240 face241 face242 face243 face244 face245
face246 face247 face248 face249 face250 face251
face252 face253 face254 face255 face256 face257
face258 face259 face260 face261 face262 face263
face264 face265 face266 face267 face268 face269
face270 face271 face272 face273 face274 face275
face276 face277 face278 face279 face280 face281
face282 face283 face284 face285 face286 face287
face288 face289 face290 face291 face292 face293
face294 face295 face296 face297 face298 face299
face300 face301 face302 face303 face304 face305
face306 face307 face308 face309 face310 face311
face312 face313 face314 face315 face316 face317
face318 face319 face320 face321 face322 face323
face324 face325 face326 face327 face328 face329
face330 face331 face332 face333 face334 face335
face336 face337 face338 face339 face340 face341
face342 face343 face344 face345 face346 face347
face348 face349 face350 face351 face352 face353
face354 face355 face356 face357 face358 face359
face360 face361 face362 face363 face364 face365
face366 face367 face368
THIS MOVES THE FACES THAT WE ARE USING TO PLIT THE BOTTOM PLENUM SURFACE
face move jetcircle jetcenter outbox face222 face223 face224
face225 face226 face227 face228 face229 face230
face231 face232 face233 face234 face235 face236
face237 face238 face239 face240 face241 face242
face243 face244 face245 face246 face247 face248
face249 face250 face251 face252 face253 face254
face255 face256 face257 face258 face259 face260
face261 face262 face263 face264 face265 face266
face267 face268 face269 face270 face271 face272
face273 face274 face275 face276 face277 face278
face279 face280 face281 face282 face283 face284
face285 face286 face287 face288 face289 face290
face291 face292 face293 face294 face295 face296
face297 face298 face299 face300 face301 face302
69
face303 face304 face305 face306 face307 face308
face309 face310 face311 face312 face313 face314
face315 face316 face317 face318 face319 face320
face321 face322 face323 face324 face325 face326
face327 face328 face329 face330 face331 face332
face333 face334 face335 face336 face337 face338
face339 face340 face341 face342 face343 face344
face345 face346 face347 face348 face349 face350
face351 face352 face353 face354 face355 face356
face357 face358 face359 face360 face361 face362
face363 face364 face365 face366 face367 face368 offset 0
0 -$zp
SPLITS THE BOTTOM FACE OF THE PLENUM WITH THE FACES THAT ARE USED TO SPLIT
face split face114 connected keeptool faces jetcircle jetcenter
outbox face222 face223 face224 face225 face226 face227
face228 face229 face230 face231 face232 face233
face234 face235 face236 face237 face238 face239
face240 face241 face242 face243 face244 face245
face246 face247 face248 face249 face250 face251
face252 face253 face254 face255 face256 face257
face258 face259 face260 face261 face262 face263
face264 face265 face266 face267 face268 face269
face270 face271 face272 face273 face274 face275
face276 face277 face278 face279 face280 face281
face282 face283 face284 face285 face286 face287
face288 face289 face290 face291 face292 face293
face294 face295 face296 face297 face298 face299
face300 face301 face302 face303 face304 face305
face306 face307 face308 face309 face310 face311
face312 face313 face314 face315 face316 face317
face318 face319 face320 face321 face322 face323
face324 face325 face326 face327 face328 face329
face330 face331 face332 face333 face334 face335
face336 face337 face338 face339 face340 face341
face342 face343 face344 face345 face346 face347
face348 face349 face350 face351 face352 face353
face354 face355 face356 face357 face358 face359
face360 face361 face362 face363 face364 face365
face366 face367 face368
COPIES THE FACES THAT WE USED TO SPLIT TO BOTTOM OF THE PLENUM TO THE TOP OF
THE CHANNEL
face cmove jetcircle jetcenter outbox face222 face223 face224
face225 face226 face227 face228 face229 face230
face231 face232 face233 face234 face235 face236
face237 face238 face239 face240 face241 face242
face243 face244 face245 face246 face247 face248
face249 face250 face251 face252 face253 face254
face255 face256 face257 face258 face259 face260
face261 face262 face263 face264 face265 face266
face267 face268 face269 face270 face271 face272
face273 face274 face275 face276 face277 face278
face279 face280 face281 face282 face283 face284
70
face285 face286 face287 face288 face289 face290
face291 face292 face293 face294 face295 face296
face297 face298 face299 face300 face301 face302
face303 face304 face305 face306 face307 face308
face309 face310 face311 face312 face313 face314
face315 face316 face317 face318 face319 face320
face321 face322 face323 face324 face325 face326
face327 face328 face329 face330 face331 face332
face333 face334 face335 face336 face337 face338
face339 face340 face341 face342 face343 face344
face345 face346 face347 face348 face349 face350
face351 face352 face353 face354 face355 face356
face357 face358 face359 face360 face361 face362
face363 face364 face365 face366 face367 face368 multiple 1 offset 0
0 -$d
NAME OF COPIED NEW FACES
face1104 face1105 face1106 face1107 face1108 face1109 face1110 face1111
face1112 face1113 face1114 face1115 face1116 face1117 face1118 face1119
face1120 face1121 face1122 face1123 face1124 face1125 face1126 face1127
face1128 face1129 face1130 face1131 face1132 face1133 face1134 face1135
face1136 face1137 face1138 face1139 face1140 face1141 face1142 face1143
face1144 face1145 face1146 face1147 face1148 face1149 face1150 face1151
face1152 face1153 face1154 face1155 face1156 face1157 face1158 face1159
face1160 face1161 face1162 face1163 face1164 face1165 face1166 face1167
face1168 face1169 face1170 face1171 face1172 face1173 face1174 face1175
face1176 face1177 face1178 face1179 face1180 face1181 face1182 face1183
face1184 face1185 face1186 face1187 face1188 face1189 face1190 face1191
face1192 face1193 face1194 face1195 face1196 face1197 face1198 face1199
face1200 face1201 face1202 face1203 face1204 face1205 face1206 face1207
face1208 face1209 face1210 face1211 face1212 face1213 face1214 face1215
face1216 face1217 face1218 face1219 face1220 face1221 face1222 face1223
face1224 face1225 face1226 face1227 face1228 face1229 face1230 face1231
face1232 face1233 face1234 face1235 face1236 face1237 face1238 face1239
face1240 face1241 face1242 face1243 face1244 face1245 face1246 face1247
face1248 face1249 face1250 face1251 face1252 face1253
THIS SPLITS THE TOP OF THE CHANNEL WITH THE NEW COPIED FACES
face split face209 connected keeptool faces face1104 face1105 face1106 face1107
face1108 face1109 face1110 face1111 face1112 face1113 face1114 face1115
face1116 face1117 face1118 face1119 face1120 face1121 face1122 face1123
face1124 face1125 face1126 face1127 face1128 face1129 face1130 face1131
face1132 face1133 face1134 face1135 face1136 face1137 face1138 face1139
face1140 face1141 face1142 face1143 face1144 face1145 face1146 face1147
face1148 face1149 face1150 face1151 face1152 face1153 face1154 face1155
face1156 face1157 face1158 face1159 face1160 face1161 face1162 face1163
face1164 face1165 face1166 face1167 face1168 face1169 face1170 face1171
face1172 face1173 face1174 face1175 face1176 face1177 face1178 face1179
face1180 face1181 face1182 face1183 face1184 face1185 face1186 face1187
face1188 face1189 face1190 face1191 face1192 face1193 face1194 face1195
face1196 face1197 face1198 face1199 face1200 face1201 face1202 face1203
face1204 face1205 face1206 face1207 face1208 face1209 face1210 face1211
face1212 face1213 face1214 face1215 face1216 face1217 face1218 face1219
face1220 face1221 face1222 face1223 face1224 face1225 face1226 face1227
71
face1228 face1229 face1230 face1231 face1232 face1233 face1234 face1235
face1236 face1237 face1238 face1239 face1240 face1241 face1242 face1243
face1244 face1245 face1246 face1247 face1248 face1249 face1250 face1251
face1252 face1253
THIS UNITES THE RECTANGLE OUTSIDE FACES AND THE SEMICIRCLE SO THAT IT MAKES
A RECTANGLE WIHOUT THE CENTERJET
face unite faces jetcircle face223 real
face unite faces face222 outbox real
face unite faces face228 face226 real
face unite faces face225 face227 real
face unite faces face231 face233 real
face unite faces face232 face230 real
face unite faces face236 face238 real
face unite faces face237 face235 real
face unite faces face241 face243 real
face unite faces face242 face240 real
face unite faces face248 face246 real
face unite faces face245 face247 real
face unite faces face253 face251 real
face unite faces face252 face250 real
face unite faces face256 face258 real
face unite faces face257 face255 real
face unite faces face263 face261 real
face unite faces face260 face262 real
face unite faces face268 face266 real
face unite faces face265 face264 real
face unite faces face265 face267 real
face unite faces face273 face271 real
face unite faces face272 face270 real
face unite faces face276 face278 real
face unite faces face277 face275 real
face unite faces face281 face283 real
face unite faces face282 face280 real
face unite faces face286 face288 real
face unite faces face287 face285 real
face unite faces face291 face293 real
face unite faces face292 face290 real
face unite faces face296 face298 real
face unite faces face297 face295 real
face unite faces face301 face303 real
face unite faces face302 face300 real
face unite faces face306 face308 real
face unite faces face307 face305 real
face unite faces face316 face318 real
face unite faces face312 face310 real
face unite faces face311 face313 real
face unite faces face315 face317 real
face unite faces face321 face323 real
face unite faces face322 face320 real
face unite faces face326 face328 real
face unite faces face327 face325 real
face unite faces face331 face333 real
face unite faces face332 face330 real
face unite faces face336 face338 real
72
face unite faces face337 face335 real
face unite faces face347 face345 real
face unite faces face346 face348 real
face unite faces face342 face340 real
face unite faces face341 face343 real
face unite faces face356 face358 real
face unite faces face357 face355 real
face unite faces face352 face350 real
face unite faces face351 face353 real
face unite faces face361 face363 real
face unite faces face366 face368 real
face unite faces face360 face362 real
face unite faces face365 face367 real
SPLITTING ALL THE FACES OF THE CIRCLES IN THE BOTTOM OF THE PLENUM
face split face912 connected keeptool faces face222
face split face117 connected keeptool faces face228
face split face117 connected keeptool faces face225
face split face922 connected keeptool faces face232
face split face124 connected keeptool faces face236
face split face124 connected keeptool faces face237
face split face932 connected keeptool faces face242
face split face131 connected keeptool faces face248
face split face131 connected keeptool faces face245
face split face942 connected keeptool faces face252
face split face138 connected keeptool faces face256
face split face138 connected keeptool faces face257
face split face952 connected keeptool faces face260
face split face145 connected keeptool faces face268
face split face145 connected keeptool faces face265
face split face962 connected keeptool faces face272
face split face152 connected keeptool faces face276
face split face152 connected keeptool faces face277
face split face972 connected keeptool faces face282
face split face159 connected keeptool faces face286
face split face159 connected keeptool faces face287
face split face982 connected keeptool faces face292
face split face166 connected keeptool faces face296
face split face166 connected keeptool faces face297
face split face992 connected keeptool faces face302
face split face173 connected keeptool faces face306
face split face173 connected keeptool faces face307
face split face1002 connected keeptool faces face312
face split face180 connected keeptool faces face316
face split face180 connected keeptool faces face315
73
face split face1012 connected keeptool faces face322
face split face187 connected keeptool faces face326
face split face187 connected keeptool faces face327
face split face1022 connected keeptool faces face332
face split face194 connected keeptool faces face336
face split face194 connected keeptool faces face337
face split face1032 connected keeptool faces face342
face split face201 connected keeptool faces face346
face split face201 connected keeptool faces face347
face split face1042 connected keeptool faces face352
face split face208 connected keeptool faces face356
face split face208 connected keeptool faces face357
face split face1052 connected keeptool faces face360
face split face215 connected keeptool faces face366
face split face215 connected keeptool faces face365
THIS UNITES THE RECTANGLE OUTSIDE FACES AND THE SEMICIRCLE SO THAT IT MAKES
A RECTANGLE WIHOUT THE CENTERJET
face unite faces face1104 face1108 real
face unite faces face1107 face1106 real
face unite faces face1113 face1111 real
face unite faces face1112 face1110 real
face unite faces face1118 face1116 real
face unite faces face1117 face1115 real
face unite faces face1123 face1121 real
face unite faces face1122 face1120 real
face unite faces face1128 face1126 real
face unite faces face1127 face1125 real
face unite faces face1133 face1131 real
face unite faces face1132 face1130 real
face unite faces face1138 face1136 real
face unite faces face1137 face1135 real
face unite faces face1143 face1141 real
face unite faces face1142 face1140 real
face unite faces face1148 face1146 real
face unite faces face1147 face1145 real
face unite faces face1153 face1151 real
face unite faces face1152 face1150 real
face unite faces face1158 face1156 real
face unite faces face1157 face1155 real
face unite faces face1163 face1161 real
face unite faces face1162 face1160 real
face unite faces face1168 face1166 real
face unite faces face1167 face1165 real
face unite faces face1173 face1171 real
face unite faces face1172 face1170 real
face unite faces face1178 face1176 real
face unite faces face1177 face1175 real
face unite faces face1183 face1181 real
74
face unite faces face1182 face1180 real
face unite faces face1186 face1188 real
face unite faces face1187 face1185 real
face unite faces face1193 face1191 real
face unite faces face1192 face1190 real
face unite faces face1198 face1196 real
face unite faces face1197 face1195 real
face unite faces face1203 face1201 real
face unite faces face1202 face1200 real
face unite faces face1206 face1208 real
face unite faces face1207 face1205 real
face unite faces face1213 face1211 real
face unite faces face1212 face1210 real
face unite faces face1216 face1218 real
face unite faces face1217 face1215 real
face unite faces face1221 face1223 real
face unite faces face1222 face1220 real
face unite faces face1228 face1226 real
face unite faces face1227 face1225 real
face unite faces face1233 face1231 real
face unite faces face1232 face1230 real
face unite faces face1238 face1236 real
face unite faces face1237 face1235 real
face unite faces face1243 face1241 real
face unite faces face1242 face1240 real
face unite faces face1248 face1246 real
face unite faces face1247 face1245 real
face unite faces face1253 face1251 real
face unite faces face1252 face1250 real
SPLITTING ALL THE FACES OF THE CIRCLES IN THE TOP OF THE CHANNEL
face split face1257 connected keeptool faces face1107
face split face115 connected keeptool faces face1113
face split face115 connected keeptool faces face1112
face split face1267 connected keeptool faces face1117
face split face122 connected keeptool faces face1123
face split face122 connected keeptool faces face1122
face split face1277 connected keeptool faces face1127
face split face129 connected keeptool faces face1133
face split face129 connected keeptool faces face1132
face split face1287 connected keeptool faces face1137
face split face136 connected keeptool faces face1143
face split face136 connected keeptool faces face1142
face split face1297 connected keeptool faces face1147
face split face143 connected keeptool faces face1153
face split face143 connected keeptool faces face1152
face split face1307 connected keeptool faces face1157
face split face150 connected keeptool faces face1163
face split face150 connected keeptool faces face1162
75
face split face1317 connected keeptool faces face1167
face split face157 connected keeptool faces face1173
face split face157 connected keeptool faces face1172
face split face1327 connected keeptool faces face1177
face split face164 connected keeptool faces face1183
face split face164 connected keeptool faces face1182
face split face1337 connected keeptool faces face1187
face split face171 connected keeptool faces face1193
face split face171 connected keeptool faces face1192
face split face1347 connected keeptool faces face1197
face split face178 connected keeptool faces face1203
face split face178 connected keeptool faces face1202
face split face1357 connected keeptool faces face1207
face split face185 connected keeptool faces face1213
face split face185 connected keeptool faces face1212
face split face1367 connected keeptool faces face1217
face split face192 connected keeptool faces face1221
face split face192 connected keeptool faces face1222
face split face1377 connected keeptool faces face1227
face split face199 connected keeptool faces face1233
face split face199 connected keeptool faces face1232
face split face1387 connected keeptool faces face1237
face split face206 connected keeptool faces face1243
face split face206 connected keeptool faces face1242
face split face1397 connected keeptool faces face1247
face split face213 connected keeptool faces face1253
face split face213 connected keeptool faces face1252
face split face1452 connected keeptool faces face224
face split face1456 connected keeptool faces face234
face split face1460 connected keeptool faces face244
face split face1464 connected keeptool faces face254
face split face1468 connected keeptool faces face264
face split face1472 connected keeptool faces face274
face split face1476 connected keeptool faces face284
face split face1480 connected keeptool faces face294
face split face1484 connected keeptool faces face304
face split face1488 connected keeptool faces face314
face split face1492 connected keeptool faces face324
face split face1496 connected keeptool faces face334
face split face1500 connected keeptool faces face344
face split face1504 connected keeptool faces face354
face split face1508 connected keeptool faces face364
DELETING ALL THE FACES USED TO MAKE THE CUTS
face delete jetcircle face222 face228 face225 jetcenter
76
face224 face231 face232 face236 face237 face229
face1456 face241 face242 face239 face248 face244
face245 face253 face249 face252 face254 face256
face257 face263 face259 face260 face268 face264
face265 face273 face272 face269 face276 face277
face274 face281 face282 face286 face279 face287
face284 face291 face292 face296 face297 face289
face294 face301 face299 face302 face306 face307
face304 face311 face312 face316 face315 face309
face314 face321 face322 face326 face327 face319
face324 face331 face332 face329 face336 face334
face337 face341 face342 face339 face346 face344
face347 face351 face352 face349 face356 face354
face357 face361 face359 face360 face366 face364
face365 lowertopology
face delete face1104 face1105 face1107 face1113 face1112
face115 face234 face1118 face1114 face1117 face1123
face1122 face122 face1138 face1128 face1127 face1124
face1133 face1132 face129 face1134 face1137 face1143
face136 face1142 face1148 face1144 face1147 face1153
face143 face1152 face1158 face1154 face1157 face1163
face150 face1162 face1168 face1164 face1167 face1173
face157 face1172 face1178 face1174 face1177 face1183
face164 face1182 face1186 face1184 face1187 face1193
face171 face1192 face1198 face1194 face1197 face1203
face178 face1202 face1206 face1204 face1207 face1213
face185 face1212 face1216 face1214 face1217 face1221
face192 face1222 face1228 face1224 face1227 face1233
face199 face1232 face1238 face1234 face1237 face1243
face206 face1242 face1248 face1244 face1247 face1253
face213 face1252 lowertopology
face delete face1109 face1119 face1129 face1139 face1149 face1159
face1169 face1179 face1189 face1199 face1209 face1219
face1229 face1239 face1249 lowertopology
face create CP1 width 600 height 75 offset 300 (225+($d)2) 0 xyplane rectangle
face create CP2 width 600 height 75 offset 300 (225+($d)2) ($zc) xyplane rectangle
face create CP3 width 600 height 75 offset 300 (225+($d)2) ($zc+$d) xyplane rectangle
face create CP4 width 600 height 75 offset 300 (225+($d)2) ($zc+$d+$zp) xyplane rectangle
face split face6 connected faces CP4
face split face114 connected faces CP3
face split face209 connected faces CP2
face split face1 connected faces CP1
GEOMETRY IS FINISHED
face modify face912 side vertex6437 vertex6436
77
face modify face1600 side vertex7302 vertex7303
face modify face117 side vertex6446 vertex6447
face modify face646 side vertex3312
face modify face646 side vertex3313
face modify face647 side vertex3432 vertex3433
face modify face372 side vertex2040 vertex2041
face modify face376 side vertex2100 vertex2101
face modify face377 side vertex2221 vertex2220
LINKING ALL THE JET CENTERS
face link face1450 face640 edges edge6949 edge3518 vertices
vertex6437 vertex3253 reverse
face link face1450 face1257 edges edge6949 edge7340 vertices
vertex6437 vertex6797 reverse
face link face1257 face370 edges edge7340 edge2139 vertices
vertex6797 vertex2041 reverse
face link face1257 face1454 edges edge7340 edge6975 vertices
vertex6797 vertex6461 reverse
face link face1454 face649 edges edge6975 edge3519 vertices
vertex6461 vertex3255 reverse
face link face1454 face1267 edges edge6975 edge7377 vertices
vertex6461 vertex6831 reverse
face link face1267 face379 edges edge7377 edge2141 vertices
vertex6831 vertex2043 reverse
face link face1267 face1458 edges edge7377 edge7001 vertices
vertex6831 vertex6485 reverse
face link face1458 face659 edges edge7001 edge3520 vertices
vertex6485 vertex3257 reverse
face link face1458 face1277 edges edge7001 edge7414 vertices
vertex6485 vertex6865 reverse
face link face1277 face389 edges edge7414 edge2143 vertices
vertex6865 vertex2045 reverse
face link face1277 face1462 edges edge7414 edge7027 vertices
vertex6865 vertex6509 reverse
face link face1462 face669 edges edge7027 edge3521 vertices
vertex6509 vertex3259 reverse
face link face1462 face1287 edges edge7027 edge7451 vertices
vertex6509 vertex6899 reverse
face link face1287 face399 edges edge7451 edge2145 vertices
vertex6899 vertex2047 reverse
face link face1287 face1466 edges edge7451 edge7053 vertices
vertex6899 vertex6533 reverse
face link face1466 face679 edges edge7053 edge3522 vertices
vertex6533 vertex3261 reverse
face link face1466 face1297 edges edge7053 edge7488 vertices
vertex6533 vertex6933 reverse
face link face1297 face409 edges edge7488 edge2147 vertices
vertex6933 vertex2049 reverse
face link face1297 face1470 edges edge7488 edge7079 vertices
vertex6933 vertex6557 reverse
face link face1470 face689 edges edge7079 edge3523 vertices
vertex6557 vertex3263 reverse
face link face1470 face1307 edges edge7079 edge7525 vertices
vertex6557 vertex6967 reverse
face link face1307 face419 edges edge7525 edge2149 vertices
78
vertex6967 vertex2051 reverse
face link face1307 face1474 edges edge7525 edge7105 vertices
vertex6967 vertex6581 reverse
face link face1474 face1317 edges edge7105 edge7562 vertices
vertex6581 vertex7001 reverse
face link face1474 face699 edges edge7105 edge3524 vertices
vertex6581 vertex3265 reverse
face link face1317 face429 edges edge7562 edge2151 vertices
vertex7001 vertex2053 reverse
face link face1317 face1478 edges edge7562 edge7131 vertices
vertex7001 vertex6605 reverse
face link face1478 face1327 edges edge7131 edge7599 vertices
vertex6605 vertex7035 reverse
face link face1478 face709 edges edge7131 edge3525 vertices
vertex6605 vertex3267 reverse
face link face1327 face439 edges edge7599 edge2153 vertices
vertex7035 vertex2055 reverse
face link face1327 face1482 edges edge7599 edge7157 vertices
vertex7035 vertex6629 reverse
face link face1482 face719 edges edge7157 edge3526 vertices
vertex6629 vertex3269 reverse
face link face1482 face1337 edges edge7157 edge7636 vertices
vertex6629 vertex7069 reverse
face link face1337 face449 edges edge7636 edge2155 vertices
vertex7069 vertex2057 reverse
face link face1337 face1486 edges edge7636 edge7183 vertices
vertex7069 vertex6653 reverse
face link face1486 face1347 edges edge7183 edge7673 vertices
vertex6653 vertex7103 reverse
face link face1347 face459 edges edge7673 edge2157 vertices
vertex7103 vertex2059 reverse
face link face1486 face729 edges edge7183 edge3527 vertices
vertex6653 vertex3271 reverse
face link face1347 face1490 edges edge7673 edge7209 vertices
vertex7103 vertex6677 reverse
face link face1490 face1357 edges edge7209 edge7710 vertices
vertex6677 vertex7137 reverse
face link face1490 face739 edges edge7209 edge3528 vertices
vertex6677 vertex3273 reverse
face link face1357 face469 edges edge7710 edge2159 vertices
vertex7137 vertex2061 reverse
face link face1357 face1494 edges edge7710 edge7235 vertices
vertex7137 vertex6701 reverse
face link face1494 face1367 edges edge7235 edge7747 vertices
vertex6701 vertex7171 reverse
face link face1494 face749 edges edge7235 edge3529 vertices
vertex6701 vertex3275 reverse
face link face1367 face479 edges edge7747 edge2161 vertices
vertex7171 vertex2063 reverse
face link face1367 face1498 edges edge7747 edge7261 vertices
vertex7171 vertex6725 reverse
face link face1498 face1377 edges edge7261 edge7784 vertices
vertex6725 vertex7205 reverse
face link face1377 face489 edges edge7784 edge2163 vertices
vertex7205 vertex2065 reverse
face link face1498 face759 edges edge7261 edge3530 vertices
79
vertex6725 vertex3277 reverse
face link face1377 face1502 edges edge7784 edge7287 vertices
vertex7205 vertex6749 reverse
face link face1502 face1387 edges edge7287 edge7821 vertices
vertex6749 vertex7239 reverse
face link face1387 face499 edges edge7821 edge2165 vertices
vertex7239 vertex2067 reverse
face link face1387 face1506 edges edge7821 edge7313 vertices
vertex7239 vertex6773 reverse
face link face1502 face769 edges edge7287 edge3531 vertices
vertex6749 vertex3279 reverse
face link face1506 face1397 edges edge7313 edge7858 vertices
vertex6773 vertex7273 reverse
face link face1506 face779 edges edge7313 edge3532 vertices
vertex6773 vertex3281 reverse
face link face1397 face509 edges edge7858 edge2167 vertices
vertex7273 vertex2069 reverse
LINKING ALL THE COMPLETE JETCENTERS
face link face1452 face644 edges edge7891 edge3773 vertices
vertex7303 vertex3433
face link face1452 face115 edges edge7891 edge7364 vertices
vertex7303 vertex6819
face link face1452 face1456 edges edge7891 edge7900 vertices
vertex7303 vertex7311
face link face1456 face654 edges edge7900 edge3774 vertices
vertex7311 vertex3435
face link face1456 face122 edges edge7900 edge7401 vertices
vertex7311 vertex6853
face link face1456 face1460 edges edge7900 edge7909 vertices
vertex7311 vertex7319
face link face1460 face1464 edges edge7909 edge7918 vertices
vertex7319 vertex7327
face link face1460 face129 edges edge7909 edge7438 vertices
vertex7319 vertex6887
face link face1460 face664 edges edge7909 edge3775 vertices
vertex7319 vertex3437
face link face1464 face674 edges edge7918 edge3776 vertices
vertex7327 vertex3439
face link face1464 face136 edges edge7918 edge7475 vertices
vertex7327 vertex6921
face link face1464 face1468 edges edge7918 edge7927 vertices
vertex7327 vertex7335
face link face1472 face1468 edges edge7936 edge7927 vertices
vertex7343 vertex7335
face link face1468 face143 edges edge7927 edge7512 vertices
vertex7335 vertex6955
face link face1468 face684 edges edge7927 edge3777 vertices
vertex7335 vertex3441
face link face1472 face694 edges edge7936 edge3778 vertices
vertex7343 vertex3443
face link face1472 face150 edges edge7936 edge7549 vertices
vertex7343 vertex6989
face link face1472 face1476 edges edge7936 edge7945 vertices
80
vertex7343 vertex7351
face link face1476 face1480 edges edge7945 edge7954 vertices
vertex7351 vertex7359
face link face1476 face157 edges edge7945 edge7586 vertices
vertex7351 vertex7023
face link face1476 face704 edges edge7945 edge3779 vertices
vertex7351 vertex3445
face link face1480 face714 edges edge7954 edge3780 vertices
vertex7359 vertex3447
face link face1480 face164 edges edge7954 edge7623 vertices
vertex7359 vertex7057
face link face1480 face1484 edges edge7954 edge7963 vertices
vertex7359 vertex7367
face link face1484 face171 edges edge7963 edge7660 vertices
vertex7367 vertex7091
face link face1484 face724 edges edge7963 edge3781 vertices
vertex7367 vertex3449
face link face1480 face1488 edges edge7954 edge7972 vertices
vertex7359 vertex7375
face link face1488 face178 edges edge7972 edge7697 vertices
vertex7375 vertex7125
face link face1488 face734 edges edge7972 edge3782 vertices
vertex7375 vertex3451
face link face1488 face1492 edges edge7972 edge7981 vertices
vertex7375 vertex7383
face link face1492 face744 edges edge7981 edge3783 vertices
vertex7383 vertex3453
face link face1492 face185 edges edge7981 edge7734 vertices
vertex7383 vertex7159
face link face1492 face1496 edges edge7981 edge7990 vertices
vertex7383 vertex7391
face link face1496 face754 edges edge7990 edge3784 vertices
vertex7391 vertex3455
face link face1496 face192 edges edge7990 edge7771 vertices
vertex7391 vertex7193
face link face1496 face1500 edges edge7990 edge7999 vertices
vertex7391 vertex7399
face link face1500 face1504 edges edge7999 edge8008 vertices
vertex7399 vertex7407
face link face1504 face1508 edges edge8008 edge8017 vertices
vertex7407 vertex7415
face link face1500 face199 edges edge7999 edge7808 vertices
vertex7399 vertex7227
face link face1500 face764 edges edge7999 edge3785 vertices
vertex7399 vertex3457
face link face1504 face774 edges edge8008 edge3786 vertices
vertex7407 vertex3459
face link face1508 face784 edges edge8017 edge3787 vertices
vertex7415 vertex3461
face link face1504 face206 edges edge8008 edge7845 vertices
vertex7407 vertex7261
face link face1508 face213 edges edge8017 edge7882 vertices
vertex7415 vertex7295
linking the jetcenters of the bottom of the channel one of them has to be reversed but the otherones are not
81
face link face115 face374 edges edge7364 edge2394 vertices
vertex6819 vertex2221 reverse
face link face374 face384 edges edge2394 edge2396 vertices
vertex2221 vertex2223
face link face384 face394 edges edge2396 edge2398 vertices
vertex2223 vertex2225
face link face394 face404 edges edge2398 edge2400 vertices
vertex2225 vertex2227
face link face404 face414 edges edge2400 edge2402 vertices
vertex2227 vertex2229
face link face414 face424 edges edge2402 edge2404 vertices
vertex2229 vertex2231
face link face424 face434 edges edge2404 edge2406 vertices
vertex2231 vertex2233
face link face434 face444 edges edge2406 edge2408 vertices
vertex2233 vertex2235
face link face444 face454 edges edge2408 edge2410 vertices
vertex2235 vertex2237
face link face454 face464 edges edge2410 edge2412 vertices
vertex2237 vertex2239
face link face464 face474 edges edge2412 edge2414 vertices
vertex2239 vertex2241
face link face474 face484 edges edge2414 edge2416 vertices
vertex2241 vertex2243
face link face484 face494 edges edge2416 edge2418 vertices
vertex2243 vertex2245
face link face494 face504 edges edge2418 edge2420 vertices
vertex2245 vertex2247
face link face504 face514 edges edge2420 edge2422 vertices
vertex2247 vertex2249
UP TO THIS POINT ALL THE FACES ARE CONNCTED SUCCESSFULLY
LINKING THE FIRST THREE JET TELEPHONES
face link face912 face117 edges edge6950 edge6960 vertices
vertex6437 vertex6446 reverse
face link face912 face1600 edges edge6950 edge7890 vertices
vertex6437 vertex7303 reverse
face link face912 face372 edges edge6950 edge2168 vertices
vertex6437 vertex2041
face link face117 face376 edges edge6959 edge2304 vertices
vertex6447 vertex2101 reverse
face link face1600 face377 edges edge7890 edge2423 vertices
vertex7303 vertex2221 reverse
face link face372 face382 edges edge2168 edge2169 vertices
vertex2041 vertex2043
face link face377 face387 edges edge2423 edge2424 vertices
vertex2221 vertex2223
face link face376 face386 edges edge2304 edge2306 vertices
vertex2101 vertex2103
face link face387 face397 edges edge2424 edge2425 vertices
vertex2223 vertex2225
face link face386 face396 edges edge2306 edge2308 vertices
82
vertex2103 vertex2105
face link face382 face392 edges edge2169 edge2170 vertices
vertex2043 vertex2045
face link face382 face392 edges edge2169 edge2170 vertices
vertex2043 vertex2045
face link face382 face392 edges edge2169 edge2170 vertices
vertex2043 vertex2045
face link face382 face392 edges edge2169 edge2170 vertices
vertex2043 vertex2045
face link face397 face407 edges edge2425 edge2426 vertices
vertex2225 vertex2227
face link face392 face402 edges edge2170 edge2171 vertices
vertex2045 vertex2047
face link face396 face406 edges edge2290 edge2291 vertices
vertex2104 vertex2106
face link face407 face417 edges edge2426 edge2427 vertices
vertex2227 vertex2229
face link face417 face427 edges edge2427 edge2428 vertices
vertex2229 vertex2231
face link face427 face437 edges edge2428 edge2429 vertices
vertex2231 vertex2233
face link face437 face447 edges edge2429 edge2430 vertices
vertex2233 vertex2235
face link face447 face457 edges edge2430 edge2431 vertices
vertex2235 vertex2237
face link face457 face467 edges edge2431 edge2432 vertices
vertex2237 vertex2239
face link face467 face477 edges edge2432 edge2433 vertices
vertex2239 vertex2241
face link face477 face487 edges edge2433 edge2434 vertices
vertex2241 vertex2243
face link face487 face487 edges edge2434 edge2434 vertices
vertex2243 vertex2243
face link face487 face487 edges edge2434 edge2434 vertices
vertex2243 vertex2243
face link face487 face487 edges edge2434 edge2434 vertices
vertex2243 vertex2243
face link face487 face497 edges edge2434 edge2435 vertices
vertex2243 vertex2245
face link face497 face507 edges edge2435 edge2436 vertices
vertex2245 vertex2247
face link face507 face517 edges edge2436 edge2437 vertices
vertex2247 vertex2249
face link face406 face416 edges edge2291 edge2292 vertices
vertex2106 vertex2108
face link face416 face426 edges edge2292 edge2293 vertices
vertex2108 vertex2110
face link face426 face436 edges edge2293 edge2294 vertices
vertex2110 vertex2112
face link face436 face446 edges edge2294 edge2295 vertices
vertex2112 vertex2114
face link face446 face456 edges edge2295 edge2296 vertices
vertex2114 vertex2116
face link face456 face466 edges edge2296 edge2297 vertices
vertex2116 vertex2118
face link face466 face476 edges edge2297 edge2298 vertices
83
vertex2118 vertex2120
face link face486 face496 edges edge2299 edge2300 vertices
vertex2122 vertex2124
face link face476 face486 edges edge2298 edge2299 vertices
vertex2120 vertex2122
face link face496 face506 edges edge2300 edge2301 vertices
vertex2124 vertex2126
face link face506 face516 edges edge2301 edge2302 vertices
vertex2126 vertex2128
face link face392 face402 edges edge2142 edge2144 vertices
vertex2044 vertex2046
face link face402 face412 edges edge2171 edge2172 vertices
vertex2047 vertex2049
face link face412 face422 edges edge2172 edge2173 vertices
vertex2049 vertex2051
face link face422 face432 edges edge2173 edge2174 vertices
vertex2051 vertex2053
face link face432 face442 edges edge2174 edge2175 vertices
vertex2053 vertex2055
face link face442 face452 edges edge2175 edge2176 vertices
vertex2055 vertex2057
face link face452 face462 edges edge2176 edge2177 vertices
vertex2057 vertex2059
face link face462 face472 edges edge2177 edge2178 vertices
vertex2059 vertex2061
face link face472 face482 edges edge2178 edge2179 vertices
vertex2061 vertex2063
face link face482 face492 edges edge2179 edge2180 vertices
vertex2063 vertex2065
face link face492 face502 edges edge2180 edge2181 vertices
vertex2065 vertex2067
face link face502 face512 edges edge2181 edge2182 vertices
vertex2067 vertex2069
LINKING THE TELEPHONES OF THE BOTTOM OF THE PLENUM
face link face912 face922 edges edge6950 edge6976 vertices
vertex6437 vertex6461
face link face922 face932 edges edge6976 edge7002 vertices
vertex6461 vertex6485
face link face932 face942 edges edge7002 edge7028 vertices
vertex6485 vertex6509
face link face942 face952 edges edge7028 edge7054 vertices
vertex6509 vertex6533
face link face952 face962 edges edge7054 edge7080 vertices
vertex6533 vertex6557
face link face962 face972 edges edge7080 edge7106 vertices
vertex6557 vertex6581
face link face972 face982 edges edge7106 edge7132 vertices
vertex6581 vertex6605
face link face982 face992 edges edge7132 edge7158 vertices
vertex6605 vertex6629
face link face992 face1002 edges edge7158 edge7184 vertices
vertex6629 vertex6653
face link face1002 face1012 edges edge7184 edge7210 vertices
vertex6653 vertex6677
84
face link face1012 face1022 edges edge7210 edge7236 vertices
vertex6677 vertex6701
face link face1032 face1042 edges edge7262 edge7288 vertices
vertex6725 vertex6749
face link face1042 face1052 edges edge7288 edge7314 vertices
vertex6749 vertex6773
face link face117 face124 edges edge6960 edge6986 vertices
vertex6446 vertex6470
face link face124 face131 edges edge6986 edge7012 vertices
vertex6470 vertex6494
face link face131 face138 edges edge7012 edge7038 vertices
vertex6494 vertex6518
face link face138 face145 edges edge7038 edge7064 vertices
vertex6518 vertex6542
face link face145 face152 edges edge7064 edge7090 vertices
vertex6542 vertex6566
face link face152 face159 edges edge7090 edge7116 vertices
vertex6566 vertex6590
face link face159 face166 edges edge7116 edge7142 vertices
vertex6590 vertex6614
face link face166 face173 edges edge7142 edge7168 vertices
vertex6614 vertex6638
face link face173 face180 edges edge7168 edge7194 vertices
vertex6638 vertex6662
face link face180 face187 edges edge7194 edge7220 vertices
vertex6662 vertex6686
face link face187 face194 edges edge7220 edge7246 vertices
vertex6686 vertex6710
face link face194 face201 edges edge7246 edge7272 vertices
vertex6710 vertex6734
face link face1022 face1032 edges edge7236 edge7262 vertices
vertex6701 vertex6725
face link face1032 face1042 edges edge7262 edge7288 vertices
vertex6725 vertex6749
face link face201 face208 edges edge7271 edge7297 vertices
vertex6735 vertex6759
face link face208 face215 edges edge7297 edge7323 vertices
vertex6759 vertex6783
face link face1600 face1602 edges edge7890 edge7899 vertices
vertex7303 vertex7311
face link face1602 face1604 edges edge7899 edge7908 vertices
vertex7311 vertex7319
face link face1604 face1606 edges edge7908 edge7917 vertices
vertex7319 vertex7327
face link face1606 face1608 edges edge7917 edge7926 vertices
vertex7327 vertex7335
face link face1608 face1610 edges edge7926 edge7935 vertices
vertex7335 vertex7343
face link face1610 face1612 edges edge7935 edge7944 vertices
vertex7343 vertex7351
face link face1612 face1614 edges edge7944 edge7953 vertices
vertex7351 vertex7359
face link face1614 face1616 edges edge7953 edge7962 vertices
vertex7359 vertex7367
face link face1616 face1618 edges edge7962 edge7971 vertices
vertex7367 vertex7375
85
face link face1618 face1620 edges edge7971 edge7980 vertices
vertex7375 vertex7383
face link face1620 face1622 edges edge7980 edge7989 vertices
vertex7383 vertex7391
face link face1622 face1624 edges edge7989 edge7998 vertices
vertex7391 vertex7399
face link face1624 face1626 edges edge7998 edge8007 vertices
vertex7399 vertex7407
face link face1626 face1628 edges edge8007 edge8016 vertices
vertex7407 vertex7415
LINKING ALL THE TELEPHONES OF THE TOP OF THE CHANNEL
face link face912 face1510 edges edge6950 edge7339 vertices
vertex6437 vertex6797 reverse
face link face117 face1512 edges edge6959 edge7349 vertices
vertex6447 vertex6807
face link face1600 face1514 edges edge7890 edge7363 vertices
vertex7303 vertex6819
face link face1510 face1516 edges edge7339 edge7376 vertices
vertex6797 vertex6831
face link face1516 face1522 edges edge7376 edge7413 vertices
vertex6831 vertex6865
face link face1522 face1528 edges edge7413 edge7450 vertices
vertex6865 vertex6899
face link face1528 face1534 edges edge7450 edge7487 vertices
vertex6899 vertex6933
face link face1534 face1540 edges edge7487 edge7524 vertices
vertex6933 vertex6967
face link face1540 face1546 edges edge7524 edge7561 vertices
vertex6967 vertex7001
face link face1546 face1552 edges edge7561 edge7598 vertices
vertex7001 vertex7035
face link face1552 face1558 edges edge7598 edge7635 vertices
vertex7035 vertex7069
face link face1558 face1564 edges edge7635 edge7672 vertices
vertex7069 vertex7103
face link face1564 face1570 edges edge7672 edge7709 vertices
vertex7103 vertex7137
face link face1570 face1576 edges edge7709 edge7746 vertices
vertex7137 vertex7171
face link face1576 face1582 edges edge7746 edge7783 vertices
vertex7171 vertex7205
face link face1582 face1588 edges edge7783 edge7820 vertices
vertex7205 vertex7239
face link face1588 face1594 edges edge7820 edge7857 vertices
vertex7239 vertex7273
face link face1512 face1518 edges edge7350 edge7387 vertices
vertex6806 vertex6840
face link face1518 face1524 edges edge7387 edge7424 vertices
vertex6840 vertex6874
face link face1524 face1530 edges edge7424 edge7461 vertices
vertex6874 vertex6908
face link face1530 face1536 edges edge7461 edge7498 vertices
vertex6908 vertex6942
face link face1536 face1542 edges edge7498 edge7535 vertices
86
vertex6942 vertex6976
face link face1542 face1548 edges edge7535 edge7572 vertices
vertex6976 vertex7010
face link face1548 face1554 edges edge7572 edge7609 vertices
vertex7010 vertex7044
face link face1554 face1560 edges edge7609 edge7646 vertices
vertex7044 vertex7078
face link face1560 face1566 edges edge7646 edge7683 vertices
vertex7078 vertex7112
face link face1566 face1572 edges edge7683 edge7720 vertices
vertex7112 vertex7146
face link face1572 face1578 edges edge7720 edge7757 vertices
vertex7146 vertex7180
face link face1578 face1584 edges edge7757 edge7794 vertices
vertex7180 vertex7214
face link face1584 face1590 edges edge7794 edge7831 vertices
vertex7214 vertex7248
face link face1590 face1596 edges edge7831 edge7868 vertices
vertex7248 vertex7282
face link face1514 face1520 edges edge7363 edge7400 vertices
vertex6819 vertex6853
face link face1520 face1526 edges edge7400 edge7437 vertices
vertex6853 vertex6887
face link face1526 face1532 edges edge7437 edge7474 vertices
vertex6887 vertex6921
face link face1532 face1538 edges edge7474 edge7511 vertices
vertex6921 vertex6955
face link face1538 face1544 edges edge7511 edge7548 vertices
vertex6955 vertex6989
face link face1544 face1550 edges edge7548 edge7585 vertices
vertex6989 vertex7023
face link face1550 face1556 edges edge7585 edge7622 vertices
vertex7023 vertex7057
face link face1556 face1562 edges edge7622 edge7659 vertices
vertex7057 vertex7091
face link face1562 face1568 edges edge7659 edge7696 vertices
vertex7091 vertex7125
face link face1568 face1574 edges edge7696 edge7733 vertices
vertex7125 vertex7159
face link face1574 face1580 edges edge7733 edge7770 vertices
vertex7159 vertex7193
face link face1580 face1586 edges edge7770 edge7807 vertices
vertex7193 vertex7227
face link face1586 face1592 edges edge7807 edge7844 vertices
vertex7227 vertex7261
face link face1592 face1598 edges edge7844 edge7881 vertices
vertex7261 vertex7295
LINKING ALL THE TELEPHONES OF THE TOP OF THE PLENUM
face link face912 face642 edges edge6950 edge3489 vertices
vertex6437 vertex3253 reverse
face link face642 face647 edges edge3489 edge3744 vertices
vertex3253 vertex3433
face link face117 face646 edges edge6959 edge3638 vertices
vertex6447 vertex3313
87
face link face642 face652 edges edge3489 edge3491 vertices
vertex3253 vertex3255
face link face652 face662 edges edge3491 edge3493 vertices
vertex3255 vertex3257
face link face662 face672 edges edge3493 edge3495 vertices
vertex3257 vertex3259
face link face672 face682 edges edge3495 edge3497 vertices
vertex3259 vertex3261
face link face682 face692 edges edge3497 edge3499 vertices
vertex3261 vertex3263
face link face692 face702 edges edge3499 edge3501 vertices
vertex3263 vertex3265
face link face702 face712 edges edge3501 edge3503 vertices
vertex3265 vertex3267
face link face712 face722 edges edge3503 edge3505 vertices
vertex3267 vertex3269
face link face722 face732 edges edge3505 edge3507 vertices
vertex3269 vertex3271
face link face732 face742 edges edge3507 edge3509 vertices
vertex3271 vertex3273
face link face742 face752 edges edge3509 edge3511 vertices
vertex3273 vertex3275
face link face752 face762 edges edge3511 edge3513 vertices
vertex3275 vertex3277
face link face762 face772 edges edge3513 edge3515 vertices
vertex3277 vertex3279
face link face772 face782 edges edge3515 edge3517 vertices
vertex3279 vertex3281
face link face646 face656 edges edge3653 edge3655 vertices
vertex3312 vertex3314
face link face656 face666 edges edge3655 edge3657 vertices
vertex3314 vertex3316
face link face666 face676 edges edge3657 edge3659 vertices
vertex3316 vertex3318
face link face676 face686 edges edge3659 edge3661 vertices
vertex3318 vertex3320
face link face686 face696 edges edge3661 edge3663 vertices
vertex3320 vertex3322
face link face696 face706 edges edge3663 edge3665 vertices
vertex3322 vertex3324
face link face706 face716 edges edge3665 edge3667 vertices
vertex3324 vertex3326
face link face716 face726 edges edge3667 edge3669 vertices
vertex3326 vertex3328
face link face726 face736 edges edge3669 edge3671 vertices
vertex3328 vertex3330
face link face736 face746 edges edge3671 edge3673 vertices
vertex3330 vertex3332
face link face746 face756 edges edge3673 edge3675 vertices
vertex3332 vertex3334
face link face756 face766 edges edge3675 edge3677 vertices
vertex3334 vertex3336
face link face766 face776 edges edge3677 edge3679 vertices
vertex3336 vertex3338
face link face776 face786 edges edge3679 edge3681 vertices
88
vertex3338 vertex3340
face link face647 face657 edges edge3744 edge3746 vertices
vertex3433 vertex3435
face link face657 face667 edges edge3746 edge3748 vertices
vertex3435 vertex3437
face link face667 face677 edges edge3748 edge3750 vertices
vertex3437 vertex3439
face link face677 face687 edges edge3750 edge3752 vertices
vertex3439 vertex3441
face link face687 face697 edges edge3752 edge3754 vertices
vertex3441 vertex3443
face link face697 face707 edges edge3754 edge3756 vertices
vertex3443 vertex3445
face link face707 face717 edges edge3756 edge3758 vertices
vertex3445 vertex3447
face link face717 face727 edges edge3758 edge3760 vertices
vertex3447 vertex3449
face link face727 face737 edges edge3760 edge3762 vertices
vertex3449 vertex3451
face link face737 face747 edges edge3762 edge3764 vertices
vertex3451 vertex3453
face link face747 face757 edges edge3764 edge3766 vertices
vertex3453 vertex3455
face link face757 face767 edges edge3766 edge3768 vertices
vertex3455 vertex3457
face link face767 face777 edges edge3768 edge3770 vertices
vertex3457 vertex3459
face link face777 face787 edges edge3770 edge3772 vertices
vertex3459 vertex3461
face link face647 face1600 edges edge3685 edge6963 vertices
vertex3345 vertex6449
LINKING OUTBOXES ON THE PLENUM
face modify face911 side vertex4404 vertex4405
face modify face918 side vertex4405 vertex4404
face link face911 face915 edges edge4778 edge4898 vertices
vertex4374 vertex4434
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vertex4480 vertex3463 reverse
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vertex4405 vertex3283 reverse
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89
vertex3471 vertex3473
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face link face725 face735 edges edge3841 edge3842 vertices
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face link face745 face755 edges edge3843 edge3844 vertices
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face link face755 face765 edges edge3844 edge3845 vertices
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face link face765 face775 edges edge3845 edge3846 vertices
vertex3487 vertex3489
face link face775 face785 edges edge3846 edge3847 vertices
vertex3489 vertex3491
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face link face658 face668 edges edge3690 edge3694 vertices
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face link face708 face718 edges edge3710 edge3714 vertices
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face link face718 face728 edges edge3714 edge3718 vertices
vertex3389 vertex3395
face link face728 face738 edges edge3718 edge3722 vertices
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face link face758 face768 edges edge3730 edge3734 vertices
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face link face660 face670 edges edge3580 edge3581 vertices
vertex3287 vertex3289
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vertex3289 vertex3291
face link face680 face690 edges edge3582 edge3583 vertices
90
vertex3291 vertex3293
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vertex4482 vertex4484
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vertex4484 vertex4486
face link face945 face955 edges edge4905 edge4907 vertices
vertex4486 vertex4488
face link face955 face965 edges edge4907 edge4909 vertices
vertex4488 vertex4490
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vertex4490 vertex4492
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vertex4492 vertex4494
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vertex4494 vertex4496
face link face995 face1005 edges edge4915 edge4917 vertices
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face link face1005 face1015 edges edge4917 edge4919 vertices
vertex4498 vertex4500
face link face1015 face1025 edges edge4919 edge4921 vertices
vertex4500 vertex4502
face link face1025 face1035 edges edge4921 edge4923 vertices
vertex4502 vertex4504
face link face1035 face1045 edges edge4923 edge4925 vertices
vertex4504 vertex4506
face link face1045 face1055 edges edge4925 edge4927 vertices
vertex4506 vertex4508
face link face918 face928 edges edge4825 edge4828 vertices
vertex4436 vertex4439
face link face928 face938 edges edge4828 edge4831 vertices
vertex4439 vertex4442
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face link face948 face958 edges edge4834 edge4837 vertices
vertex4445 vertex4448
face link face958 face968 edges edge4837 edge4840 vertices
91
vertex4448 vertex4451
face link face968 face978 edges edge4840 edge4843 vertices
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face link face988 face998 edges edge4846 edge4849 vertices
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face link face998 face1008 edges edge4849 edge4852 vertices
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face link face1018 face1028 edges edge4855 edge4858 vertices
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face link face1028 face1038 edges edge4858 edge4861 vertices
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face link face1048 face1058 edges edge4864 edge4867 vertices
vertex4475 vertex4478
face link face911 face920 edges edge108 edge118 vertices
vertex88 vertex94
face link face920 face930 edges edge118 edge128 vertices
vertex94 vertex100
face link face930 face940 edges edge4783 edge4785 vertices
vertex4409 vertex4411
face link face940 face950 edges edge4785 edge4787 vertices
vertex4411 vertex4413
face link face950 face960 edges edge4787 edge4789 vertices
vertex4413 vertex4415
face link face960 face970 edges edge4789 edge4791 vertices
vertex4415 vertex4417
face link face970 face980 edges edge4791 edge4793 vertices
vertex4417 vertex4419
face link face980 face990 edges edge4793 edge4795 vertices
vertex4419 vertex4421
face link face990 face1000 edges edge4795 edge4797 vertices
vertex4421 vertex4423
face link face1000 face1010 edges edge4797 edge4799 vertices
vertex4423 vertex4425
face link face1010 face1020 edges edge4799 edge4801 vertices
vertex4425 vertex4427
face link face1020 face1030 edges edge4801 edge4803 vertices
vertex4427 vertex4429
face link face1030 face1040 edges edge4803 edge4805 vertices
vertex4429 vertex4431
face link face1040 face1050 edges edge4805 edge4807 vertices
vertex4431 vertex4433
LINKING THE TOP OF THE CHANEL OUTBOXES
face modify face1256 side vertex6322 vertex6321
face modify face1263 side vertex6322 vertex6321
face modify face1260 side vertex6397 vertex6396
92
face link face1256 face1260 edges edge6803 edge6923 vertices
vertex6322 vertex6397
face link face1256 face371 edges edge6774 edge2053 vertices
vertex6292 vertex1955 reverse
face link face371 face375 edges edge2053 edge2336 vertices
vertex1955 vertex2135
face link face1263 face378 edges edge6820 edge2228 vertices
vertex6322 vertex2071 reverse
face link face1263 face1273 edges edge6820 edge6823 vertices
vertex6322 vertex6324
face link face1273 face1283 edges edge6823 edge6826 vertices
vertex6324 vertex6326
face link face1283 face1293 edges edge6826 edge6829 vertices
vertex6326 vertex6328
face link face1293 face1303 edges edge6829 edge6832 vertices
vertex6328 vertex6330
face link face1303 face1313 edges edge6832 edge6835 vertices
vertex6330 vertex6332
face link face1313 face1323 edges edge6835 edge6838 vertices
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face link face1323 face1333 edges edge6838 edge6841 vertices
vertex6334 vertex6336
face link face1333 face1343 edges edge6841 edge6844 vertices
vertex6336 vertex6338
face link face1343 face1353 edges edge6844 edge6847 vertices
vertex6338 vertex6340
face link face1353 face1363 edges edge6847 edge6850 vertices
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face link face1363 face1373 edges edge6850 edge6853 vertices
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face link face1373 face1383 edges edge6853 edge6856 vertices
vertex6344 vertex6346
face link face1383 face1393 edges edge6856 edge6859 vertices
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face link face1393 face1403 edges edge6859 edge6862 vertices
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face link face1265 face1275 edges edge6776 edge6778 vertices
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face link face1275 face1285 edges edge6778 edge6780 vertices
vertex6296 vertex6298
face link face1285 face1295 edges edge6780 edge6782 vertices
vertex6298 vertex6300
face link face1295 face1305 edges edge6782 edge6784 vertices
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face link face1305 face1315 edges edge6784 edge6786 vertices
vertex6302 vertex6304
face link face1315 face1325 edges edge6786 edge6788 vertices
vertex6304 vertex6306
face link face1325 face1335 edges edge6788 edge6790 vertices
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face link face1335 face1345 edges edge6790 edge6792 vertices
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face link face1345 face1355 edges edge6792 edge6794 vertices
vertex6310 vertex6312
93
face link face1355 face1365 edges edge6794 edge6796 vertices
vertex6312 vertex6314
face link face1365 face1375 edges edge6796 edge6798 vertices
vertex6314 vertex6316
face link face1375 face1385 edges edge6798 edge6800 vertices
vertex6316 vertex6318
face link face1385 face1395 edges edge6800 edge6802 vertices
vertex6318 vertex6320
face link face1260 face1270 edges edge6894 edge6896 vertices
vertex6353 vertex6356
face link face1270 face1280 edges edge6896 edge6898 vertices
vertex6356 vertex6359
face link face1280 face1290 edges edge6898 edge6900 vertices
vertex6359 vertex6362
face link face1290 face1300 edges edge6900 edge6902 vertices
vertex6362 vertex6365
face link face1300 face1310 edges edge6902 edge6904 vertices
vertex6365 vertex6368
face link face1310 face1320 edges edge6904 edge6906 vertices
vertex6368 vertex6371
face link face1320 face1330 edges edge6906 edge6908 vertices
vertex6371 vertex6374
face link face1330 face1340 edges edge6908 edge6910 vertices
vertex6374 vertex6377
face link face1340 face1350 edges edge6910 edge6912 vertices
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face link face1350 face1360 edges edge6912 edge6914 vertices
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face link face1360 face1370 edges edge6914 edge6916 vertices
vertex6383 vertex6386
face link face1370 face1380 edges edge6916 edge6918 vertices
vertex6386 vertex6389
face link face1380 face1390 edges edge6918 edge6920 vertices
vertex6389 vertex6392
face link face1390 face1400 edges edge6920 edge6922 vertices
vertex6392 vertex6395
LINKING THE BOTTOM OF THE CHANEL OUTBOXES
face link face375 face385 edges edge2440 edge2443 vertices
vertex2251 vertex2253
face link face385 face395 edges edge2443 edge2446 vertices
vertex2253 vertex2255
face link face395 face405 edges edge2446 edge2449 vertices
vertex2255 vertex2257
face link face405 face415 edges edge2449 edge2452 vertices
vertex2257 vertex2259
face link face415 face425 edges edge2452 edge2455 vertices
vertex2259 vertex2261
face link face425 face435 edges edge2455 edge2458 vertices
vertex2261 vertex2263
face link face435 face445 edges edge2458 edge2461 vertices
vertex2263 vertex2265
face link face445 face455 edges edge2461 edge2464 vertices
vertex2265 vertex2267
face link face455 face465 edges edge2464 edge2467 vertices
94
vertex2267 vertex2269
face link face465 face475 edges edge2467 edge2470 vertices
vertex2269 vertex2271
face link face475 face485 edges edge2470 edge2473 vertices
vertex2271 vertex2273
face link face485 face495 edges edge2473 edge2476 vertices
vertex2273 vertex2275
face link face495 face505 edges edge2476 edge2479 vertices
vertex2275 vertex2277
face link face505 face515 edges edge2479 edge2482 vertices
vertex2277 vertex2279
face link face378 face388 edges edge2245 edge2248 vertices
vertex2135 vertex2141
face link face388 face398 edges edge2248 edge2251 vertices
vertex2141 vertex2147
face link face398 face408 edges edge2251 edge2254 vertices
vertex2147 vertex2153
face link face408 face418 edges edge2254 edge2257 vertices
vertex2153 vertex2159
face link face418 face428 edges edge2257 edge2260 vertices
vertex2159 vertex2165
face link face428 face438 edges edge2260 edge2263 vertices
vertex2165 vertex2171
face link face438 face448 edges edge2263 edge2266 vertices
vertex2171 vertex2177
face link face448 face458 edges edge2266 edge2269 vertices
vertex2177 vertex2183
face link face458 face468 edges edge2269 edge2272 vertices
vertex2183 vertex2189
face link face468 face478 edges edge2272 edge2275 vertices
vertex2189 vertex2195
face link face478 face488 edges edge2275 edge2278 vertices
vertex2195 vertex2201
face link face488 face498 edges edge2278 edge2281 vertices
vertex2201 vertex2207
face link face498 face508 edges edge2281 edge2284 vertices
vertex2207 vertex2213
face link face508 face518 edges edge2284 edge2287 vertices
vertex2213 vertex2219
face link face371 face380 edges edge2185 edge2188 vertices
vertex2071 vertex2073
face link face380 face390 edges edge2188 edge2191 vertices
vertex2073 vertex2075
face link face390 face400 edges edge2191 edge2194 vertices
vertex2075 vertex2077
face link face400 face410 edges edge2194 edge2197 vertices
vertex2077 vertex2079
face link face410 face420 edges edge2197 edge2200 vertices
vertex2079 vertex2081
face link face420 face430 edges edge2200 edge2203 vertices
vertex2081 vertex2083
face link face430 face440 edges edge2203 edge2206 vertices
vertex2083 vertex2085
face link face440 face450 edges edge2206 edge2209 vertices
vertex2085 vertex2087
face link face450 face460 edges edge2209 edge2212 vertices
95
vertex2087 vertex2089
face link face460 face470 edges edge2212 edge2215 vertices
vertex2089 vertex2091
face link face470 face480 edges edge2215 edge2218 vertices
vertex2091 vertex2093
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vertex2093 vertex2095
face link face490 face500 edges edge2221 edge2224 vertices
vertex2095 vertex2097
face link face500 face510 edges edge2224 edge2227 vertices
vertex2097 vertex2099
TOP SIDE BOX beginning of channel
face link face1649 face1633 edges edge97 edge3533 vertices
vertex4374 vertex3162 reverse
TOP SIDE BOXES
face link face1650 face1651 edges edge4749 edge4751 vertices
vertex4376 vertex4378
face link face1652 face1653 edges edge4753 edge4755 vertices
vertex4380 vertex4382
face link face1653 face1654 edges edge4755 edge4757 vertices
vertex4382 vertex4384
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vertex4384 vertex4386
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vertex4386 vertex4388
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vertex4388 vertex4390
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vertex4390 vertex4392
face link face1657 face1658 edges edge4765 edge4767 vertices
vertex4392 vertex4394
face link face1658 face1659 edges edge4767 edge4769 vertices
vertex4394 vertex4396
face link face1659 face1660 edges edge4769 edge4771 vertices
vertex4396 vertex4398
face link face1660 face1661 edges edge4771 edge4773 vertices
vertex4398 vertex4400
face link face1661 face1662 edges edge4773 edge4775 vertices
vertex4400 vertex4402
face link face1650 face1634 edges edge4900 edge8036 vertices
vertex4481 vertex3464 reverse
face link face1634 face1635 edges edge8036 edge8037 vertices
vertex3464 vertex3466
face link face1635 face1636 edges edge8037 edge8038 vertices
vertex3466 vertex3468
face link face1636 face1637 edges edge8038 edge8039 vertices
vertex3468 vertex3470
face link face1637 face1638 edges edge8039 edge8040 vertices
vertex3470 vertex3472
face link face1638 face1639 edges edge8040 edge8041 vertices
vertex3472 vertex3474
face link face1639 face6 edges edge8041 edge8042 vertices
96
vertex3474 vertex3476
face link face6 face1640 edges edge8042 edge8043 vertices
vertex3476 vertex3478
face link face1640 face1641 edges edge8043 edge8044 vertices
vertex3478 vertex3480
face link face1641 face1642 edges edge8044 edge8045 vertices
vertex3480 vertex3482
face link face1642 face1643 edges edge8045 edge8046 vertices
vertex3482 vertex3484
face link face1643 face1644 edges edge8046 edge8047 vertices
vertex3484 vertex3486
face link face1644 face1645 edges edge8047 edge8048 vertices
vertex3486 vertex3488
face link face1645 face1646 edges edge8048 edge8049 vertices
vertex3488 vertex3490
face link face1651 face1652 edges edge4751 edge4753 vertices
vertex4378 vertex4380
TOP SIDE BOX END OF CHANNEL
face link face1647 face1663 edges edge8050 edge99 vertices
vertex7433 vertex7435 reverse
TOP SIDE BOX BACK OF CHANNEL
face link face1648 face1664 edges edge12 edge8069 vertices
vertex8 vertex84 reverse
BOTTOM SIDE BOX
face link face1665 face1681 edges edge6773 edge2048 vertices
vertex6291 vertex1950 reverse
face link face1680 face1696 edges edge8071 edge8105 vertices
vertex7436 vertex7438 reverse
face link face1666 face1667 edges edge6894 edge6896 vertices
vertex6397 vertex6399
face link face1667 face1668 edges edge6896 edge6898 vertices
vertex6399 vertex6401
face link face1668 face1669 edges edge6898 edge6900 vertices
vertex6401 vertex6403
face link face1669 face1670 edges edge6900 edge6902 vertices
vertex6403 vertex6405
face link face1670 face1671 edges edge6902 edge6904 vertices
vertex6405 vertex6407
face link face1671 face209 edges edge6904 edge6906 vertices
vertex6407 vertex6409
face link face209 face1672 edges edge6906 edge6908 vertices
vertex6409 vertex6411
face link face1672 face1673 edges edge6908 edge6910 vertices
vertex6411 vertex6413
face link face1673 face1674 edges edge6910 edge6912 vertices
vertex6413 vertex6415
face link face1674 face1675 edges edge6912 edge6914 vertices
vertex6415 vertex6417
face link face1675 face1676 edges edge6914 edge6916 vertices
vertex6417 vertex6419
97
face link face1676 face1677 edges edge6916 edge6918 vertices
vertex6419 vertex6421
face link face1677 face1678 edges edge6918 edge6920 vertices
vertex6421 vertex6423
face link face1666 face1682 edges edge6894 edge8090 vertices
vertex6397 vertex2251 reverse
face link face1682 face1683 edges edge8090 edge8091 vertices
vertex2251 vertex2253
face link face1683 face1684 edges edge8091 edge8092 vertices
vertex2253 vertex2255
face link face1684 face1685 edges edge8092 edge8093 vertices
vertex2255 vertex2257
face link face1685 face1686 edges edge8093 edge8094 vertices
vertex2257 vertex2259
face link face1686 face1687 edges edge8094 edge8095 vertices
vertex2259 vertex2261
face link face1687 face1688 edges edge8095 edge8096 vertices
vertex2261 vertex2263
face link face1688 face1 edges edge8096 edge8097 vertices
vertex2263 vertex2265
face link face1 face1689 edges edge8097 edge8098 vertices
vertex2265 vertex2267
face link face1689 face1690 edges edge8098 edge8099 vertices
vertex2267 vertex2269
face link face1690 face1691 edges edge8099 edge8100 vertices
vertex2269 vertex2271
face link face1691 face1692 edges edge8100 edge8101 vertices
vertex2271 vertex2273
face link face1692 face1693 edges edge8101 edge8102 vertices
vertex2273 vertex2275
face link face1693 face1694 edges edge8102 edge8103 vertices
vertex2275 vertex2277
face link face1679 face1695 edges edge89 edge2227 vertices
vertex6320 vertex2039 reverse
MESHING BEGINS HERE
BOUNDARY LAYERS BEGINS HERE
BOUNDARY LAYER FOR THE bottom of plenum
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer1 face face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
98
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 edge edge97
edge4748 edge106 edge6946 edge6947 edge107 edge4749
edge4750 edge116 edge6972 edge6973 edge117 edge4751
edge4752 edge126 edge6998 edge6999 edge127 edge4753
edge4754 edge136 edge7024 edge7025 edge137 edge4755
edge4756 edge146 edge7050 edge7051 edge147 edge4757
edge4758 edge156 edge7076 edge7077 edge157 edge4759
edge4760 edge166 edge7102 edge7103 edge167 edge4761
edge4762 edge176 edge7128 edge7129 edge177 edge4763
edge4764 edge186 edge7154 edge7155 edge187 edge4765
edge4766 edge196 edge7180 edge7181 edge197 edge4767
edge4768 edge206 edge7206 edge7207 edge207 edge4769
edge4770 edge216 edge7232 edge7233 edge217 edge4771
edge4772 edge226 edge7258 edge7259 edge227 edge4773
edge4774 edge236 edge7284 edge7285 edge237 edge4775
edge4776 edge246 edge7310 edge7311 edge247 edge4777 add
MESHING THE PLENUM
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer2 face face4 face4 face5 face110
face110 edge edge99 edge8069 edge100 edge8052 edge98 add
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer4 face face1649 face1664 face1664
face1664 face1663 edge edge8052 edge98 edge100 edge8069
edge99 add
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer4 face face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face4 face2 face2 face2 face2 face2 face4
face5 face110 face110 edge edge9 edge3398 edge3399
edge3400 edge3401 edge3402 edge3403 edge3404 edge3406
edge3405 edge3407 edge3408 edge3409 edge3415 edge3410
edge3411 edge3412 edge3413 edge3414 edge3416 edge3417
edge3418 edge3419 edge3420 edge3421 edge3422 edge3423
edge3424 edge3425 edge3426 edge3427 edge3428 edge3429
edge3430 edge3431 edge3432 edge3433 edge3434 edge3435
edge3436 edge3437 edge3438 edge3439 edge3440 edge3441
edge3442 edge3443 edge3444 edge3445 edge3446 edge3447
99
edge3448 edge3449 edge3450 edge3451 edge3457 edge3452
edge3453 edge3454 edge3455 edge3456 edge3458 edge3459
edge3460 edge3461 edge3462 edge3463 edge3464 edge3465
edge3466 edge3467 edge3468 edge3469 edge3475 edge3481
edge3470 edge3471 edge3472 edge3473 edge3474 edge3476
edge3477 edge3478 edge3479 edge3480 edge3487 edge11
edge3482 edge3483 edge3484 edge3485 edge3486 edge8051
edge12 edge10 edge8034 add
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer5 face face1663 face1664 face1664
face1664 face1649 edge edge99 edge8069 edge100 edge98
edge8052 add
BOUNDARY LAYER OF THE HOLES
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer1 face face642 edge edge3534 add
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer7 face face117 face1600 edge edge4824
edge110 add
BONDARY LAYER OF THE CHANNEL
TARGET WALL BOUNDARY LAYER
BBBL
BBL
BBL
BBBL
BBL
BBL
BBBLLLLL
blayer create first $firstch growth $growthch rows $rowsch transition 1 trows 0
uniform
blayer attach b_layer8 face face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
100
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face105 face105 face106
face104 face104 edge edge2048 edge2049 edge2050 edge2051
edge2052 edge2053 edge2054 edge2055 edge2056 edge2057
edge2058 edge2059 edge2060 edge2061 edge2062 edge2063
edge2064 edge2065 edge2066 edge2072 edge2067 edge2068
edge2069 edge2070 edge2071 edge2084 edge2078 edge2073
edge2074 edge2075 edge2076 edge2077 edge2079 edge2080
edge2081 edge2082 edge2083 edge2090 edge2096 edge2085
edge2086 edge2087 edge2088 edge2089 edge2091 edge2092
edge2093 edge2094 edge2095 edge2102 edge2108 edge2097
edge2098 edge2099 edge2100 edge2101 edge2103 edge2104
edge2105 edge2106 edge2107 edge2114 edge2120 edge2109
edge2110 edge2111 edge2112 edge2113 edge2115 edge2116
edge2117 edge2118 edge2119 edge2126 edge2132 edge2121
edge2122 edge2123 edge2124 edge2125 edge2127 edge2128
edge2129 edge2130 edge2131 edge2133 edge2134 edge2136
edge2137 edge1 edge2135 edge8088 edge3 edge4 edge8105
edge2 add
blayer create first $firstch growth $growthch rows $rowsch transition 1 trows 0
uniform
blayer attach b_layer9 face face1681 face1696 face1696
face1696 face1695 edge edge2 edge8105 edge4 edge3
edge8088 add
blayer create first $firstch growth $growthch rows $rowsch transition 1 trows 0
uniform
blayer attach b_layer10 face face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face105 face105
face106 face104 face104 edge edge6743 edge101
edge7336 edge7337 edge102 edge6744 edge6745 edge111
edge7373 edge7374 edge112 edge6746 edge6747 edge121
edge7410 edge7411 edge122 edge6748 edge6749 edge131
edge7447 edge7448 edge132 edge6750 edge6751 edge141
edge7484 edge7485 edge142 edge6752 edge6755 edge6753
edge151 edge6754 edge7521 edge7522 edge152 edge161
101
edge6756 edge6757 edge7558 edge7559 edge162 edge171
edge7595 edge7596 edge172 edge6758 edge6759 edge181
edge7632 edge7633 edge182 edge6760 edge6761 edge191
edge7669 edge7670 edge192 edge6762 edge6763 edge6767
edge6765 edge201 edge7706 edge7707 edge202 edge6764
edge211 edge6766 edge7743 edge7744 edge212 edge6769
edge221 edge6768 edge7780 edge7781 edge222 edge6771
edge231 edge6770 edge7817 edge7818 edge232 edge241
edge7854 edge7855 edge242 edge6772 edge89 edge8070
edge91 edge92 edge8087 edge90 add
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer11 face face4 face5 face2 face5
face110 face2 edge edge8 edge8 edge6 edge7 edge7
edge5 add
blayer create first $firstch growth $growthch rows $rowsch transition 1 trows 0
uniform
blayer attach b_layer12 face face106 face104 face103 face105
edge edge87 edge87 edge85 edge88 add
BOUNDARY LAYERS ENDS HERE
edge picklink edge6948 edge6949
edge mesh edge6949 edge6948 successive ratio1 1 intervals $NumbNodes
edge picklink edge6950
edge mesh edge6950 successive ratio1 1 intervals ($NumbNodes2)
face mesh face1450 map
edge picklink edge6963 edge6947
edge mesh edge6947 edge6963 successive ratio1 1 intervals ($Numbtelnodes+$rows)
face mesh face912 map
edge picklink edge6961 edge6960 edge7889 edge7890
edge mesh edge7890 edge7889 edge6960 edge6961 successive ratio1 1
intervals ($NumbNodes)
edge picklink edge6959 edge7891
edge mesh edge7891 edge6959 successive ratio1 1 intervals ($NumbNodes2)
face mesh face1452 map
face mesh face1600 face117 map
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer12 face face2 face110 face5 face110
face2 face4 face5 face4 edge edge5 edge5 edge7
edge7 edge6 edge6 edge8 edge8 add
Meshing constants
$NumbNodes=5
$Numbtelnodes=6
$PLobnodes=5
$Chobnodes=5
$Plbenodes=($NumbNodes(4)+$rows)
$plsqnodes=($NumbNodes(3))
102
$Pllsnodes=($NumbNodes+$rows)
$Nojetcells=10
edge picklink edge3686 edge3402
edge mesh edge3686 edge3402 successive ratio1 1 intervals ($PLobnodes)
edge picklink edge6744 edge6864
edge mesh edge6864 edge6744 successive ratio1 1 intervals 5
face link face1260 face375 edges edge6923 edge2440 vertices
vertex6397 vertex2251 reverse
face modify face915 side vertex4479 vertex4480
face mesh face915 face918 face911 map size 1
face mesh face1260 face1263 face1256 map size 1
edge picklink edge8068 edge8053
edge mesh edge8068 edge8053 successive ratio1 1 intervals ($Plbenodes)
edge picklink edge8086 edge8071
edge mesh edge8071 edge8086 successive ratio1 1 intervals ($CHbenodes)
edge delete edge8053 edge8068 keepsettings onlymesh
edge mesh edge8053 edge8068 successive ratio1 1 intervals ($Plbenodes)
edge delete edge8090 keepsettings onlymesh
edge picklink edge8090
edge mesh edge8090 successive ratio1 1 intervals ($plsqnodes)
edge delete edge8054 keepsettings onlymesh
edge picklink edge8054
edge mesh edge8054 successive ratio1 1 intervals ($plsqnodes)
face mesh face1647 face1679 face1678 face1646 face1633
face1665 map
edge delete edge98 edge8087 keepsettings onlymesh
edge picklink edge8087 edge98
edge mesh edge98 successive ratio1 1 intervals ($Pllsnodes)
edge mesh edge8087 successive ratio1 1 intervals ($CHlsnodes)
face mesh face1648 face1680 map
COOPERING ALL THE JETS
volume mesh volume3 cooper source face1600 face1452 face117
face1514 face1512 face115 intervals ($Nojetcells)
volume mesh volume5 cooper source face1456 face1602 face124
face1518 face1520 face122 intervals ($Nojetcells)
volume mesh volume7 cooper source face1460 face1604 face131
face1526 face1524 face129 intervals ($Nojetcells)
volume mesh volume9 cooper source face1464 face1606 face138
face1532 face1530 face136 intervals ($Nojetcells)
volume mesh volume11 cooper source face1468 face1608 face145
face1538 face143 face1536 intervals ($Nojetcells)
volume mesh volume13 cooper source face1472 face1610 face152
face1544 face1542 face150 intervals ($Nojetcells)
volume mesh volume15 cooper source face1476 face1612 face159
face1550 face1548 face157 intervals ($Nojetcells)
volume mesh volume17 cooper source face1480 face1614 face166
face1556 face1554 face164 intervals ($Nojetcells)
volume mesh volume19 cooper source face1484 face1616 face173
face1562 face171 face1560 intervals ($Nojetcells)
volume mesh volume21 cooper source face1488 face1618 face180
face1568 face1566 face178 intervals ($Nojetcells)
103
volume mesh volume23 cooper source face1492 face1620 face187
face1574 face1572 face185 intervals ($Nojetcells)
volume mesh volume25 cooper source face1496 face1622 face194
face1578 face1580 face192 intervals ($Nojetcells)
volume mesh volume27 cooper source face1624 face1500 face201
face1586 face1584 face199 intervals ($Nojetcells)
volume mesh volume29 cooper source face1504 face1626 face208
face1592 face1590 face206 intervals ($Nojetcells)
volume mesh volume31 cooper source face1628 face1508 face215
face1596 face1598 face213 intervals ($Nojetcells)
volume mesh volume30 cooper source face1506 face1052 face1594
face1397 intervals ($Nojetcells)
volume mesh volume28 cooper source face1502 face1042 face1588
face1387 intervals ($Nojetcells)
volume mesh volume26 cooper source face1498 face1032 face1582
face1377 intervals ($Nojetcells)
volume mesh volume24 cooper source face1494 face1022 face1576
face1367 intervals ($Nojetcells)
volume mesh volume22 cooper source face1490 face1012 face1570
face1357 intervals ($Nojetcells)
volume mesh volume20 cooper source face1486 face1002 face1564
face1347 intervals ($Nojetcells)
volume mesh volume18 cooper source face1482 face992 face1558
face1337 intervals ($Nojetcells)
volume mesh volume16 cooper source face1478 face982 face1552
face1327 intervals ($Nojetcells)
volume mesh volume14 cooper source face1474 face972 face1546
face1317 intervals ($Nojetcells)
volume mesh volume12 cooper source face1470 face962 face1540
face1307 intervals ($Nojetcells)
volume mesh volume10 cooper source face1466 face952 face1534
face1297 intervals ($Nojetcells)
volume mesh volume8 cooper source face1462 face942 face1528
face1287 intervals ($Nojetcells)
volume mesh volume6 cooper source face1458 face932 face1522
face1277 intervals ($Nojetcells)
volume mesh volume4 cooper source face1454 face922 face1516
face1267 intervals ($Nojetcells)
volume mesh cylinder cooper source face1450 face912 face1510
face1257 intervals ($Nojetcells)
window modify invisible mesh
volume mesh volume34 cooper source face1649 face1650 face1651
face1652 face1653 face1654 face1655 face1664 face1639
face1638 face1637 face1636 face1635 face1634 face1633
face1648 face1610 face1608 face1606 face1604 face1602
face1600 face1472 face962 face1468 face952 face1464
face942 face1460 face932 face1456 face922 face1452
face912 face915 face918 face911 face925 face928
face920 face935 face938 face930 face945 face948
face940 face955 face958 face950 face965 face968
face960 face694 face689 face684 face679 face674
face669 face664 face659 face654 face649 face644
face640 face697 face696 face692 face687 face686
face682 face677 face676 face672 face667 face666
104
face662 face657 face656 face652 face647 face646
face642 face695 face698 face690 face685 face688
face680 face675 face678 face670 face665 face668
face660 face655 face658 face650 face645 face648
face641 face152 face1470 face145 face1466 face138
face1462 face131 face1458 face124 face1454 face117
face1450 face1657 face1658 face1659 face1660 face1661
face1662 face1663 face788 face1656 face1474 face159
face1647 face1646 face1645 face1644 face1643 face1642
face1641 face1640 face1478 face1628 face1626 face1624
face1622 face1620 face1618 face1616 face1614 face1612
face1508 face1052 face1504 face1042 face1500 face1032
face1496 face1022 face1492 face1012 face1488 face1002
face1484 face992 face1480 face982 face1476 face972
face975 face978 face970 face985 face988 face980
face995 face998 face990 face1005 face1008 face1000
face1015 face1018 face1010 face1025 face1028 face1020
face1035 face1038 face1030 face1045 face1048 face1040
face1050 face114 face1058 face774 face769 face764
face759 face754 face749 face744 face739 face734
face729 face724 face719 face714 face709 face704
face699 face777 face776 face772 face767 face766
face762 face757 face756 face752 face747 face746
face742 face737 face736 face732 face727 face726
face722 face717 face716 face712 face707 face706
face702 face779 face784 face787 face775 face778
face770 face765 face768 face760 face755 face758
face750 face745 face748 face740 face735 face738
face730 face725 face728 face720 face715 face718
face710 face705 face708 face700 face782 face786
face785 face6 face780 face1055 face215 face1506
face208 face1502 face201 face1498 face194 face1494
face187 face1490 face180 face1486 face173 face1482
face166 intervals ($Plzdnodes)
volume delete body onlymesh
volume mesh body cooper source face1689 face1690 face1691
face1692 face1693 face1681 face1682 face1683 face1684
face1685 face1686 face1687 face1688 face1696 face1671
face1670 face1669 face1668 face1667 face1666 face1665
face1677 face1676 face1675 face1674 face1673 face1672
face1680 face199 face1584 face1377 face192 face1578
face1367 face185 face1572 face1357 face178 face1566
face1347 face171 face1560 face1337 face164 face1554
face1327 face157 face1548 face1317 face150 face1542
face1307 face143 face1536 face1297 face136 face1530
face1287 face129 face1524 face1277 face122 face1518
face1267 face115 face1512 face1257 face1380 face1383
face1375 face1370 face1373 face1365 face1360 face1363
face1355 face1350 face1353 face1345 face1340 face1343
face1335 face1330 face1333 face1325 face1320 face1323
face1315 face1310 face1313 face1305 face1300 face1303
face1295 face1290 face1293 face1285 face1280 face1283
face1275 face1270 face1273 face1265 face1260 face1263
face1256 face209 face374 face370 face384 face379
face394 face389 face404 face399 face414 face409
105
face424 face419 face434 face429 face444 face439
face454 face449 face464 face459 face474 face469
face484 face479 face494 face489 face377 face376
face372 face387 face386 face382 face397 face396
face392 face407 face406 face402 face417 face416
face412 face427 face426 face422 face437 face436
face432 face447 face446 face442 face457 face456
face452 face467 face466 face462 face477 face476
face472 face487 face486 face482 face497 face496
face492 face375 face378 face371 face385 face388
face380 face395 face398 face390 face405 face408
face400 face415 face418 face410 face425 face428
face420 face435 face438 face430 face445 face448
face440 face455 face458 face450 face465 face468
face460 face475 face478 face470 face485 face488
face480 face495 face498 face490 face1 face1586
face1582 face1580 face1576 face1574 face1570 face1568
face1564 face1562 face1558 face1556 face1552 face1550
face1546 face1544 face1540 face1538 face1534 face1532
face1528 face1526 face1522 face1520 face1516 face1514
face1510 face1403 face518 face1588 face1592 face1594
face1694 face1695 face1598 face1679 face1678 face515
face516 face510 face500 face508 face505 face213
face1596 face1397 face206 face1590 face1387 face517
face514 face512 face502 face506 face507 face509
face499 face504 face1400 face1395 face1385 face1390
face1393 intervals ($Chzdnodes)
BOUNDARY CONDITIONS
physics create Symmetry btype SYMMETRY face face2 face103
face211 face204 face197 face190 face183 face176
face169 face162 face155 face148 face141 face134
face127 face120 face112
physics create Wall btype SYMMETRY face face110 face5 face1649
face1664 face918 face915 face911 face925 face1650
face928 face920 face935 face938 face930 face1652
face1651 face948 face945 face940 face1653 face1654
face958 face955 face950 face1655 face965 face968
face960 face978 face975 face970 face1656 face114
face985 face988 face980 face995 face998 face990
face1657 face1005 face1008 face1000 face1658 face1015
face1018 face1010 face1659 face1028 face1025 face1020
face1035 face1660 face1038 face1030 face1045 face1661
face1048 face1040 face1055 face1662 face1058 face1050
face1663 face4 face1395 face1679 face1403 face1400
face1680 face1385 face1678 face1393 face1390 face1375
face1677 face1383 face1380 face1676 face1365 face1373
face1370 face1675 face1355 face1363 face1360 face1674
face1345 face1353 face1350 face1673 face1335 face1343
face1340 face1672 face1325 face1333 face1330 face209
face1315 face1323 face1320 face1671 face1305 face1313
face1310 face1670 face1295 face1303 face1300 face1669
106
face1285 face1293 face1290 face1668 face1275 face1283
face1280 face1667 face1265 face1273 face1270 face1666
face1256 face1263 face1260 face1665 face214 face91
face207 face85 face200 face79 face193 face73 face186
face67 face179 face61 face172 face55 face165 face49
face158 face43 face151 face37 face144 face31 face137
face25 face130 face19 face123 face13 face116 face8
physics modify Wall btype WALL face face110 face5 face1649
face1664 face918 face915 face911 face925 face1650
face928 face920 face935 face938 face930 face1652
face1651 face948 face945 face940 face1653 face1654
face958 face955 face950 face1655 face965 face968
face960 face978 face975 face970 face1656 face114
face985 face988 face980 face995 face998 face990
face1657 face1005 face1008 face1000 face1658 face1015
face1018 face1010 face1659 face1028 face1025 face1020
face1035 face1660 face1038 face1030 face1045 face1661
face1048 face1040 face1055 face1662 face1058 face1050
face1663 face4 face1395 face1679 face1403 face1400
face1680 face1385 face1678 face1393 face1390 face1375
face1677 face1383 face1380 face1676 face1365 face1373
face1370 face1675 face1355 face1363 face1360 face1674
face1345 face1353 face1350 face1673 face1335 face1343
face1340 face1672 face1325 face1333 face1330 face209
face1315 face1323 face1320 face1671 face1305 face1313
face1310 face1670 face1295 face1303 face1300 face1669
face1285 face1293 face1290 face1668 face1275 face1283
face1280 face1667 face1265 face1273 face1270 face1666
face1256 face1263 face1260 face1665 face214 face91
face207 face85 face200 face79 face193 face73 face186
face67 face179 face61 face172 face55 face165 face49
face158 face43 face151 face37 face144 face31 face137
face25 face130 face19 face123 face13 face116 face8
physics create Heat Fluxes btype WALL face face104 face106
face370 face379 face389 face372 face382 face392
face371 face380 face390 face378 face388 face398
face376 face386 face396 face374 face384 face394
face377 face387 face397 face375 face385 face395
face1681 face1682 face1683 face1684 face1696 face402
face412 face422 face432 face442 face400 face410
face420 face430 face440 face408 face418 face428
face438 face448 face406 face416 face426 face436
face446 face404 face414 face424 face434 face444
face407 face417 face427 face437 face447 face405
face415 face425 face435 face445 face1688 face1685
face1686 face1687 face452 face462 face472 face482
face492 face1693 face450 face460 face470 face480
face490 face1692 face458 face468 face478 face488
face498 face1 face456 face466 face476 face486 face496
face454 face464 face474 face484 face494 face457
face467 face477 face487 face497 face1691 face455
face465 face475 face485 face495 face1689 face1690
face518 face502 face512 face1695 face500 face510
face1694 face508 face506 face516 face504 face514
face507 face517 face515 face505
physics create Mass flow inlet btype SYMMETRY face face640 face649
107
face659 face642 face652 face662 face672 face641
face650 face660 face670 face648 face658 face668
face678 face646 face656 face666 face676 face644
face654 face664 face674 face647 face657 face667
face677 face645 face655 face665 face675 face1633
face1634 face1635 face1636 face1637 face1648 face679
face689 face699 face682 face692 face702 face712
face680 face690 face700 face710 face688 face698
face708 face718 face6 face686 face696 face706 face716
face684 face694 face704 face714 face687 face697
face707 face717 face685 face695 face705 face715
face1640 face1638 face1639 face719 face729 face739
face749 face722 face732 face742 face752 face762
face720 face730 face740 face750 face760 face728
face738 face748 face758 face768 face726 face736
face746 face756 face766 face724 face734 face744
face754 face764 face727 face737 face747 face757
face767 face725 face735 face745 face755 face765
face1645 face1641 face1642 face1643 face1644 face788
face769 face779 face772 face782 face770 face780
face778 face776 face786 face774 face784 face777
face787 face775 face785 face1647 face1646
physics create Outflow btype OUTFLOW face face105
108
REFERENCES
Al-Aqal O M A 2003 ldquoHeat transfer distributions on the walls of a narrow channel
with jet impingement and cross flowrdquo PhD Thesis University of Pittsburgh
Bunker Ronald S 2007 Gas Turbine Heat Transfer Ten Remaining Hot Gas Path
Challengesrdquo Journal of Turbomachinery April Vol 129 pp 193-201
Downs James P Landis Kenneth K 2009 ldquoTurbine Cooling Systems Design- Past
Present and Futurerdquo Proceedings of ASME Turbo Expo 2009 June 8-12 2009
GT2009-59991
Florschuetz LW Berry R A Metzger D E 1980 ldquoPeriodic streamswise variations of
heat transfer coefficients for inline and staggered arrays of circular jets with cross
flow of spent airrdquo ASME J of Heat Transfer 102 p 132-137
Florschuetz L W Truman C R Metzger D E 1981 ldquoStreamwise Flow and Heat
Transfer Distributions for Jet Array Impingement with Cross flowrdquo Journal of
Heat Transfer Vol 103 pp 337
Florschuetz L W Isoda Y 1983 ldquoFlow Distributions and Discharge Coefficient for
Jet Array Impingement With Initial Cross flowrdquo Journal of Engineering for
Power Vol 105 pp 296
Incropera Frank P DeWitt D P 2002 Fundamentals of Heat and Mass Transfer John
Wiley amp Sons Inc New Jersey pp 491-493
Liu Quan Kapat J May 2006 ldquoStudy of Heat Transfer Characteristics of Impinging
Air Jet Using Pressure and Temperature Sensitive Luminescent Paintrdquo UCF
Dissertation
109
Martin H 1977 ldquoImpinging jet flow heat and mass transferrdquo Advances in heat transfer
Vol 13
Ricklick Mark Kapat J December 2009 ldquoCharacterization of an Inline Row
Impingement Channel for Turbine Blade Cooling Applicationsrdquo UCF
Dissertation
Zuckerman N Lior N 2005 ldquoImpingement Heat transfer Correlations and Numerical
Modelingrdquo Journal of Heat Transfer Vol 127 pp 544
iv
ACKNOWLEDGEMENTS
I would like to acknowledge my mentor and advisor Dr Jay Kapat for all his
support and encouragement I would also like to thank my committee members Dr Ali
Gordon and Dr Weiwei Deng
I would also like to give a million thanks to Perry Johnson Lucky Tran Bryan
Bernier and William Clark for their help with the CFD portion of this study and for
letting me run on their computers Special thanks go to Mark Ricklick for helping me
throughout this project To everyone at CATER Mark Miller Michelle Valantino
Jimmy Kullberg Greg Natsui Michael Torrance Jeff Nguyen Nghia Tran Abhishek
Saha Kaylee Dorman Matt Golsen and everyone else that were once caterers a big thank
you for making these two years of work at the lab unforgettable
v
TABLE OF CONTENTS
ABSTRACT ii
ACKNOWLEDGEMENTS iv
LIST OF FIGURES vii
NOMENCLATURE ix
CHAPTER ONE INTRODUCTION 1
11 Gas Turbine as a Heat Engine 1
12 Cooling of Hot Components 2
CHAPTER TWO LITERATURE REVIEW 9
21 Impingement Literature Cornerstone 9
22 Relevant Impingement Channel Studies 11
23 Computational Studies on Impingement Channels 12
CHAPTER THREE EXPERIMENTAL SETUP AND TECHNIQUES 15
31 Temperature Measurements with TSP 15
32 Experimental Setup of Suction Channel 21
33 Data Processing and Reduction 24
34 Uncertainty Analysis 27
35 Lateral Conduction Analysis 28
CHAPTER FOUR HEAT TRANSFER RESULTS 32
vi
41 Heat Transfer Validation 32
42 Heat Transfer Results 33
43 XD Comparisons 40
44 3D Comparison of the Heat Transfer Profiles 45
45 Thermal Performance Calculations 48
CHAPTER FIVE COMPUTATIONAL FLUID DYNAMICS 52
51 Problem Setup 52
52 CFD Results 58
CHAPTER SIX CONCLUSIONS 63
APPENDICES 64
Appendix A 64
Appendix B 66
REFERENCES 108
vii
LIST OF FIGURES
Figure 1 Brayton Cycle Flow Path and T-s Diagram (Adapted from UPTB Website) 1
Figure 2 Thermal Loading Throughout a Turbine Blade (Daniels 1982) 3
Figure 3 Allowable Turbine Inlet Temperature vs Cooling Techniques over the Years
(Clifford 1985) 4
Figure 4 Turbine Inlet Temperature Increase with the help of TBC New Super Alloys
and Cooling Technologies (Kapat and Kiesow Lectures 2010) 4
Figure 5 Turbine Stator Cooled with Impingement Coupled with Film Cooling
(Florschuetz 1980) 5
Figure 6 Rotor Blade Cooling Configuration (Gladden 1988) 6
Figure 7 Cross-section of Turbine Airfoil with Cooling Channels (Han et al 1984) 6
Figure 8 Relative Temperatures for Hot Gas Metal Temperature and Coolant
Temperature (Cardwell 2005) 7
Figure 9 (a) The Development of the Wall Jet (b) Jet Diffusion to Surroundings (Liu
2006) 8
Figure 10 Simplified Jablonski Diagram (Adapted from ISSI Website) 17
Figure 11 Heater Strips Painted with TSP Too Closely 21
Figure 12 Flow Loop of Impingement Channel 22
Figure 13 Top View of Jet Plate 22
Figure 14 Front View of Impingement Channel 23
Figure 15 Target Wall Test Section with Heater Leads 23
Figure 16 Heat Transfer Coefficient Uncertainty Tree 27
viii
Figure 17 Temperature Profile of First Five Impingement Rows 29
Figure 18 Detailed View of First Heat Transfer Peak with a Polynomial Curve Fit 30
Figure 19 Control Volume Heat Transfer Analysis 30
Figure 20 Heat Loss through Convection and Lateral Conduction 31
Figure 21 Validation Spanwise Averaged Results 32
Figure 22 Target Wall Heat Transfer Coefficient Distributions 34
Figure 23 Span-averaged Target Wall Heat Transfer Distribution 35
Figure 24 Side Wall Heat Transfer Coefficient Distributions 36
Figure 25 Span-averaged Side wall Heat Transfer Distribution 37
Figure 26 XD=15 Target Wall Heat Transfer Profile 41
Figure 27 XD=15 Span-averaged Target Wall Heat Transfer Distribution 42
Figure 28 Target Wall Span-average Comparison of XD=5 and 15 at High Re 43
Figure 29 Side Wall Heat transfer Coefficient Profile 44
Figure 30 XD=15 Side Wall Span-averaged Heat Transfer Coefficients 45
Figure 31 3D Heat Transfer Profile for ZD=6 XD=5 46
Figure 32 3D Heat Transfer Profile for ZD=8 XD=5 47
Figure 33 3D Heat Transfer Profile for ZD=6 XD=15 48
Figure 34 Pressure Drop Ratio with Respect to Smooth Channel 49
Figure 35 Heat Transfer Enhancement 50
Figure 36 Thermal Performance at Constant Pressure Drop 50
Figure 37 Thermal Performance at Constant Pumping Power 51
Figure 38 Horizontal Plane of Impingement Channel Geometry 53
Figure 39 Target Side and Front End Wall y+ Values 54
ix
Figure 40 Finished Mesh with Boundary Conditions 55
Figure 41 Grid Independence Study 57
Figure 42 Residual Plots for the 26M Cell Run 57
Figure 43 Total Pressure Contours 58
Figure 44 Velocity Magnitude Contours 59
Figure 45 Turbulent Kinetic Energy Contours 60
Figure 46 Static Temperature Contours 60
Figure 47 Target and Side Wall Heat Transfer Coefficient Contours 61
Figure 48 Closer View of First few Rows of Impingement HTC Contours 61
Figure 49 Pathlines Generating from the First Row of Jets 62
NOMENCLATURE
Cross Sectional Area
Heater Surface Area (m2)
Specific Heat at Constant Pressure (kJkgK)
D Jet Diameter (m)
Channel Hydraulic Diameter (m)
Friction Factor
Heat Transfer Coefficient (HTC) (Wm2K)
Average Heat Transfer Coefficient (Wm2K)
Channel Length (m)
Mass Flow Rate (kgs)
Static Pressure (kPa)
x
Total Pressure (kPa)
Pr Prandtl Number
Heat Flux (Wm2)
Total Heat Input (W)
Heater Resistance (ohm)
Re Reynolds Number
SW Side Wall
Temperature (K)
TW Target Wall
Voltage Potential
Streamwise Location
y Spanwise Location
z Height from Target Wall
X Streamwise Distance (m)
Y Spanwise Distance (m)
Z Impingement Height (m)
Thermal Performance Parameter
Ratio of Specific Heats
Air Density (kgm3)
Subscripts
C Cold
H Hot
xi
Carnot Describing a Carnot cycle
Exit
Effective
Quantity Lost to the Environment
Reference Value
Wall Value
Base Line Value
1
CHAPTER ONE INTRODUCTION
11 Gas Turbine as a Heat Engine
Gas turbine is a form of heat engine where the hot reservoir is created by the
combustion of fuel and the cold reservoir is the open atmosphere It is well known that
the maximum efficiency of any heat engine is denoted as the Carnot efficiency
A more accurate cycle is used to describe the processes inside a gas turbine ndash the
Brayton Cycle The Brayton cycle as seen in Figure 1 is composed of four processes In
a gas turbine air is drawn in at state 1 it is compressed until it reaches state 2 The
compressed air is mixed with fuel and ignited as it passes through the combustor The hot
air then passes through the turbines where work is extracted The process from state 4 to
state 1 happens throughout the atmosphere therefore the Brayton cycle is an open loop
cycle as the same air is not continuously being fed through the motor
Figure 1 Brayton Cycle Flow Path and T-s Diagram (Adapted from UPTB Website)
The Brayton cycle has an isentropic efficiency similar to the carnot the Brayton
cycle efficiency is defined as
2
It can be seen that increasing the temperature at which air enters the first turbine
stage T3 increases the overall efficiency of the turbine Moreover increasing the
pressure ratio Pr also aids in the increase of the efficiency One of the hurdles of
increasing T3 is the fact that the post combustion gas is a few hundred degrees Celsius
above the melting point of the super alloys used to make the turbine stator vanes and
rotor blades For this reason it is important to cool the hot components of the gas turbine
in order to assure a reasonable life for the machine
12 Cooling of Hot Components
The transition duct that connects the combustor to the first stage turbine as well
as the first stage of the turbine are the parts that are subject to the harshest thermal
loadings and must therefore be cooled aggressively to maintain them in working
conditions for a long period of time Since the first stage guide vanes and rotor extrude
into the flow they are subject to the highest convection coefficients These heat transfer
coefficients can reach up to 4000 Wm2K (Downs 2009) Figure 2 shows the different
magnitudes of convection coefficient around the blade High heat transfer coefficients
occur where the air stagnates into the leading edge of the airfoil This high heat transfer
region is not only caused by the lack of a thermal boundary layer to protect the airfoil but
also because the effective heat transfer driving temperature is the recovery temperature
At the high Mach numbers that occur in turbines the ratio of total to static temperatures
is significant causing the leading edge to have the highest effective heat load Another
3
peak occurs on the suction side of the blade as the boundary layer created by the airfoil
switches from being a laminar boundary layer into a turbulent one Due to the nozzling
effect of the turbine rotor and stators the flow gathers speed toward the trailing edge of
the airfoil leading to higher convection coefficients on the pressure side of the airfoil
Figure 2 Thermal Loading Throughout a Turbine Blade (Daniels 1982)
Simple convection channels were implemented in the early nineteen sixties as
years passed the cooling techniques became more and more sophisticated allowing the
free stream temperature to increase to previously impossible levels Currently the use of
film cooling coupled with backside impingement leads the turbine cooling technology
The trend of allowable turbine inlet temperature is shown in Figure 3 from this figure it
can be seen that the allowable free stream temperature has increased around 600 degrees
in the past 50 years The addition of thermal barrier coatings also helps in the increase in
allowable combustion temperatures by creating an extra resistance that the heat needs to
move through as it moves from the combustion gasses into the coolant air It is impotatnt
to notice that as seen in Figure 4 the increase in turbine inlet temperatures is done with
the combined benefits of new alloys TBC and cooling technologies
4
Figure 3 Allowable Turbine Inlet Temperature vs Cooling Techniques over the Years (Clifford 1985)
Figure 4 Turbine Inlet Temperature Increase with the help of TBC New Super Alloys and Cooling
Technologies (Kapat and Kiesow Lectures 2010)
The cooling of inlet guide vanes can be done with the use of impingement inserts
inside the airfoils As air passes through the miniscule holes in the inserts a jet is formed
which then impinges on the wall of the airfoil producing one of the largest single phase
heat transfer coefficients This already impinged coolant air is then bled out as film
5
cooling as well as bled out through the trailing edge Figure 5 shows a stator vane with
the impingement insert in black the film cooling extraction as well as the trailing edge
bleed
Figure 5 Turbine Stator Cooled with Impingement Coupled with Film Cooling (Florschuetz 1980)
The cooling of turbine airfoils with the use of an impingement insert is only
possible in stationary components as the rotating ones are subject to centrifugal loadings
making it unfeasible to cool them with this setup Rotor blades are typically cooled with
serpentine passages that have heat transfer enhancing features such as ribs dimples and
other turbulators these serpentine passages are located in the mid chord of the blade On
the trailing edge a bank of pins are used to obtain high convective coefficients in the thin
region the coolant is the bled out to compensate for the boundary layer created around
the airfoil Rows of impingement holes cool the leading edge The spent air is then bled
out through showerhead cooling Figure 6 and Figure 7 show in detail the cooling
channels around two similar airfoils airfoils
6
Figure 6 Rotor Blade Cooling Configuration (Gladden 1988)
Figure 7 Cross-section of Turbine Airfoil with Cooling Channels (Han et al 1984)
7
The coolant air is bled out from the later stages of the compressor This air is
expensive as it has been compressed and not under gown the heat addition by
combustion It is imperative that the minimum amount of coolant is used in these cooling
configurations The cooling must also be as uniform as possible to reduce thermal
stresses within the blades leading to a higher component life Figure 8 shows freestream
metal and coolant temperatures of the flow blade and coolant air It can be seen that a
decrease of 25degrees in the surface temperature of the blade can provide an airfoil with
twice the working life Impingement cooling has great potential to provide high heat
transfer coefficients at a small flow rate Impingement of a jet onto a surface provides
high heat transfer coefficients due to a starting boundary layer as well as its high
turbulence When the jet is located around 3 diameters from the target surface the heat
transfer profile has two peaks one located at the stagnation region and the other located
between one and 3 diameters from the stagnation region As the jet is moved away from
the target wall the secondary peak diminishes leaving a profile with a maximum at the
stagnation region decreasing radialy
Figure 8 Relative Temperatures for Hot Gas Metal Temperature and Coolant Temperature (Cardwell 2005)
Cardwell N D 2005
8
Figure 9 shows a diagram of a jet impinging on a target surface The potential
core is the part of the jet that has not been affected by the surrounding stagnant fluid As
the jet moves towards the target wall its momentum diffuses into the surrounding fluid
decreasing the velocity at which it reaches the target wall and potentially decreasing the
corresponding heat transfer coefficient Studies have shown (Martin 1973 for example)
that the potential core may last anywhere between 7 to 10 diameters The successful
impingement of the potential core yields significantly higher heat transfer coefficients
than a fully diffused jet this comes however at a cost of higher pressure drop across the
jet plate as well as a highly non uniform heat transfer profile
Figure 9 (a) The Development of the Wall Jet (b) Jet Diffusion to Surroundings (Liu 2006)
9
CHAPTER TWO LITERATURE REVIEW
21 Impingement Literature Cornerstone
From the early days of simple convective cooling channels in turbine airfoils
studies have been done on modes of enhancing heat transfer coefficients while
maintaining a low pressure drop and minimum mass flow rate Heat transfer
characteristics of single round nozzle impingement were studied in the late 1960rsquos and
early 1970rsquos The collected works of many authors is combined into ldquoHeat and Mass
Transfer between Impinging Gas Jets and Solid Surfacesrdquo by Holger Martin 1977 The
paper collects works from multiple authors who studied single round nozzle impingement
effects on heat and mass transfer coefficients In this compilation non dimensional jet to
target spacing was studied they ranged from ZD=12-10 providing plots of Sherwood
number as a function of radius for four different jet to target spacings The local
Sherwood number was also given for a slot jet for HS ranging from 5 to 20 Studies on
impingement jet arrays were also gathered alongside an array of slot jets Correlations
were given for multiple setups present in the paper Circular jet arrays and slot arrays are
studied in detail with both analytical and experimental approaches The paper also
combines studies done on swirling jets turbulence enhancers on the target surface
impingement on concave surfaces and angle of attack variations Optimization studies
were also done to find the optimal spacing for round and slot jet arrays
Florschuetz studied the heat transfer characteristics of an array of jets impinging
on a flat surface This study was guided towards finding an optimal spacing for an array
for jets used to cool the midchord of turbine airfoils similar to that found in Figure 5 His
main contributions include a Nusselt number correlation as a function of jet to target
10
spacing jet Reynolds number and other flow and geometric parameters He found that an
increase in hole spacing and channel height resulted in a decrease of heat transfer He
also provided a one dimensional jet mass flux and channel mass flux correlations
His Nusselt number correlation takes the form of
Where A B and n are dependent by the two different types of arrays inline or staggered
Liu studied new techniques in temperature and pressure measurements of a single
slot jet with the use of temperature sensitive paint or TSP and pressure sensitive paint or
PSP In his work both measurement techniques are explained in detail Since TSP is the
only tool from that study currently used in this work it will be explained further in the
experimental setup section
11
22 Relevant Impingement Channel Studies
Al-Aqal 2003 studied three different types of impingement channels The use of
TLC was implemented in this work to obtain heat transfer distributions for the target
wall The three different configurations varied the number of holes in the streamwise and
spanwise directions The first channel had a single row of 6 streamwise jets the second
consisted of 2 rows of 12 streamwise holes summing up to a total of 24 holes The last
channel is a triple spanwise row with 18 streamwise jets This last geometry is the most
similar to the one present in the current study The third geometry will be used to
compare results There are differences however the total width of the channel is of 16
diameters as opposed to 8 in this study The streamwise jet spacing is also different Al-
Aqal used an XD of 65 compared to XD = 5 in this study The jet to target plate
spacings are similar on two occasions as he studied a ZD=4 6 and 8 while this work
uses a ZD = 6 8 and 10 Average jet Reynolds numbers also fall within the range of this
study as they range between 5000 and 33000 The author provides span averaged plots
for all cases and Reynolds numbers convenient when comparing the results
Ricklick 2009 studied a channel similar to the one found in this study His
channel was composed of a single row of 15 jets with a YcD = 4 XD = 5 and 15 and
ZD = 1 3 and 5 Two channels were tested one was pressure fed while the other was fed
by suction TSP was used to gather temperature data of all four wetted surfaces on the
pressure channel and two surfaces on the suction channel Since the maximum jet Mach
number was less than 03 the flow was assumed to be incompressible leading to the
conclusion that both channels contain identical flow patterns Thin foil heaters were used
to create the required heat flux for the channel Besides channel geometry Reynolds
12
numbers and heater geometry Ricklicksrsquo experimental setup is identical to the one
presented in this work The author also provided an ample comparison of his results to
literature He provided thermal performances of the entire channel at different Reynolds
numbers and channel heights
A small CFD study was also done A paved mesh was created on the target wall
with finer mesh near the impingement locations The resulting y+ at the wall was higher
than one yielding potentially faulty heat transfer values however this is acceptable since
the CFD was used as a tool to better understand the flow physics and help understand the
experimental heat transfer profiles
23 Computational Studies on Impingement Channels
El-Gabry did a numerical study of jet impingement with cross flow Two different
turbulence models were compared in their ability to predict surface Nusselt number The
Yang-Shih and standard k-ε models were used to compute the flow generated by jets
angled at 30 60 and 90 degrees with cross flow The computational results were
compared to previous experimental work by El-Gabry Comparisons to experimental
results at ZD = 1 and 2 90deg injection angle between Yang-Shih and standard k-ε The
error in the average Nu from the experimental results and both turbulence models were
calculated It was found that the Yang-Shih model behaved well at low Reynolds
numbers with the average Nusselt number being 5 off from the experimental value
while the standard k-ε was off my 94 As jet Reynolds number was increased the error
of the standard k-ε model dropped to as low as 39 while the error from the Yang-shih
model increased to -76 The span average plots show the experimental data Nusselt
number alongside the span averages of the results acquired by the Yang-Shih and
13
standard k-ε models High Nusselt numbers occur at the impingement location decreasing
thereafter after another impingement location is found The frequencies of these
variations are all the same for the experimental and the two numerical solutions The
amplitude of fluctuations between the impingement locations and the areas in between
are much larger for both of the numerical results however the Yang-Shih model over
predicts at the high Reynolds number for the ZD=2 case Since the amplitude of
fluctuations is greater for the CFD solutions it is important to note that even though the
error in average Nusselt number is not great the actual differences in the profile are much
greater upwards of 20 difference of heat transfer coefficients between the experimental
and numerical heat transfer peaks Other variations were studied (Injection angles for
example) but will not be discussed as their importance to the current study is minimal
Zuckerman compared a much wider set of turbulence models in their ability to
successfully predict Nusselt numbers caused by jet impingement The models tested were
k ndash ε k-ω Reynolds Stress Model algebraic stress models shear stress transport and
lastly the υ2f turbulence model DNS runs are extremely time consuming to run
therefore LES was run on its behalf to provide results for the unsteady turbulence
models The paper summarizes all the different models used their computational cost
impingement heat transfer coefficient and their ability to predict the second peak in heat
transfer As expected DNSLES provide the best prediction of both stagnation and
secondary peak heat transfer coefficient however this comes at a large computational
cost The k ndash ε and k-ω provide poor heat transfer results for the stagnation region where
they can have 30 error from the correct value The Realizable k ndash ε model provides
14
better heat transfer results while still maintaining a low computational cost The highest
accuracy to cost ratio was achieved by the υ2f model where it predicts the heat transfer
coefficient for the surface with a minimum of 2 error while not being as expensive as
the other unsteady models such as DNS and LES Ideally the CFD portion of this work
would be run with the υ2f model however since the code used to run the simulation
FLUENT does not have the υ2f model a realizable k ndash ε model will be used with
enhanced wall functions for both thermal and velocity gradients
15
CHAPTER THREE EXPERIMENTAL SETUP AND TECHNIQUES
31 Temperature Measurements with TSP
Temperature sensitive paint or TSP provides the capability of measuring
temperatures over the painted area This measurement technique supersedes the
advantages of other temperature measurement devices such as thermocouples because it
provides the user with data over a large area rather than point temperatures given by
thermocouples
Uni-Coat TSP is purchased from ISSI It is very robust to different working
conditions Calibration done on one batch of paint can be used for multiple cans as the
product is highly consistent The paint is calibrated in a dark booth a painted coupon is
placed on the hot side of a thermoelectric heat pump working on the Peltier effect
thermal paste is used to minimize contact resistance between the hot side and the TSP
coupon Calibrated thermocouples are placed in between the TSP and the thermoelectric
heat pump A reference temperature and picture are taken and the calibration commences
At least 5 or 6 data points should be taken to form the calibration Intensity ratios are
taken between the hot and cold pictures They are then plotted versus their corresponding
temperature
The paint consists of fluorescent molecules suspended in a binder These
molecules with a certain wavelength of light will be exited to a higher energy level The
molecules then can dissipate some of the energy by transferring it vibrationally to its
neighboring binder particles and dissipate the remainder of the energy by radiating it as a
photon as the molecule comes down to its original ground state Since the amount of
16
energy that the particle can transmit to others through vibration is directly proportional on
temperature and the total initial energy is fixed by measuring the ratio of the intensity at
a known temperature (reference picture) and intensity of the unknown temperature
feeding it through the correlation the unknown temperature can be found to an
uncertainty of 1 K Figure 10 shows a simplified Jablonski diagram adapted from the
suppliers website The blue arrows signify the blue light used to excite the luminescent
molecule Tris(22rsquo-bipyridyl) Ruthenium(II) Chloride Hexahydrate with a shellac binder
in our case The shellac binder is impermeable to oxygen opposite of that found in PSP
due to PSP relying on the presence of oxygen for it to function Once the particle is
excited it can give off the energy in two different ways one is by emitting it back out as
another photon of the same energy and therefore wavelength The second mode of the
particle to lose its energy is through vibrational relaxation This second process is directly
dependent on the temperature ie the higher the temperature the higher the probability
for it to lose energy to its surroundings Once it loses some energy to the surrounding
particles it releases the remainder of the energy as a photon of less energy of that which
excited it originally hence why a long pass filter is installed in the CCD camera For a
more descriptive explanation of the way TSP works refer to Liu 2006
17
Figure 10 Simplified Jablonski Diagram (Adapted from ISSI Website)
Throughout the past two years there have been numerous projects at CATER that
have used TSP Painting surfaces with TSP should be done carefully by someone who
has experience with spray painting since every single can costs $500 A single can should
be able to paint an area the size of an acrylic plate that is 36rdquo wide and 24rdquotallThe
sidewalls and the target wall of the impingement channel were painted with the use of
less than one can Painting on different surfaces is difficult for example when painting
Rohacell the paint canister can be held very close to the surface while spraying due to
the surface being somewhat porous and rough however when painting straight onto
metal heater strips the can should be placed as far back as possible for the first run
Ideally for the first pass through only a slight mist should be applied If the can is being
held too close to the surface the paint will run Figure 11 shows a set of heater strips that
has been painted too closely leading the paint to drip down Ideally the paint would be
applied to the surface in as many coats as possible Of course this would be time
18
demanding and impractical therefore with the knowledge that I have gained through the
multiple TSP paintings on different surfaces I have compiled a list of TSP dos and
donrsquots
Dos
Clean the surface to be painted with acetone or break parts cleaner Break
parts cleaner is preferable over acetone as it does not leave an oily residual
after cleaning
Paint the first coat as thin as possible Most of the surface should not be
covered There should be an even mist of miniscule TSP circles This will
give the later coats something to attach to
When positioning the test section to paint make sure to wipe it one last
time as small dust particles may have attached to the surface
Stop if you see small bumps in the paint This is caused by dust particles
collecting all the paint around it while it is still wet due to surface tension
Clean the surface and repaint This should be noticeable in the first few
coats If you see this pattern happening do not continue thinking it will be
covered by future coats What will happen is the problem will get worse
and worse ultimately the surface will have to be cleaned again and
repainted
When painting test sections try to paint the smallest section as possible
This will not only save paint but will make it very simple for the post
processing code to crop out the unpainted areas
19
Let the finished painted surface to sit at least for 90 minutes after the last
coat before baking There have been problems when baking steel and
acrylic test sections with the paint cracking while baking right after the
last coat Normally the finished surface is left to dry overnight and baked
first thing in the morning
For test sections that are too large to be baked in the oven the heat gun
may be used Carefully place a thermocouple in a central location with
blue painters tape The heating should be uniform and should not take
more than 20 minutes of continuous blowing When the thermocouple
reaches 80-90 C the plate can be assumed to be baked To introduce a
factor of safety in the baking it does not hurt to bake it longer than it
normally takes
Once the test section is mounted and ready to run cover it with cloth that
does not let any light through This will protect the paint for further uses
This is especially important on test sections that can be used multiple
times like the ones found in this study
When the test is running turn off the LED lights This light is the most
damaging to the TSP as it degrades the quality of the fluorescent
molecules
If there is a particular head of the TSP can that you prefer over others you
can remove it once the can is empty It is difficult to get used to a single
kind of nozzle being able to transfer it from can to can is a must if
painting consistency is to be kept
20
Donrsquots
Do not clean a test section that has already been used with too much
acetone The acetone is volatile evaporating quickly cooling the test
section rapidly If this test section has had heaters attached to it and run
previously the acrylic will crack due to uneven stresses inside of it
If paint is dripping stop painting immediately Clean the surface and start
over Hold the can far from the surface in order for it not to drip
Do not use TSP to teach new apprentices undergrads or graduate students
how to paint Regular spray paint is two orders of magnitude lower in cost
while the painting process is exactly the same
Do not paint with the doors closed The paint contains carcinogens that
can harm the lungs Always use a respirator and keep the room well
ventilated In-situ painting and baking has not been tried however it may
be a real option if the test section is difficult to disassemble and easily
accessible to painting and baking
If there is a can of paint that contains too little paint for the test section
that needs to be painted try to find a new can The mixing of two different
cans of TSP can be dangerous at times however it has been noticed over
the years that ISSI provides a very robust and dependable product that
does not vary significantly from batch to batch
21
Figure 11 Heater Strips Painted with TSP Too Closely
32 Experimental Setup of Suction Channel
The impingement channel is fed under suction As seen in Figure 12 air enters
through the plenum it crosses the jet plate as it gains speed to form the jets
which then impinge on the target wall The flow then passes through a venturi
flow meter and finally through the blower into the atmosphere A bypass valve is
used to control the flow rate of the impingement channel
22
Figure 12 Flow Loop of Impingement Channel
The impingement channel consists of 15 streamwise rows of 3 spanwise jets each The
total width of the channel YcD is of 8 diameters while the streamwise spacing between
the rows is XD=5 the spanwise distance between the holes is of YD=2 Figure 13shows
the top view of the jet plate The plate is counter bored to ensure that a nearly flat
velocity profile of the jet is achieved Figure 14 shows the front view of the channel Z is
denoted as the distance between the jet and target plates Side walls are interchangeable
to change the height of the channel to 6 8 and 10 diameters Two thirds of the
streamwise rows can be covered to change the XD from 5 to 15
Figure 13 Top View of Jet Plate
23
Figure 14 Front View of Impingement Channel
The target and sidewalls had heaters made specifically for them in a serpentine
style This was necessary to increase the resistance as the VARIACs used to power them
only had a maximum current output of 20 amps The heater strips are two diameters
wide at each end copper tape with conductive adhesive was used to connect the leads to
the power supply The heater consists of 50 micron thick steel sheet sandwiched between
two pieces of Kapton tape The heater is attached to the painted surface with the use of
double sided Kapton tape The target test section can be seen in Figure 15 also seen in
this figure are the two Teflon gaskets lined on the sides of the target plate With the target
wall bolted onto the sidewall the gasket is compressed generating a strong seal
Figure 15 Target Wall Test Section with Heater Leads
24
For this study the test matrix shown in Table 1 will be run Target and side wall
data will be taken at three different impingement heights at two different Reynolds
numbers of 7500 and 15000 denoted by A and B respectively A streamwise jet spacing
study is also done by testing the target and side wall heat transfer at an XD=15 for the
low impingement height channel
Table 1 Test Matrix
XD ZD Wall Re
5
10 TW
7500
15000
SW 7500
15000
8 TW
7500
15000
SW 7500
15000
6 TW
7500
15000
SW 7500
15000
15 6 TW
7500
15000
SW 7500
15000
33 Data Processing and Reduction
As described previously when taking temperature measurements with the use of TSP
reference temperatures are noted and a reference picture is taken The experiment is the
run once the experiment reaches steady state a new set of 4 pictures is taken Given the
calibration curve temperatures are backed out
25
Given the amount of heat generated inside the heater
Dividing by the heated area to get heat flux
Heat loss tests were run to consider how much of the heat flux generated by the heaters
goes through the backside instead of into the flow It was found that 25 of the heat flux
leaks out to the atmosphere through the acrylic In order to account for this heat leakage
it must be subtracted from the calculated value to become
Where Ah is the effective heated area given by
Where Aunheated is an estimate of how much unheated area is between the heater strips (~
3 of the total area)
To obtain heat transfer coefficient
Where Tref is the reference temperature Typically set in literature to be the jet
temperature
To obtain the average Reynolds number for the jets the total mass flow rate is used
Where Dj is the jet diameter and μ is dynamic viscosity (1983kgm s at 300K)
26
Pressure measurements were taken at the sidewall after the last jet entered the channel
These pressure measurements were used to determine the thermal performance of the
tallest two channels (ZD = 8 and 10)
The thermal performance at constant pumping power is found by using the equation
Where h is the average heat transfer coefficient for the target wall of them impingement
channel and ho is the heat transfer coefficient obtained by passing the same amount of
flow through a smooth duct ie the Dittus-Boelter correlation The friction factor f is
found with the use of
Where Ppl is the plenum static pressure assumed to be atmospheric and Plast jet is
the pressure read after the last jet V is the volumetric flow rate divided by the cross-
sectional area of the duct after the last impingement row The hydraulic diameter of the
channel is set to be
The baseline friction factor was calculated with the use of the Moody chart the hydraulic
diameter and the total mass flow rate though the channel Thermal performance at
constant pressure drop was also calculated with
27
34 Uncertainty Analysis
A simple uncertainty analysis was done to estimate the error in calculation of the
heat transfer coefficient from the given outputs of the test data From the bare basic
measurements for voltage area current temperature of thermocouples and temperature
profiles of paint a simple uncertainty analysis can be done to estimate the error for the
calculated heat transfer coefficient Figure 16 shows the different sources of error in the
calculation of heat transfer coefficient The effective uncertainty was calculated by taking
the root of the sum of the squares of all the individual percentage errors The
experimental uncertainty for heat transfer coefficient was of 703 This error may be
reduced by acquiring higher temperatures of the TSP reading current with a more
accurate ammeter or reading reference temperatures with the use of a thermopile instead
of a single thermocouple
Figure 16 Heat Transfer Coefficient Uncertainty Tree
28
35 Lateral Conduction Analysis
To take into account the lateral conduction occurring inside the heater foil while
the test is running two simple 1D conduction and convection equations were used to
quantify the amount of heat moving through the heater laterally and the amount of heat
convecting into the air The lateral conduction is expected to be at a maximum at the
places where there are large spatial variations of surface temperature which is why the
ZD = 6 XD = 5 case at high Re is chosen to be studied Figure 17 shows the
temperature distribution of the aforementioned case Four cold spots can be seen by their
distinct blue and yellow color located at the stagnation regions The maximum
temperature gradient occurs between the third jet impingement and the middle region
between jets The temperature difference was seen to be of 13degC The distance in between
these two temperatures is of 25D=01875m The corresponding heat flux between these
two points was calculated to be 13000Wm2 with ksteel~20Wm K A region of 1cm by
1cm was then created and the amount of heat calculated through conduction and
convection were compared To acquire the amount of heat removed through conduction
a heat flux of 13000Wm2 was imposed through an area of 01m by 00005m this
equaled to 00277 W The amount of heat moved through convection was calculated by
multiplying the heat flux used during the test by the area of the square 0001m2 the
resulting heat moving through the heater onto the air is 6 W Since the heat moving
through to the air is two orders of magnitudes larger than the heat moving laterally the
effective lateral conduction can be neglected
29
Figure 17 Temperature Profile of First Five Impingement Rows
A second order approach was also taken to quantify the amount of lateral
conduction in the heater The temperature gradient was taken from high peaks in heat
transfer caused by the second row of impingement of the same ZD=6 XD=5 channel at
high Re Figure 18 shows the high heat transfer coefficients created by the second row of
jets A quadratic curve fit was obtained by for this small region so that a continuous
equation of heat transfer coefficients as a function of streamwise distance was quantified
30
Figure 18 Detailed View of First Heat Transfer Peak with a Polynomial Curve Fit
The net heat gained by a differential volume from lateral conduction is the
difference in the temperature gradient at the entrance and the exit multiplied by the
thermal conductivity and cross sectional area Using this method shown in Figure 19 the
net change in convective heat transfer due to lateral conduction can be studied
Figure 19 Control Volume Heat Transfer Analysis
By taking the difference between the out flowing heat trough the right side and
the inflowing heat from the left side a net gain or loss can be found Figure 20 shows the
y = -470630x2 + 31244x - 14842Rsup2 = 09934
300
310
320
330
340
350
360
370
380
0 001 002 003 004 005
HTC
(W
m2K
)
x (m)
Heat Transfer Peak
Poly (Heat Transfer Peak)
31
difference in magnitude between the out flowing heat through convection seen in red and
the net inflow of heat from lateral conduction in blue From these calculations it was also
found that the amount of heat moving through lateral conduction is tow orders of
magnitude smaller than the amount of heat moving out through convection leading to the
belief that even at high temperature gradients lateral conduction does not play an
important role in the ongoing heat transfer processes in the impingement channel A more
detailed calculation of this work can be seen in appendix A
Figure 20 Heat Loss through Convection and Lateral Conduction
002 003 004 0051 10
5
1 104
1 103
001
qconv x( )
qnet x( )
x x
32
CHAPTER FOUR HEAT TRANSFER RESULTS
41 Heat Transfer Validation
In order to obtain confidence in our experimental setup an experiment was made
to test something that has already been published in literature A smooth channel was the
obvious choice as it was easy to setup by taking off the end cap and blocking all the holes
with smooth blue painters tape on the flow side and metal tape on the plenum side to
ensure no leaks into the channel from the jet plate The smooth channel has been studied
widely and multiple correlations exist one of these equations is the Dittus-Boelter
correlation (Incropera 2007) The test was run using the ZD=6 side wall so that the
hydraulic diameter was a minimum Figure 21 shows the span averaged results versus
non dimensional distance into the channel
Figure 21 Validation Spanwise Averaged Results
0
10
20
30
40
50
60
0 1 2 3 4 5 6 7 8 9
HTC
(W
m2K
)
XDc
Span Avg
Dittus Boelter
33
The plot shows decreasing heat transfer coefficient with increasing XDc due to
the developing thermal boundary layer The span average does not reach the Dittus-
Boelter due to it not being fully developed in the limited space it is given Typical flows
can take up to 60 diameters to achieve a fully developed profile with the current setup
the maximum length of the channel was of 9 diameters The profile however seems to
have an asymptote at the Dittus-Boelter correlation value leading to the belief that if the
channel was longer that value given by the correlation would be reached One important
factor to take into account in determining whether the experimental setup is validated is
the fact that the Dittus-Boelter correlation has an uncertainty near 30 Since the span
average at high XDc is well within 30 from the calculated value it is safe to assume
that the current experimental setup is validated
42 Heat Transfer Results
Heat transfer results are compared based on variations in channel height and
average jet Reynolds number As discussed earlier there are numerous other parameters
also affecting the heat transfer in these channels As these parameters are changed flow
structures within the channel are expected to be altered as well as discussed in the
literature Two of the major contributors to heat transfer in these channels are the
successful jet impingement and the resulting cross flow The same domain is captured in
both the local and averaged results
Figure 22 through Figure 25 highlights the heat transfer distribution for the cases
with a jet to jet spacing of 5 diameters in the streamwise direction and of 2 in the
spanwise direction It is evident that the smallest channel height (ZD=6) performs the
best at all Reynolds numbers on all surfaces It is also interesting to note the similarity
34
in the target wall profiles between case 528A and B where the curves are very similar
other than the obvious offset due to the change of the Reynolds number At this large
spacing we also see the degradation of the jets a few diameters downstream of each
impingement location The downstream shifts of the peaks are evident after the second
and third row of jets Also evident in these plots is the deflection of the impinging jet and
the wall jets from the cross flow The cross flow is forced to flow around the jet
deflecting the spread of the wall jet in the downstream direction Impingement locations
are also very evident at low XD however as XD and therefore the cross flow increase
the magnitude of the peaks start decreasing and eventually level out to pure internal flow
Figure 22 Target Wall Heat Transfer Coefficient Distributions
35
Figure 23 Span-averaged Target Wall Heat Transfer Distribution
36
Figure 24 Side Wall Heat Transfer Coefficient Distributions
37
Figure 25 Span-averaged Side wall Heat Transfer Distribution
Figure 23 and Figure 25 show similar details with impingement peaks clearly
diminishing and shifting in the downstream direction The cross flow clearly has some
negative influence on these geometries when compared to the more traditional
impingement highest on the order of 1 to 5 jet diameters The heat transfer profiles of the
target wall for all heights seen in Figure 22 and Figure 24 show the rapid decay in heat
transfer after the third jet This can be explained by understanding that the first jet does
not have any cross flow to deflect it the second jet only has the first jet worth of
momentum deflecting it downstream however since the channel is so tall the
momentum of the cross flow after the first and second jet are not enough to greatly
disturb the incoming jets After the third jet however the cross flow builds up enough
momentum to greatly affect the integrity of the jets downstream causing the span-
0
20
40
60
80
100
120
140
160
2 12 22 32 42 52 62 72
HTC
(W
m2K
)
XD
5210B_SW 528A_SW Jet Location
526A_TW 526B_TW
38
averaged heat transfer to rapidly drop The point at which the crossflow starts taking a
considerable effect occurs around XD =35 The target wall profile of the ZD=10
channel shows the outside jets on the second row of jet deflecting downstream It can be
conjectured that the bending of the outside jets downstream is caused by the wall jet
created by the first row of jets separating from the side wall and deflecting the outside
jets of the following rows of jets The heat transfer profile for the ZD case excludes the
first jet due to shadows being present when the data was taken
Also evident from this spanwise averaged data is the increase in heat transfer
with increases in Reynolds numbers and decreases in impingement height Results tend
to be the closest from case to case at the first impingement jet This is a reasonable
result as the effects of cross flow have little to no effect at the first few impingement
locations The impact of the jet would then be the driving force at these locations and
would be similar between cases except if the potential core is not reaching the target
surface The potential core of a jet tends to last between 6 and 10 diameters from its
origin It can be seen that the difference in heat transfer coefficient in the first two jets for
the ZD=8 and ZD=10 channel is much different than the corresponding difference
between the ZD=6 and ZD=8 heights This decreased difference between the heights of
the peaks may be attributed to the potential core reaching the target wall at the heights of
6 and 8 diameters leading to similar profiles and may not be reaching the surface at the
height of 10 diameters The heat transfer values of the peaks diminish in the downstream
direction The range of fluctuation also drops that is the profile becomes more uniform
at large XD This drop in fluctuation is more visible at the tallest channel height
(ZD=10) and less pronounced at the smallest channel This is due to the jet in the small
39
channel having to travel a shorter distance to impinge on the target plate leaving the
crossflow less time for it to deflect the jet as opposed to the tall channel where the jet has
to travel almost twice the distance as the ZD=6 channel for it to impinge on the target
wall This effect cannot be solely explained by the built up cross flow in the channel
Mixing loses also take part in the degradation of the stagnation size of the downstream
jets The mixing losses have much greater effect on the taller channels due to the same
reason that the cross flow has a higher impact on them too the jets have to travel a large
distance before hitting the target plate leading the stagnant or moving surrounding air to
be a sink of its downward momentum for a longer time and distance than the respective
smaller channels The heat transfer coefficient of the side wall was also analyzed
Similar effects are expected on the side wall due to the expected impact of the wall jet
As expected the strength of the cross flow is not enough to prevent wall jets from
successfully impacting the side wall at small XD jet locations however the crossflow
takes dominance at around XD=25 Also evident in these plots is the concentration of the
wall jet impact to the bottom of the channel on the order of 1-2 diameters in height It is
interesting to note that for the 5210B case in Figure 24 as the first jet diffuses outward
it impacts the sidewall at a height of ZD=6 The height at which the diffused jet affects
the sidewall heat transfer coefficient decreases as the crossflow increases The stagnation
regions are also deflected in the downstream direction similar to the target surface
results These effects are most evident in the 5210B Similar characteristics can be
explained from the spanwise-averaged plots shown in Figure 25 These results again
clearly show the effects of increasing the impingement height and increases in Reynolds
number As the height is increased the effect of the wall jet is significantly reduced
40
partially due to the increased surface area much of which is not affected by the wall jet
The diminishing effect of the cross flow accumulation is also evident in these plots as the
heat transfer peaks decrease in the downstream direction
43 XD Comparisons
The streamwise jet spacing was changed from XD=5 to 15 by covering two out
of three rows of jets This was done by covering the impingement holes inside the
channel with smooth blue painters tape and sealing the plenum side of the jet plate with
metal tape to ensure no leakage The profile is expected to be less uniform than the case
where XD=5 due to the large spreading of the high heat transfer peaks Due to the large
separation between the rows of jets there is a lower amount of downward momentum
than the equivalent XD=5 geometry for this reason it is expected to see a lower heat
transfer peak due to the jets momentum diffusing out faster to the stagnant air decreasing
the effective impingement velocity Figure 26 shows the target wall heat transfer
distribution Similar to the XD=5 profile it can be seen that the heat transfer due to the
jet impingement drastically reduces after the third jet This phenomenon leads us to
believe that at both Reynolds numbers the cross flow generated by the first three jets is
powerful enough to effectively deflect the fourth jet downstream diminishing its heat
transfer performance The similarity seen in Figure 26 between high and low Reynolds
number implies that the downstream deflection of the jets is not dependent on the jet
Reynolds numbers
41
Figure 26 XD=15 Target Wall Heat Transfer Profile
42
Figure 27 XD=15 Span-averaged Target Wall Heat Transfer Distribution
On the span averaged plots seen in Figure 27 the downstream deflection of the
jets is evident however as described previously the shifts in the peaks of heat transfer
occur at the same xD for both Reynolds numbers The amplitude of fluctuation of heat
transfer coefficients for the high Reynolds number case is larger than that of the low
Reynolds number Both profiles seem to start to level off at the end of the impingement
channel with the lowest span average being located just before the fourth jet at both
Reynolds numbers
A comparison of target wall heat transfer coefficients between XD =15 and 5 is
shown in Figure 28 At first glance it is clearly visible that the XD=15 average heat
transfer coefficient is smaller than its XD=5 counterpart This is also noticed by Ricklick
where he showed average HTC profiles for larger XD to be smaller than those at lower
XD (Ricklick 2009) This may occur due to there not being as high downward
0
50
100
150
200
250
300
350
0 20 40 60 80
HTC
(W
m2
K)
XD
Low Re
High Re
Impingement Location
43
momentum for the XD=15 case as compared to the XD=5 due to the lack of close jets
The stagnant air around the spaced out jets is taking away more of its momentum
decreasing the effective impingement Reynolds number Also important to notice is the
fact that since the XD=5 case has three times the flow impinged into it the cross flow
velocity and therefore Reynolds number will be three times as large increasing the heat
transfer coefficient
Figure 28 Target Wall Span-average Comparison of XD=5 and 15 at High Re
The side walls also show similar patterns to their XD=15 counterparts Strong
wall jet impingement can be seen on the side wall at low xD and zD Figure 29 shows
areas where the wall jet generated by the target wall impinges on the sidewall Similar to
the profile seen in Figure 24 the high heat transfer region reaches upward in the z
direction up to a height of 4-5 diameters for the first jet This high heat transfer stagnation
region decreases as xD increases to the point where the wall jet created by the last jet is
negligible when coupled with pure channel flow
0
50
100
150
200
250
300
350
400
0 10 20 30 40 50 60 70 80
HTC
(W
m2K
)
XD
XD = 5 XD = 15 Jet Location
- Blocked for XD =15
44
Figure 29 Side Wall Heat transfer Coefficient Profile
The span averaged plot seen in Figure 30 shows a nearly flat profile with peaks
located at the stagnation regions of the wall jets Thw downstream deflection for the
XD=15 case is much more pronounced than the one for the XD=5 case This is due to
the jet not being constrained by the wall jets generated by the previous and latter
impingement locations In the XD=15 case the wall jet is free to move downstream
more so than the XD=5 due to it not being disturbed by anything other than the cross
flow
45
Figure 30 XD=15 Side Wall Span-averaged Heat Transfer Coefficients
44 3D Comparison of the Heat Transfer Profiles
In order to further understand the targetsidewall interactions both heat transfer profiles
were positioned in an isometric view representative of the channel One important thing
to note is that both target and side wall profiles are not on the same scale This form of
data display is only qualitative way to describe the heat transfer profiles Figure 31 shows
the 3D profile of the XD=5 ZD=6 case The both stagnation regions of the jet onto the
target wall and the wall jet into the sidewall can be seen to occur at the same location for
the first three streamwise rows After the fourth and fifth row the wall jet diminishes in
magnitude Also visible in this view is the increasing heat transfer at low zD towards the
end of the channel of the side wall The constant input of mass and downward momentum
into the channel causes the cross flow generated by the previous jets to be squeezed into
the lower third of the channel increasing the velocity and the heat transfer of the target
wall
0
20
40
60
80
100
120
0 20 40 60 80
HTC
(W
m2K
)
XD
Low Re High Re Jet Locations
46
Figure 31 3D Heat Transfer Profile for ZD=6 XD=5
Similar patterns are seen in the taller ZD=8 channel seen in Figure 32 The wall jet
generate by the third streamwise row of jets is been deflected downward more than its
ZD=6 counterpart This can be attributed to the fact that the jet located at the ZD=8
channel has lost much of its momentum and is more easily bent downstream by the cross
flow generated by the first two jets The ZD=8 sidewall shows similar increasing heat
transfer at high xD however the increase is not as drastic as the one found in the ZD=6
channel This is caused due to the extra two diameters the jets have to cover to impinge
on the surface since the ZD=8 channel is one third larger than the ZD=6 one the flow
has to have more area to flow through The last few jets only deflect the cross flow
downward about 4 diameters this leaves two diameters for the flow to pass through on
the ZD=6 channel causing the velocity to increase rapidly and therefore increasing the
heat transfer coefficient at the low zD Since the ZD=8 channel has four remaining
47
diameters for the flow to move through it does not deflect it as much as the ZD=6
channel does only increasing the cross flow velocity and resulting heat transfer
coefficient slightly over the area at low zD and high xD
Figure 32 3D Heat Transfer Profile for ZD=8 XD=5
The 3D heat transfer profile for ZD=6 and xD=15 channel seen in Figure 33 shows
similar details to those seen in the XD=5 channels The stagnation regions of the jet and
wall jet occur at the same x location for the first three rows of jets the wall jet generated
by the fourth row of jets is deflected downstream only generating as small region of high
convective coefficients at the side wall The region located at the top right corner of the
side wall is colored red signifying high heat transfer however this area is generated by
the heaters providing non uniform heat flux at this location This region of high heat
transfer coefficients also occur at xD=0-4 of the target wall where the heater coil bends
48
Figure 33 3D Heat Transfer Profile for ZD=6 XD=15
45 Thermal Performance Calculations
Thermal performance calculations were done on the two tallest channels (ZD=8 and 10)
The pumping power was calculated for both channels at two Reynolds numbers Figure
34 shows the ratio of pressures required to pull the same amount of flow through as
smooth duct as opposed to through the jet plate The ZD=10 channel at high Reynolds
number requires the largest pressure as seen in the Figure however in order to pull the
same amount of flow rate through it requires a smaller pressure difference due to the
large cross section
49
Figure 34 Pressure Drop Ratio with Respect to Smooth Channel
Next the heat transfer enhancement was calculated A total area averaged heat
transfer coefficient was taken for the target wall and compared to the smooth channel
Dittus-Boelter value while using the same total mass flow rate Figure 35 shows an
average heat transfer enhancement of four times that of a smooth channel Similar trends
were noticed in the literature (Ricklick 2009) of decreasing heat transfer enhancement
with an increase of jet Reynolds number Ricklick also showed an increase in heat
transfer enhancement with an increase of jet to target spacing similar to the one seen in
Figure 35
0
10
20
30
40
50
60
528A_TW 528B_TW 5210A_TW 5210B_TW
PP
o
50
Figure 35 Heat Transfer Enhancement
Thermal performances at constant pressure drop were then calculated by dividing
the heat transfer enhancement by the pressure increase As seen in Figure 36 all the
values fall well below 1 making the impingement channel an unfeasible mode of heat
transfer enhancement when a constant pressure is supplied
Figure 36 Thermal Performance at Constant Pressure Drop
0
05
1
15
2
25
3
35
4
45
528A_TW 528B_TW 5210A_TW 5210B_TW
hh
o
0
002
004
006
008
01
012
014
528A_TW 528B_TW 5210A_TW 5210B_TW
(hh
o)
(PP
o)
51
The thermal performance at constant pumping drop was calculated in the same
way that the constant pressure drop was calculated the only difference being the pressure
ratio term was raised to the one third power As seen in Figure 37 the thermal
performances at constant pumping power are all higher than unity this signifies that if a
surface needs to be cooled with the supply of a constant pumping power the
impingement channel is a feasible option Similar to the figure literature (Ricklick 2009)
showed a decrease of thermal performance with an increase of channel height and
Reynolds number
Figure 37 Thermal Performance at Constant Pumping Power
0
02
04
06
08
1
12
14
528A_TW 528B_TW 5210A_TW 5210B_TW
(hh
o)
(PP
o)1
3
52
CHAPTER FIVE COMPUTATIONAL FLUID DYNAMICS
51 Problem Setup
In order to further enhance the understanding of the heat transfer profiles showed
previously a computational study was performed Even though CFD does not yield
accurate quantitative results it produces good qualitative data that can be used to explain
the flow physics in the channel and therefore increase the understanding of the patterns
seen previously The channel was meshed with the use of GAMBIT Due to the
symmetry the channel was split in half in the streamwise direction All horizontal
surfaces (parallel to the target wall) were divided into 6 different regions that are later on
going to be meshed individually The six regions are seen in Figure 38 section 1 is
located at the center of every jet also referred to as ldquojet centerrdquo This region was created
to reduce the squewness of the elements near the center of the jet by allowing the mesh to
be completely linear with a squewness of zero Section two complements section 1 to
complete the impingement hole The half impingement hole located at the symmetry wall
contains the same exact region 2 however it only has one half of the jet center Section 3
was made in order to bring the polar geometry of the holes to match the cartesian aspect
of the remainder of the channel With the addition of section 3 to the channel the only
remaining sections are square or rectangular regions Region 4 lies in between
streamwise rows of jets Section 5 is located at the entrance and the exit of the channel
These sections are not square in contrast with section 4 The last remaining section is
located near the side wall of the channel extending from the beginning to the exit of the
channel
53
Figure 38 Horizontal Plane of Impingement Channel Geometry
All the faces of sections 1 and 2 are linked throughout the channel and the
plenum however in order to have greater control of the mesh in the plenum and the
channel the remaining sections 3 4 5 and 6 are not linked to every single similar face
instead they are only linked to similar faces in either the plenum or the channel
Boundary layer spacing number of rows and growth factor are placed around the
channel In order to maintain a y+ of less than unity the first cell spacing of the boundary
layer inside the channel was set to be 000001 m (01mm) This first cell spacing yielded
y+
values varying between zero and 9 at the target side and front end wall Figure 39
shows a contour of y+ values on the heated walls The maximum values occur near the
impingement locations as expected due to large shear caused by the steep velocity
gradient normal to the wall On the downstream direction the y+ also increases due to the
increase of flow rate and therefore the increased skin friction on the wall At the
impingement location of the first jet the y+ is close to zero due to the velocity having its
direction mostly normal to the surface yielding no shear
54
Figure 39 Target Side and Front End Wall y+ Values
Once the faces were linked edge meshes were created on the sides of the jet center
Section 2rsquos inner edge was also meshed using a different parameter than the one used for
the jet center in order to allow for more freedom when trying to refine the mesh These
two edge meshes is followed by meshing all of section 2 faces alongside all the jet
centers Once these were complete section 3rsquos inner edge was meshed with different
parameters for the channel and plenum Sections 4 and 5 sides that connected with the
face made by section 6 were meshed so that their spacing was similar again the plenum
and channel were meshed separately for increased control of mesh density in both of
these areas The upstream-most edge of section 6 was meshed so that the spacing is
similar to the edge mesh in sections 4 and 5 this was done in order to have aspect ratios
of the wall be as close as possible to unity Sections 3 4 5 and 6 were meshed on both
the channel and the plenum With the entire target wall plane meshed these surface
meshes are coopered upwards to connect to the opposite wall The vertical spacing has
55
also been set up differently between the channel and the plenum The holes and the
plenum were also coopered The finished mesh was then exported as a msh file
Boundary conditions were set in GAMBIT once the mesh was imported into
Fluent values were set to every face depending on their location and purpose Figure 40
shows the four different boundary conditions Face 1 (blue) was set to be a mass flow
inlet The flow rate is half of the total flow rate at a given jet Reynolds number due to it
being only half of the entire domain Face 2 (yellow) is a symmetry plane face 3 (red) is
a pressure outlet at zero gauge pressure The rest of the faces in the channel denoted by
the number 4 (white) are set to walls The target side and front end wall had a heat flux
applied to them equal to 10000Wm2
Figure 40 Finished Mesh with Boundary Conditions
The model was imported into Fluent It was scaled down by a factor of 1000 due to it
being made in GAMBIT in millimeters The energy model was turned on The Realizable
k-ε model was used with enhanced wall functions on both the pressure and thermal
gradients The boundary conditions were set as discussed previously the mass flow inlet
was set to the specific flow rate normal to the surface the heat fluxes were set on the
56
heated walls the outflow gauge pressure was set to zero Two important reference values
characteristic length and reference temperature were set to be the diameter of the jet
(0075m) and 300K respectively The spatial discretization parameters were set to second
order upwind for momentum turbulent kinetic energy turbulent dissipation rate and
energy The under-relaxation factors were set to default Four monitors were created to
aid in the determination of convergence two of them read Nusselt numbers at the
stagnation region of the first and last jet the remaining two read the exit velocity at the
first and last jet The continuity x y and x velocities and energy equations residuals
were set to be 1E-6 while k and ε residuals were set to 1E-4 The solution was initialized
on the all zones at 1ms in the positive x direction The solution was set to autosave every
100 iterations while keeping only the two newest dat files The calculation was then run
for a maximum of 7000 iterations
A grid independence study was done on the domain to find the optimal size of
mesh that provides the correct solution while minimizing the compute time Two
monitors were set to check for grid independence both of them were vertex maximum
One of them read the Nusselt number at the impingement location of the first center jet
while the second one measures the velocity at the exit of the last jet Four different mesh
sizes were run to the convergence criterion explained before their sizes were 900000
15 million 28 million and 43 million cells
57
Figure 41 Grid Independence Study
It can be seen in Figure 41 that the difference between the 28 and 43 million cell
meshes are very small a difference of under 006 for velocity and 7 for Nusselt
number It can be safe to assume that the 28 million cell mesh is large enough to provide
a mesh independent solution The GAMBIT journal file used to create this mesh is
attached to the appendix The results shown hereafter are the ones obtained by the 28
million cell mesh
Figure 42 Residual Plots for the 26M Cell Run
67
69
71
73
75
77
79
81
83
85
485
4855
486
4865
487
4875
488
4885
489
0 1 2 3 4 5
Nu
sse
lt N
um
be
r
Cell Ammount (Millions)
Grid Independence Study
Velocity
Nusselt Number
58
For future reference Figure 42 shows the residuals of the 26M cell calculation
Up until around 4400 iterations the residuals were increasing shortly thereafter the
residuals started decreasing until it converged just after 5500 iterations All runs for the
differently sized meshes had the same residual patters with the peak of residuals and
point of convergence happening at different iterations
52 CFD Results
As describe previously all the results shown here are for the mesh containing 28 million
elements Figure 43 shows the total pressure contours It can be seen that the plenum
portion is at a constant total pressure Once the jets form since there are very small losses
in the jets due to the wall friction the total pressure still remains constant Only when the
jets enter the channel and start mixing with the cross flow is that they start losing the total
pressure head It is important to notice how the first two jets have the total pressure close
to the plenum arriving at the target wall This implies a successful impingement of the
undisturbed potential core As we move downstream the total pressure is lost quite
rapidly as the jets interact with the cross flow
Figure 43 Total Pressure Contours
59
Similar details can be drawn out from Figure 44 it can be seen that the first three
jets successfully impinge on the target wall while the rest of the downstream ones are
deflected by the cross flow As mentioned by Ricklick the velocity magnitude of the last
jet is larger than that of the first jet due to there being a lower static pressure at the end of
the channel providing it with a steeper pressure gradient hence higher velocity
Figure 44 Velocity Magnitude Contours
Turbulent kinetic energy was plotted in Figure 45 it is expected to have the
highest turbulent kinetic energy near the exit of the holes where the stagnant air is in
contact with the fast moving jet The mixing between the two regimes causes very
energetic eddies to form potentially enhancing the target and side wall heat transfer
coefficient As cross flow builds up towards the end of the channel the turbulent kinetic
energy increases due to larger overall velocities and fluctuations between the cross flow
and jets
60
Figure 45 Turbulent Kinetic Energy Contours
As Ricklick showed in his work the static temperature rise is quite small for such a small
channel It can be seen in Figure 46 that the driving temperature for heat transfer is that of
the plenum It is important to notice that a wall heat flux of 10000 Wm2 was used as the
boundary condition Not even in the most powerful tests would we ever use heat fluxes
that high they normally range between 2500 to a maximum of 7000 Wm2 A heat flux of
10000 Wm2 will increase the temperature at a faster rate than what it is normally used in
experimental testing
Figure 46 Static Temperature Contours
61
Figure 47 Target and Side Wall Heat Transfer Coefficient Contours
Figure 47 shows the target and sidewall heat transfer profiles Peaks can be seen at the
first three locations similar to that seen in Figure 22 The trend decreases rapidly to
eventually become a slowly increasing heat transfer profile due to the increase of mass
flow through the channel The sidewall provides the same results clear peaks in heat
transfer where the wall jets impinge on the sidewall seen in Figure 48 in more detail The
sidewall also shows a recirculation zone in between the first row of jets and the end wall
This is caused by the wall jet from the first row hitting the back wall moving upwards in
a circular pattern and coming back down when it encounters the first impingement row
Figure 48 Closer View of First few Rows of Impingement HTC Contours
62
Figure 49 Pathlines Generating from the First Row of Jets
Figure 49 helps explain the low heat transfer region between the first row of jets and
the end wall Pathlines are generated at the exit of each hole in the first row As the
air impinges on the surface half of it moves downstream and the other half movers
upstream to this recirculation zone where it circulates for a period of time before
reuniting with the remainder of the flow to move downstream The wall jet that
moves towards the second row of jets encounters the wall jet created by the second
row of jets causing the pathlines to drastically move upwards On the side of the
channel the pathlines behave erratically with no clear pattern clearly signifying the
highly turbulent and chaotic flow structure of this impingement channel
63
CHAPTER SIX CONCLUSIONS
It has been seen from this analysis that the side walls provide significant heat
transfer in an impingement channel especially at the relatively smaller channel
height This is primarily the result of successful impact of the wall jet with the side
walls It was shown that the tallest channel (ZD=10) has the most uniform profile with
low heat transfer coefficients when compared to the other channels The peaks of the
ZD=6 and 8 channels have a very similar profile which may indicate the successful
impingement of the potential core of the jet on the target surface As XD increases the
peaks diminish and a positive slope profile is attained by the increase of cross flow
velocity as more and more jets are introduced Tall impingement channels provide the
user with a heat transfer profile that is more uniform than those provided with the use of a
smaller channel while still maintaining higher convective coefficients when compared to
a smooth flow scenario The downstream shift of the wall jets is found to be independent
of Reynolds number and heavily dependent on streamwise position It was also found that
at XD=15 the wall jets decay faster than their XD=5 counterparts From the 3D heat
transfer profiles it was seen that the cross flow generated by multiple upstream jets is
deflected downward decreasing its effective flow area increasing its velocity hence
providing higher convective coefficients at the side wall at high xD and low zD
64
APPENDICES
Appendix A
Lateral Conduction Consideration
Thickness of foil heater Heat flux
Sample volume width
Volumetric heat generation
Volume of sample volume
Temperature profile from the first row of impingement ONLY valid for 02ltxlt045
t 50m k 20W
m K qflux 6000
W
m2
1mm
V 2
t qvol
qflux
t
T x( ) 298Kqflux
470630 x2
31244x 14842 W
m2K
N 15
x 02045 02
N 102 047
002 003 004 005314
315
316
317
318
319
320
T x( )
x
A t
qnet x( ) A kxT x
m
d
d xT x( )
d
d
1
m
002 003 004 0050
5 105
1 104
15 104
2 104
qnet x( )
x
65
Now comparing the net heat gained by lateral conduction to heat generated and convected out
It can be seen that the lateral conduction into the sample volume is two orders of magnitude smaller than the heat removed by convection
qgen qvol V 6 103
W
qconv x( ) 2
qflux qnet x( )
002 003 004 0051 10
5
1 104
1 103
001
qconv x( )
qnet x( )
x x
66
Appendix B
This is the journal file run on gambit to generate the geometry faces links
boundary layer face and volume meshes as well as the boundary conditions
set diameter
$d=75
$zc=6($d)
$xc=80($d)
$yc=4($d)
$y=2($d)
$x=5($d)
$zp=5($d)
$ztot=($zc)+($d)+($zp)
$jcf=(13)
$ocf=2
Boundary layer constants
$first=01
$growth=12
$rows=4
Meshing constants
$NumbNodes=5
$Numbtelnodes=6
$PLobnodes=5
$Chobnodes=5
$Plbenodes=($NumbNodes(4)+$rows)
$plsqnodes=($NumbNodes(3))
$Pllsnodes=($NumbNodes+$rows)
$Nojetcells=10
$Chzdnodes=($zc$Nojetcells)($d)
$Plzdnodes=($zp$Nojetcells)($d)
Boundary layer constants for channel
$firstch=001
$growthch=12
$rowsch=8
$CHbenodes=($NumbNodes(4)+$rowsch)
$CHlsnodes=($NumbNodes+$rowsch)
volume create body width ($xc) depth ($yc) height ($ztot) offset ($xc2) ($yc2) ($ztot2) brick
volume create cylinder height ($ztot) radius1 ($d2) radius3 ($d2) offset ($x) 0 ($ztot2) zaxis frustum
volume cmove cylinder multiple 1 offset 0 ($y) 0
volume cmove cylinder volume3 multiple 14 offset ($x) 0 0
volume create jetplate width ($xc) depth ($yc) height ($d)offset ($xc2) ($yc2) ($d2+$zc) brick
volume split body volumes jetplate connected
volume split jetplate volumes cylinder volume3 volume4 volume5
volume6 volume7 volume8 volume9 volume10 volume11
volume12 volume13 volume14 volume15 volume16 volume17
67
volume18 volume19 volume20 volume21 volume22 volume23
volume24 volume25 volume26 volume27 volume28 volume29
volume30 volume31 connected
face create jetcenter width ($jcf$d) height ($jcf$d) offset ($x) 0 0 xyplane rectangle
face create jetcircle radius ($d2) xyplane circle
face move jetcircle offset ($x) 0 0
face create outbox width ($ocf$d) height ($ocf$d) offset ($x) 0 0 xyplane rectangle
face split outbox connected faces jetcircle jetcenter
face split jetcircle connected faces face1
face split outbox connected faces face1
face cmove jetcenter outbox jetcircle face222 face223 multiple 1 offset 0 ($y) 0
face cmove jetcenter outbox jetcircle face222 face223 face224 face225 face226
face227 face228 multiple 14 offset ($x) 0 0
volume delete jetplate lowertopology
face split face1 connected keeptool faces jetcircle jetcenter outbox
face222 face223 face224 face225 face226 face227
face228 face229 face230 face231 face232 face233
face234 face235 face236 face237 face238 face239
face240 face241 face242 face243 face244 face245
face246 face247 face248 face249 face250 face251
face252 face253 face254 face255 face256 face257
face258 face259 face260 face261 face262 face263
face264 face265 face266 face267 face268 face269
face270 face271 face272 face273 face274 face275
face276 face277 face278 face279 face280 face281
face282 face283 face284 face285 face286 face287
face288 face289 face290 face291 face292 face293
face294 face295 face296 face297 face298 face299
face300 face301 face302 face303 face304 face305
face306 face307 face308 face309 face310 face311
face312 face313 face314 face315 face316 face317
face318 face319 face320 face321 face322 face323
face324 face325 face326 face327 face328 face329
face330 face331 face332 face333 face334 face335
face336 face337 face338 face339 face340 face341
face342 face343 face344 face345 face346 face347
face348 face349 face350 face351 face352 face353
face354 face355 face356 face357 face358 face359
face360 face361 face362 face363 face364 face365
face366 face367 face368
face move jetcircle jetcenter outbox face222 face223 face224
face225 face226 face227 face228 face229 face230
face231 face232 face233 face234 face235 face236
face237 face238 face239 face240 face241 face242
face243 face244 face245 face246 face247 face248
face249 face250 face251 face252 face253 face254
face255 face256 face257 face258 face259 face260
face261 face262 face263 face264 face265 face266
face267 face268 face269 face270 face271 face272
face273 face274 face275 face276 face277 face278
face279 face280 face281 face282 face283 face284
face285 face286 face287 face288 face289 face290
face291 face292 face293 face294 face295 face296
face297 face298 face299 face300 face301 face302
face303 face304 face305 face306 face307 face308
face309 face310 face311 face312 face313 face314
68
face315 face316 face317 face318 face319 face320
face321 face322 face323 face324 face325 face326
face327 face328 face329 face330 face331 face332
face333 face334 face335 face336 face337 face338
face339 face340 face341 face342 face343 face344
face345 face346 face347 face348 face349 face350
face351 face352 face353 face354 face355 face356
face357 face358 face359 face360 face361 face362
face363 face364 face365 face366 face367 face368 offset 0
0 $ztot
THIS SPLITS THE TOP PLENUM FACE WITH THE FACES CREATED IN THE BOTTOM
face split face6 connected keeptool faces jetcircle jetcenter outbox
face222 face223 face224 face225 face226 face227
face228 face229 face230 face231 face232 face233
face234 face235 face236 face237 face238 face239
face240 face241 face242 face243 face244 face245
face246 face247 face248 face249 face250 face251
face252 face253 face254 face255 face256 face257
face258 face259 face260 face261 face262 face263
face264 face265 face266 face267 face268 face269
face270 face271 face272 face273 face274 face275
face276 face277 face278 face279 face280 face281
face282 face283 face284 face285 face286 face287
face288 face289 face290 face291 face292 face293
face294 face295 face296 face297 face298 face299
face300 face301 face302 face303 face304 face305
face306 face307 face308 face309 face310 face311
face312 face313 face314 face315 face316 face317
face318 face319 face320 face321 face322 face323
face324 face325 face326 face327 face328 face329
face330 face331 face332 face333 face334 face335
face336 face337 face338 face339 face340 face341
face342 face343 face344 face345 face346 face347
face348 face349 face350 face351 face352 face353
face354 face355 face356 face357 face358 face359
face360 face361 face362 face363 face364 face365
face366 face367 face368
THIS MOVES THE FACES THAT WE ARE USING TO PLIT THE BOTTOM PLENUM SURFACE
face move jetcircle jetcenter outbox face222 face223 face224
face225 face226 face227 face228 face229 face230
face231 face232 face233 face234 face235 face236
face237 face238 face239 face240 face241 face242
face243 face244 face245 face246 face247 face248
face249 face250 face251 face252 face253 face254
face255 face256 face257 face258 face259 face260
face261 face262 face263 face264 face265 face266
face267 face268 face269 face270 face271 face272
face273 face274 face275 face276 face277 face278
face279 face280 face281 face282 face283 face284
face285 face286 face287 face288 face289 face290
face291 face292 face293 face294 face295 face296
face297 face298 face299 face300 face301 face302
69
face303 face304 face305 face306 face307 face308
face309 face310 face311 face312 face313 face314
face315 face316 face317 face318 face319 face320
face321 face322 face323 face324 face325 face326
face327 face328 face329 face330 face331 face332
face333 face334 face335 face336 face337 face338
face339 face340 face341 face342 face343 face344
face345 face346 face347 face348 face349 face350
face351 face352 face353 face354 face355 face356
face357 face358 face359 face360 face361 face362
face363 face364 face365 face366 face367 face368 offset 0
0 -$zp
SPLITS THE BOTTOM FACE OF THE PLENUM WITH THE FACES THAT ARE USED TO SPLIT
face split face114 connected keeptool faces jetcircle jetcenter
outbox face222 face223 face224 face225 face226 face227
face228 face229 face230 face231 face232 face233
face234 face235 face236 face237 face238 face239
face240 face241 face242 face243 face244 face245
face246 face247 face248 face249 face250 face251
face252 face253 face254 face255 face256 face257
face258 face259 face260 face261 face262 face263
face264 face265 face266 face267 face268 face269
face270 face271 face272 face273 face274 face275
face276 face277 face278 face279 face280 face281
face282 face283 face284 face285 face286 face287
face288 face289 face290 face291 face292 face293
face294 face295 face296 face297 face298 face299
face300 face301 face302 face303 face304 face305
face306 face307 face308 face309 face310 face311
face312 face313 face314 face315 face316 face317
face318 face319 face320 face321 face322 face323
face324 face325 face326 face327 face328 face329
face330 face331 face332 face333 face334 face335
face336 face337 face338 face339 face340 face341
face342 face343 face344 face345 face346 face347
face348 face349 face350 face351 face352 face353
face354 face355 face356 face357 face358 face359
face360 face361 face362 face363 face364 face365
face366 face367 face368
COPIES THE FACES THAT WE USED TO SPLIT TO BOTTOM OF THE PLENUM TO THE TOP OF
THE CHANNEL
face cmove jetcircle jetcenter outbox face222 face223 face224
face225 face226 face227 face228 face229 face230
face231 face232 face233 face234 face235 face236
face237 face238 face239 face240 face241 face242
face243 face244 face245 face246 face247 face248
face249 face250 face251 face252 face253 face254
face255 face256 face257 face258 face259 face260
face261 face262 face263 face264 face265 face266
face267 face268 face269 face270 face271 face272
face273 face274 face275 face276 face277 face278
face279 face280 face281 face282 face283 face284
70
face285 face286 face287 face288 face289 face290
face291 face292 face293 face294 face295 face296
face297 face298 face299 face300 face301 face302
face303 face304 face305 face306 face307 face308
face309 face310 face311 face312 face313 face314
face315 face316 face317 face318 face319 face320
face321 face322 face323 face324 face325 face326
face327 face328 face329 face330 face331 face332
face333 face334 face335 face336 face337 face338
face339 face340 face341 face342 face343 face344
face345 face346 face347 face348 face349 face350
face351 face352 face353 face354 face355 face356
face357 face358 face359 face360 face361 face362
face363 face364 face365 face366 face367 face368 multiple 1 offset 0
0 -$d
NAME OF COPIED NEW FACES
face1104 face1105 face1106 face1107 face1108 face1109 face1110 face1111
face1112 face1113 face1114 face1115 face1116 face1117 face1118 face1119
face1120 face1121 face1122 face1123 face1124 face1125 face1126 face1127
face1128 face1129 face1130 face1131 face1132 face1133 face1134 face1135
face1136 face1137 face1138 face1139 face1140 face1141 face1142 face1143
face1144 face1145 face1146 face1147 face1148 face1149 face1150 face1151
face1152 face1153 face1154 face1155 face1156 face1157 face1158 face1159
face1160 face1161 face1162 face1163 face1164 face1165 face1166 face1167
face1168 face1169 face1170 face1171 face1172 face1173 face1174 face1175
face1176 face1177 face1178 face1179 face1180 face1181 face1182 face1183
face1184 face1185 face1186 face1187 face1188 face1189 face1190 face1191
face1192 face1193 face1194 face1195 face1196 face1197 face1198 face1199
face1200 face1201 face1202 face1203 face1204 face1205 face1206 face1207
face1208 face1209 face1210 face1211 face1212 face1213 face1214 face1215
face1216 face1217 face1218 face1219 face1220 face1221 face1222 face1223
face1224 face1225 face1226 face1227 face1228 face1229 face1230 face1231
face1232 face1233 face1234 face1235 face1236 face1237 face1238 face1239
face1240 face1241 face1242 face1243 face1244 face1245 face1246 face1247
face1248 face1249 face1250 face1251 face1252 face1253
THIS SPLITS THE TOP OF THE CHANNEL WITH THE NEW COPIED FACES
face split face209 connected keeptool faces face1104 face1105 face1106 face1107
face1108 face1109 face1110 face1111 face1112 face1113 face1114 face1115
face1116 face1117 face1118 face1119 face1120 face1121 face1122 face1123
face1124 face1125 face1126 face1127 face1128 face1129 face1130 face1131
face1132 face1133 face1134 face1135 face1136 face1137 face1138 face1139
face1140 face1141 face1142 face1143 face1144 face1145 face1146 face1147
face1148 face1149 face1150 face1151 face1152 face1153 face1154 face1155
face1156 face1157 face1158 face1159 face1160 face1161 face1162 face1163
face1164 face1165 face1166 face1167 face1168 face1169 face1170 face1171
face1172 face1173 face1174 face1175 face1176 face1177 face1178 face1179
face1180 face1181 face1182 face1183 face1184 face1185 face1186 face1187
face1188 face1189 face1190 face1191 face1192 face1193 face1194 face1195
face1196 face1197 face1198 face1199 face1200 face1201 face1202 face1203
face1204 face1205 face1206 face1207 face1208 face1209 face1210 face1211
face1212 face1213 face1214 face1215 face1216 face1217 face1218 face1219
face1220 face1221 face1222 face1223 face1224 face1225 face1226 face1227
71
face1228 face1229 face1230 face1231 face1232 face1233 face1234 face1235
face1236 face1237 face1238 face1239 face1240 face1241 face1242 face1243
face1244 face1245 face1246 face1247 face1248 face1249 face1250 face1251
face1252 face1253
THIS UNITES THE RECTANGLE OUTSIDE FACES AND THE SEMICIRCLE SO THAT IT MAKES
A RECTANGLE WIHOUT THE CENTERJET
face unite faces jetcircle face223 real
face unite faces face222 outbox real
face unite faces face228 face226 real
face unite faces face225 face227 real
face unite faces face231 face233 real
face unite faces face232 face230 real
face unite faces face236 face238 real
face unite faces face237 face235 real
face unite faces face241 face243 real
face unite faces face242 face240 real
face unite faces face248 face246 real
face unite faces face245 face247 real
face unite faces face253 face251 real
face unite faces face252 face250 real
face unite faces face256 face258 real
face unite faces face257 face255 real
face unite faces face263 face261 real
face unite faces face260 face262 real
face unite faces face268 face266 real
face unite faces face265 face264 real
face unite faces face265 face267 real
face unite faces face273 face271 real
face unite faces face272 face270 real
face unite faces face276 face278 real
face unite faces face277 face275 real
face unite faces face281 face283 real
face unite faces face282 face280 real
face unite faces face286 face288 real
face unite faces face287 face285 real
face unite faces face291 face293 real
face unite faces face292 face290 real
face unite faces face296 face298 real
face unite faces face297 face295 real
face unite faces face301 face303 real
face unite faces face302 face300 real
face unite faces face306 face308 real
face unite faces face307 face305 real
face unite faces face316 face318 real
face unite faces face312 face310 real
face unite faces face311 face313 real
face unite faces face315 face317 real
face unite faces face321 face323 real
face unite faces face322 face320 real
face unite faces face326 face328 real
face unite faces face327 face325 real
face unite faces face331 face333 real
face unite faces face332 face330 real
face unite faces face336 face338 real
72
face unite faces face337 face335 real
face unite faces face347 face345 real
face unite faces face346 face348 real
face unite faces face342 face340 real
face unite faces face341 face343 real
face unite faces face356 face358 real
face unite faces face357 face355 real
face unite faces face352 face350 real
face unite faces face351 face353 real
face unite faces face361 face363 real
face unite faces face366 face368 real
face unite faces face360 face362 real
face unite faces face365 face367 real
SPLITTING ALL THE FACES OF THE CIRCLES IN THE BOTTOM OF THE PLENUM
face split face912 connected keeptool faces face222
face split face117 connected keeptool faces face228
face split face117 connected keeptool faces face225
face split face922 connected keeptool faces face232
face split face124 connected keeptool faces face236
face split face124 connected keeptool faces face237
face split face932 connected keeptool faces face242
face split face131 connected keeptool faces face248
face split face131 connected keeptool faces face245
face split face942 connected keeptool faces face252
face split face138 connected keeptool faces face256
face split face138 connected keeptool faces face257
face split face952 connected keeptool faces face260
face split face145 connected keeptool faces face268
face split face145 connected keeptool faces face265
face split face962 connected keeptool faces face272
face split face152 connected keeptool faces face276
face split face152 connected keeptool faces face277
face split face972 connected keeptool faces face282
face split face159 connected keeptool faces face286
face split face159 connected keeptool faces face287
face split face982 connected keeptool faces face292
face split face166 connected keeptool faces face296
face split face166 connected keeptool faces face297
face split face992 connected keeptool faces face302
face split face173 connected keeptool faces face306
face split face173 connected keeptool faces face307
face split face1002 connected keeptool faces face312
face split face180 connected keeptool faces face316
face split face180 connected keeptool faces face315
73
face split face1012 connected keeptool faces face322
face split face187 connected keeptool faces face326
face split face187 connected keeptool faces face327
face split face1022 connected keeptool faces face332
face split face194 connected keeptool faces face336
face split face194 connected keeptool faces face337
face split face1032 connected keeptool faces face342
face split face201 connected keeptool faces face346
face split face201 connected keeptool faces face347
face split face1042 connected keeptool faces face352
face split face208 connected keeptool faces face356
face split face208 connected keeptool faces face357
face split face1052 connected keeptool faces face360
face split face215 connected keeptool faces face366
face split face215 connected keeptool faces face365
THIS UNITES THE RECTANGLE OUTSIDE FACES AND THE SEMICIRCLE SO THAT IT MAKES
A RECTANGLE WIHOUT THE CENTERJET
face unite faces face1104 face1108 real
face unite faces face1107 face1106 real
face unite faces face1113 face1111 real
face unite faces face1112 face1110 real
face unite faces face1118 face1116 real
face unite faces face1117 face1115 real
face unite faces face1123 face1121 real
face unite faces face1122 face1120 real
face unite faces face1128 face1126 real
face unite faces face1127 face1125 real
face unite faces face1133 face1131 real
face unite faces face1132 face1130 real
face unite faces face1138 face1136 real
face unite faces face1137 face1135 real
face unite faces face1143 face1141 real
face unite faces face1142 face1140 real
face unite faces face1148 face1146 real
face unite faces face1147 face1145 real
face unite faces face1153 face1151 real
face unite faces face1152 face1150 real
face unite faces face1158 face1156 real
face unite faces face1157 face1155 real
face unite faces face1163 face1161 real
face unite faces face1162 face1160 real
face unite faces face1168 face1166 real
face unite faces face1167 face1165 real
face unite faces face1173 face1171 real
face unite faces face1172 face1170 real
face unite faces face1178 face1176 real
face unite faces face1177 face1175 real
face unite faces face1183 face1181 real
74
face unite faces face1182 face1180 real
face unite faces face1186 face1188 real
face unite faces face1187 face1185 real
face unite faces face1193 face1191 real
face unite faces face1192 face1190 real
face unite faces face1198 face1196 real
face unite faces face1197 face1195 real
face unite faces face1203 face1201 real
face unite faces face1202 face1200 real
face unite faces face1206 face1208 real
face unite faces face1207 face1205 real
face unite faces face1213 face1211 real
face unite faces face1212 face1210 real
face unite faces face1216 face1218 real
face unite faces face1217 face1215 real
face unite faces face1221 face1223 real
face unite faces face1222 face1220 real
face unite faces face1228 face1226 real
face unite faces face1227 face1225 real
face unite faces face1233 face1231 real
face unite faces face1232 face1230 real
face unite faces face1238 face1236 real
face unite faces face1237 face1235 real
face unite faces face1243 face1241 real
face unite faces face1242 face1240 real
face unite faces face1248 face1246 real
face unite faces face1247 face1245 real
face unite faces face1253 face1251 real
face unite faces face1252 face1250 real
SPLITTING ALL THE FACES OF THE CIRCLES IN THE TOP OF THE CHANNEL
face split face1257 connected keeptool faces face1107
face split face115 connected keeptool faces face1113
face split face115 connected keeptool faces face1112
face split face1267 connected keeptool faces face1117
face split face122 connected keeptool faces face1123
face split face122 connected keeptool faces face1122
face split face1277 connected keeptool faces face1127
face split face129 connected keeptool faces face1133
face split face129 connected keeptool faces face1132
face split face1287 connected keeptool faces face1137
face split face136 connected keeptool faces face1143
face split face136 connected keeptool faces face1142
face split face1297 connected keeptool faces face1147
face split face143 connected keeptool faces face1153
face split face143 connected keeptool faces face1152
face split face1307 connected keeptool faces face1157
face split face150 connected keeptool faces face1163
face split face150 connected keeptool faces face1162
75
face split face1317 connected keeptool faces face1167
face split face157 connected keeptool faces face1173
face split face157 connected keeptool faces face1172
face split face1327 connected keeptool faces face1177
face split face164 connected keeptool faces face1183
face split face164 connected keeptool faces face1182
face split face1337 connected keeptool faces face1187
face split face171 connected keeptool faces face1193
face split face171 connected keeptool faces face1192
face split face1347 connected keeptool faces face1197
face split face178 connected keeptool faces face1203
face split face178 connected keeptool faces face1202
face split face1357 connected keeptool faces face1207
face split face185 connected keeptool faces face1213
face split face185 connected keeptool faces face1212
face split face1367 connected keeptool faces face1217
face split face192 connected keeptool faces face1221
face split face192 connected keeptool faces face1222
face split face1377 connected keeptool faces face1227
face split face199 connected keeptool faces face1233
face split face199 connected keeptool faces face1232
face split face1387 connected keeptool faces face1237
face split face206 connected keeptool faces face1243
face split face206 connected keeptool faces face1242
face split face1397 connected keeptool faces face1247
face split face213 connected keeptool faces face1253
face split face213 connected keeptool faces face1252
face split face1452 connected keeptool faces face224
face split face1456 connected keeptool faces face234
face split face1460 connected keeptool faces face244
face split face1464 connected keeptool faces face254
face split face1468 connected keeptool faces face264
face split face1472 connected keeptool faces face274
face split face1476 connected keeptool faces face284
face split face1480 connected keeptool faces face294
face split face1484 connected keeptool faces face304
face split face1488 connected keeptool faces face314
face split face1492 connected keeptool faces face324
face split face1496 connected keeptool faces face334
face split face1500 connected keeptool faces face344
face split face1504 connected keeptool faces face354
face split face1508 connected keeptool faces face364
DELETING ALL THE FACES USED TO MAKE THE CUTS
face delete jetcircle face222 face228 face225 jetcenter
76
face224 face231 face232 face236 face237 face229
face1456 face241 face242 face239 face248 face244
face245 face253 face249 face252 face254 face256
face257 face263 face259 face260 face268 face264
face265 face273 face272 face269 face276 face277
face274 face281 face282 face286 face279 face287
face284 face291 face292 face296 face297 face289
face294 face301 face299 face302 face306 face307
face304 face311 face312 face316 face315 face309
face314 face321 face322 face326 face327 face319
face324 face331 face332 face329 face336 face334
face337 face341 face342 face339 face346 face344
face347 face351 face352 face349 face356 face354
face357 face361 face359 face360 face366 face364
face365 lowertopology
face delete face1104 face1105 face1107 face1113 face1112
face115 face234 face1118 face1114 face1117 face1123
face1122 face122 face1138 face1128 face1127 face1124
face1133 face1132 face129 face1134 face1137 face1143
face136 face1142 face1148 face1144 face1147 face1153
face143 face1152 face1158 face1154 face1157 face1163
face150 face1162 face1168 face1164 face1167 face1173
face157 face1172 face1178 face1174 face1177 face1183
face164 face1182 face1186 face1184 face1187 face1193
face171 face1192 face1198 face1194 face1197 face1203
face178 face1202 face1206 face1204 face1207 face1213
face185 face1212 face1216 face1214 face1217 face1221
face192 face1222 face1228 face1224 face1227 face1233
face199 face1232 face1238 face1234 face1237 face1243
face206 face1242 face1248 face1244 face1247 face1253
face213 face1252 lowertopology
face delete face1109 face1119 face1129 face1139 face1149 face1159
face1169 face1179 face1189 face1199 face1209 face1219
face1229 face1239 face1249 lowertopology
face create CP1 width 600 height 75 offset 300 (225+($d)2) 0 xyplane rectangle
face create CP2 width 600 height 75 offset 300 (225+($d)2) ($zc) xyplane rectangle
face create CP3 width 600 height 75 offset 300 (225+($d)2) ($zc+$d) xyplane rectangle
face create CP4 width 600 height 75 offset 300 (225+($d)2) ($zc+$d+$zp) xyplane rectangle
face split face6 connected faces CP4
face split face114 connected faces CP3
face split face209 connected faces CP2
face split face1 connected faces CP1
GEOMETRY IS FINISHED
face modify face912 side vertex6437 vertex6436
77
face modify face1600 side vertex7302 vertex7303
face modify face117 side vertex6446 vertex6447
face modify face646 side vertex3312
face modify face646 side vertex3313
face modify face647 side vertex3432 vertex3433
face modify face372 side vertex2040 vertex2041
face modify face376 side vertex2100 vertex2101
face modify face377 side vertex2221 vertex2220
LINKING ALL THE JET CENTERS
face link face1450 face640 edges edge6949 edge3518 vertices
vertex6437 vertex3253 reverse
face link face1450 face1257 edges edge6949 edge7340 vertices
vertex6437 vertex6797 reverse
face link face1257 face370 edges edge7340 edge2139 vertices
vertex6797 vertex2041 reverse
face link face1257 face1454 edges edge7340 edge6975 vertices
vertex6797 vertex6461 reverse
face link face1454 face649 edges edge6975 edge3519 vertices
vertex6461 vertex3255 reverse
face link face1454 face1267 edges edge6975 edge7377 vertices
vertex6461 vertex6831 reverse
face link face1267 face379 edges edge7377 edge2141 vertices
vertex6831 vertex2043 reverse
face link face1267 face1458 edges edge7377 edge7001 vertices
vertex6831 vertex6485 reverse
face link face1458 face659 edges edge7001 edge3520 vertices
vertex6485 vertex3257 reverse
face link face1458 face1277 edges edge7001 edge7414 vertices
vertex6485 vertex6865 reverse
face link face1277 face389 edges edge7414 edge2143 vertices
vertex6865 vertex2045 reverse
face link face1277 face1462 edges edge7414 edge7027 vertices
vertex6865 vertex6509 reverse
face link face1462 face669 edges edge7027 edge3521 vertices
vertex6509 vertex3259 reverse
face link face1462 face1287 edges edge7027 edge7451 vertices
vertex6509 vertex6899 reverse
face link face1287 face399 edges edge7451 edge2145 vertices
vertex6899 vertex2047 reverse
face link face1287 face1466 edges edge7451 edge7053 vertices
vertex6899 vertex6533 reverse
face link face1466 face679 edges edge7053 edge3522 vertices
vertex6533 vertex3261 reverse
face link face1466 face1297 edges edge7053 edge7488 vertices
vertex6533 vertex6933 reverse
face link face1297 face409 edges edge7488 edge2147 vertices
vertex6933 vertex2049 reverse
face link face1297 face1470 edges edge7488 edge7079 vertices
vertex6933 vertex6557 reverse
face link face1470 face689 edges edge7079 edge3523 vertices
vertex6557 vertex3263 reverse
face link face1470 face1307 edges edge7079 edge7525 vertices
vertex6557 vertex6967 reverse
face link face1307 face419 edges edge7525 edge2149 vertices
78
vertex6967 vertex2051 reverse
face link face1307 face1474 edges edge7525 edge7105 vertices
vertex6967 vertex6581 reverse
face link face1474 face1317 edges edge7105 edge7562 vertices
vertex6581 vertex7001 reverse
face link face1474 face699 edges edge7105 edge3524 vertices
vertex6581 vertex3265 reverse
face link face1317 face429 edges edge7562 edge2151 vertices
vertex7001 vertex2053 reverse
face link face1317 face1478 edges edge7562 edge7131 vertices
vertex7001 vertex6605 reverse
face link face1478 face1327 edges edge7131 edge7599 vertices
vertex6605 vertex7035 reverse
face link face1478 face709 edges edge7131 edge3525 vertices
vertex6605 vertex3267 reverse
face link face1327 face439 edges edge7599 edge2153 vertices
vertex7035 vertex2055 reverse
face link face1327 face1482 edges edge7599 edge7157 vertices
vertex7035 vertex6629 reverse
face link face1482 face719 edges edge7157 edge3526 vertices
vertex6629 vertex3269 reverse
face link face1482 face1337 edges edge7157 edge7636 vertices
vertex6629 vertex7069 reverse
face link face1337 face449 edges edge7636 edge2155 vertices
vertex7069 vertex2057 reverse
face link face1337 face1486 edges edge7636 edge7183 vertices
vertex7069 vertex6653 reverse
face link face1486 face1347 edges edge7183 edge7673 vertices
vertex6653 vertex7103 reverse
face link face1347 face459 edges edge7673 edge2157 vertices
vertex7103 vertex2059 reverse
face link face1486 face729 edges edge7183 edge3527 vertices
vertex6653 vertex3271 reverse
face link face1347 face1490 edges edge7673 edge7209 vertices
vertex7103 vertex6677 reverse
face link face1490 face1357 edges edge7209 edge7710 vertices
vertex6677 vertex7137 reverse
face link face1490 face739 edges edge7209 edge3528 vertices
vertex6677 vertex3273 reverse
face link face1357 face469 edges edge7710 edge2159 vertices
vertex7137 vertex2061 reverse
face link face1357 face1494 edges edge7710 edge7235 vertices
vertex7137 vertex6701 reverse
face link face1494 face1367 edges edge7235 edge7747 vertices
vertex6701 vertex7171 reverse
face link face1494 face749 edges edge7235 edge3529 vertices
vertex6701 vertex3275 reverse
face link face1367 face479 edges edge7747 edge2161 vertices
vertex7171 vertex2063 reverse
face link face1367 face1498 edges edge7747 edge7261 vertices
vertex7171 vertex6725 reverse
face link face1498 face1377 edges edge7261 edge7784 vertices
vertex6725 vertex7205 reverse
face link face1377 face489 edges edge7784 edge2163 vertices
vertex7205 vertex2065 reverse
face link face1498 face759 edges edge7261 edge3530 vertices
79
vertex6725 vertex3277 reverse
face link face1377 face1502 edges edge7784 edge7287 vertices
vertex7205 vertex6749 reverse
face link face1502 face1387 edges edge7287 edge7821 vertices
vertex6749 vertex7239 reverse
face link face1387 face499 edges edge7821 edge2165 vertices
vertex7239 vertex2067 reverse
face link face1387 face1506 edges edge7821 edge7313 vertices
vertex7239 vertex6773 reverse
face link face1502 face769 edges edge7287 edge3531 vertices
vertex6749 vertex3279 reverse
face link face1506 face1397 edges edge7313 edge7858 vertices
vertex6773 vertex7273 reverse
face link face1506 face779 edges edge7313 edge3532 vertices
vertex6773 vertex3281 reverse
face link face1397 face509 edges edge7858 edge2167 vertices
vertex7273 vertex2069 reverse
LINKING ALL THE COMPLETE JETCENTERS
face link face1452 face644 edges edge7891 edge3773 vertices
vertex7303 vertex3433
face link face1452 face115 edges edge7891 edge7364 vertices
vertex7303 vertex6819
face link face1452 face1456 edges edge7891 edge7900 vertices
vertex7303 vertex7311
face link face1456 face654 edges edge7900 edge3774 vertices
vertex7311 vertex3435
face link face1456 face122 edges edge7900 edge7401 vertices
vertex7311 vertex6853
face link face1456 face1460 edges edge7900 edge7909 vertices
vertex7311 vertex7319
face link face1460 face1464 edges edge7909 edge7918 vertices
vertex7319 vertex7327
face link face1460 face129 edges edge7909 edge7438 vertices
vertex7319 vertex6887
face link face1460 face664 edges edge7909 edge3775 vertices
vertex7319 vertex3437
face link face1464 face674 edges edge7918 edge3776 vertices
vertex7327 vertex3439
face link face1464 face136 edges edge7918 edge7475 vertices
vertex7327 vertex6921
face link face1464 face1468 edges edge7918 edge7927 vertices
vertex7327 vertex7335
face link face1472 face1468 edges edge7936 edge7927 vertices
vertex7343 vertex7335
face link face1468 face143 edges edge7927 edge7512 vertices
vertex7335 vertex6955
face link face1468 face684 edges edge7927 edge3777 vertices
vertex7335 vertex3441
face link face1472 face694 edges edge7936 edge3778 vertices
vertex7343 vertex3443
face link face1472 face150 edges edge7936 edge7549 vertices
vertex7343 vertex6989
face link face1472 face1476 edges edge7936 edge7945 vertices
80
vertex7343 vertex7351
face link face1476 face1480 edges edge7945 edge7954 vertices
vertex7351 vertex7359
face link face1476 face157 edges edge7945 edge7586 vertices
vertex7351 vertex7023
face link face1476 face704 edges edge7945 edge3779 vertices
vertex7351 vertex3445
face link face1480 face714 edges edge7954 edge3780 vertices
vertex7359 vertex3447
face link face1480 face164 edges edge7954 edge7623 vertices
vertex7359 vertex7057
face link face1480 face1484 edges edge7954 edge7963 vertices
vertex7359 vertex7367
face link face1484 face171 edges edge7963 edge7660 vertices
vertex7367 vertex7091
face link face1484 face724 edges edge7963 edge3781 vertices
vertex7367 vertex3449
face link face1480 face1488 edges edge7954 edge7972 vertices
vertex7359 vertex7375
face link face1488 face178 edges edge7972 edge7697 vertices
vertex7375 vertex7125
face link face1488 face734 edges edge7972 edge3782 vertices
vertex7375 vertex3451
face link face1488 face1492 edges edge7972 edge7981 vertices
vertex7375 vertex7383
face link face1492 face744 edges edge7981 edge3783 vertices
vertex7383 vertex3453
face link face1492 face185 edges edge7981 edge7734 vertices
vertex7383 vertex7159
face link face1492 face1496 edges edge7981 edge7990 vertices
vertex7383 vertex7391
face link face1496 face754 edges edge7990 edge3784 vertices
vertex7391 vertex3455
face link face1496 face192 edges edge7990 edge7771 vertices
vertex7391 vertex7193
face link face1496 face1500 edges edge7990 edge7999 vertices
vertex7391 vertex7399
face link face1500 face1504 edges edge7999 edge8008 vertices
vertex7399 vertex7407
face link face1504 face1508 edges edge8008 edge8017 vertices
vertex7407 vertex7415
face link face1500 face199 edges edge7999 edge7808 vertices
vertex7399 vertex7227
face link face1500 face764 edges edge7999 edge3785 vertices
vertex7399 vertex3457
face link face1504 face774 edges edge8008 edge3786 vertices
vertex7407 vertex3459
face link face1508 face784 edges edge8017 edge3787 vertices
vertex7415 vertex3461
face link face1504 face206 edges edge8008 edge7845 vertices
vertex7407 vertex7261
face link face1508 face213 edges edge8017 edge7882 vertices
vertex7415 vertex7295
linking the jetcenters of the bottom of the channel one of them has to be reversed but the otherones are not
81
face link face115 face374 edges edge7364 edge2394 vertices
vertex6819 vertex2221 reverse
face link face374 face384 edges edge2394 edge2396 vertices
vertex2221 vertex2223
face link face384 face394 edges edge2396 edge2398 vertices
vertex2223 vertex2225
face link face394 face404 edges edge2398 edge2400 vertices
vertex2225 vertex2227
face link face404 face414 edges edge2400 edge2402 vertices
vertex2227 vertex2229
face link face414 face424 edges edge2402 edge2404 vertices
vertex2229 vertex2231
face link face424 face434 edges edge2404 edge2406 vertices
vertex2231 vertex2233
face link face434 face444 edges edge2406 edge2408 vertices
vertex2233 vertex2235
face link face444 face454 edges edge2408 edge2410 vertices
vertex2235 vertex2237
face link face454 face464 edges edge2410 edge2412 vertices
vertex2237 vertex2239
face link face464 face474 edges edge2412 edge2414 vertices
vertex2239 vertex2241
face link face474 face484 edges edge2414 edge2416 vertices
vertex2241 vertex2243
face link face484 face494 edges edge2416 edge2418 vertices
vertex2243 vertex2245
face link face494 face504 edges edge2418 edge2420 vertices
vertex2245 vertex2247
face link face504 face514 edges edge2420 edge2422 vertices
vertex2247 vertex2249
UP TO THIS POINT ALL THE FACES ARE CONNCTED SUCCESSFULLY
LINKING THE FIRST THREE JET TELEPHONES
face link face912 face117 edges edge6950 edge6960 vertices
vertex6437 vertex6446 reverse
face link face912 face1600 edges edge6950 edge7890 vertices
vertex6437 vertex7303 reverse
face link face912 face372 edges edge6950 edge2168 vertices
vertex6437 vertex2041
face link face117 face376 edges edge6959 edge2304 vertices
vertex6447 vertex2101 reverse
face link face1600 face377 edges edge7890 edge2423 vertices
vertex7303 vertex2221 reverse
face link face372 face382 edges edge2168 edge2169 vertices
vertex2041 vertex2043
face link face377 face387 edges edge2423 edge2424 vertices
vertex2221 vertex2223
face link face376 face386 edges edge2304 edge2306 vertices
vertex2101 vertex2103
face link face387 face397 edges edge2424 edge2425 vertices
vertex2223 vertex2225
face link face386 face396 edges edge2306 edge2308 vertices
82
vertex2103 vertex2105
face link face382 face392 edges edge2169 edge2170 vertices
vertex2043 vertex2045
face link face382 face392 edges edge2169 edge2170 vertices
vertex2043 vertex2045
face link face382 face392 edges edge2169 edge2170 vertices
vertex2043 vertex2045
face link face382 face392 edges edge2169 edge2170 vertices
vertex2043 vertex2045
face link face397 face407 edges edge2425 edge2426 vertices
vertex2225 vertex2227
face link face392 face402 edges edge2170 edge2171 vertices
vertex2045 vertex2047
face link face396 face406 edges edge2290 edge2291 vertices
vertex2104 vertex2106
face link face407 face417 edges edge2426 edge2427 vertices
vertex2227 vertex2229
face link face417 face427 edges edge2427 edge2428 vertices
vertex2229 vertex2231
face link face427 face437 edges edge2428 edge2429 vertices
vertex2231 vertex2233
face link face437 face447 edges edge2429 edge2430 vertices
vertex2233 vertex2235
face link face447 face457 edges edge2430 edge2431 vertices
vertex2235 vertex2237
face link face457 face467 edges edge2431 edge2432 vertices
vertex2237 vertex2239
face link face467 face477 edges edge2432 edge2433 vertices
vertex2239 vertex2241
face link face477 face487 edges edge2433 edge2434 vertices
vertex2241 vertex2243
face link face487 face487 edges edge2434 edge2434 vertices
vertex2243 vertex2243
face link face487 face487 edges edge2434 edge2434 vertices
vertex2243 vertex2243
face link face487 face487 edges edge2434 edge2434 vertices
vertex2243 vertex2243
face link face487 face497 edges edge2434 edge2435 vertices
vertex2243 vertex2245
face link face497 face507 edges edge2435 edge2436 vertices
vertex2245 vertex2247
face link face507 face517 edges edge2436 edge2437 vertices
vertex2247 vertex2249
face link face406 face416 edges edge2291 edge2292 vertices
vertex2106 vertex2108
face link face416 face426 edges edge2292 edge2293 vertices
vertex2108 vertex2110
face link face426 face436 edges edge2293 edge2294 vertices
vertex2110 vertex2112
face link face436 face446 edges edge2294 edge2295 vertices
vertex2112 vertex2114
face link face446 face456 edges edge2295 edge2296 vertices
vertex2114 vertex2116
face link face456 face466 edges edge2296 edge2297 vertices
vertex2116 vertex2118
face link face466 face476 edges edge2297 edge2298 vertices
83
vertex2118 vertex2120
face link face486 face496 edges edge2299 edge2300 vertices
vertex2122 vertex2124
face link face476 face486 edges edge2298 edge2299 vertices
vertex2120 vertex2122
face link face496 face506 edges edge2300 edge2301 vertices
vertex2124 vertex2126
face link face506 face516 edges edge2301 edge2302 vertices
vertex2126 vertex2128
face link face392 face402 edges edge2142 edge2144 vertices
vertex2044 vertex2046
face link face402 face412 edges edge2171 edge2172 vertices
vertex2047 vertex2049
face link face412 face422 edges edge2172 edge2173 vertices
vertex2049 vertex2051
face link face422 face432 edges edge2173 edge2174 vertices
vertex2051 vertex2053
face link face432 face442 edges edge2174 edge2175 vertices
vertex2053 vertex2055
face link face442 face452 edges edge2175 edge2176 vertices
vertex2055 vertex2057
face link face452 face462 edges edge2176 edge2177 vertices
vertex2057 vertex2059
face link face462 face472 edges edge2177 edge2178 vertices
vertex2059 vertex2061
face link face472 face482 edges edge2178 edge2179 vertices
vertex2061 vertex2063
face link face482 face492 edges edge2179 edge2180 vertices
vertex2063 vertex2065
face link face492 face502 edges edge2180 edge2181 vertices
vertex2065 vertex2067
face link face502 face512 edges edge2181 edge2182 vertices
vertex2067 vertex2069
LINKING THE TELEPHONES OF THE BOTTOM OF THE PLENUM
face link face912 face922 edges edge6950 edge6976 vertices
vertex6437 vertex6461
face link face922 face932 edges edge6976 edge7002 vertices
vertex6461 vertex6485
face link face932 face942 edges edge7002 edge7028 vertices
vertex6485 vertex6509
face link face942 face952 edges edge7028 edge7054 vertices
vertex6509 vertex6533
face link face952 face962 edges edge7054 edge7080 vertices
vertex6533 vertex6557
face link face962 face972 edges edge7080 edge7106 vertices
vertex6557 vertex6581
face link face972 face982 edges edge7106 edge7132 vertices
vertex6581 vertex6605
face link face982 face992 edges edge7132 edge7158 vertices
vertex6605 vertex6629
face link face992 face1002 edges edge7158 edge7184 vertices
vertex6629 vertex6653
face link face1002 face1012 edges edge7184 edge7210 vertices
vertex6653 vertex6677
84
face link face1012 face1022 edges edge7210 edge7236 vertices
vertex6677 vertex6701
face link face1032 face1042 edges edge7262 edge7288 vertices
vertex6725 vertex6749
face link face1042 face1052 edges edge7288 edge7314 vertices
vertex6749 vertex6773
face link face117 face124 edges edge6960 edge6986 vertices
vertex6446 vertex6470
face link face124 face131 edges edge6986 edge7012 vertices
vertex6470 vertex6494
face link face131 face138 edges edge7012 edge7038 vertices
vertex6494 vertex6518
face link face138 face145 edges edge7038 edge7064 vertices
vertex6518 vertex6542
face link face145 face152 edges edge7064 edge7090 vertices
vertex6542 vertex6566
face link face152 face159 edges edge7090 edge7116 vertices
vertex6566 vertex6590
face link face159 face166 edges edge7116 edge7142 vertices
vertex6590 vertex6614
face link face166 face173 edges edge7142 edge7168 vertices
vertex6614 vertex6638
face link face173 face180 edges edge7168 edge7194 vertices
vertex6638 vertex6662
face link face180 face187 edges edge7194 edge7220 vertices
vertex6662 vertex6686
face link face187 face194 edges edge7220 edge7246 vertices
vertex6686 vertex6710
face link face194 face201 edges edge7246 edge7272 vertices
vertex6710 vertex6734
face link face1022 face1032 edges edge7236 edge7262 vertices
vertex6701 vertex6725
face link face1032 face1042 edges edge7262 edge7288 vertices
vertex6725 vertex6749
face link face201 face208 edges edge7271 edge7297 vertices
vertex6735 vertex6759
face link face208 face215 edges edge7297 edge7323 vertices
vertex6759 vertex6783
face link face1600 face1602 edges edge7890 edge7899 vertices
vertex7303 vertex7311
face link face1602 face1604 edges edge7899 edge7908 vertices
vertex7311 vertex7319
face link face1604 face1606 edges edge7908 edge7917 vertices
vertex7319 vertex7327
face link face1606 face1608 edges edge7917 edge7926 vertices
vertex7327 vertex7335
face link face1608 face1610 edges edge7926 edge7935 vertices
vertex7335 vertex7343
face link face1610 face1612 edges edge7935 edge7944 vertices
vertex7343 vertex7351
face link face1612 face1614 edges edge7944 edge7953 vertices
vertex7351 vertex7359
face link face1614 face1616 edges edge7953 edge7962 vertices
vertex7359 vertex7367
face link face1616 face1618 edges edge7962 edge7971 vertices
vertex7367 vertex7375
85
face link face1618 face1620 edges edge7971 edge7980 vertices
vertex7375 vertex7383
face link face1620 face1622 edges edge7980 edge7989 vertices
vertex7383 vertex7391
face link face1622 face1624 edges edge7989 edge7998 vertices
vertex7391 vertex7399
face link face1624 face1626 edges edge7998 edge8007 vertices
vertex7399 vertex7407
face link face1626 face1628 edges edge8007 edge8016 vertices
vertex7407 vertex7415
LINKING ALL THE TELEPHONES OF THE TOP OF THE CHANNEL
face link face912 face1510 edges edge6950 edge7339 vertices
vertex6437 vertex6797 reverse
face link face117 face1512 edges edge6959 edge7349 vertices
vertex6447 vertex6807
face link face1600 face1514 edges edge7890 edge7363 vertices
vertex7303 vertex6819
face link face1510 face1516 edges edge7339 edge7376 vertices
vertex6797 vertex6831
face link face1516 face1522 edges edge7376 edge7413 vertices
vertex6831 vertex6865
face link face1522 face1528 edges edge7413 edge7450 vertices
vertex6865 vertex6899
face link face1528 face1534 edges edge7450 edge7487 vertices
vertex6899 vertex6933
face link face1534 face1540 edges edge7487 edge7524 vertices
vertex6933 vertex6967
face link face1540 face1546 edges edge7524 edge7561 vertices
vertex6967 vertex7001
face link face1546 face1552 edges edge7561 edge7598 vertices
vertex7001 vertex7035
face link face1552 face1558 edges edge7598 edge7635 vertices
vertex7035 vertex7069
face link face1558 face1564 edges edge7635 edge7672 vertices
vertex7069 vertex7103
face link face1564 face1570 edges edge7672 edge7709 vertices
vertex7103 vertex7137
face link face1570 face1576 edges edge7709 edge7746 vertices
vertex7137 vertex7171
face link face1576 face1582 edges edge7746 edge7783 vertices
vertex7171 vertex7205
face link face1582 face1588 edges edge7783 edge7820 vertices
vertex7205 vertex7239
face link face1588 face1594 edges edge7820 edge7857 vertices
vertex7239 vertex7273
face link face1512 face1518 edges edge7350 edge7387 vertices
vertex6806 vertex6840
face link face1518 face1524 edges edge7387 edge7424 vertices
vertex6840 vertex6874
face link face1524 face1530 edges edge7424 edge7461 vertices
vertex6874 vertex6908
face link face1530 face1536 edges edge7461 edge7498 vertices
vertex6908 vertex6942
face link face1536 face1542 edges edge7498 edge7535 vertices
86
vertex6942 vertex6976
face link face1542 face1548 edges edge7535 edge7572 vertices
vertex6976 vertex7010
face link face1548 face1554 edges edge7572 edge7609 vertices
vertex7010 vertex7044
face link face1554 face1560 edges edge7609 edge7646 vertices
vertex7044 vertex7078
face link face1560 face1566 edges edge7646 edge7683 vertices
vertex7078 vertex7112
face link face1566 face1572 edges edge7683 edge7720 vertices
vertex7112 vertex7146
face link face1572 face1578 edges edge7720 edge7757 vertices
vertex7146 vertex7180
face link face1578 face1584 edges edge7757 edge7794 vertices
vertex7180 vertex7214
face link face1584 face1590 edges edge7794 edge7831 vertices
vertex7214 vertex7248
face link face1590 face1596 edges edge7831 edge7868 vertices
vertex7248 vertex7282
face link face1514 face1520 edges edge7363 edge7400 vertices
vertex6819 vertex6853
face link face1520 face1526 edges edge7400 edge7437 vertices
vertex6853 vertex6887
face link face1526 face1532 edges edge7437 edge7474 vertices
vertex6887 vertex6921
face link face1532 face1538 edges edge7474 edge7511 vertices
vertex6921 vertex6955
face link face1538 face1544 edges edge7511 edge7548 vertices
vertex6955 vertex6989
face link face1544 face1550 edges edge7548 edge7585 vertices
vertex6989 vertex7023
face link face1550 face1556 edges edge7585 edge7622 vertices
vertex7023 vertex7057
face link face1556 face1562 edges edge7622 edge7659 vertices
vertex7057 vertex7091
face link face1562 face1568 edges edge7659 edge7696 vertices
vertex7091 vertex7125
face link face1568 face1574 edges edge7696 edge7733 vertices
vertex7125 vertex7159
face link face1574 face1580 edges edge7733 edge7770 vertices
vertex7159 vertex7193
face link face1580 face1586 edges edge7770 edge7807 vertices
vertex7193 vertex7227
face link face1586 face1592 edges edge7807 edge7844 vertices
vertex7227 vertex7261
face link face1592 face1598 edges edge7844 edge7881 vertices
vertex7261 vertex7295
LINKING ALL THE TELEPHONES OF THE TOP OF THE PLENUM
face link face912 face642 edges edge6950 edge3489 vertices
vertex6437 vertex3253 reverse
face link face642 face647 edges edge3489 edge3744 vertices
vertex3253 vertex3433
face link face117 face646 edges edge6959 edge3638 vertices
vertex6447 vertex3313
87
face link face642 face652 edges edge3489 edge3491 vertices
vertex3253 vertex3255
face link face652 face662 edges edge3491 edge3493 vertices
vertex3255 vertex3257
face link face662 face672 edges edge3493 edge3495 vertices
vertex3257 vertex3259
face link face672 face682 edges edge3495 edge3497 vertices
vertex3259 vertex3261
face link face682 face692 edges edge3497 edge3499 vertices
vertex3261 vertex3263
face link face692 face702 edges edge3499 edge3501 vertices
vertex3263 vertex3265
face link face702 face712 edges edge3501 edge3503 vertices
vertex3265 vertex3267
face link face712 face722 edges edge3503 edge3505 vertices
vertex3267 vertex3269
face link face722 face732 edges edge3505 edge3507 vertices
vertex3269 vertex3271
face link face732 face742 edges edge3507 edge3509 vertices
vertex3271 vertex3273
face link face742 face752 edges edge3509 edge3511 vertices
vertex3273 vertex3275
face link face752 face762 edges edge3511 edge3513 vertices
vertex3275 vertex3277
face link face762 face772 edges edge3513 edge3515 vertices
vertex3277 vertex3279
face link face772 face782 edges edge3515 edge3517 vertices
vertex3279 vertex3281
face link face646 face656 edges edge3653 edge3655 vertices
vertex3312 vertex3314
face link face656 face666 edges edge3655 edge3657 vertices
vertex3314 vertex3316
face link face666 face676 edges edge3657 edge3659 vertices
vertex3316 vertex3318
face link face676 face686 edges edge3659 edge3661 vertices
vertex3318 vertex3320
face link face686 face696 edges edge3661 edge3663 vertices
vertex3320 vertex3322
face link face696 face706 edges edge3663 edge3665 vertices
vertex3322 vertex3324
face link face706 face716 edges edge3665 edge3667 vertices
vertex3324 vertex3326
face link face716 face726 edges edge3667 edge3669 vertices
vertex3326 vertex3328
face link face726 face736 edges edge3669 edge3671 vertices
vertex3328 vertex3330
face link face736 face746 edges edge3671 edge3673 vertices
vertex3330 vertex3332
face link face746 face756 edges edge3673 edge3675 vertices
vertex3332 vertex3334
face link face756 face766 edges edge3675 edge3677 vertices
vertex3334 vertex3336
face link face766 face776 edges edge3677 edge3679 vertices
vertex3336 vertex3338
face link face776 face786 edges edge3679 edge3681 vertices
88
vertex3338 vertex3340
face link face647 face657 edges edge3744 edge3746 vertices
vertex3433 vertex3435
face link face657 face667 edges edge3746 edge3748 vertices
vertex3435 vertex3437
face link face667 face677 edges edge3748 edge3750 vertices
vertex3437 vertex3439
face link face677 face687 edges edge3750 edge3752 vertices
vertex3439 vertex3441
face link face687 face697 edges edge3752 edge3754 vertices
vertex3441 vertex3443
face link face697 face707 edges edge3754 edge3756 vertices
vertex3443 vertex3445
face link face707 face717 edges edge3756 edge3758 vertices
vertex3445 vertex3447
face link face717 face727 edges edge3758 edge3760 vertices
vertex3447 vertex3449
face link face727 face737 edges edge3760 edge3762 vertices
vertex3449 vertex3451
face link face737 face747 edges edge3762 edge3764 vertices
vertex3451 vertex3453
face link face747 face757 edges edge3764 edge3766 vertices
vertex3453 vertex3455
face link face757 face767 edges edge3766 edge3768 vertices
vertex3455 vertex3457
face link face767 face777 edges edge3768 edge3770 vertices
vertex3457 vertex3459
face link face777 face787 edges edge3770 edge3772 vertices
vertex3459 vertex3461
face link face647 face1600 edges edge3685 edge6963 vertices
vertex3345 vertex6449
LINKING OUTBOXES ON THE PLENUM
face modify face911 side vertex4404 vertex4405
face modify face918 side vertex4405 vertex4404
face link face911 face915 edges edge4778 edge4898 vertices
vertex4374 vertex4434
face link face915 face645 edges edge4899 edge3833 vertices
vertex4480 vertex3463 reverse
face link face911 face641 edges edge4779 edge3578 vertices
vertex4405 vertex3283 reverse
face link face918 face648 edges edge4825 edge3686 vertices
vertex4436 vertex3347 reverse
face link face645 face655 edges edge3833 edge3834 vertices
vertex3463 vertex3465
face link face655 face665 edges edge3834 edge3835 vertices
vertex3465 vertex3467
face link face665 face675 edges edge3835 edge3836 vertices
vertex3467 vertex3469
face link face675 face685 edges edge3836 edge3837 vertices
vertex3469 vertex3471
face link face685 face695 edges edge3837 edge3838 vertices
89
vertex3471 vertex3473
face link face695 face705 edges edge3838 edge3839 vertices
vertex3473 vertex3475
face link face705 face715 edges edge3839 edge3840 vertices
vertex3475 vertex3477
face link face715 face725 edges edge3840 edge3841 vertices
vertex3477 vertex3479
face link face725 face735 edges edge3841 edge3842 vertices
vertex3479 vertex3481
face link face735 face745 edges edge3842 edge3843 vertices
vertex3481 vertex3483
face link face745 face755 edges edge3843 edge3844 vertices
vertex3483 vertex3485
face link face755 face765 edges edge3844 edge3845 vertices
vertex3485 vertex3487
face link face765 face775 edges edge3845 edge3846 vertices
vertex3487 vertex3489
face link face775 face785 edges edge3846 edge3847 vertices
vertex3489 vertex3491
face link face648 face658 edges edge3686 edge3690 vertices
vertex3347 vertex3353
face link face658 face668 edges edge3690 edge3694 vertices
vertex3353 vertex3359
face link face668 face678 edges edge3694 edge3698 vertices
vertex3359 vertex3365
face link face678 face688 edges edge3698 edge3702 vertices
vertex3365 vertex3371
face link face688 face698 edges edge3702 edge3706 vertices
vertex3371 vertex3377
face link face698 face708 edges edge3706 edge3710 vertices
vertex3377 vertex3383
face link face708 face718 edges edge3710 edge3714 vertices
vertex3383 vertex3389
face link face718 face728 edges edge3714 edge3718 vertices
vertex3389 vertex3395
face link face728 face738 edges edge3718 edge3722 vertices
vertex3395 vertex3401
face link face738 face748 edges edge3722 edge3726 vertices
vertex3401 vertex3407
face link face748 face758 edges edge3726 edge3730 vertices
vertex3407 vertex3413
face link face758 face768 edges edge3730 edge3734 vertices
vertex3413 vertex3419
face link face768 face778 edges edge3734 edge3738 vertices
vertex3419 vertex3425
face link face778 face788 edges edge3738 edge3742 vertices
vertex3425 vertex3431
face link face641 face650 edges edge3578 edge3579 vertices
vertex3283 vertex3285
face link face650 face660 edges edge3579 edge3580 vertices
vertex3285 vertex3287
face link face660 face670 edges edge3580 edge3581 vertices
vertex3287 vertex3289
face link face670 face680 edges edge3581 edge3582 vertices
vertex3289 vertex3291
face link face680 face690 edges edge3582 edge3583 vertices
90
vertex3291 vertex3293
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LINKING THE TOP OF THE CHANEL OUTBOXES
face modify face1256 side vertex6322 vertex6321
face modify face1263 side vertex6322 vertex6321
face modify face1260 side vertex6397 vertex6396
92
face link face1256 face1260 edges edge6803 edge6923 vertices
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93
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LINKING THE BOTTOM OF THE CHANEL OUTBOXES
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94
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95
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TOP SIDE BOX beginning of channel
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TOP SIDE BOXES
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96
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TOP SIDE BOX END OF CHANNEL
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TOP SIDE BOX BACK OF CHANNEL
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vertex8 vertex84 reverse
BOTTOM SIDE BOX
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97
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MESHING BEGINS HERE
BOUNDARY LAYERS BEGINS HERE
BOUNDARY LAYER FOR THE bottom of plenum
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer1 face face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
98
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 edge edge97
edge4748 edge106 edge6946 edge6947 edge107 edge4749
edge4750 edge116 edge6972 edge6973 edge117 edge4751
edge4752 edge126 edge6998 edge6999 edge127 edge4753
edge4754 edge136 edge7024 edge7025 edge137 edge4755
edge4756 edge146 edge7050 edge7051 edge147 edge4757
edge4758 edge156 edge7076 edge7077 edge157 edge4759
edge4760 edge166 edge7102 edge7103 edge167 edge4761
edge4762 edge176 edge7128 edge7129 edge177 edge4763
edge4764 edge186 edge7154 edge7155 edge187 edge4765
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edge4768 edge206 edge7206 edge7207 edge207 edge4769
edge4770 edge216 edge7232 edge7233 edge217 edge4771
edge4772 edge226 edge7258 edge7259 edge227 edge4773
edge4774 edge236 edge7284 edge7285 edge237 edge4775
edge4776 edge246 edge7310 edge7311 edge247 edge4777 add
MESHING THE PLENUM
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer2 face face4 face4 face5 face110
face110 edge edge99 edge8069 edge100 edge8052 edge98 add
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer4 face face1649 face1664 face1664
face1664 face1663 edge edge8052 edge98 edge100 edge8069
edge99 add
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer4 face face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face4 face2 face2 face2 face2 face2 face4
face5 face110 face110 edge edge9 edge3398 edge3399
edge3400 edge3401 edge3402 edge3403 edge3404 edge3406
edge3405 edge3407 edge3408 edge3409 edge3415 edge3410
edge3411 edge3412 edge3413 edge3414 edge3416 edge3417
edge3418 edge3419 edge3420 edge3421 edge3422 edge3423
edge3424 edge3425 edge3426 edge3427 edge3428 edge3429
edge3430 edge3431 edge3432 edge3433 edge3434 edge3435
edge3436 edge3437 edge3438 edge3439 edge3440 edge3441
edge3442 edge3443 edge3444 edge3445 edge3446 edge3447
99
edge3448 edge3449 edge3450 edge3451 edge3457 edge3452
edge3453 edge3454 edge3455 edge3456 edge3458 edge3459
edge3460 edge3461 edge3462 edge3463 edge3464 edge3465
edge3466 edge3467 edge3468 edge3469 edge3475 edge3481
edge3470 edge3471 edge3472 edge3473 edge3474 edge3476
edge3477 edge3478 edge3479 edge3480 edge3487 edge11
edge3482 edge3483 edge3484 edge3485 edge3486 edge8051
edge12 edge10 edge8034 add
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer5 face face1663 face1664 face1664
face1664 face1649 edge edge99 edge8069 edge100 edge98
edge8052 add
BOUNDARY LAYER OF THE HOLES
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer1 face face642 edge edge3534 add
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer7 face face117 face1600 edge edge4824
edge110 add
BONDARY LAYER OF THE CHANNEL
TARGET WALL BOUNDARY LAYER
BBBL
BBL
BBL
BBBL
BBL
BBL
BBBLLLLL
blayer create first $firstch growth $growthch rows $rowsch transition 1 trows 0
uniform
blayer attach b_layer8 face face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
100
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face105 face105 face106
face104 face104 edge edge2048 edge2049 edge2050 edge2051
edge2052 edge2053 edge2054 edge2055 edge2056 edge2057
edge2058 edge2059 edge2060 edge2061 edge2062 edge2063
edge2064 edge2065 edge2066 edge2072 edge2067 edge2068
edge2069 edge2070 edge2071 edge2084 edge2078 edge2073
edge2074 edge2075 edge2076 edge2077 edge2079 edge2080
edge2081 edge2082 edge2083 edge2090 edge2096 edge2085
edge2086 edge2087 edge2088 edge2089 edge2091 edge2092
edge2093 edge2094 edge2095 edge2102 edge2108 edge2097
edge2098 edge2099 edge2100 edge2101 edge2103 edge2104
edge2105 edge2106 edge2107 edge2114 edge2120 edge2109
edge2110 edge2111 edge2112 edge2113 edge2115 edge2116
edge2117 edge2118 edge2119 edge2126 edge2132 edge2121
edge2122 edge2123 edge2124 edge2125 edge2127 edge2128
edge2129 edge2130 edge2131 edge2133 edge2134 edge2136
edge2137 edge1 edge2135 edge8088 edge3 edge4 edge8105
edge2 add
blayer create first $firstch growth $growthch rows $rowsch transition 1 trows 0
uniform
blayer attach b_layer9 face face1681 face1696 face1696
face1696 face1695 edge edge2 edge8105 edge4 edge3
edge8088 add
blayer create first $firstch growth $growthch rows $rowsch transition 1 trows 0
uniform
blayer attach b_layer10 face face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face105 face105
face106 face104 face104 edge edge6743 edge101
edge7336 edge7337 edge102 edge6744 edge6745 edge111
edge7373 edge7374 edge112 edge6746 edge6747 edge121
edge7410 edge7411 edge122 edge6748 edge6749 edge131
edge7447 edge7448 edge132 edge6750 edge6751 edge141
edge7484 edge7485 edge142 edge6752 edge6755 edge6753
edge151 edge6754 edge7521 edge7522 edge152 edge161
101
edge6756 edge6757 edge7558 edge7559 edge162 edge171
edge7595 edge7596 edge172 edge6758 edge6759 edge181
edge7632 edge7633 edge182 edge6760 edge6761 edge191
edge7669 edge7670 edge192 edge6762 edge6763 edge6767
edge6765 edge201 edge7706 edge7707 edge202 edge6764
edge211 edge6766 edge7743 edge7744 edge212 edge6769
edge221 edge6768 edge7780 edge7781 edge222 edge6771
edge231 edge6770 edge7817 edge7818 edge232 edge241
edge7854 edge7855 edge242 edge6772 edge89 edge8070
edge91 edge92 edge8087 edge90 add
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer11 face face4 face5 face2 face5
face110 face2 edge edge8 edge8 edge6 edge7 edge7
edge5 add
blayer create first $firstch growth $growthch rows $rowsch transition 1 trows 0
uniform
blayer attach b_layer12 face face106 face104 face103 face105
edge edge87 edge87 edge85 edge88 add
BOUNDARY LAYERS ENDS HERE
edge picklink edge6948 edge6949
edge mesh edge6949 edge6948 successive ratio1 1 intervals $NumbNodes
edge picklink edge6950
edge mesh edge6950 successive ratio1 1 intervals ($NumbNodes2)
face mesh face1450 map
edge picklink edge6963 edge6947
edge mesh edge6947 edge6963 successive ratio1 1 intervals ($Numbtelnodes+$rows)
face mesh face912 map
edge picklink edge6961 edge6960 edge7889 edge7890
edge mesh edge7890 edge7889 edge6960 edge6961 successive ratio1 1
intervals ($NumbNodes)
edge picklink edge6959 edge7891
edge mesh edge7891 edge6959 successive ratio1 1 intervals ($NumbNodes2)
face mesh face1452 map
face mesh face1600 face117 map
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer12 face face2 face110 face5 face110
face2 face4 face5 face4 edge edge5 edge5 edge7
edge7 edge6 edge6 edge8 edge8 add
Meshing constants
$NumbNodes=5
$Numbtelnodes=6
$PLobnodes=5
$Chobnodes=5
$Plbenodes=($NumbNodes(4)+$rows)
$plsqnodes=($NumbNodes(3))
102
$Pllsnodes=($NumbNodes+$rows)
$Nojetcells=10
edge picklink edge3686 edge3402
edge mesh edge3686 edge3402 successive ratio1 1 intervals ($PLobnodes)
edge picklink edge6744 edge6864
edge mesh edge6864 edge6744 successive ratio1 1 intervals 5
face link face1260 face375 edges edge6923 edge2440 vertices
vertex6397 vertex2251 reverse
face modify face915 side vertex4479 vertex4480
face mesh face915 face918 face911 map size 1
face mesh face1260 face1263 face1256 map size 1
edge picklink edge8068 edge8053
edge mesh edge8068 edge8053 successive ratio1 1 intervals ($Plbenodes)
edge picklink edge8086 edge8071
edge mesh edge8071 edge8086 successive ratio1 1 intervals ($CHbenodes)
edge delete edge8053 edge8068 keepsettings onlymesh
edge mesh edge8053 edge8068 successive ratio1 1 intervals ($Plbenodes)
edge delete edge8090 keepsettings onlymesh
edge picklink edge8090
edge mesh edge8090 successive ratio1 1 intervals ($plsqnodes)
edge delete edge8054 keepsettings onlymesh
edge picklink edge8054
edge mesh edge8054 successive ratio1 1 intervals ($plsqnodes)
face mesh face1647 face1679 face1678 face1646 face1633
face1665 map
edge delete edge98 edge8087 keepsettings onlymesh
edge picklink edge8087 edge98
edge mesh edge98 successive ratio1 1 intervals ($Pllsnodes)
edge mesh edge8087 successive ratio1 1 intervals ($CHlsnodes)
face mesh face1648 face1680 map
COOPERING ALL THE JETS
volume mesh volume3 cooper source face1600 face1452 face117
face1514 face1512 face115 intervals ($Nojetcells)
volume mesh volume5 cooper source face1456 face1602 face124
face1518 face1520 face122 intervals ($Nojetcells)
volume mesh volume7 cooper source face1460 face1604 face131
face1526 face1524 face129 intervals ($Nojetcells)
volume mesh volume9 cooper source face1464 face1606 face138
face1532 face1530 face136 intervals ($Nojetcells)
volume mesh volume11 cooper source face1468 face1608 face145
face1538 face143 face1536 intervals ($Nojetcells)
volume mesh volume13 cooper source face1472 face1610 face152
face1544 face1542 face150 intervals ($Nojetcells)
volume mesh volume15 cooper source face1476 face1612 face159
face1550 face1548 face157 intervals ($Nojetcells)
volume mesh volume17 cooper source face1480 face1614 face166
face1556 face1554 face164 intervals ($Nojetcells)
volume mesh volume19 cooper source face1484 face1616 face173
face1562 face171 face1560 intervals ($Nojetcells)
volume mesh volume21 cooper source face1488 face1618 face180
face1568 face1566 face178 intervals ($Nojetcells)
103
volume mesh volume23 cooper source face1492 face1620 face187
face1574 face1572 face185 intervals ($Nojetcells)
volume mesh volume25 cooper source face1496 face1622 face194
face1578 face1580 face192 intervals ($Nojetcells)
volume mesh volume27 cooper source face1624 face1500 face201
face1586 face1584 face199 intervals ($Nojetcells)
volume mesh volume29 cooper source face1504 face1626 face208
face1592 face1590 face206 intervals ($Nojetcells)
volume mesh volume31 cooper source face1628 face1508 face215
face1596 face1598 face213 intervals ($Nojetcells)
volume mesh volume30 cooper source face1506 face1052 face1594
face1397 intervals ($Nojetcells)
volume mesh volume28 cooper source face1502 face1042 face1588
face1387 intervals ($Nojetcells)
volume mesh volume26 cooper source face1498 face1032 face1582
face1377 intervals ($Nojetcells)
volume mesh volume24 cooper source face1494 face1022 face1576
face1367 intervals ($Nojetcells)
volume mesh volume22 cooper source face1490 face1012 face1570
face1357 intervals ($Nojetcells)
volume mesh volume20 cooper source face1486 face1002 face1564
face1347 intervals ($Nojetcells)
volume mesh volume18 cooper source face1482 face992 face1558
face1337 intervals ($Nojetcells)
volume mesh volume16 cooper source face1478 face982 face1552
face1327 intervals ($Nojetcells)
volume mesh volume14 cooper source face1474 face972 face1546
face1317 intervals ($Nojetcells)
volume mesh volume12 cooper source face1470 face962 face1540
face1307 intervals ($Nojetcells)
volume mesh volume10 cooper source face1466 face952 face1534
face1297 intervals ($Nojetcells)
volume mesh volume8 cooper source face1462 face942 face1528
face1287 intervals ($Nojetcells)
volume mesh volume6 cooper source face1458 face932 face1522
face1277 intervals ($Nojetcells)
volume mesh volume4 cooper source face1454 face922 face1516
face1267 intervals ($Nojetcells)
volume mesh cylinder cooper source face1450 face912 face1510
face1257 intervals ($Nojetcells)
window modify invisible mesh
volume mesh volume34 cooper source face1649 face1650 face1651
face1652 face1653 face1654 face1655 face1664 face1639
face1638 face1637 face1636 face1635 face1634 face1633
face1648 face1610 face1608 face1606 face1604 face1602
face1600 face1472 face962 face1468 face952 face1464
face942 face1460 face932 face1456 face922 face1452
face912 face915 face918 face911 face925 face928
face920 face935 face938 face930 face945 face948
face940 face955 face958 face950 face965 face968
face960 face694 face689 face684 face679 face674
face669 face664 face659 face654 face649 face644
face640 face697 face696 face692 face687 face686
face682 face677 face676 face672 face667 face666
104
face662 face657 face656 face652 face647 face646
face642 face695 face698 face690 face685 face688
face680 face675 face678 face670 face665 face668
face660 face655 face658 face650 face645 face648
face641 face152 face1470 face145 face1466 face138
face1462 face131 face1458 face124 face1454 face117
face1450 face1657 face1658 face1659 face1660 face1661
face1662 face1663 face788 face1656 face1474 face159
face1647 face1646 face1645 face1644 face1643 face1642
face1641 face1640 face1478 face1628 face1626 face1624
face1622 face1620 face1618 face1616 face1614 face1612
face1508 face1052 face1504 face1042 face1500 face1032
face1496 face1022 face1492 face1012 face1488 face1002
face1484 face992 face1480 face982 face1476 face972
face975 face978 face970 face985 face988 face980
face995 face998 face990 face1005 face1008 face1000
face1015 face1018 face1010 face1025 face1028 face1020
face1035 face1038 face1030 face1045 face1048 face1040
face1050 face114 face1058 face774 face769 face764
face759 face754 face749 face744 face739 face734
face729 face724 face719 face714 face709 face704
face699 face777 face776 face772 face767 face766
face762 face757 face756 face752 face747 face746
face742 face737 face736 face732 face727 face726
face722 face717 face716 face712 face707 face706
face702 face779 face784 face787 face775 face778
face770 face765 face768 face760 face755 face758
face750 face745 face748 face740 face735 face738
face730 face725 face728 face720 face715 face718
face710 face705 face708 face700 face782 face786
face785 face6 face780 face1055 face215 face1506
face208 face1502 face201 face1498 face194 face1494
face187 face1490 face180 face1486 face173 face1482
face166 intervals ($Plzdnodes)
volume delete body onlymesh
volume mesh body cooper source face1689 face1690 face1691
face1692 face1693 face1681 face1682 face1683 face1684
face1685 face1686 face1687 face1688 face1696 face1671
face1670 face1669 face1668 face1667 face1666 face1665
face1677 face1676 face1675 face1674 face1673 face1672
face1680 face199 face1584 face1377 face192 face1578
face1367 face185 face1572 face1357 face178 face1566
face1347 face171 face1560 face1337 face164 face1554
face1327 face157 face1548 face1317 face150 face1542
face1307 face143 face1536 face1297 face136 face1530
face1287 face129 face1524 face1277 face122 face1518
face1267 face115 face1512 face1257 face1380 face1383
face1375 face1370 face1373 face1365 face1360 face1363
face1355 face1350 face1353 face1345 face1340 face1343
face1335 face1330 face1333 face1325 face1320 face1323
face1315 face1310 face1313 face1305 face1300 face1303
face1295 face1290 face1293 face1285 face1280 face1283
face1275 face1270 face1273 face1265 face1260 face1263
face1256 face209 face374 face370 face384 face379
face394 face389 face404 face399 face414 face409
105
face424 face419 face434 face429 face444 face439
face454 face449 face464 face459 face474 face469
face484 face479 face494 face489 face377 face376
face372 face387 face386 face382 face397 face396
face392 face407 face406 face402 face417 face416
face412 face427 face426 face422 face437 face436
face432 face447 face446 face442 face457 face456
face452 face467 face466 face462 face477 face476
face472 face487 face486 face482 face497 face496
face492 face375 face378 face371 face385 face388
face380 face395 face398 face390 face405 face408
face400 face415 face418 face410 face425 face428
face420 face435 face438 face430 face445 face448
face440 face455 face458 face450 face465 face468
face460 face475 face478 face470 face485 face488
face480 face495 face498 face490 face1 face1586
face1582 face1580 face1576 face1574 face1570 face1568
face1564 face1562 face1558 face1556 face1552 face1550
face1546 face1544 face1540 face1538 face1534 face1532
face1528 face1526 face1522 face1520 face1516 face1514
face1510 face1403 face518 face1588 face1592 face1594
face1694 face1695 face1598 face1679 face1678 face515
face516 face510 face500 face508 face505 face213
face1596 face1397 face206 face1590 face1387 face517
face514 face512 face502 face506 face507 face509
face499 face504 face1400 face1395 face1385 face1390
face1393 intervals ($Chzdnodes)
BOUNDARY CONDITIONS
physics create Symmetry btype SYMMETRY face face2 face103
face211 face204 face197 face190 face183 face176
face169 face162 face155 face148 face141 face134
face127 face120 face112
physics create Wall btype SYMMETRY face face110 face5 face1649
face1664 face918 face915 face911 face925 face1650
face928 face920 face935 face938 face930 face1652
face1651 face948 face945 face940 face1653 face1654
face958 face955 face950 face1655 face965 face968
face960 face978 face975 face970 face1656 face114
face985 face988 face980 face995 face998 face990
face1657 face1005 face1008 face1000 face1658 face1015
face1018 face1010 face1659 face1028 face1025 face1020
face1035 face1660 face1038 face1030 face1045 face1661
face1048 face1040 face1055 face1662 face1058 face1050
face1663 face4 face1395 face1679 face1403 face1400
face1680 face1385 face1678 face1393 face1390 face1375
face1677 face1383 face1380 face1676 face1365 face1373
face1370 face1675 face1355 face1363 face1360 face1674
face1345 face1353 face1350 face1673 face1335 face1343
face1340 face1672 face1325 face1333 face1330 face209
face1315 face1323 face1320 face1671 face1305 face1313
face1310 face1670 face1295 face1303 face1300 face1669
106
face1285 face1293 face1290 face1668 face1275 face1283
face1280 face1667 face1265 face1273 face1270 face1666
face1256 face1263 face1260 face1665 face214 face91
face207 face85 face200 face79 face193 face73 face186
face67 face179 face61 face172 face55 face165 face49
face158 face43 face151 face37 face144 face31 face137
face25 face130 face19 face123 face13 face116 face8
physics modify Wall btype WALL face face110 face5 face1649
face1664 face918 face915 face911 face925 face1650
face928 face920 face935 face938 face930 face1652
face1651 face948 face945 face940 face1653 face1654
face958 face955 face950 face1655 face965 face968
face960 face978 face975 face970 face1656 face114
face985 face988 face980 face995 face998 face990
face1657 face1005 face1008 face1000 face1658 face1015
face1018 face1010 face1659 face1028 face1025 face1020
face1035 face1660 face1038 face1030 face1045 face1661
face1048 face1040 face1055 face1662 face1058 face1050
face1663 face4 face1395 face1679 face1403 face1400
face1680 face1385 face1678 face1393 face1390 face1375
face1677 face1383 face1380 face1676 face1365 face1373
face1370 face1675 face1355 face1363 face1360 face1674
face1345 face1353 face1350 face1673 face1335 face1343
face1340 face1672 face1325 face1333 face1330 face209
face1315 face1323 face1320 face1671 face1305 face1313
face1310 face1670 face1295 face1303 face1300 face1669
face1285 face1293 face1290 face1668 face1275 face1283
face1280 face1667 face1265 face1273 face1270 face1666
face1256 face1263 face1260 face1665 face214 face91
face207 face85 face200 face79 face193 face73 face186
face67 face179 face61 face172 face55 face165 face49
face158 face43 face151 face37 face144 face31 face137
face25 face130 face19 face123 face13 face116 face8
physics create Heat Fluxes btype WALL face face104 face106
face370 face379 face389 face372 face382 face392
face371 face380 face390 face378 face388 face398
face376 face386 face396 face374 face384 face394
face377 face387 face397 face375 face385 face395
face1681 face1682 face1683 face1684 face1696 face402
face412 face422 face432 face442 face400 face410
face420 face430 face440 face408 face418 face428
face438 face448 face406 face416 face426 face436
face446 face404 face414 face424 face434 face444
face407 face417 face427 face437 face447 face405
face415 face425 face435 face445 face1688 face1685
face1686 face1687 face452 face462 face472 face482
face492 face1693 face450 face460 face470 face480
face490 face1692 face458 face468 face478 face488
face498 face1 face456 face466 face476 face486 face496
face454 face464 face474 face484 face494 face457
face467 face477 face487 face497 face1691 face455
face465 face475 face485 face495 face1689 face1690
face518 face502 face512 face1695 face500 face510
face1694 face508 face506 face516 face504 face514
face507 face517 face515 face505
physics create Mass flow inlet btype SYMMETRY face face640 face649
107
face659 face642 face652 face662 face672 face641
face650 face660 face670 face648 face658 face668
face678 face646 face656 face666 face676 face644
face654 face664 face674 face647 face657 face667
face677 face645 face655 face665 face675 face1633
face1634 face1635 face1636 face1637 face1648 face679
face689 face699 face682 face692 face702 face712
face680 face690 face700 face710 face688 face698
face708 face718 face6 face686 face696 face706 face716
face684 face694 face704 face714 face687 face697
face707 face717 face685 face695 face705 face715
face1640 face1638 face1639 face719 face729 face739
face749 face722 face732 face742 face752 face762
face720 face730 face740 face750 face760 face728
face738 face748 face758 face768 face726 face736
face746 face756 face766 face724 face734 face744
face754 face764 face727 face737 face747 face757
face767 face725 face735 face745 face755 face765
face1645 face1641 face1642 face1643 face1644 face788
face769 face779 face772 face782 face770 face780
face778 face776 face786 face774 face784 face777
face787 face775 face785 face1647 face1646
physics create Outflow btype OUTFLOW face face105
108
REFERENCES
Al-Aqal O M A 2003 ldquoHeat transfer distributions on the walls of a narrow channel
with jet impingement and cross flowrdquo PhD Thesis University of Pittsburgh
Bunker Ronald S 2007 Gas Turbine Heat Transfer Ten Remaining Hot Gas Path
Challengesrdquo Journal of Turbomachinery April Vol 129 pp 193-201
Downs James P Landis Kenneth K 2009 ldquoTurbine Cooling Systems Design- Past
Present and Futurerdquo Proceedings of ASME Turbo Expo 2009 June 8-12 2009
GT2009-59991
Florschuetz LW Berry R A Metzger D E 1980 ldquoPeriodic streamswise variations of
heat transfer coefficients for inline and staggered arrays of circular jets with cross
flow of spent airrdquo ASME J of Heat Transfer 102 p 132-137
Florschuetz L W Truman C R Metzger D E 1981 ldquoStreamwise Flow and Heat
Transfer Distributions for Jet Array Impingement with Cross flowrdquo Journal of
Heat Transfer Vol 103 pp 337
Florschuetz L W Isoda Y 1983 ldquoFlow Distributions and Discharge Coefficient for
Jet Array Impingement With Initial Cross flowrdquo Journal of Engineering for
Power Vol 105 pp 296
Incropera Frank P DeWitt D P 2002 Fundamentals of Heat and Mass Transfer John
Wiley amp Sons Inc New Jersey pp 491-493
Liu Quan Kapat J May 2006 ldquoStudy of Heat Transfer Characteristics of Impinging
Air Jet Using Pressure and Temperature Sensitive Luminescent Paintrdquo UCF
Dissertation
109
Martin H 1977 ldquoImpinging jet flow heat and mass transferrdquo Advances in heat transfer
Vol 13
Ricklick Mark Kapat J December 2009 ldquoCharacterization of an Inline Row
Impingement Channel for Turbine Blade Cooling Applicationsrdquo UCF
Dissertation
Zuckerman N Lior N 2005 ldquoImpingement Heat transfer Correlations and Numerical
Modelingrdquo Journal of Heat Transfer Vol 127 pp 544
v
TABLE OF CONTENTS
ABSTRACT ii
ACKNOWLEDGEMENTS iv
LIST OF FIGURES vii
NOMENCLATURE ix
CHAPTER ONE INTRODUCTION 1
11 Gas Turbine as a Heat Engine 1
12 Cooling of Hot Components 2
CHAPTER TWO LITERATURE REVIEW 9
21 Impingement Literature Cornerstone 9
22 Relevant Impingement Channel Studies 11
23 Computational Studies on Impingement Channels 12
CHAPTER THREE EXPERIMENTAL SETUP AND TECHNIQUES 15
31 Temperature Measurements with TSP 15
32 Experimental Setup of Suction Channel 21
33 Data Processing and Reduction 24
34 Uncertainty Analysis 27
35 Lateral Conduction Analysis 28
CHAPTER FOUR HEAT TRANSFER RESULTS 32
vi
41 Heat Transfer Validation 32
42 Heat Transfer Results 33
43 XD Comparisons 40
44 3D Comparison of the Heat Transfer Profiles 45
45 Thermal Performance Calculations 48
CHAPTER FIVE COMPUTATIONAL FLUID DYNAMICS 52
51 Problem Setup 52
52 CFD Results 58
CHAPTER SIX CONCLUSIONS 63
APPENDICES 64
Appendix A 64
Appendix B 66
REFERENCES 108
vii
LIST OF FIGURES
Figure 1 Brayton Cycle Flow Path and T-s Diagram (Adapted from UPTB Website) 1
Figure 2 Thermal Loading Throughout a Turbine Blade (Daniels 1982) 3
Figure 3 Allowable Turbine Inlet Temperature vs Cooling Techniques over the Years
(Clifford 1985) 4
Figure 4 Turbine Inlet Temperature Increase with the help of TBC New Super Alloys
and Cooling Technologies (Kapat and Kiesow Lectures 2010) 4
Figure 5 Turbine Stator Cooled with Impingement Coupled with Film Cooling
(Florschuetz 1980) 5
Figure 6 Rotor Blade Cooling Configuration (Gladden 1988) 6
Figure 7 Cross-section of Turbine Airfoil with Cooling Channels (Han et al 1984) 6
Figure 8 Relative Temperatures for Hot Gas Metal Temperature and Coolant
Temperature (Cardwell 2005) 7
Figure 9 (a) The Development of the Wall Jet (b) Jet Diffusion to Surroundings (Liu
2006) 8
Figure 10 Simplified Jablonski Diagram (Adapted from ISSI Website) 17
Figure 11 Heater Strips Painted with TSP Too Closely 21
Figure 12 Flow Loop of Impingement Channel 22
Figure 13 Top View of Jet Plate 22
Figure 14 Front View of Impingement Channel 23
Figure 15 Target Wall Test Section with Heater Leads 23
Figure 16 Heat Transfer Coefficient Uncertainty Tree 27
viii
Figure 17 Temperature Profile of First Five Impingement Rows 29
Figure 18 Detailed View of First Heat Transfer Peak with a Polynomial Curve Fit 30
Figure 19 Control Volume Heat Transfer Analysis 30
Figure 20 Heat Loss through Convection and Lateral Conduction 31
Figure 21 Validation Spanwise Averaged Results 32
Figure 22 Target Wall Heat Transfer Coefficient Distributions 34
Figure 23 Span-averaged Target Wall Heat Transfer Distribution 35
Figure 24 Side Wall Heat Transfer Coefficient Distributions 36
Figure 25 Span-averaged Side wall Heat Transfer Distribution 37
Figure 26 XD=15 Target Wall Heat Transfer Profile 41
Figure 27 XD=15 Span-averaged Target Wall Heat Transfer Distribution 42
Figure 28 Target Wall Span-average Comparison of XD=5 and 15 at High Re 43
Figure 29 Side Wall Heat transfer Coefficient Profile 44
Figure 30 XD=15 Side Wall Span-averaged Heat Transfer Coefficients 45
Figure 31 3D Heat Transfer Profile for ZD=6 XD=5 46
Figure 32 3D Heat Transfer Profile for ZD=8 XD=5 47
Figure 33 3D Heat Transfer Profile for ZD=6 XD=15 48
Figure 34 Pressure Drop Ratio with Respect to Smooth Channel 49
Figure 35 Heat Transfer Enhancement 50
Figure 36 Thermal Performance at Constant Pressure Drop 50
Figure 37 Thermal Performance at Constant Pumping Power 51
Figure 38 Horizontal Plane of Impingement Channel Geometry 53
Figure 39 Target Side and Front End Wall y+ Values 54
ix
Figure 40 Finished Mesh with Boundary Conditions 55
Figure 41 Grid Independence Study 57
Figure 42 Residual Plots for the 26M Cell Run 57
Figure 43 Total Pressure Contours 58
Figure 44 Velocity Magnitude Contours 59
Figure 45 Turbulent Kinetic Energy Contours 60
Figure 46 Static Temperature Contours 60
Figure 47 Target and Side Wall Heat Transfer Coefficient Contours 61
Figure 48 Closer View of First few Rows of Impingement HTC Contours 61
Figure 49 Pathlines Generating from the First Row of Jets 62
NOMENCLATURE
Cross Sectional Area
Heater Surface Area (m2)
Specific Heat at Constant Pressure (kJkgK)
D Jet Diameter (m)
Channel Hydraulic Diameter (m)
Friction Factor
Heat Transfer Coefficient (HTC) (Wm2K)
Average Heat Transfer Coefficient (Wm2K)
Channel Length (m)
Mass Flow Rate (kgs)
Static Pressure (kPa)
x
Total Pressure (kPa)
Pr Prandtl Number
Heat Flux (Wm2)
Total Heat Input (W)
Heater Resistance (ohm)
Re Reynolds Number
SW Side Wall
Temperature (K)
TW Target Wall
Voltage Potential
Streamwise Location
y Spanwise Location
z Height from Target Wall
X Streamwise Distance (m)
Y Spanwise Distance (m)
Z Impingement Height (m)
Thermal Performance Parameter
Ratio of Specific Heats
Air Density (kgm3)
Subscripts
C Cold
H Hot
xi
Carnot Describing a Carnot cycle
Exit
Effective
Quantity Lost to the Environment
Reference Value
Wall Value
Base Line Value
1
CHAPTER ONE INTRODUCTION
11 Gas Turbine as a Heat Engine
Gas turbine is a form of heat engine where the hot reservoir is created by the
combustion of fuel and the cold reservoir is the open atmosphere It is well known that
the maximum efficiency of any heat engine is denoted as the Carnot efficiency
A more accurate cycle is used to describe the processes inside a gas turbine ndash the
Brayton Cycle The Brayton cycle as seen in Figure 1 is composed of four processes In
a gas turbine air is drawn in at state 1 it is compressed until it reaches state 2 The
compressed air is mixed with fuel and ignited as it passes through the combustor The hot
air then passes through the turbines where work is extracted The process from state 4 to
state 1 happens throughout the atmosphere therefore the Brayton cycle is an open loop
cycle as the same air is not continuously being fed through the motor
Figure 1 Brayton Cycle Flow Path and T-s Diagram (Adapted from UPTB Website)
The Brayton cycle has an isentropic efficiency similar to the carnot the Brayton
cycle efficiency is defined as
2
It can be seen that increasing the temperature at which air enters the first turbine
stage T3 increases the overall efficiency of the turbine Moreover increasing the
pressure ratio Pr also aids in the increase of the efficiency One of the hurdles of
increasing T3 is the fact that the post combustion gas is a few hundred degrees Celsius
above the melting point of the super alloys used to make the turbine stator vanes and
rotor blades For this reason it is important to cool the hot components of the gas turbine
in order to assure a reasonable life for the machine
12 Cooling of Hot Components
The transition duct that connects the combustor to the first stage turbine as well
as the first stage of the turbine are the parts that are subject to the harshest thermal
loadings and must therefore be cooled aggressively to maintain them in working
conditions for a long period of time Since the first stage guide vanes and rotor extrude
into the flow they are subject to the highest convection coefficients These heat transfer
coefficients can reach up to 4000 Wm2K (Downs 2009) Figure 2 shows the different
magnitudes of convection coefficient around the blade High heat transfer coefficients
occur where the air stagnates into the leading edge of the airfoil This high heat transfer
region is not only caused by the lack of a thermal boundary layer to protect the airfoil but
also because the effective heat transfer driving temperature is the recovery temperature
At the high Mach numbers that occur in turbines the ratio of total to static temperatures
is significant causing the leading edge to have the highest effective heat load Another
3
peak occurs on the suction side of the blade as the boundary layer created by the airfoil
switches from being a laminar boundary layer into a turbulent one Due to the nozzling
effect of the turbine rotor and stators the flow gathers speed toward the trailing edge of
the airfoil leading to higher convection coefficients on the pressure side of the airfoil
Figure 2 Thermal Loading Throughout a Turbine Blade (Daniels 1982)
Simple convection channels were implemented in the early nineteen sixties as
years passed the cooling techniques became more and more sophisticated allowing the
free stream temperature to increase to previously impossible levels Currently the use of
film cooling coupled with backside impingement leads the turbine cooling technology
The trend of allowable turbine inlet temperature is shown in Figure 3 from this figure it
can be seen that the allowable free stream temperature has increased around 600 degrees
in the past 50 years The addition of thermal barrier coatings also helps in the increase in
allowable combustion temperatures by creating an extra resistance that the heat needs to
move through as it moves from the combustion gasses into the coolant air It is impotatnt
to notice that as seen in Figure 4 the increase in turbine inlet temperatures is done with
the combined benefits of new alloys TBC and cooling technologies
4
Figure 3 Allowable Turbine Inlet Temperature vs Cooling Techniques over the Years (Clifford 1985)
Figure 4 Turbine Inlet Temperature Increase with the help of TBC New Super Alloys and Cooling
Technologies (Kapat and Kiesow Lectures 2010)
The cooling of inlet guide vanes can be done with the use of impingement inserts
inside the airfoils As air passes through the miniscule holes in the inserts a jet is formed
which then impinges on the wall of the airfoil producing one of the largest single phase
heat transfer coefficients This already impinged coolant air is then bled out as film
5
cooling as well as bled out through the trailing edge Figure 5 shows a stator vane with
the impingement insert in black the film cooling extraction as well as the trailing edge
bleed
Figure 5 Turbine Stator Cooled with Impingement Coupled with Film Cooling (Florschuetz 1980)
The cooling of turbine airfoils with the use of an impingement insert is only
possible in stationary components as the rotating ones are subject to centrifugal loadings
making it unfeasible to cool them with this setup Rotor blades are typically cooled with
serpentine passages that have heat transfer enhancing features such as ribs dimples and
other turbulators these serpentine passages are located in the mid chord of the blade On
the trailing edge a bank of pins are used to obtain high convective coefficients in the thin
region the coolant is the bled out to compensate for the boundary layer created around
the airfoil Rows of impingement holes cool the leading edge The spent air is then bled
out through showerhead cooling Figure 6 and Figure 7 show in detail the cooling
channels around two similar airfoils airfoils
6
Figure 6 Rotor Blade Cooling Configuration (Gladden 1988)
Figure 7 Cross-section of Turbine Airfoil with Cooling Channels (Han et al 1984)
7
The coolant air is bled out from the later stages of the compressor This air is
expensive as it has been compressed and not under gown the heat addition by
combustion It is imperative that the minimum amount of coolant is used in these cooling
configurations The cooling must also be as uniform as possible to reduce thermal
stresses within the blades leading to a higher component life Figure 8 shows freestream
metal and coolant temperatures of the flow blade and coolant air It can be seen that a
decrease of 25degrees in the surface temperature of the blade can provide an airfoil with
twice the working life Impingement cooling has great potential to provide high heat
transfer coefficients at a small flow rate Impingement of a jet onto a surface provides
high heat transfer coefficients due to a starting boundary layer as well as its high
turbulence When the jet is located around 3 diameters from the target surface the heat
transfer profile has two peaks one located at the stagnation region and the other located
between one and 3 diameters from the stagnation region As the jet is moved away from
the target wall the secondary peak diminishes leaving a profile with a maximum at the
stagnation region decreasing radialy
Figure 8 Relative Temperatures for Hot Gas Metal Temperature and Coolant Temperature (Cardwell 2005)
Cardwell N D 2005
8
Figure 9 shows a diagram of a jet impinging on a target surface The potential
core is the part of the jet that has not been affected by the surrounding stagnant fluid As
the jet moves towards the target wall its momentum diffuses into the surrounding fluid
decreasing the velocity at which it reaches the target wall and potentially decreasing the
corresponding heat transfer coefficient Studies have shown (Martin 1973 for example)
that the potential core may last anywhere between 7 to 10 diameters The successful
impingement of the potential core yields significantly higher heat transfer coefficients
than a fully diffused jet this comes however at a cost of higher pressure drop across the
jet plate as well as a highly non uniform heat transfer profile
Figure 9 (a) The Development of the Wall Jet (b) Jet Diffusion to Surroundings (Liu 2006)
9
CHAPTER TWO LITERATURE REVIEW
21 Impingement Literature Cornerstone
From the early days of simple convective cooling channels in turbine airfoils
studies have been done on modes of enhancing heat transfer coefficients while
maintaining a low pressure drop and minimum mass flow rate Heat transfer
characteristics of single round nozzle impingement were studied in the late 1960rsquos and
early 1970rsquos The collected works of many authors is combined into ldquoHeat and Mass
Transfer between Impinging Gas Jets and Solid Surfacesrdquo by Holger Martin 1977 The
paper collects works from multiple authors who studied single round nozzle impingement
effects on heat and mass transfer coefficients In this compilation non dimensional jet to
target spacing was studied they ranged from ZD=12-10 providing plots of Sherwood
number as a function of radius for four different jet to target spacings The local
Sherwood number was also given for a slot jet for HS ranging from 5 to 20 Studies on
impingement jet arrays were also gathered alongside an array of slot jets Correlations
were given for multiple setups present in the paper Circular jet arrays and slot arrays are
studied in detail with both analytical and experimental approaches The paper also
combines studies done on swirling jets turbulence enhancers on the target surface
impingement on concave surfaces and angle of attack variations Optimization studies
were also done to find the optimal spacing for round and slot jet arrays
Florschuetz studied the heat transfer characteristics of an array of jets impinging
on a flat surface This study was guided towards finding an optimal spacing for an array
for jets used to cool the midchord of turbine airfoils similar to that found in Figure 5 His
main contributions include a Nusselt number correlation as a function of jet to target
10
spacing jet Reynolds number and other flow and geometric parameters He found that an
increase in hole spacing and channel height resulted in a decrease of heat transfer He
also provided a one dimensional jet mass flux and channel mass flux correlations
His Nusselt number correlation takes the form of
Where A B and n are dependent by the two different types of arrays inline or staggered
Liu studied new techniques in temperature and pressure measurements of a single
slot jet with the use of temperature sensitive paint or TSP and pressure sensitive paint or
PSP In his work both measurement techniques are explained in detail Since TSP is the
only tool from that study currently used in this work it will be explained further in the
experimental setup section
11
22 Relevant Impingement Channel Studies
Al-Aqal 2003 studied three different types of impingement channels The use of
TLC was implemented in this work to obtain heat transfer distributions for the target
wall The three different configurations varied the number of holes in the streamwise and
spanwise directions The first channel had a single row of 6 streamwise jets the second
consisted of 2 rows of 12 streamwise holes summing up to a total of 24 holes The last
channel is a triple spanwise row with 18 streamwise jets This last geometry is the most
similar to the one present in the current study The third geometry will be used to
compare results There are differences however the total width of the channel is of 16
diameters as opposed to 8 in this study The streamwise jet spacing is also different Al-
Aqal used an XD of 65 compared to XD = 5 in this study The jet to target plate
spacings are similar on two occasions as he studied a ZD=4 6 and 8 while this work
uses a ZD = 6 8 and 10 Average jet Reynolds numbers also fall within the range of this
study as they range between 5000 and 33000 The author provides span averaged plots
for all cases and Reynolds numbers convenient when comparing the results
Ricklick 2009 studied a channel similar to the one found in this study His
channel was composed of a single row of 15 jets with a YcD = 4 XD = 5 and 15 and
ZD = 1 3 and 5 Two channels were tested one was pressure fed while the other was fed
by suction TSP was used to gather temperature data of all four wetted surfaces on the
pressure channel and two surfaces on the suction channel Since the maximum jet Mach
number was less than 03 the flow was assumed to be incompressible leading to the
conclusion that both channels contain identical flow patterns Thin foil heaters were used
to create the required heat flux for the channel Besides channel geometry Reynolds
12
numbers and heater geometry Ricklicksrsquo experimental setup is identical to the one
presented in this work The author also provided an ample comparison of his results to
literature He provided thermal performances of the entire channel at different Reynolds
numbers and channel heights
A small CFD study was also done A paved mesh was created on the target wall
with finer mesh near the impingement locations The resulting y+ at the wall was higher
than one yielding potentially faulty heat transfer values however this is acceptable since
the CFD was used as a tool to better understand the flow physics and help understand the
experimental heat transfer profiles
23 Computational Studies on Impingement Channels
El-Gabry did a numerical study of jet impingement with cross flow Two different
turbulence models were compared in their ability to predict surface Nusselt number The
Yang-Shih and standard k-ε models were used to compute the flow generated by jets
angled at 30 60 and 90 degrees with cross flow The computational results were
compared to previous experimental work by El-Gabry Comparisons to experimental
results at ZD = 1 and 2 90deg injection angle between Yang-Shih and standard k-ε The
error in the average Nu from the experimental results and both turbulence models were
calculated It was found that the Yang-Shih model behaved well at low Reynolds
numbers with the average Nusselt number being 5 off from the experimental value
while the standard k-ε was off my 94 As jet Reynolds number was increased the error
of the standard k-ε model dropped to as low as 39 while the error from the Yang-shih
model increased to -76 The span average plots show the experimental data Nusselt
number alongside the span averages of the results acquired by the Yang-Shih and
13
standard k-ε models High Nusselt numbers occur at the impingement location decreasing
thereafter after another impingement location is found The frequencies of these
variations are all the same for the experimental and the two numerical solutions The
amplitude of fluctuations between the impingement locations and the areas in between
are much larger for both of the numerical results however the Yang-Shih model over
predicts at the high Reynolds number for the ZD=2 case Since the amplitude of
fluctuations is greater for the CFD solutions it is important to note that even though the
error in average Nusselt number is not great the actual differences in the profile are much
greater upwards of 20 difference of heat transfer coefficients between the experimental
and numerical heat transfer peaks Other variations were studied (Injection angles for
example) but will not be discussed as their importance to the current study is minimal
Zuckerman compared a much wider set of turbulence models in their ability to
successfully predict Nusselt numbers caused by jet impingement The models tested were
k ndash ε k-ω Reynolds Stress Model algebraic stress models shear stress transport and
lastly the υ2f turbulence model DNS runs are extremely time consuming to run
therefore LES was run on its behalf to provide results for the unsteady turbulence
models The paper summarizes all the different models used their computational cost
impingement heat transfer coefficient and their ability to predict the second peak in heat
transfer As expected DNSLES provide the best prediction of both stagnation and
secondary peak heat transfer coefficient however this comes at a large computational
cost The k ndash ε and k-ω provide poor heat transfer results for the stagnation region where
they can have 30 error from the correct value The Realizable k ndash ε model provides
14
better heat transfer results while still maintaining a low computational cost The highest
accuracy to cost ratio was achieved by the υ2f model where it predicts the heat transfer
coefficient for the surface with a minimum of 2 error while not being as expensive as
the other unsteady models such as DNS and LES Ideally the CFD portion of this work
would be run with the υ2f model however since the code used to run the simulation
FLUENT does not have the υ2f model a realizable k ndash ε model will be used with
enhanced wall functions for both thermal and velocity gradients
15
CHAPTER THREE EXPERIMENTAL SETUP AND TECHNIQUES
31 Temperature Measurements with TSP
Temperature sensitive paint or TSP provides the capability of measuring
temperatures over the painted area This measurement technique supersedes the
advantages of other temperature measurement devices such as thermocouples because it
provides the user with data over a large area rather than point temperatures given by
thermocouples
Uni-Coat TSP is purchased from ISSI It is very robust to different working
conditions Calibration done on one batch of paint can be used for multiple cans as the
product is highly consistent The paint is calibrated in a dark booth a painted coupon is
placed on the hot side of a thermoelectric heat pump working on the Peltier effect
thermal paste is used to minimize contact resistance between the hot side and the TSP
coupon Calibrated thermocouples are placed in between the TSP and the thermoelectric
heat pump A reference temperature and picture are taken and the calibration commences
At least 5 or 6 data points should be taken to form the calibration Intensity ratios are
taken between the hot and cold pictures They are then plotted versus their corresponding
temperature
The paint consists of fluorescent molecules suspended in a binder These
molecules with a certain wavelength of light will be exited to a higher energy level The
molecules then can dissipate some of the energy by transferring it vibrationally to its
neighboring binder particles and dissipate the remainder of the energy by radiating it as a
photon as the molecule comes down to its original ground state Since the amount of
16
energy that the particle can transmit to others through vibration is directly proportional on
temperature and the total initial energy is fixed by measuring the ratio of the intensity at
a known temperature (reference picture) and intensity of the unknown temperature
feeding it through the correlation the unknown temperature can be found to an
uncertainty of 1 K Figure 10 shows a simplified Jablonski diagram adapted from the
suppliers website The blue arrows signify the blue light used to excite the luminescent
molecule Tris(22rsquo-bipyridyl) Ruthenium(II) Chloride Hexahydrate with a shellac binder
in our case The shellac binder is impermeable to oxygen opposite of that found in PSP
due to PSP relying on the presence of oxygen for it to function Once the particle is
excited it can give off the energy in two different ways one is by emitting it back out as
another photon of the same energy and therefore wavelength The second mode of the
particle to lose its energy is through vibrational relaxation This second process is directly
dependent on the temperature ie the higher the temperature the higher the probability
for it to lose energy to its surroundings Once it loses some energy to the surrounding
particles it releases the remainder of the energy as a photon of less energy of that which
excited it originally hence why a long pass filter is installed in the CCD camera For a
more descriptive explanation of the way TSP works refer to Liu 2006
17
Figure 10 Simplified Jablonski Diagram (Adapted from ISSI Website)
Throughout the past two years there have been numerous projects at CATER that
have used TSP Painting surfaces with TSP should be done carefully by someone who
has experience with spray painting since every single can costs $500 A single can should
be able to paint an area the size of an acrylic plate that is 36rdquo wide and 24rdquotallThe
sidewalls and the target wall of the impingement channel were painted with the use of
less than one can Painting on different surfaces is difficult for example when painting
Rohacell the paint canister can be held very close to the surface while spraying due to
the surface being somewhat porous and rough however when painting straight onto
metal heater strips the can should be placed as far back as possible for the first run
Ideally for the first pass through only a slight mist should be applied If the can is being
held too close to the surface the paint will run Figure 11 shows a set of heater strips that
has been painted too closely leading the paint to drip down Ideally the paint would be
applied to the surface in as many coats as possible Of course this would be time
18
demanding and impractical therefore with the knowledge that I have gained through the
multiple TSP paintings on different surfaces I have compiled a list of TSP dos and
donrsquots
Dos
Clean the surface to be painted with acetone or break parts cleaner Break
parts cleaner is preferable over acetone as it does not leave an oily residual
after cleaning
Paint the first coat as thin as possible Most of the surface should not be
covered There should be an even mist of miniscule TSP circles This will
give the later coats something to attach to
When positioning the test section to paint make sure to wipe it one last
time as small dust particles may have attached to the surface
Stop if you see small bumps in the paint This is caused by dust particles
collecting all the paint around it while it is still wet due to surface tension
Clean the surface and repaint This should be noticeable in the first few
coats If you see this pattern happening do not continue thinking it will be
covered by future coats What will happen is the problem will get worse
and worse ultimately the surface will have to be cleaned again and
repainted
When painting test sections try to paint the smallest section as possible
This will not only save paint but will make it very simple for the post
processing code to crop out the unpainted areas
19
Let the finished painted surface to sit at least for 90 minutes after the last
coat before baking There have been problems when baking steel and
acrylic test sections with the paint cracking while baking right after the
last coat Normally the finished surface is left to dry overnight and baked
first thing in the morning
For test sections that are too large to be baked in the oven the heat gun
may be used Carefully place a thermocouple in a central location with
blue painters tape The heating should be uniform and should not take
more than 20 minutes of continuous blowing When the thermocouple
reaches 80-90 C the plate can be assumed to be baked To introduce a
factor of safety in the baking it does not hurt to bake it longer than it
normally takes
Once the test section is mounted and ready to run cover it with cloth that
does not let any light through This will protect the paint for further uses
This is especially important on test sections that can be used multiple
times like the ones found in this study
When the test is running turn off the LED lights This light is the most
damaging to the TSP as it degrades the quality of the fluorescent
molecules
If there is a particular head of the TSP can that you prefer over others you
can remove it once the can is empty It is difficult to get used to a single
kind of nozzle being able to transfer it from can to can is a must if
painting consistency is to be kept
20
Donrsquots
Do not clean a test section that has already been used with too much
acetone The acetone is volatile evaporating quickly cooling the test
section rapidly If this test section has had heaters attached to it and run
previously the acrylic will crack due to uneven stresses inside of it
If paint is dripping stop painting immediately Clean the surface and start
over Hold the can far from the surface in order for it not to drip
Do not use TSP to teach new apprentices undergrads or graduate students
how to paint Regular spray paint is two orders of magnitude lower in cost
while the painting process is exactly the same
Do not paint with the doors closed The paint contains carcinogens that
can harm the lungs Always use a respirator and keep the room well
ventilated In-situ painting and baking has not been tried however it may
be a real option if the test section is difficult to disassemble and easily
accessible to painting and baking
If there is a can of paint that contains too little paint for the test section
that needs to be painted try to find a new can The mixing of two different
cans of TSP can be dangerous at times however it has been noticed over
the years that ISSI provides a very robust and dependable product that
does not vary significantly from batch to batch
21
Figure 11 Heater Strips Painted with TSP Too Closely
32 Experimental Setup of Suction Channel
The impingement channel is fed under suction As seen in Figure 12 air enters
through the plenum it crosses the jet plate as it gains speed to form the jets
which then impinge on the target wall The flow then passes through a venturi
flow meter and finally through the blower into the atmosphere A bypass valve is
used to control the flow rate of the impingement channel
22
Figure 12 Flow Loop of Impingement Channel
The impingement channel consists of 15 streamwise rows of 3 spanwise jets each The
total width of the channel YcD is of 8 diameters while the streamwise spacing between
the rows is XD=5 the spanwise distance between the holes is of YD=2 Figure 13shows
the top view of the jet plate The plate is counter bored to ensure that a nearly flat
velocity profile of the jet is achieved Figure 14 shows the front view of the channel Z is
denoted as the distance between the jet and target plates Side walls are interchangeable
to change the height of the channel to 6 8 and 10 diameters Two thirds of the
streamwise rows can be covered to change the XD from 5 to 15
Figure 13 Top View of Jet Plate
23
Figure 14 Front View of Impingement Channel
The target and sidewalls had heaters made specifically for them in a serpentine
style This was necessary to increase the resistance as the VARIACs used to power them
only had a maximum current output of 20 amps The heater strips are two diameters
wide at each end copper tape with conductive adhesive was used to connect the leads to
the power supply The heater consists of 50 micron thick steel sheet sandwiched between
two pieces of Kapton tape The heater is attached to the painted surface with the use of
double sided Kapton tape The target test section can be seen in Figure 15 also seen in
this figure are the two Teflon gaskets lined on the sides of the target plate With the target
wall bolted onto the sidewall the gasket is compressed generating a strong seal
Figure 15 Target Wall Test Section with Heater Leads
24
For this study the test matrix shown in Table 1 will be run Target and side wall
data will be taken at three different impingement heights at two different Reynolds
numbers of 7500 and 15000 denoted by A and B respectively A streamwise jet spacing
study is also done by testing the target and side wall heat transfer at an XD=15 for the
low impingement height channel
Table 1 Test Matrix
XD ZD Wall Re
5
10 TW
7500
15000
SW 7500
15000
8 TW
7500
15000
SW 7500
15000
6 TW
7500
15000
SW 7500
15000
15 6 TW
7500
15000
SW 7500
15000
33 Data Processing and Reduction
As described previously when taking temperature measurements with the use of TSP
reference temperatures are noted and a reference picture is taken The experiment is the
run once the experiment reaches steady state a new set of 4 pictures is taken Given the
calibration curve temperatures are backed out
25
Given the amount of heat generated inside the heater
Dividing by the heated area to get heat flux
Heat loss tests were run to consider how much of the heat flux generated by the heaters
goes through the backside instead of into the flow It was found that 25 of the heat flux
leaks out to the atmosphere through the acrylic In order to account for this heat leakage
it must be subtracted from the calculated value to become
Where Ah is the effective heated area given by
Where Aunheated is an estimate of how much unheated area is between the heater strips (~
3 of the total area)
To obtain heat transfer coefficient
Where Tref is the reference temperature Typically set in literature to be the jet
temperature
To obtain the average Reynolds number for the jets the total mass flow rate is used
Where Dj is the jet diameter and μ is dynamic viscosity (1983kgm s at 300K)
26
Pressure measurements were taken at the sidewall after the last jet entered the channel
These pressure measurements were used to determine the thermal performance of the
tallest two channels (ZD = 8 and 10)
The thermal performance at constant pumping power is found by using the equation
Where h is the average heat transfer coefficient for the target wall of them impingement
channel and ho is the heat transfer coefficient obtained by passing the same amount of
flow through a smooth duct ie the Dittus-Boelter correlation The friction factor f is
found with the use of
Where Ppl is the plenum static pressure assumed to be atmospheric and Plast jet is
the pressure read after the last jet V is the volumetric flow rate divided by the cross-
sectional area of the duct after the last impingement row The hydraulic diameter of the
channel is set to be
The baseline friction factor was calculated with the use of the Moody chart the hydraulic
diameter and the total mass flow rate though the channel Thermal performance at
constant pressure drop was also calculated with
27
34 Uncertainty Analysis
A simple uncertainty analysis was done to estimate the error in calculation of the
heat transfer coefficient from the given outputs of the test data From the bare basic
measurements for voltage area current temperature of thermocouples and temperature
profiles of paint a simple uncertainty analysis can be done to estimate the error for the
calculated heat transfer coefficient Figure 16 shows the different sources of error in the
calculation of heat transfer coefficient The effective uncertainty was calculated by taking
the root of the sum of the squares of all the individual percentage errors The
experimental uncertainty for heat transfer coefficient was of 703 This error may be
reduced by acquiring higher temperatures of the TSP reading current with a more
accurate ammeter or reading reference temperatures with the use of a thermopile instead
of a single thermocouple
Figure 16 Heat Transfer Coefficient Uncertainty Tree
28
35 Lateral Conduction Analysis
To take into account the lateral conduction occurring inside the heater foil while
the test is running two simple 1D conduction and convection equations were used to
quantify the amount of heat moving through the heater laterally and the amount of heat
convecting into the air The lateral conduction is expected to be at a maximum at the
places where there are large spatial variations of surface temperature which is why the
ZD = 6 XD = 5 case at high Re is chosen to be studied Figure 17 shows the
temperature distribution of the aforementioned case Four cold spots can be seen by their
distinct blue and yellow color located at the stagnation regions The maximum
temperature gradient occurs between the third jet impingement and the middle region
between jets The temperature difference was seen to be of 13degC The distance in between
these two temperatures is of 25D=01875m The corresponding heat flux between these
two points was calculated to be 13000Wm2 with ksteel~20Wm K A region of 1cm by
1cm was then created and the amount of heat calculated through conduction and
convection were compared To acquire the amount of heat removed through conduction
a heat flux of 13000Wm2 was imposed through an area of 01m by 00005m this
equaled to 00277 W The amount of heat moved through convection was calculated by
multiplying the heat flux used during the test by the area of the square 0001m2 the
resulting heat moving through the heater onto the air is 6 W Since the heat moving
through to the air is two orders of magnitudes larger than the heat moving laterally the
effective lateral conduction can be neglected
29
Figure 17 Temperature Profile of First Five Impingement Rows
A second order approach was also taken to quantify the amount of lateral
conduction in the heater The temperature gradient was taken from high peaks in heat
transfer caused by the second row of impingement of the same ZD=6 XD=5 channel at
high Re Figure 18 shows the high heat transfer coefficients created by the second row of
jets A quadratic curve fit was obtained by for this small region so that a continuous
equation of heat transfer coefficients as a function of streamwise distance was quantified
30
Figure 18 Detailed View of First Heat Transfer Peak with a Polynomial Curve Fit
The net heat gained by a differential volume from lateral conduction is the
difference in the temperature gradient at the entrance and the exit multiplied by the
thermal conductivity and cross sectional area Using this method shown in Figure 19 the
net change in convective heat transfer due to lateral conduction can be studied
Figure 19 Control Volume Heat Transfer Analysis
By taking the difference between the out flowing heat trough the right side and
the inflowing heat from the left side a net gain or loss can be found Figure 20 shows the
y = -470630x2 + 31244x - 14842Rsup2 = 09934
300
310
320
330
340
350
360
370
380
0 001 002 003 004 005
HTC
(W
m2K
)
x (m)
Heat Transfer Peak
Poly (Heat Transfer Peak)
31
difference in magnitude between the out flowing heat through convection seen in red and
the net inflow of heat from lateral conduction in blue From these calculations it was also
found that the amount of heat moving through lateral conduction is tow orders of
magnitude smaller than the amount of heat moving out through convection leading to the
belief that even at high temperature gradients lateral conduction does not play an
important role in the ongoing heat transfer processes in the impingement channel A more
detailed calculation of this work can be seen in appendix A
Figure 20 Heat Loss through Convection and Lateral Conduction
002 003 004 0051 10
5
1 104
1 103
001
qconv x( )
qnet x( )
x x
32
CHAPTER FOUR HEAT TRANSFER RESULTS
41 Heat Transfer Validation
In order to obtain confidence in our experimental setup an experiment was made
to test something that has already been published in literature A smooth channel was the
obvious choice as it was easy to setup by taking off the end cap and blocking all the holes
with smooth blue painters tape on the flow side and metal tape on the plenum side to
ensure no leaks into the channel from the jet plate The smooth channel has been studied
widely and multiple correlations exist one of these equations is the Dittus-Boelter
correlation (Incropera 2007) The test was run using the ZD=6 side wall so that the
hydraulic diameter was a minimum Figure 21 shows the span averaged results versus
non dimensional distance into the channel
Figure 21 Validation Spanwise Averaged Results
0
10
20
30
40
50
60
0 1 2 3 4 5 6 7 8 9
HTC
(W
m2K
)
XDc
Span Avg
Dittus Boelter
33
The plot shows decreasing heat transfer coefficient with increasing XDc due to
the developing thermal boundary layer The span average does not reach the Dittus-
Boelter due to it not being fully developed in the limited space it is given Typical flows
can take up to 60 diameters to achieve a fully developed profile with the current setup
the maximum length of the channel was of 9 diameters The profile however seems to
have an asymptote at the Dittus-Boelter correlation value leading to the belief that if the
channel was longer that value given by the correlation would be reached One important
factor to take into account in determining whether the experimental setup is validated is
the fact that the Dittus-Boelter correlation has an uncertainty near 30 Since the span
average at high XDc is well within 30 from the calculated value it is safe to assume
that the current experimental setup is validated
42 Heat Transfer Results
Heat transfer results are compared based on variations in channel height and
average jet Reynolds number As discussed earlier there are numerous other parameters
also affecting the heat transfer in these channels As these parameters are changed flow
structures within the channel are expected to be altered as well as discussed in the
literature Two of the major contributors to heat transfer in these channels are the
successful jet impingement and the resulting cross flow The same domain is captured in
both the local and averaged results
Figure 22 through Figure 25 highlights the heat transfer distribution for the cases
with a jet to jet spacing of 5 diameters in the streamwise direction and of 2 in the
spanwise direction It is evident that the smallest channel height (ZD=6) performs the
best at all Reynolds numbers on all surfaces It is also interesting to note the similarity
34
in the target wall profiles between case 528A and B where the curves are very similar
other than the obvious offset due to the change of the Reynolds number At this large
spacing we also see the degradation of the jets a few diameters downstream of each
impingement location The downstream shifts of the peaks are evident after the second
and third row of jets Also evident in these plots is the deflection of the impinging jet and
the wall jets from the cross flow The cross flow is forced to flow around the jet
deflecting the spread of the wall jet in the downstream direction Impingement locations
are also very evident at low XD however as XD and therefore the cross flow increase
the magnitude of the peaks start decreasing and eventually level out to pure internal flow
Figure 22 Target Wall Heat Transfer Coefficient Distributions
35
Figure 23 Span-averaged Target Wall Heat Transfer Distribution
36
Figure 24 Side Wall Heat Transfer Coefficient Distributions
37
Figure 25 Span-averaged Side wall Heat Transfer Distribution
Figure 23 and Figure 25 show similar details with impingement peaks clearly
diminishing and shifting in the downstream direction The cross flow clearly has some
negative influence on these geometries when compared to the more traditional
impingement highest on the order of 1 to 5 jet diameters The heat transfer profiles of the
target wall for all heights seen in Figure 22 and Figure 24 show the rapid decay in heat
transfer after the third jet This can be explained by understanding that the first jet does
not have any cross flow to deflect it the second jet only has the first jet worth of
momentum deflecting it downstream however since the channel is so tall the
momentum of the cross flow after the first and second jet are not enough to greatly
disturb the incoming jets After the third jet however the cross flow builds up enough
momentum to greatly affect the integrity of the jets downstream causing the span-
0
20
40
60
80
100
120
140
160
2 12 22 32 42 52 62 72
HTC
(W
m2K
)
XD
5210B_SW 528A_SW Jet Location
526A_TW 526B_TW
38
averaged heat transfer to rapidly drop The point at which the crossflow starts taking a
considerable effect occurs around XD =35 The target wall profile of the ZD=10
channel shows the outside jets on the second row of jet deflecting downstream It can be
conjectured that the bending of the outside jets downstream is caused by the wall jet
created by the first row of jets separating from the side wall and deflecting the outside
jets of the following rows of jets The heat transfer profile for the ZD case excludes the
first jet due to shadows being present when the data was taken
Also evident from this spanwise averaged data is the increase in heat transfer
with increases in Reynolds numbers and decreases in impingement height Results tend
to be the closest from case to case at the first impingement jet This is a reasonable
result as the effects of cross flow have little to no effect at the first few impingement
locations The impact of the jet would then be the driving force at these locations and
would be similar between cases except if the potential core is not reaching the target
surface The potential core of a jet tends to last between 6 and 10 diameters from its
origin It can be seen that the difference in heat transfer coefficient in the first two jets for
the ZD=8 and ZD=10 channel is much different than the corresponding difference
between the ZD=6 and ZD=8 heights This decreased difference between the heights of
the peaks may be attributed to the potential core reaching the target wall at the heights of
6 and 8 diameters leading to similar profiles and may not be reaching the surface at the
height of 10 diameters The heat transfer values of the peaks diminish in the downstream
direction The range of fluctuation also drops that is the profile becomes more uniform
at large XD This drop in fluctuation is more visible at the tallest channel height
(ZD=10) and less pronounced at the smallest channel This is due to the jet in the small
39
channel having to travel a shorter distance to impinge on the target plate leaving the
crossflow less time for it to deflect the jet as opposed to the tall channel where the jet has
to travel almost twice the distance as the ZD=6 channel for it to impinge on the target
wall This effect cannot be solely explained by the built up cross flow in the channel
Mixing loses also take part in the degradation of the stagnation size of the downstream
jets The mixing losses have much greater effect on the taller channels due to the same
reason that the cross flow has a higher impact on them too the jets have to travel a large
distance before hitting the target plate leading the stagnant or moving surrounding air to
be a sink of its downward momentum for a longer time and distance than the respective
smaller channels The heat transfer coefficient of the side wall was also analyzed
Similar effects are expected on the side wall due to the expected impact of the wall jet
As expected the strength of the cross flow is not enough to prevent wall jets from
successfully impacting the side wall at small XD jet locations however the crossflow
takes dominance at around XD=25 Also evident in these plots is the concentration of the
wall jet impact to the bottom of the channel on the order of 1-2 diameters in height It is
interesting to note that for the 5210B case in Figure 24 as the first jet diffuses outward
it impacts the sidewall at a height of ZD=6 The height at which the diffused jet affects
the sidewall heat transfer coefficient decreases as the crossflow increases The stagnation
regions are also deflected in the downstream direction similar to the target surface
results These effects are most evident in the 5210B Similar characteristics can be
explained from the spanwise-averaged plots shown in Figure 25 These results again
clearly show the effects of increasing the impingement height and increases in Reynolds
number As the height is increased the effect of the wall jet is significantly reduced
40
partially due to the increased surface area much of which is not affected by the wall jet
The diminishing effect of the cross flow accumulation is also evident in these plots as the
heat transfer peaks decrease in the downstream direction
43 XD Comparisons
The streamwise jet spacing was changed from XD=5 to 15 by covering two out
of three rows of jets This was done by covering the impingement holes inside the
channel with smooth blue painters tape and sealing the plenum side of the jet plate with
metal tape to ensure no leakage The profile is expected to be less uniform than the case
where XD=5 due to the large spreading of the high heat transfer peaks Due to the large
separation between the rows of jets there is a lower amount of downward momentum
than the equivalent XD=5 geometry for this reason it is expected to see a lower heat
transfer peak due to the jets momentum diffusing out faster to the stagnant air decreasing
the effective impingement velocity Figure 26 shows the target wall heat transfer
distribution Similar to the XD=5 profile it can be seen that the heat transfer due to the
jet impingement drastically reduces after the third jet This phenomenon leads us to
believe that at both Reynolds numbers the cross flow generated by the first three jets is
powerful enough to effectively deflect the fourth jet downstream diminishing its heat
transfer performance The similarity seen in Figure 26 between high and low Reynolds
number implies that the downstream deflection of the jets is not dependent on the jet
Reynolds numbers
41
Figure 26 XD=15 Target Wall Heat Transfer Profile
42
Figure 27 XD=15 Span-averaged Target Wall Heat Transfer Distribution
On the span averaged plots seen in Figure 27 the downstream deflection of the
jets is evident however as described previously the shifts in the peaks of heat transfer
occur at the same xD for both Reynolds numbers The amplitude of fluctuation of heat
transfer coefficients for the high Reynolds number case is larger than that of the low
Reynolds number Both profiles seem to start to level off at the end of the impingement
channel with the lowest span average being located just before the fourth jet at both
Reynolds numbers
A comparison of target wall heat transfer coefficients between XD =15 and 5 is
shown in Figure 28 At first glance it is clearly visible that the XD=15 average heat
transfer coefficient is smaller than its XD=5 counterpart This is also noticed by Ricklick
where he showed average HTC profiles for larger XD to be smaller than those at lower
XD (Ricklick 2009) This may occur due to there not being as high downward
0
50
100
150
200
250
300
350
0 20 40 60 80
HTC
(W
m2
K)
XD
Low Re
High Re
Impingement Location
43
momentum for the XD=15 case as compared to the XD=5 due to the lack of close jets
The stagnant air around the spaced out jets is taking away more of its momentum
decreasing the effective impingement Reynolds number Also important to notice is the
fact that since the XD=5 case has three times the flow impinged into it the cross flow
velocity and therefore Reynolds number will be three times as large increasing the heat
transfer coefficient
Figure 28 Target Wall Span-average Comparison of XD=5 and 15 at High Re
The side walls also show similar patterns to their XD=15 counterparts Strong
wall jet impingement can be seen on the side wall at low xD and zD Figure 29 shows
areas where the wall jet generated by the target wall impinges on the sidewall Similar to
the profile seen in Figure 24 the high heat transfer region reaches upward in the z
direction up to a height of 4-5 diameters for the first jet This high heat transfer stagnation
region decreases as xD increases to the point where the wall jet created by the last jet is
negligible when coupled with pure channel flow
0
50
100
150
200
250
300
350
400
0 10 20 30 40 50 60 70 80
HTC
(W
m2K
)
XD
XD = 5 XD = 15 Jet Location
- Blocked for XD =15
44
Figure 29 Side Wall Heat transfer Coefficient Profile
The span averaged plot seen in Figure 30 shows a nearly flat profile with peaks
located at the stagnation regions of the wall jets Thw downstream deflection for the
XD=15 case is much more pronounced than the one for the XD=5 case This is due to
the jet not being constrained by the wall jets generated by the previous and latter
impingement locations In the XD=15 case the wall jet is free to move downstream
more so than the XD=5 due to it not being disturbed by anything other than the cross
flow
45
Figure 30 XD=15 Side Wall Span-averaged Heat Transfer Coefficients
44 3D Comparison of the Heat Transfer Profiles
In order to further understand the targetsidewall interactions both heat transfer profiles
were positioned in an isometric view representative of the channel One important thing
to note is that both target and side wall profiles are not on the same scale This form of
data display is only qualitative way to describe the heat transfer profiles Figure 31 shows
the 3D profile of the XD=5 ZD=6 case The both stagnation regions of the jet onto the
target wall and the wall jet into the sidewall can be seen to occur at the same location for
the first three streamwise rows After the fourth and fifth row the wall jet diminishes in
magnitude Also visible in this view is the increasing heat transfer at low zD towards the
end of the channel of the side wall The constant input of mass and downward momentum
into the channel causes the cross flow generated by the previous jets to be squeezed into
the lower third of the channel increasing the velocity and the heat transfer of the target
wall
0
20
40
60
80
100
120
0 20 40 60 80
HTC
(W
m2K
)
XD
Low Re High Re Jet Locations
46
Figure 31 3D Heat Transfer Profile for ZD=6 XD=5
Similar patterns are seen in the taller ZD=8 channel seen in Figure 32 The wall jet
generate by the third streamwise row of jets is been deflected downward more than its
ZD=6 counterpart This can be attributed to the fact that the jet located at the ZD=8
channel has lost much of its momentum and is more easily bent downstream by the cross
flow generated by the first two jets The ZD=8 sidewall shows similar increasing heat
transfer at high xD however the increase is not as drastic as the one found in the ZD=6
channel This is caused due to the extra two diameters the jets have to cover to impinge
on the surface since the ZD=8 channel is one third larger than the ZD=6 one the flow
has to have more area to flow through The last few jets only deflect the cross flow
downward about 4 diameters this leaves two diameters for the flow to pass through on
the ZD=6 channel causing the velocity to increase rapidly and therefore increasing the
heat transfer coefficient at the low zD Since the ZD=8 channel has four remaining
47
diameters for the flow to move through it does not deflect it as much as the ZD=6
channel does only increasing the cross flow velocity and resulting heat transfer
coefficient slightly over the area at low zD and high xD
Figure 32 3D Heat Transfer Profile for ZD=8 XD=5
The 3D heat transfer profile for ZD=6 and xD=15 channel seen in Figure 33 shows
similar details to those seen in the XD=5 channels The stagnation regions of the jet and
wall jet occur at the same x location for the first three rows of jets the wall jet generated
by the fourth row of jets is deflected downstream only generating as small region of high
convective coefficients at the side wall The region located at the top right corner of the
side wall is colored red signifying high heat transfer however this area is generated by
the heaters providing non uniform heat flux at this location This region of high heat
transfer coefficients also occur at xD=0-4 of the target wall where the heater coil bends
48
Figure 33 3D Heat Transfer Profile for ZD=6 XD=15
45 Thermal Performance Calculations
Thermal performance calculations were done on the two tallest channels (ZD=8 and 10)
The pumping power was calculated for both channels at two Reynolds numbers Figure
34 shows the ratio of pressures required to pull the same amount of flow through as
smooth duct as opposed to through the jet plate The ZD=10 channel at high Reynolds
number requires the largest pressure as seen in the Figure however in order to pull the
same amount of flow rate through it requires a smaller pressure difference due to the
large cross section
49
Figure 34 Pressure Drop Ratio with Respect to Smooth Channel
Next the heat transfer enhancement was calculated A total area averaged heat
transfer coefficient was taken for the target wall and compared to the smooth channel
Dittus-Boelter value while using the same total mass flow rate Figure 35 shows an
average heat transfer enhancement of four times that of a smooth channel Similar trends
were noticed in the literature (Ricklick 2009) of decreasing heat transfer enhancement
with an increase of jet Reynolds number Ricklick also showed an increase in heat
transfer enhancement with an increase of jet to target spacing similar to the one seen in
Figure 35
0
10
20
30
40
50
60
528A_TW 528B_TW 5210A_TW 5210B_TW
PP
o
50
Figure 35 Heat Transfer Enhancement
Thermal performances at constant pressure drop were then calculated by dividing
the heat transfer enhancement by the pressure increase As seen in Figure 36 all the
values fall well below 1 making the impingement channel an unfeasible mode of heat
transfer enhancement when a constant pressure is supplied
Figure 36 Thermal Performance at Constant Pressure Drop
0
05
1
15
2
25
3
35
4
45
528A_TW 528B_TW 5210A_TW 5210B_TW
hh
o
0
002
004
006
008
01
012
014
528A_TW 528B_TW 5210A_TW 5210B_TW
(hh
o)
(PP
o)
51
The thermal performance at constant pumping drop was calculated in the same
way that the constant pressure drop was calculated the only difference being the pressure
ratio term was raised to the one third power As seen in Figure 37 the thermal
performances at constant pumping power are all higher than unity this signifies that if a
surface needs to be cooled with the supply of a constant pumping power the
impingement channel is a feasible option Similar to the figure literature (Ricklick 2009)
showed a decrease of thermal performance with an increase of channel height and
Reynolds number
Figure 37 Thermal Performance at Constant Pumping Power
0
02
04
06
08
1
12
14
528A_TW 528B_TW 5210A_TW 5210B_TW
(hh
o)
(PP
o)1
3
52
CHAPTER FIVE COMPUTATIONAL FLUID DYNAMICS
51 Problem Setup
In order to further enhance the understanding of the heat transfer profiles showed
previously a computational study was performed Even though CFD does not yield
accurate quantitative results it produces good qualitative data that can be used to explain
the flow physics in the channel and therefore increase the understanding of the patterns
seen previously The channel was meshed with the use of GAMBIT Due to the
symmetry the channel was split in half in the streamwise direction All horizontal
surfaces (parallel to the target wall) were divided into 6 different regions that are later on
going to be meshed individually The six regions are seen in Figure 38 section 1 is
located at the center of every jet also referred to as ldquojet centerrdquo This region was created
to reduce the squewness of the elements near the center of the jet by allowing the mesh to
be completely linear with a squewness of zero Section two complements section 1 to
complete the impingement hole The half impingement hole located at the symmetry wall
contains the same exact region 2 however it only has one half of the jet center Section 3
was made in order to bring the polar geometry of the holes to match the cartesian aspect
of the remainder of the channel With the addition of section 3 to the channel the only
remaining sections are square or rectangular regions Region 4 lies in between
streamwise rows of jets Section 5 is located at the entrance and the exit of the channel
These sections are not square in contrast with section 4 The last remaining section is
located near the side wall of the channel extending from the beginning to the exit of the
channel
53
Figure 38 Horizontal Plane of Impingement Channel Geometry
All the faces of sections 1 and 2 are linked throughout the channel and the
plenum however in order to have greater control of the mesh in the plenum and the
channel the remaining sections 3 4 5 and 6 are not linked to every single similar face
instead they are only linked to similar faces in either the plenum or the channel
Boundary layer spacing number of rows and growth factor are placed around the
channel In order to maintain a y+ of less than unity the first cell spacing of the boundary
layer inside the channel was set to be 000001 m (01mm) This first cell spacing yielded
y+
values varying between zero and 9 at the target side and front end wall Figure 39
shows a contour of y+ values on the heated walls The maximum values occur near the
impingement locations as expected due to large shear caused by the steep velocity
gradient normal to the wall On the downstream direction the y+ also increases due to the
increase of flow rate and therefore the increased skin friction on the wall At the
impingement location of the first jet the y+ is close to zero due to the velocity having its
direction mostly normal to the surface yielding no shear
54
Figure 39 Target Side and Front End Wall y+ Values
Once the faces were linked edge meshes were created on the sides of the jet center
Section 2rsquos inner edge was also meshed using a different parameter than the one used for
the jet center in order to allow for more freedom when trying to refine the mesh These
two edge meshes is followed by meshing all of section 2 faces alongside all the jet
centers Once these were complete section 3rsquos inner edge was meshed with different
parameters for the channel and plenum Sections 4 and 5 sides that connected with the
face made by section 6 were meshed so that their spacing was similar again the plenum
and channel were meshed separately for increased control of mesh density in both of
these areas The upstream-most edge of section 6 was meshed so that the spacing is
similar to the edge mesh in sections 4 and 5 this was done in order to have aspect ratios
of the wall be as close as possible to unity Sections 3 4 5 and 6 were meshed on both
the channel and the plenum With the entire target wall plane meshed these surface
meshes are coopered upwards to connect to the opposite wall The vertical spacing has
55
also been set up differently between the channel and the plenum The holes and the
plenum were also coopered The finished mesh was then exported as a msh file
Boundary conditions were set in GAMBIT once the mesh was imported into
Fluent values were set to every face depending on their location and purpose Figure 40
shows the four different boundary conditions Face 1 (blue) was set to be a mass flow
inlet The flow rate is half of the total flow rate at a given jet Reynolds number due to it
being only half of the entire domain Face 2 (yellow) is a symmetry plane face 3 (red) is
a pressure outlet at zero gauge pressure The rest of the faces in the channel denoted by
the number 4 (white) are set to walls The target side and front end wall had a heat flux
applied to them equal to 10000Wm2
Figure 40 Finished Mesh with Boundary Conditions
The model was imported into Fluent It was scaled down by a factor of 1000 due to it
being made in GAMBIT in millimeters The energy model was turned on The Realizable
k-ε model was used with enhanced wall functions on both the pressure and thermal
gradients The boundary conditions were set as discussed previously the mass flow inlet
was set to the specific flow rate normal to the surface the heat fluxes were set on the
56
heated walls the outflow gauge pressure was set to zero Two important reference values
characteristic length and reference temperature were set to be the diameter of the jet
(0075m) and 300K respectively The spatial discretization parameters were set to second
order upwind for momentum turbulent kinetic energy turbulent dissipation rate and
energy The under-relaxation factors were set to default Four monitors were created to
aid in the determination of convergence two of them read Nusselt numbers at the
stagnation region of the first and last jet the remaining two read the exit velocity at the
first and last jet The continuity x y and x velocities and energy equations residuals
were set to be 1E-6 while k and ε residuals were set to 1E-4 The solution was initialized
on the all zones at 1ms in the positive x direction The solution was set to autosave every
100 iterations while keeping only the two newest dat files The calculation was then run
for a maximum of 7000 iterations
A grid independence study was done on the domain to find the optimal size of
mesh that provides the correct solution while minimizing the compute time Two
monitors were set to check for grid independence both of them were vertex maximum
One of them read the Nusselt number at the impingement location of the first center jet
while the second one measures the velocity at the exit of the last jet Four different mesh
sizes were run to the convergence criterion explained before their sizes were 900000
15 million 28 million and 43 million cells
57
Figure 41 Grid Independence Study
It can be seen in Figure 41 that the difference between the 28 and 43 million cell
meshes are very small a difference of under 006 for velocity and 7 for Nusselt
number It can be safe to assume that the 28 million cell mesh is large enough to provide
a mesh independent solution The GAMBIT journal file used to create this mesh is
attached to the appendix The results shown hereafter are the ones obtained by the 28
million cell mesh
Figure 42 Residual Plots for the 26M Cell Run
67
69
71
73
75
77
79
81
83
85
485
4855
486
4865
487
4875
488
4885
489
0 1 2 3 4 5
Nu
sse
lt N
um
be
r
Cell Ammount (Millions)
Grid Independence Study
Velocity
Nusselt Number
58
For future reference Figure 42 shows the residuals of the 26M cell calculation
Up until around 4400 iterations the residuals were increasing shortly thereafter the
residuals started decreasing until it converged just after 5500 iterations All runs for the
differently sized meshes had the same residual patters with the peak of residuals and
point of convergence happening at different iterations
52 CFD Results
As describe previously all the results shown here are for the mesh containing 28 million
elements Figure 43 shows the total pressure contours It can be seen that the plenum
portion is at a constant total pressure Once the jets form since there are very small losses
in the jets due to the wall friction the total pressure still remains constant Only when the
jets enter the channel and start mixing with the cross flow is that they start losing the total
pressure head It is important to notice how the first two jets have the total pressure close
to the plenum arriving at the target wall This implies a successful impingement of the
undisturbed potential core As we move downstream the total pressure is lost quite
rapidly as the jets interact with the cross flow
Figure 43 Total Pressure Contours
59
Similar details can be drawn out from Figure 44 it can be seen that the first three
jets successfully impinge on the target wall while the rest of the downstream ones are
deflected by the cross flow As mentioned by Ricklick the velocity magnitude of the last
jet is larger than that of the first jet due to there being a lower static pressure at the end of
the channel providing it with a steeper pressure gradient hence higher velocity
Figure 44 Velocity Magnitude Contours
Turbulent kinetic energy was plotted in Figure 45 it is expected to have the
highest turbulent kinetic energy near the exit of the holes where the stagnant air is in
contact with the fast moving jet The mixing between the two regimes causes very
energetic eddies to form potentially enhancing the target and side wall heat transfer
coefficient As cross flow builds up towards the end of the channel the turbulent kinetic
energy increases due to larger overall velocities and fluctuations between the cross flow
and jets
60
Figure 45 Turbulent Kinetic Energy Contours
As Ricklick showed in his work the static temperature rise is quite small for such a small
channel It can be seen in Figure 46 that the driving temperature for heat transfer is that of
the plenum It is important to notice that a wall heat flux of 10000 Wm2 was used as the
boundary condition Not even in the most powerful tests would we ever use heat fluxes
that high they normally range between 2500 to a maximum of 7000 Wm2 A heat flux of
10000 Wm2 will increase the temperature at a faster rate than what it is normally used in
experimental testing
Figure 46 Static Temperature Contours
61
Figure 47 Target and Side Wall Heat Transfer Coefficient Contours
Figure 47 shows the target and sidewall heat transfer profiles Peaks can be seen at the
first three locations similar to that seen in Figure 22 The trend decreases rapidly to
eventually become a slowly increasing heat transfer profile due to the increase of mass
flow through the channel The sidewall provides the same results clear peaks in heat
transfer where the wall jets impinge on the sidewall seen in Figure 48 in more detail The
sidewall also shows a recirculation zone in between the first row of jets and the end wall
This is caused by the wall jet from the first row hitting the back wall moving upwards in
a circular pattern and coming back down when it encounters the first impingement row
Figure 48 Closer View of First few Rows of Impingement HTC Contours
62
Figure 49 Pathlines Generating from the First Row of Jets
Figure 49 helps explain the low heat transfer region between the first row of jets and
the end wall Pathlines are generated at the exit of each hole in the first row As the
air impinges on the surface half of it moves downstream and the other half movers
upstream to this recirculation zone where it circulates for a period of time before
reuniting with the remainder of the flow to move downstream The wall jet that
moves towards the second row of jets encounters the wall jet created by the second
row of jets causing the pathlines to drastically move upwards On the side of the
channel the pathlines behave erratically with no clear pattern clearly signifying the
highly turbulent and chaotic flow structure of this impingement channel
63
CHAPTER SIX CONCLUSIONS
It has been seen from this analysis that the side walls provide significant heat
transfer in an impingement channel especially at the relatively smaller channel
height This is primarily the result of successful impact of the wall jet with the side
walls It was shown that the tallest channel (ZD=10) has the most uniform profile with
low heat transfer coefficients when compared to the other channels The peaks of the
ZD=6 and 8 channels have a very similar profile which may indicate the successful
impingement of the potential core of the jet on the target surface As XD increases the
peaks diminish and a positive slope profile is attained by the increase of cross flow
velocity as more and more jets are introduced Tall impingement channels provide the
user with a heat transfer profile that is more uniform than those provided with the use of a
smaller channel while still maintaining higher convective coefficients when compared to
a smooth flow scenario The downstream shift of the wall jets is found to be independent
of Reynolds number and heavily dependent on streamwise position It was also found that
at XD=15 the wall jets decay faster than their XD=5 counterparts From the 3D heat
transfer profiles it was seen that the cross flow generated by multiple upstream jets is
deflected downward decreasing its effective flow area increasing its velocity hence
providing higher convective coefficients at the side wall at high xD and low zD
64
APPENDICES
Appendix A
Lateral Conduction Consideration
Thickness of foil heater Heat flux
Sample volume width
Volumetric heat generation
Volume of sample volume
Temperature profile from the first row of impingement ONLY valid for 02ltxlt045
t 50m k 20W
m K qflux 6000
W
m2
1mm
V 2
t qvol
qflux
t
T x( ) 298Kqflux
470630 x2
31244x 14842 W
m2K
N 15
x 02045 02
N 102 047
002 003 004 005314
315
316
317
318
319
320
T x( )
x
A t
qnet x( ) A kxT x
m
d
d xT x( )
d
d
1
m
002 003 004 0050
5 105
1 104
15 104
2 104
qnet x( )
x
65
Now comparing the net heat gained by lateral conduction to heat generated and convected out
It can be seen that the lateral conduction into the sample volume is two orders of magnitude smaller than the heat removed by convection
qgen qvol V 6 103
W
qconv x( ) 2
qflux qnet x( )
002 003 004 0051 10
5
1 104
1 103
001
qconv x( )
qnet x( )
x x
66
Appendix B
This is the journal file run on gambit to generate the geometry faces links
boundary layer face and volume meshes as well as the boundary conditions
set diameter
$d=75
$zc=6($d)
$xc=80($d)
$yc=4($d)
$y=2($d)
$x=5($d)
$zp=5($d)
$ztot=($zc)+($d)+($zp)
$jcf=(13)
$ocf=2
Boundary layer constants
$first=01
$growth=12
$rows=4
Meshing constants
$NumbNodes=5
$Numbtelnodes=6
$PLobnodes=5
$Chobnodes=5
$Plbenodes=($NumbNodes(4)+$rows)
$plsqnodes=($NumbNodes(3))
$Pllsnodes=($NumbNodes+$rows)
$Nojetcells=10
$Chzdnodes=($zc$Nojetcells)($d)
$Plzdnodes=($zp$Nojetcells)($d)
Boundary layer constants for channel
$firstch=001
$growthch=12
$rowsch=8
$CHbenodes=($NumbNodes(4)+$rowsch)
$CHlsnodes=($NumbNodes+$rowsch)
volume create body width ($xc) depth ($yc) height ($ztot) offset ($xc2) ($yc2) ($ztot2) brick
volume create cylinder height ($ztot) radius1 ($d2) radius3 ($d2) offset ($x) 0 ($ztot2) zaxis frustum
volume cmove cylinder multiple 1 offset 0 ($y) 0
volume cmove cylinder volume3 multiple 14 offset ($x) 0 0
volume create jetplate width ($xc) depth ($yc) height ($d)offset ($xc2) ($yc2) ($d2+$zc) brick
volume split body volumes jetplate connected
volume split jetplate volumes cylinder volume3 volume4 volume5
volume6 volume7 volume8 volume9 volume10 volume11
volume12 volume13 volume14 volume15 volume16 volume17
67
volume18 volume19 volume20 volume21 volume22 volume23
volume24 volume25 volume26 volume27 volume28 volume29
volume30 volume31 connected
face create jetcenter width ($jcf$d) height ($jcf$d) offset ($x) 0 0 xyplane rectangle
face create jetcircle radius ($d2) xyplane circle
face move jetcircle offset ($x) 0 0
face create outbox width ($ocf$d) height ($ocf$d) offset ($x) 0 0 xyplane rectangle
face split outbox connected faces jetcircle jetcenter
face split jetcircle connected faces face1
face split outbox connected faces face1
face cmove jetcenter outbox jetcircle face222 face223 multiple 1 offset 0 ($y) 0
face cmove jetcenter outbox jetcircle face222 face223 face224 face225 face226
face227 face228 multiple 14 offset ($x) 0 0
volume delete jetplate lowertopology
face split face1 connected keeptool faces jetcircle jetcenter outbox
face222 face223 face224 face225 face226 face227
face228 face229 face230 face231 face232 face233
face234 face235 face236 face237 face238 face239
face240 face241 face242 face243 face244 face245
face246 face247 face248 face249 face250 face251
face252 face253 face254 face255 face256 face257
face258 face259 face260 face261 face262 face263
face264 face265 face266 face267 face268 face269
face270 face271 face272 face273 face274 face275
face276 face277 face278 face279 face280 face281
face282 face283 face284 face285 face286 face287
face288 face289 face290 face291 face292 face293
face294 face295 face296 face297 face298 face299
face300 face301 face302 face303 face304 face305
face306 face307 face308 face309 face310 face311
face312 face313 face314 face315 face316 face317
face318 face319 face320 face321 face322 face323
face324 face325 face326 face327 face328 face329
face330 face331 face332 face333 face334 face335
face336 face337 face338 face339 face340 face341
face342 face343 face344 face345 face346 face347
face348 face349 face350 face351 face352 face353
face354 face355 face356 face357 face358 face359
face360 face361 face362 face363 face364 face365
face366 face367 face368
face move jetcircle jetcenter outbox face222 face223 face224
face225 face226 face227 face228 face229 face230
face231 face232 face233 face234 face235 face236
face237 face238 face239 face240 face241 face242
face243 face244 face245 face246 face247 face248
face249 face250 face251 face252 face253 face254
face255 face256 face257 face258 face259 face260
face261 face262 face263 face264 face265 face266
face267 face268 face269 face270 face271 face272
face273 face274 face275 face276 face277 face278
face279 face280 face281 face282 face283 face284
face285 face286 face287 face288 face289 face290
face291 face292 face293 face294 face295 face296
face297 face298 face299 face300 face301 face302
face303 face304 face305 face306 face307 face308
face309 face310 face311 face312 face313 face314
68
face315 face316 face317 face318 face319 face320
face321 face322 face323 face324 face325 face326
face327 face328 face329 face330 face331 face332
face333 face334 face335 face336 face337 face338
face339 face340 face341 face342 face343 face344
face345 face346 face347 face348 face349 face350
face351 face352 face353 face354 face355 face356
face357 face358 face359 face360 face361 face362
face363 face364 face365 face366 face367 face368 offset 0
0 $ztot
THIS SPLITS THE TOP PLENUM FACE WITH THE FACES CREATED IN THE BOTTOM
face split face6 connected keeptool faces jetcircle jetcenter outbox
face222 face223 face224 face225 face226 face227
face228 face229 face230 face231 face232 face233
face234 face235 face236 face237 face238 face239
face240 face241 face242 face243 face244 face245
face246 face247 face248 face249 face250 face251
face252 face253 face254 face255 face256 face257
face258 face259 face260 face261 face262 face263
face264 face265 face266 face267 face268 face269
face270 face271 face272 face273 face274 face275
face276 face277 face278 face279 face280 face281
face282 face283 face284 face285 face286 face287
face288 face289 face290 face291 face292 face293
face294 face295 face296 face297 face298 face299
face300 face301 face302 face303 face304 face305
face306 face307 face308 face309 face310 face311
face312 face313 face314 face315 face316 face317
face318 face319 face320 face321 face322 face323
face324 face325 face326 face327 face328 face329
face330 face331 face332 face333 face334 face335
face336 face337 face338 face339 face340 face341
face342 face343 face344 face345 face346 face347
face348 face349 face350 face351 face352 face353
face354 face355 face356 face357 face358 face359
face360 face361 face362 face363 face364 face365
face366 face367 face368
THIS MOVES THE FACES THAT WE ARE USING TO PLIT THE BOTTOM PLENUM SURFACE
face move jetcircle jetcenter outbox face222 face223 face224
face225 face226 face227 face228 face229 face230
face231 face232 face233 face234 face235 face236
face237 face238 face239 face240 face241 face242
face243 face244 face245 face246 face247 face248
face249 face250 face251 face252 face253 face254
face255 face256 face257 face258 face259 face260
face261 face262 face263 face264 face265 face266
face267 face268 face269 face270 face271 face272
face273 face274 face275 face276 face277 face278
face279 face280 face281 face282 face283 face284
face285 face286 face287 face288 face289 face290
face291 face292 face293 face294 face295 face296
face297 face298 face299 face300 face301 face302
69
face303 face304 face305 face306 face307 face308
face309 face310 face311 face312 face313 face314
face315 face316 face317 face318 face319 face320
face321 face322 face323 face324 face325 face326
face327 face328 face329 face330 face331 face332
face333 face334 face335 face336 face337 face338
face339 face340 face341 face342 face343 face344
face345 face346 face347 face348 face349 face350
face351 face352 face353 face354 face355 face356
face357 face358 face359 face360 face361 face362
face363 face364 face365 face366 face367 face368 offset 0
0 -$zp
SPLITS THE BOTTOM FACE OF THE PLENUM WITH THE FACES THAT ARE USED TO SPLIT
face split face114 connected keeptool faces jetcircle jetcenter
outbox face222 face223 face224 face225 face226 face227
face228 face229 face230 face231 face232 face233
face234 face235 face236 face237 face238 face239
face240 face241 face242 face243 face244 face245
face246 face247 face248 face249 face250 face251
face252 face253 face254 face255 face256 face257
face258 face259 face260 face261 face262 face263
face264 face265 face266 face267 face268 face269
face270 face271 face272 face273 face274 face275
face276 face277 face278 face279 face280 face281
face282 face283 face284 face285 face286 face287
face288 face289 face290 face291 face292 face293
face294 face295 face296 face297 face298 face299
face300 face301 face302 face303 face304 face305
face306 face307 face308 face309 face310 face311
face312 face313 face314 face315 face316 face317
face318 face319 face320 face321 face322 face323
face324 face325 face326 face327 face328 face329
face330 face331 face332 face333 face334 face335
face336 face337 face338 face339 face340 face341
face342 face343 face344 face345 face346 face347
face348 face349 face350 face351 face352 face353
face354 face355 face356 face357 face358 face359
face360 face361 face362 face363 face364 face365
face366 face367 face368
COPIES THE FACES THAT WE USED TO SPLIT TO BOTTOM OF THE PLENUM TO THE TOP OF
THE CHANNEL
face cmove jetcircle jetcenter outbox face222 face223 face224
face225 face226 face227 face228 face229 face230
face231 face232 face233 face234 face235 face236
face237 face238 face239 face240 face241 face242
face243 face244 face245 face246 face247 face248
face249 face250 face251 face252 face253 face254
face255 face256 face257 face258 face259 face260
face261 face262 face263 face264 face265 face266
face267 face268 face269 face270 face271 face272
face273 face274 face275 face276 face277 face278
face279 face280 face281 face282 face283 face284
70
face285 face286 face287 face288 face289 face290
face291 face292 face293 face294 face295 face296
face297 face298 face299 face300 face301 face302
face303 face304 face305 face306 face307 face308
face309 face310 face311 face312 face313 face314
face315 face316 face317 face318 face319 face320
face321 face322 face323 face324 face325 face326
face327 face328 face329 face330 face331 face332
face333 face334 face335 face336 face337 face338
face339 face340 face341 face342 face343 face344
face345 face346 face347 face348 face349 face350
face351 face352 face353 face354 face355 face356
face357 face358 face359 face360 face361 face362
face363 face364 face365 face366 face367 face368 multiple 1 offset 0
0 -$d
NAME OF COPIED NEW FACES
face1104 face1105 face1106 face1107 face1108 face1109 face1110 face1111
face1112 face1113 face1114 face1115 face1116 face1117 face1118 face1119
face1120 face1121 face1122 face1123 face1124 face1125 face1126 face1127
face1128 face1129 face1130 face1131 face1132 face1133 face1134 face1135
face1136 face1137 face1138 face1139 face1140 face1141 face1142 face1143
face1144 face1145 face1146 face1147 face1148 face1149 face1150 face1151
face1152 face1153 face1154 face1155 face1156 face1157 face1158 face1159
face1160 face1161 face1162 face1163 face1164 face1165 face1166 face1167
face1168 face1169 face1170 face1171 face1172 face1173 face1174 face1175
face1176 face1177 face1178 face1179 face1180 face1181 face1182 face1183
face1184 face1185 face1186 face1187 face1188 face1189 face1190 face1191
face1192 face1193 face1194 face1195 face1196 face1197 face1198 face1199
face1200 face1201 face1202 face1203 face1204 face1205 face1206 face1207
face1208 face1209 face1210 face1211 face1212 face1213 face1214 face1215
face1216 face1217 face1218 face1219 face1220 face1221 face1222 face1223
face1224 face1225 face1226 face1227 face1228 face1229 face1230 face1231
face1232 face1233 face1234 face1235 face1236 face1237 face1238 face1239
face1240 face1241 face1242 face1243 face1244 face1245 face1246 face1247
face1248 face1249 face1250 face1251 face1252 face1253
THIS SPLITS THE TOP OF THE CHANNEL WITH THE NEW COPIED FACES
face split face209 connected keeptool faces face1104 face1105 face1106 face1107
face1108 face1109 face1110 face1111 face1112 face1113 face1114 face1115
face1116 face1117 face1118 face1119 face1120 face1121 face1122 face1123
face1124 face1125 face1126 face1127 face1128 face1129 face1130 face1131
face1132 face1133 face1134 face1135 face1136 face1137 face1138 face1139
face1140 face1141 face1142 face1143 face1144 face1145 face1146 face1147
face1148 face1149 face1150 face1151 face1152 face1153 face1154 face1155
face1156 face1157 face1158 face1159 face1160 face1161 face1162 face1163
face1164 face1165 face1166 face1167 face1168 face1169 face1170 face1171
face1172 face1173 face1174 face1175 face1176 face1177 face1178 face1179
face1180 face1181 face1182 face1183 face1184 face1185 face1186 face1187
face1188 face1189 face1190 face1191 face1192 face1193 face1194 face1195
face1196 face1197 face1198 face1199 face1200 face1201 face1202 face1203
face1204 face1205 face1206 face1207 face1208 face1209 face1210 face1211
face1212 face1213 face1214 face1215 face1216 face1217 face1218 face1219
face1220 face1221 face1222 face1223 face1224 face1225 face1226 face1227
71
face1228 face1229 face1230 face1231 face1232 face1233 face1234 face1235
face1236 face1237 face1238 face1239 face1240 face1241 face1242 face1243
face1244 face1245 face1246 face1247 face1248 face1249 face1250 face1251
face1252 face1253
THIS UNITES THE RECTANGLE OUTSIDE FACES AND THE SEMICIRCLE SO THAT IT MAKES
A RECTANGLE WIHOUT THE CENTERJET
face unite faces jetcircle face223 real
face unite faces face222 outbox real
face unite faces face228 face226 real
face unite faces face225 face227 real
face unite faces face231 face233 real
face unite faces face232 face230 real
face unite faces face236 face238 real
face unite faces face237 face235 real
face unite faces face241 face243 real
face unite faces face242 face240 real
face unite faces face248 face246 real
face unite faces face245 face247 real
face unite faces face253 face251 real
face unite faces face252 face250 real
face unite faces face256 face258 real
face unite faces face257 face255 real
face unite faces face263 face261 real
face unite faces face260 face262 real
face unite faces face268 face266 real
face unite faces face265 face264 real
face unite faces face265 face267 real
face unite faces face273 face271 real
face unite faces face272 face270 real
face unite faces face276 face278 real
face unite faces face277 face275 real
face unite faces face281 face283 real
face unite faces face282 face280 real
face unite faces face286 face288 real
face unite faces face287 face285 real
face unite faces face291 face293 real
face unite faces face292 face290 real
face unite faces face296 face298 real
face unite faces face297 face295 real
face unite faces face301 face303 real
face unite faces face302 face300 real
face unite faces face306 face308 real
face unite faces face307 face305 real
face unite faces face316 face318 real
face unite faces face312 face310 real
face unite faces face311 face313 real
face unite faces face315 face317 real
face unite faces face321 face323 real
face unite faces face322 face320 real
face unite faces face326 face328 real
face unite faces face327 face325 real
face unite faces face331 face333 real
face unite faces face332 face330 real
face unite faces face336 face338 real
72
face unite faces face337 face335 real
face unite faces face347 face345 real
face unite faces face346 face348 real
face unite faces face342 face340 real
face unite faces face341 face343 real
face unite faces face356 face358 real
face unite faces face357 face355 real
face unite faces face352 face350 real
face unite faces face351 face353 real
face unite faces face361 face363 real
face unite faces face366 face368 real
face unite faces face360 face362 real
face unite faces face365 face367 real
SPLITTING ALL THE FACES OF THE CIRCLES IN THE BOTTOM OF THE PLENUM
face split face912 connected keeptool faces face222
face split face117 connected keeptool faces face228
face split face117 connected keeptool faces face225
face split face922 connected keeptool faces face232
face split face124 connected keeptool faces face236
face split face124 connected keeptool faces face237
face split face932 connected keeptool faces face242
face split face131 connected keeptool faces face248
face split face131 connected keeptool faces face245
face split face942 connected keeptool faces face252
face split face138 connected keeptool faces face256
face split face138 connected keeptool faces face257
face split face952 connected keeptool faces face260
face split face145 connected keeptool faces face268
face split face145 connected keeptool faces face265
face split face962 connected keeptool faces face272
face split face152 connected keeptool faces face276
face split face152 connected keeptool faces face277
face split face972 connected keeptool faces face282
face split face159 connected keeptool faces face286
face split face159 connected keeptool faces face287
face split face982 connected keeptool faces face292
face split face166 connected keeptool faces face296
face split face166 connected keeptool faces face297
face split face992 connected keeptool faces face302
face split face173 connected keeptool faces face306
face split face173 connected keeptool faces face307
face split face1002 connected keeptool faces face312
face split face180 connected keeptool faces face316
face split face180 connected keeptool faces face315
73
face split face1012 connected keeptool faces face322
face split face187 connected keeptool faces face326
face split face187 connected keeptool faces face327
face split face1022 connected keeptool faces face332
face split face194 connected keeptool faces face336
face split face194 connected keeptool faces face337
face split face1032 connected keeptool faces face342
face split face201 connected keeptool faces face346
face split face201 connected keeptool faces face347
face split face1042 connected keeptool faces face352
face split face208 connected keeptool faces face356
face split face208 connected keeptool faces face357
face split face1052 connected keeptool faces face360
face split face215 connected keeptool faces face366
face split face215 connected keeptool faces face365
THIS UNITES THE RECTANGLE OUTSIDE FACES AND THE SEMICIRCLE SO THAT IT MAKES
A RECTANGLE WIHOUT THE CENTERJET
face unite faces face1104 face1108 real
face unite faces face1107 face1106 real
face unite faces face1113 face1111 real
face unite faces face1112 face1110 real
face unite faces face1118 face1116 real
face unite faces face1117 face1115 real
face unite faces face1123 face1121 real
face unite faces face1122 face1120 real
face unite faces face1128 face1126 real
face unite faces face1127 face1125 real
face unite faces face1133 face1131 real
face unite faces face1132 face1130 real
face unite faces face1138 face1136 real
face unite faces face1137 face1135 real
face unite faces face1143 face1141 real
face unite faces face1142 face1140 real
face unite faces face1148 face1146 real
face unite faces face1147 face1145 real
face unite faces face1153 face1151 real
face unite faces face1152 face1150 real
face unite faces face1158 face1156 real
face unite faces face1157 face1155 real
face unite faces face1163 face1161 real
face unite faces face1162 face1160 real
face unite faces face1168 face1166 real
face unite faces face1167 face1165 real
face unite faces face1173 face1171 real
face unite faces face1172 face1170 real
face unite faces face1178 face1176 real
face unite faces face1177 face1175 real
face unite faces face1183 face1181 real
74
face unite faces face1182 face1180 real
face unite faces face1186 face1188 real
face unite faces face1187 face1185 real
face unite faces face1193 face1191 real
face unite faces face1192 face1190 real
face unite faces face1198 face1196 real
face unite faces face1197 face1195 real
face unite faces face1203 face1201 real
face unite faces face1202 face1200 real
face unite faces face1206 face1208 real
face unite faces face1207 face1205 real
face unite faces face1213 face1211 real
face unite faces face1212 face1210 real
face unite faces face1216 face1218 real
face unite faces face1217 face1215 real
face unite faces face1221 face1223 real
face unite faces face1222 face1220 real
face unite faces face1228 face1226 real
face unite faces face1227 face1225 real
face unite faces face1233 face1231 real
face unite faces face1232 face1230 real
face unite faces face1238 face1236 real
face unite faces face1237 face1235 real
face unite faces face1243 face1241 real
face unite faces face1242 face1240 real
face unite faces face1248 face1246 real
face unite faces face1247 face1245 real
face unite faces face1253 face1251 real
face unite faces face1252 face1250 real
SPLITTING ALL THE FACES OF THE CIRCLES IN THE TOP OF THE CHANNEL
face split face1257 connected keeptool faces face1107
face split face115 connected keeptool faces face1113
face split face115 connected keeptool faces face1112
face split face1267 connected keeptool faces face1117
face split face122 connected keeptool faces face1123
face split face122 connected keeptool faces face1122
face split face1277 connected keeptool faces face1127
face split face129 connected keeptool faces face1133
face split face129 connected keeptool faces face1132
face split face1287 connected keeptool faces face1137
face split face136 connected keeptool faces face1143
face split face136 connected keeptool faces face1142
face split face1297 connected keeptool faces face1147
face split face143 connected keeptool faces face1153
face split face143 connected keeptool faces face1152
face split face1307 connected keeptool faces face1157
face split face150 connected keeptool faces face1163
face split face150 connected keeptool faces face1162
75
face split face1317 connected keeptool faces face1167
face split face157 connected keeptool faces face1173
face split face157 connected keeptool faces face1172
face split face1327 connected keeptool faces face1177
face split face164 connected keeptool faces face1183
face split face164 connected keeptool faces face1182
face split face1337 connected keeptool faces face1187
face split face171 connected keeptool faces face1193
face split face171 connected keeptool faces face1192
face split face1347 connected keeptool faces face1197
face split face178 connected keeptool faces face1203
face split face178 connected keeptool faces face1202
face split face1357 connected keeptool faces face1207
face split face185 connected keeptool faces face1213
face split face185 connected keeptool faces face1212
face split face1367 connected keeptool faces face1217
face split face192 connected keeptool faces face1221
face split face192 connected keeptool faces face1222
face split face1377 connected keeptool faces face1227
face split face199 connected keeptool faces face1233
face split face199 connected keeptool faces face1232
face split face1387 connected keeptool faces face1237
face split face206 connected keeptool faces face1243
face split face206 connected keeptool faces face1242
face split face1397 connected keeptool faces face1247
face split face213 connected keeptool faces face1253
face split face213 connected keeptool faces face1252
face split face1452 connected keeptool faces face224
face split face1456 connected keeptool faces face234
face split face1460 connected keeptool faces face244
face split face1464 connected keeptool faces face254
face split face1468 connected keeptool faces face264
face split face1472 connected keeptool faces face274
face split face1476 connected keeptool faces face284
face split face1480 connected keeptool faces face294
face split face1484 connected keeptool faces face304
face split face1488 connected keeptool faces face314
face split face1492 connected keeptool faces face324
face split face1496 connected keeptool faces face334
face split face1500 connected keeptool faces face344
face split face1504 connected keeptool faces face354
face split face1508 connected keeptool faces face364
DELETING ALL THE FACES USED TO MAKE THE CUTS
face delete jetcircle face222 face228 face225 jetcenter
76
face224 face231 face232 face236 face237 face229
face1456 face241 face242 face239 face248 face244
face245 face253 face249 face252 face254 face256
face257 face263 face259 face260 face268 face264
face265 face273 face272 face269 face276 face277
face274 face281 face282 face286 face279 face287
face284 face291 face292 face296 face297 face289
face294 face301 face299 face302 face306 face307
face304 face311 face312 face316 face315 face309
face314 face321 face322 face326 face327 face319
face324 face331 face332 face329 face336 face334
face337 face341 face342 face339 face346 face344
face347 face351 face352 face349 face356 face354
face357 face361 face359 face360 face366 face364
face365 lowertopology
face delete face1104 face1105 face1107 face1113 face1112
face115 face234 face1118 face1114 face1117 face1123
face1122 face122 face1138 face1128 face1127 face1124
face1133 face1132 face129 face1134 face1137 face1143
face136 face1142 face1148 face1144 face1147 face1153
face143 face1152 face1158 face1154 face1157 face1163
face150 face1162 face1168 face1164 face1167 face1173
face157 face1172 face1178 face1174 face1177 face1183
face164 face1182 face1186 face1184 face1187 face1193
face171 face1192 face1198 face1194 face1197 face1203
face178 face1202 face1206 face1204 face1207 face1213
face185 face1212 face1216 face1214 face1217 face1221
face192 face1222 face1228 face1224 face1227 face1233
face199 face1232 face1238 face1234 face1237 face1243
face206 face1242 face1248 face1244 face1247 face1253
face213 face1252 lowertopology
face delete face1109 face1119 face1129 face1139 face1149 face1159
face1169 face1179 face1189 face1199 face1209 face1219
face1229 face1239 face1249 lowertopology
face create CP1 width 600 height 75 offset 300 (225+($d)2) 0 xyplane rectangle
face create CP2 width 600 height 75 offset 300 (225+($d)2) ($zc) xyplane rectangle
face create CP3 width 600 height 75 offset 300 (225+($d)2) ($zc+$d) xyplane rectangle
face create CP4 width 600 height 75 offset 300 (225+($d)2) ($zc+$d+$zp) xyplane rectangle
face split face6 connected faces CP4
face split face114 connected faces CP3
face split face209 connected faces CP2
face split face1 connected faces CP1
GEOMETRY IS FINISHED
face modify face912 side vertex6437 vertex6436
77
face modify face1600 side vertex7302 vertex7303
face modify face117 side vertex6446 vertex6447
face modify face646 side vertex3312
face modify face646 side vertex3313
face modify face647 side vertex3432 vertex3433
face modify face372 side vertex2040 vertex2041
face modify face376 side vertex2100 vertex2101
face modify face377 side vertex2221 vertex2220
LINKING ALL THE JET CENTERS
face link face1450 face640 edges edge6949 edge3518 vertices
vertex6437 vertex3253 reverse
face link face1450 face1257 edges edge6949 edge7340 vertices
vertex6437 vertex6797 reverse
face link face1257 face370 edges edge7340 edge2139 vertices
vertex6797 vertex2041 reverse
face link face1257 face1454 edges edge7340 edge6975 vertices
vertex6797 vertex6461 reverse
face link face1454 face649 edges edge6975 edge3519 vertices
vertex6461 vertex3255 reverse
face link face1454 face1267 edges edge6975 edge7377 vertices
vertex6461 vertex6831 reverse
face link face1267 face379 edges edge7377 edge2141 vertices
vertex6831 vertex2043 reverse
face link face1267 face1458 edges edge7377 edge7001 vertices
vertex6831 vertex6485 reverse
face link face1458 face659 edges edge7001 edge3520 vertices
vertex6485 vertex3257 reverse
face link face1458 face1277 edges edge7001 edge7414 vertices
vertex6485 vertex6865 reverse
face link face1277 face389 edges edge7414 edge2143 vertices
vertex6865 vertex2045 reverse
face link face1277 face1462 edges edge7414 edge7027 vertices
vertex6865 vertex6509 reverse
face link face1462 face669 edges edge7027 edge3521 vertices
vertex6509 vertex3259 reverse
face link face1462 face1287 edges edge7027 edge7451 vertices
vertex6509 vertex6899 reverse
face link face1287 face399 edges edge7451 edge2145 vertices
vertex6899 vertex2047 reverse
face link face1287 face1466 edges edge7451 edge7053 vertices
vertex6899 vertex6533 reverse
face link face1466 face679 edges edge7053 edge3522 vertices
vertex6533 vertex3261 reverse
face link face1466 face1297 edges edge7053 edge7488 vertices
vertex6533 vertex6933 reverse
face link face1297 face409 edges edge7488 edge2147 vertices
vertex6933 vertex2049 reverse
face link face1297 face1470 edges edge7488 edge7079 vertices
vertex6933 vertex6557 reverse
face link face1470 face689 edges edge7079 edge3523 vertices
vertex6557 vertex3263 reverse
face link face1470 face1307 edges edge7079 edge7525 vertices
vertex6557 vertex6967 reverse
face link face1307 face419 edges edge7525 edge2149 vertices
78
vertex6967 vertex2051 reverse
face link face1307 face1474 edges edge7525 edge7105 vertices
vertex6967 vertex6581 reverse
face link face1474 face1317 edges edge7105 edge7562 vertices
vertex6581 vertex7001 reverse
face link face1474 face699 edges edge7105 edge3524 vertices
vertex6581 vertex3265 reverse
face link face1317 face429 edges edge7562 edge2151 vertices
vertex7001 vertex2053 reverse
face link face1317 face1478 edges edge7562 edge7131 vertices
vertex7001 vertex6605 reverse
face link face1478 face1327 edges edge7131 edge7599 vertices
vertex6605 vertex7035 reverse
face link face1478 face709 edges edge7131 edge3525 vertices
vertex6605 vertex3267 reverse
face link face1327 face439 edges edge7599 edge2153 vertices
vertex7035 vertex2055 reverse
face link face1327 face1482 edges edge7599 edge7157 vertices
vertex7035 vertex6629 reverse
face link face1482 face719 edges edge7157 edge3526 vertices
vertex6629 vertex3269 reverse
face link face1482 face1337 edges edge7157 edge7636 vertices
vertex6629 vertex7069 reverse
face link face1337 face449 edges edge7636 edge2155 vertices
vertex7069 vertex2057 reverse
face link face1337 face1486 edges edge7636 edge7183 vertices
vertex7069 vertex6653 reverse
face link face1486 face1347 edges edge7183 edge7673 vertices
vertex6653 vertex7103 reverse
face link face1347 face459 edges edge7673 edge2157 vertices
vertex7103 vertex2059 reverse
face link face1486 face729 edges edge7183 edge3527 vertices
vertex6653 vertex3271 reverse
face link face1347 face1490 edges edge7673 edge7209 vertices
vertex7103 vertex6677 reverse
face link face1490 face1357 edges edge7209 edge7710 vertices
vertex6677 vertex7137 reverse
face link face1490 face739 edges edge7209 edge3528 vertices
vertex6677 vertex3273 reverse
face link face1357 face469 edges edge7710 edge2159 vertices
vertex7137 vertex2061 reverse
face link face1357 face1494 edges edge7710 edge7235 vertices
vertex7137 vertex6701 reverse
face link face1494 face1367 edges edge7235 edge7747 vertices
vertex6701 vertex7171 reverse
face link face1494 face749 edges edge7235 edge3529 vertices
vertex6701 vertex3275 reverse
face link face1367 face479 edges edge7747 edge2161 vertices
vertex7171 vertex2063 reverse
face link face1367 face1498 edges edge7747 edge7261 vertices
vertex7171 vertex6725 reverse
face link face1498 face1377 edges edge7261 edge7784 vertices
vertex6725 vertex7205 reverse
face link face1377 face489 edges edge7784 edge2163 vertices
vertex7205 vertex2065 reverse
face link face1498 face759 edges edge7261 edge3530 vertices
79
vertex6725 vertex3277 reverse
face link face1377 face1502 edges edge7784 edge7287 vertices
vertex7205 vertex6749 reverse
face link face1502 face1387 edges edge7287 edge7821 vertices
vertex6749 vertex7239 reverse
face link face1387 face499 edges edge7821 edge2165 vertices
vertex7239 vertex2067 reverse
face link face1387 face1506 edges edge7821 edge7313 vertices
vertex7239 vertex6773 reverse
face link face1502 face769 edges edge7287 edge3531 vertices
vertex6749 vertex3279 reverse
face link face1506 face1397 edges edge7313 edge7858 vertices
vertex6773 vertex7273 reverse
face link face1506 face779 edges edge7313 edge3532 vertices
vertex6773 vertex3281 reverse
face link face1397 face509 edges edge7858 edge2167 vertices
vertex7273 vertex2069 reverse
LINKING ALL THE COMPLETE JETCENTERS
face link face1452 face644 edges edge7891 edge3773 vertices
vertex7303 vertex3433
face link face1452 face115 edges edge7891 edge7364 vertices
vertex7303 vertex6819
face link face1452 face1456 edges edge7891 edge7900 vertices
vertex7303 vertex7311
face link face1456 face654 edges edge7900 edge3774 vertices
vertex7311 vertex3435
face link face1456 face122 edges edge7900 edge7401 vertices
vertex7311 vertex6853
face link face1456 face1460 edges edge7900 edge7909 vertices
vertex7311 vertex7319
face link face1460 face1464 edges edge7909 edge7918 vertices
vertex7319 vertex7327
face link face1460 face129 edges edge7909 edge7438 vertices
vertex7319 vertex6887
face link face1460 face664 edges edge7909 edge3775 vertices
vertex7319 vertex3437
face link face1464 face674 edges edge7918 edge3776 vertices
vertex7327 vertex3439
face link face1464 face136 edges edge7918 edge7475 vertices
vertex7327 vertex6921
face link face1464 face1468 edges edge7918 edge7927 vertices
vertex7327 vertex7335
face link face1472 face1468 edges edge7936 edge7927 vertices
vertex7343 vertex7335
face link face1468 face143 edges edge7927 edge7512 vertices
vertex7335 vertex6955
face link face1468 face684 edges edge7927 edge3777 vertices
vertex7335 vertex3441
face link face1472 face694 edges edge7936 edge3778 vertices
vertex7343 vertex3443
face link face1472 face150 edges edge7936 edge7549 vertices
vertex7343 vertex6989
face link face1472 face1476 edges edge7936 edge7945 vertices
80
vertex7343 vertex7351
face link face1476 face1480 edges edge7945 edge7954 vertices
vertex7351 vertex7359
face link face1476 face157 edges edge7945 edge7586 vertices
vertex7351 vertex7023
face link face1476 face704 edges edge7945 edge3779 vertices
vertex7351 vertex3445
face link face1480 face714 edges edge7954 edge3780 vertices
vertex7359 vertex3447
face link face1480 face164 edges edge7954 edge7623 vertices
vertex7359 vertex7057
face link face1480 face1484 edges edge7954 edge7963 vertices
vertex7359 vertex7367
face link face1484 face171 edges edge7963 edge7660 vertices
vertex7367 vertex7091
face link face1484 face724 edges edge7963 edge3781 vertices
vertex7367 vertex3449
face link face1480 face1488 edges edge7954 edge7972 vertices
vertex7359 vertex7375
face link face1488 face178 edges edge7972 edge7697 vertices
vertex7375 vertex7125
face link face1488 face734 edges edge7972 edge3782 vertices
vertex7375 vertex3451
face link face1488 face1492 edges edge7972 edge7981 vertices
vertex7375 vertex7383
face link face1492 face744 edges edge7981 edge3783 vertices
vertex7383 vertex3453
face link face1492 face185 edges edge7981 edge7734 vertices
vertex7383 vertex7159
face link face1492 face1496 edges edge7981 edge7990 vertices
vertex7383 vertex7391
face link face1496 face754 edges edge7990 edge3784 vertices
vertex7391 vertex3455
face link face1496 face192 edges edge7990 edge7771 vertices
vertex7391 vertex7193
face link face1496 face1500 edges edge7990 edge7999 vertices
vertex7391 vertex7399
face link face1500 face1504 edges edge7999 edge8008 vertices
vertex7399 vertex7407
face link face1504 face1508 edges edge8008 edge8017 vertices
vertex7407 vertex7415
face link face1500 face199 edges edge7999 edge7808 vertices
vertex7399 vertex7227
face link face1500 face764 edges edge7999 edge3785 vertices
vertex7399 vertex3457
face link face1504 face774 edges edge8008 edge3786 vertices
vertex7407 vertex3459
face link face1508 face784 edges edge8017 edge3787 vertices
vertex7415 vertex3461
face link face1504 face206 edges edge8008 edge7845 vertices
vertex7407 vertex7261
face link face1508 face213 edges edge8017 edge7882 vertices
vertex7415 vertex7295
linking the jetcenters of the bottom of the channel one of them has to be reversed but the otherones are not
81
face link face115 face374 edges edge7364 edge2394 vertices
vertex6819 vertex2221 reverse
face link face374 face384 edges edge2394 edge2396 vertices
vertex2221 vertex2223
face link face384 face394 edges edge2396 edge2398 vertices
vertex2223 vertex2225
face link face394 face404 edges edge2398 edge2400 vertices
vertex2225 vertex2227
face link face404 face414 edges edge2400 edge2402 vertices
vertex2227 vertex2229
face link face414 face424 edges edge2402 edge2404 vertices
vertex2229 vertex2231
face link face424 face434 edges edge2404 edge2406 vertices
vertex2231 vertex2233
face link face434 face444 edges edge2406 edge2408 vertices
vertex2233 vertex2235
face link face444 face454 edges edge2408 edge2410 vertices
vertex2235 vertex2237
face link face454 face464 edges edge2410 edge2412 vertices
vertex2237 vertex2239
face link face464 face474 edges edge2412 edge2414 vertices
vertex2239 vertex2241
face link face474 face484 edges edge2414 edge2416 vertices
vertex2241 vertex2243
face link face484 face494 edges edge2416 edge2418 vertices
vertex2243 vertex2245
face link face494 face504 edges edge2418 edge2420 vertices
vertex2245 vertex2247
face link face504 face514 edges edge2420 edge2422 vertices
vertex2247 vertex2249
UP TO THIS POINT ALL THE FACES ARE CONNCTED SUCCESSFULLY
LINKING THE FIRST THREE JET TELEPHONES
face link face912 face117 edges edge6950 edge6960 vertices
vertex6437 vertex6446 reverse
face link face912 face1600 edges edge6950 edge7890 vertices
vertex6437 vertex7303 reverse
face link face912 face372 edges edge6950 edge2168 vertices
vertex6437 vertex2041
face link face117 face376 edges edge6959 edge2304 vertices
vertex6447 vertex2101 reverse
face link face1600 face377 edges edge7890 edge2423 vertices
vertex7303 vertex2221 reverse
face link face372 face382 edges edge2168 edge2169 vertices
vertex2041 vertex2043
face link face377 face387 edges edge2423 edge2424 vertices
vertex2221 vertex2223
face link face376 face386 edges edge2304 edge2306 vertices
vertex2101 vertex2103
face link face387 face397 edges edge2424 edge2425 vertices
vertex2223 vertex2225
face link face386 face396 edges edge2306 edge2308 vertices
82
vertex2103 vertex2105
face link face382 face392 edges edge2169 edge2170 vertices
vertex2043 vertex2045
face link face382 face392 edges edge2169 edge2170 vertices
vertex2043 vertex2045
face link face382 face392 edges edge2169 edge2170 vertices
vertex2043 vertex2045
face link face382 face392 edges edge2169 edge2170 vertices
vertex2043 vertex2045
face link face397 face407 edges edge2425 edge2426 vertices
vertex2225 vertex2227
face link face392 face402 edges edge2170 edge2171 vertices
vertex2045 vertex2047
face link face396 face406 edges edge2290 edge2291 vertices
vertex2104 vertex2106
face link face407 face417 edges edge2426 edge2427 vertices
vertex2227 vertex2229
face link face417 face427 edges edge2427 edge2428 vertices
vertex2229 vertex2231
face link face427 face437 edges edge2428 edge2429 vertices
vertex2231 vertex2233
face link face437 face447 edges edge2429 edge2430 vertices
vertex2233 vertex2235
face link face447 face457 edges edge2430 edge2431 vertices
vertex2235 vertex2237
face link face457 face467 edges edge2431 edge2432 vertices
vertex2237 vertex2239
face link face467 face477 edges edge2432 edge2433 vertices
vertex2239 vertex2241
face link face477 face487 edges edge2433 edge2434 vertices
vertex2241 vertex2243
face link face487 face487 edges edge2434 edge2434 vertices
vertex2243 vertex2243
face link face487 face487 edges edge2434 edge2434 vertices
vertex2243 vertex2243
face link face487 face487 edges edge2434 edge2434 vertices
vertex2243 vertex2243
face link face487 face497 edges edge2434 edge2435 vertices
vertex2243 vertex2245
face link face497 face507 edges edge2435 edge2436 vertices
vertex2245 vertex2247
face link face507 face517 edges edge2436 edge2437 vertices
vertex2247 vertex2249
face link face406 face416 edges edge2291 edge2292 vertices
vertex2106 vertex2108
face link face416 face426 edges edge2292 edge2293 vertices
vertex2108 vertex2110
face link face426 face436 edges edge2293 edge2294 vertices
vertex2110 vertex2112
face link face436 face446 edges edge2294 edge2295 vertices
vertex2112 vertex2114
face link face446 face456 edges edge2295 edge2296 vertices
vertex2114 vertex2116
face link face456 face466 edges edge2296 edge2297 vertices
vertex2116 vertex2118
face link face466 face476 edges edge2297 edge2298 vertices
83
vertex2118 vertex2120
face link face486 face496 edges edge2299 edge2300 vertices
vertex2122 vertex2124
face link face476 face486 edges edge2298 edge2299 vertices
vertex2120 vertex2122
face link face496 face506 edges edge2300 edge2301 vertices
vertex2124 vertex2126
face link face506 face516 edges edge2301 edge2302 vertices
vertex2126 vertex2128
face link face392 face402 edges edge2142 edge2144 vertices
vertex2044 vertex2046
face link face402 face412 edges edge2171 edge2172 vertices
vertex2047 vertex2049
face link face412 face422 edges edge2172 edge2173 vertices
vertex2049 vertex2051
face link face422 face432 edges edge2173 edge2174 vertices
vertex2051 vertex2053
face link face432 face442 edges edge2174 edge2175 vertices
vertex2053 vertex2055
face link face442 face452 edges edge2175 edge2176 vertices
vertex2055 vertex2057
face link face452 face462 edges edge2176 edge2177 vertices
vertex2057 vertex2059
face link face462 face472 edges edge2177 edge2178 vertices
vertex2059 vertex2061
face link face472 face482 edges edge2178 edge2179 vertices
vertex2061 vertex2063
face link face482 face492 edges edge2179 edge2180 vertices
vertex2063 vertex2065
face link face492 face502 edges edge2180 edge2181 vertices
vertex2065 vertex2067
face link face502 face512 edges edge2181 edge2182 vertices
vertex2067 vertex2069
LINKING THE TELEPHONES OF THE BOTTOM OF THE PLENUM
face link face912 face922 edges edge6950 edge6976 vertices
vertex6437 vertex6461
face link face922 face932 edges edge6976 edge7002 vertices
vertex6461 vertex6485
face link face932 face942 edges edge7002 edge7028 vertices
vertex6485 vertex6509
face link face942 face952 edges edge7028 edge7054 vertices
vertex6509 vertex6533
face link face952 face962 edges edge7054 edge7080 vertices
vertex6533 vertex6557
face link face962 face972 edges edge7080 edge7106 vertices
vertex6557 vertex6581
face link face972 face982 edges edge7106 edge7132 vertices
vertex6581 vertex6605
face link face982 face992 edges edge7132 edge7158 vertices
vertex6605 vertex6629
face link face992 face1002 edges edge7158 edge7184 vertices
vertex6629 vertex6653
face link face1002 face1012 edges edge7184 edge7210 vertices
vertex6653 vertex6677
84
face link face1012 face1022 edges edge7210 edge7236 vertices
vertex6677 vertex6701
face link face1032 face1042 edges edge7262 edge7288 vertices
vertex6725 vertex6749
face link face1042 face1052 edges edge7288 edge7314 vertices
vertex6749 vertex6773
face link face117 face124 edges edge6960 edge6986 vertices
vertex6446 vertex6470
face link face124 face131 edges edge6986 edge7012 vertices
vertex6470 vertex6494
face link face131 face138 edges edge7012 edge7038 vertices
vertex6494 vertex6518
face link face138 face145 edges edge7038 edge7064 vertices
vertex6518 vertex6542
face link face145 face152 edges edge7064 edge7090 vertices
vertex6542 vertex6566
face link face152 face159 edges edge7090 edge7116 vertices
vertex6566 vertex6590
face link face159 face166 edges edge7116 edge7142 vertices
vertex6590 vertex6614
face link face166 face173 edges edge7142 edge7168 vertices
vertex6614 vertex6638
face link face173 face180 edges edge7168 edge7194 vertices
vertex6638 vertex6662
face link face180 face187 edges edge7194 edge7220 vertices
vertex6662 vertex6686
face link face187 face194 edges edge7220 edge7246 vertices
vertex6686 vertex6710
face link face194 face201 edges edge7246 edge7272 vertices
vertex6710 vertex6734
face link face1022 face1032 edges edge7236 edge7262 vertices
vertex6701 vertex6725
face link face1032 face1042 edges edge7262 edge7288 vertices
vertex6725 vertex6749
face link face201 face208 edges edge7271 edge7297 vertices
vertex6735 vertex6759
face link face208 face215 edges edge7297 edge7323 vertices
vertex6759 vertex6783
face link face1600 face1602 edges edge7890 edge7899 vertices
vertex7303 vertex7311
face link face1602 face1604 edges edge7899 edge7908 vertices
vertex7311 vertex7319
face link face1604 face1606 edges edge7908 edge7917 vertices
vertex7319 vertex7327
face link face1606 face1608 edges edge7917 edge7926 vertices
vertex7327 vertex7335
face link face1608 face1610 edges edge7926 edge7935 vertices
vertex7335 vertex7343
face link face1610 face1612 edges edge7935 edge7944 vertices
vertex7343 vertex7351
face link face1612 face1614 edges edge7944 edge7953 vertices
vertex7351 vertex7359
face link face1614 face1616 edges edge7953 edge7962 vertices
vertex7359 vertex7367
face link face1616 face1618 edges edge7962 edge7971 vertices
vertex7367 vertex7375
85
face link face1618 face1620 edges edge7971 edge7980 vertices
vertex7375 vertex7383
face link face1620 face1622 edges edge7980 edge7989 vertices
vertex7383 vertex7391
face link face1622 face1624 edges edge7989 edge7998 vertices
vertex7391 vertex7399
face link face1624 face1626 edges edge7998 edge8007 vertices
vertex7399 vertex7407
face link face1626 face1628 edges edge8007 edge8016 vertices
vertex7407 vertex7415
LINKING ALL THE TELEPHONES OF THE TOP OF THE CHANNEL
face link face912 face1510 edges edge6950 edge7339 vertices
vertex6437 vertex6797 reverse
face link face117 face1512 edges edge6959 edge7349 vertices
vertex6447 vertex6807
face link face1600 face1514 edges edge7890 edge7363 vertices
vertex7303 vertex6819
face link face1510 face1516 edges edge7339 edge7376 vertices
vertex6797 vertex6831
face link face1516 face1522 edges edge7376 edge7413 vertices
vertex6831 vertex6865
face link face1522 face1528 edges edge7413 edge7450 vertices
vertex6865 vertex6899
face link face1528 face1534 edges edge7450 edge7487 vertices
vertex6899 vertex6933
face link face1534 face1540 edges edge7487 edge7524 vertices
vertex6933 vertex6967
face link face1540 face1546 edges edge7524 edge7561 vertices
vertex6967 vertex7001
face link face1546 face1552 edges edge7561 edge7598 vertices
vertex7001 vertex7035
face link face1552 face1558 edges edge7598 edge7635 vertices
vertex7035 vertex7069
face link face1558 face1564 edges edge7635 edge7672 vertices
vertex7069 vertex7103
face link face1564 face1570 edges edge7672 edge7709 vertices
vertex7103 vertex7137
face link face1570 face1576 edges edge7709 edge7746 vertices
vertex7137 vertex7171
face link face1576 face1582 edges edge7746 edge7783 vertices
vertex7171 vertex7205
face link face1582 face1588 edges edge7783 edge7820 vertices
vertex7205 vertex7239
face link face1588 face1594 edges edge7820 edge7857 vertices
vertex7239 vertex7273
face link face1512 face1518 edges edge7350 edge7387 vertices
vertex6806 vertex6840
face link face1518 face1524 edges edge7387 edge7424 vertices
vertex6840 vertex6874
face link face1524 face1530 edges edge7424 edge7461 vertices
vertex6874 vertex6908
face link face1530 face1536 edges edge7461 edge7498 vertices
vertex6908 vertex6942
face link face1536 face1542 edges edge7498 edge7535 vertices
86
vertex6942 vertex6976
face link face1542 face1548 edges edge7535 edge7572 vertices
vertex6976 vertex7010
face link face1548 face1554 edges edge7572 edge7609 vertices
vertex7010 vertex7044
face link face1554 face1560 edges edge7609 edge7646 vertices
vertex7044 vertex7078
face link face1560 face1566 edges edge7646 edge7683 vertices
vertex7078 vertex7112
face link face1566 face1572 edges edge7683 edge7720 vertices
vertex7112 vertex7146
face link face1572 face1578 edges edge7720 edge7757 vertices
vertex7146 vertex7180
face link face1578 face1584 edges edge7757 edge7794 vertices
vertex7180 vertex7214
face link face1584 face1590 edges edge7794 edge7831 vertices
vertex7214 vertex7248
face link face1590 face1596 edges edge7831 edge7868 vertices
vertex7248 vertex7282
face link face1514 face1520 edges edge7363 edge7400 vertices
vertex6819 vertex6853
face link face1520 face1526 edges edge7400 edge7437 vertices
vertex6853 vertex6887
face link face1526 face1532 edges edge7437 edge7474 vertices
vertex6887 vertex6921
face link face1532 face1538 edges edge7474 edge7511 vertices
vertex6921 vertex6955
face link face1538 face1544 edges edge7511 edge7548 vertices
vertex6955 vertex6989
face link face1544 face1550 edges edge7548 edge7585 vertices
vertex6989 vertex7023
face link face1550 face1556 edges edge7585 edge7622 vertices
vertex7023 vertex7057
face link face1556 face1562 edges edge7622 edge7659 vertices
vertex7057 vertex7091
face link face1562 face1568 edges edge7659 edge7696 vertices
vertex7091 vertex7125
face link face1568 face1574 edges edge7696 edge7733 vertices
vertex7125 vertex7159
face link face1574 face1580 edges edge7733 edge7770 vertices
vertex7159 vertex7193
face link face1580 face1586 edges edge7770 edge7807 vertices
vertex7193 vertex7227
face link face1586 face1592 edges edge7807 edge7844 vertices
vertex7227 vertex7261
face link face1592 face1598 edges edge7844 edge7881 vertices
vertex7261 vertex7295
LINKING ALL THE TELEPHONES OF THE TOP OF THE PLENUM
face link face912 face642 edges edge6950 edge3489 vertices
vertex6437 vertex3253 reverse
face link face642 face647 edges edge3489 edge3744 vertices
vertex3253 vertex3433
face link face117 face646 edges edge6959 edge3638 vertices
vertex6447 vertex3313
87
face link face642 face652 edges edge3489 edge3491 vertices
vertex3253 vertex3255
face link face652 face662 edges edge3491 edge3493 vertices
vertex3255 vertex3257
face link face662 face672 edges edge3493 edge3495 vertices
vertex3257 vertex3259
face link face672 face682 edges edge3495 edge3497 vertices
vertex3259 vertex3261
face link face682 face692 edges edge3497 edge3499 vertices
vertex3261 vertex3263
face link face692 face702 edges edge3499 edge3501 vertices
vertex3263 vertex3265
face link face702 face712 edges edge3501 edge3503 vertices
vertex3265 vertex3267
face link face712 face722 edges edge3503 edge3505 vertices
vertex3267 vertex3269
face link face722 face732 edges edge3505 edge3507 vertices
vertex3269 vertex3271
face link face732 face742 edges edge3507 edge3509 vertices
vertex3271 vertex3273
face link face742 face752 edges edge3509 edge3511 vertices
vertex3273 vertex3275
face link face752 face762 edges edge3511 edge3513 vertices
vertex3275 vertex3277
face link face762 face772 edges edge3513 edge3515 vertices
vertex3277 vertex3279
face link face772 face782 edges edge3515 edge3517 vertices
vertex3279 vertex3281
face link face646 face656 edges edge3653 edge3655 vertices
vertex3312 vertex3314
face link face656 face666 edges edge3655 edge3657 vertices
vertex3314 vertex3316
face link face666 face676 edges edge3657 edge3659 vertices
vertex3316 vertex3318
face link face676 face686 edges edge3659 edge3661 vertices
vertex3318 vertex3320
face link face686 face696 edges edge3661 edge3663 vertices
vertex3320 vertex3322
face link face696 face706 edges edge3663 edge3665 vertices
vertex3322 vertex3324
face link face706 face716 edges edge3665 edge3667 vertices
vertex3324 vertex3326
face link face716 face726 edges edge3667 edge3669 vertices
vertex3326 vertex3328
face link face726 face736 edges edge3669 edge3671 vertices
vertex3328 vertex3330
face link face736 face746 edges edge3671 edge3673 vertices
vertex3330 vertex3332
face link face746 face756 edges edge3673 edge3675 vertices
vertex3332 vertex3334
face link face756 face766 edges edge3675 edge3677 vertices
vertex3334 vertex3336
face link face766 face776 edges edge3677 edge3679 vertices
vertex3336 vertex3338
face link face776 face786 edges edge3679 edge3681 vertices
88
vertex3338 vertex3340
face link face647 face657 edges edge3744 edge3746 vertices
vertex3433 vertex3435
face link face657 face667 edges edge3746 edge3748 vertices
vertex3435 vertex3437
face link face667 face677 edges edge3748 edge3750 vertices
vertex3437 vertex3439
face link face677 face687 edges edge3750 edge3752 vertices
vertex3439 vertex3441
face link face687 face697 edges edge3752 edge3754 vertices
vertex3441 vertex3443
face link face697 face707 edges edge3754 edge3756 vertices
vertex3443 vertex3445
face link face707 face717 edges edge3756 edge3758 vertices
vertex3445 vertex3447
face link face717 face727 edges edge3758 edge3760 vertices
vertex3447 vertex3449
face link face727 face737 edges edge3760 edge3762 vertices
vertex3449 vertex3451
face link face737 face747 edges edge3762 edge3764 vertices
vertex3451 vertex3453
face link face747 face757 edges edge3764 edge3766 vertices
vertex3453 vertex3455
face link face757 face767 edges edge3766 edge3768 vertices
vertex3455 vertex3457
face link face767 face777 edges edge3768 edge3770 vertices
vertex3457 vertex3459
face link face777 face787 edges edge3770 edge3772 vertices
vertex3459 vertex3461
face link face647 face1600 edges edge3685 edge6963 vertices
vertex3345 vertex6449
LINKING OUTBOXES ON THE PLENUM
face modify face911 side vertex4404 vertex4405
face modify face918 side vertex4405 vertex4404
face link face911 face915 edges edge4778 edge4898 vertices
vertex4374 vertex4434
face link face915 face645 edges edge4899 edge3833 vertices
vertex4480 vertex3463 reverse
face link face911 face641 edges edge4779 edge3578 vertices
vertex4405 vertex3283 reverse
face link face918 face648 edges edge4825 edge3686 vertices
vertex4436 vertex3347 reverse
face link face645 face655 edges edge3833 edge3834 vertices
vertex3463 vertex3465
face link face655 face665 edges edge3834 edge3835 vertices
vertex3465 vertex3467
face link face665 face675 edges edge3835 edge3836 vertices
vertex3467 vertex3469
face link face675 face685 edges edge3836 edge3837 vertices
vertex3469 vertex3471
face link face685 face695 edges edge3837 edge3838 vertices
89
vertex3471 vertex3473
face link face695 face705 edges edge3838 edge3839 vertices
vertex3473 vertex3475
face link face705 face715 edges edge3839 edge3840 vertices
vertex3475 vertex3477
face link face715 face725 edges edge3840 edge3841 vertices
vertex3477 vertex3479
face link face725 face735 edges edge3841 edge3842 vertices
vertex3479 vertex3481
face link face735 face745 edges edge3842 edge3843 vertices
vertex3481 vertex3483
face link face745 face755 edges edge3843 edge3844 vertices
vertex3483 vertex3485
face link face755 face765 edges edge3844 edge3845 vertices
vertex3485 vertex3487
face link face765 face775 edges edge3845 edge3846 vertices
vertex3487 vertex3489
face link face775 face785 edges edge3846 edge3847 vertices
vertex3489 vertex3491
face link face648 face658 edges edge3686 edge3690 vertices
vertex3347 vertex3353
face link face658 face668 edges edge3690 edge3694 vertices
vertex3353 vertex3359
face link face668 face678 edges edge3694 edge3698 vertices
vertex3359 vertex3365
face link face678 face688 edges edge3698 edge3702 vertices
vertex3365 vertex3371
face link face688 face698 edges edge3702 edge3706 vertices
vertex3371 vertex3377
face link face698 face708 edges edge3706 edge3710 vertices
vertex3377 vertex3383
face link face708 face718 edges edge3710 edge3714 vertices
vertex3383 vertex3389
face link face718 face728 edges edge3714 edge3718 vertices
vertex3389 vertex3395
face link face728 face738 edges edge3718 edge3722 vertices
vertex3395 vertex3401
face link face738 face748 edges edge3722 edge3726 vertices
vertex3401 vertex3407
face link face748 face758 edges edge3726 edge3730 vertices
vertex3407 vertex3413
face link face758 face768 edges edge3730 edge3734 vertices
vertex3413 vertex3419
face link face768 face778 edges edge3734 edge3738 vertices
vertex3419 vertex3425
face link face778 face788 edges edge3738 edge3742 vertices
vertex3425 vertex3431
face link face641 face650 edges edge3578 edge3579 vertices
vertex3283 vertex3285
face link face650 face660 edges edge3579 edge3580 vertices
vertex3285 vertex3287
face link face660 face670 edges edge3580 edge3581 vertices
vertex3287 vertex3289
face link face670 face680 edges edge3581 edge3582 vertices
vertex3289 vertex3291
face link face680 face690 edges edge3582 edge3583 vertices
90
vertex3291 vertex3293
face link face690 face700 edges edge3583 edge3584 vertices
vertex3293 vertex3295
face link face700 face710 edges edge3584 edge3585 vertices
vertex3295 vertex3297
face link face710 face720 edges edge3585 edge3586 vertices
vertex3297 vertex3299
face link face720 face730 edges edge3586 edge3587 vertices
vertex3299 vertex3301
face link face730 face740 edges edge3587 edge3588 vertices
vertex3301 vertex3303
face link face740 face750 edges edge3588 edge3589 vertices
vertex3303 vertex3305
face link face750 face760 edges edge3589 edge3590 vertices
vertex3305 vertex3307
face link face760 face770 edges edge3590 edge3591 vertices
vertex3307 vertex3309
face link face770 face780 edges edge3591 edge3592 vertices
vertex3309 vertex3311
face link face915 face925 edges edge4899 edge4901 vertices
vertex4480 vertex4482
face link face925 face935 edges edge4901 edge4903 vertices
vertex4482 vertex4484
face link face935 face945 edges edge4903 edge4905 vertices
vertex4484 vertex4486
face link face945 face955 edges edge4905 edge4907 vertices
vertex4486 vertex4488
face link face955 face965 edges edge4907 edge4909 vertices
vertex4488 vertex4490
face link face965 face975 edges edge4909 edge4911 vertices
vertex4490 vertex4492
face link face975 face985 edges edge4911 edge4913 vertices
vertex4492 vertex4494
face link face985 face995 edges edge4913 edge4915 vertices
vertex4494 vertex4496
face link face995 face1005 edges edge4915 edge4917 vertices
vertex4496 vertex4498
face link face1005 face1015 edges edge4917 edge4919 vertices
vertex4498 vertex4500
face link face1015 face1025 edges edge4919 edge4921 vertices
vertex4500 vertex4502
face link face1025 face1035 edges edge4921 edge4923 vertices
vertex4502 vertex4504
face link face1035 face1045 edges edge4923 edge4925 vertices
vertex4504 vertex4506
face link face1045 face1055 edges edge4925 edge4927 vertices
vertex4506 vertex4508
face link face918 face928 edges edge4825 edge4828 vertices
vertex4436 vertex4439
face link face928 face938 edges edge4828 edge4831 vertices
vertex4439 vertex4442
face link face938 face948 edges edge4831 edge4834 vertices
vertex4442 vertex4445
face link face948 face958 edges edge4834 edge4837 vertices
vertex4445 vertex4448
face link face958 face968 edges edge4837 edge4840 vertices
91
vertex4448 vertex4451
face link face968 face978 edges edge4840 edge4843 vertices
vertex4451 vertex4454
face link face978 face988 edges edge4843 edge4846 vertices
vertex4454 vertex4457
face link face988 face998 edges edge4846 edge4849 vertices
vertex4457 vertex4460
face link face998 face1008 edges edge4849 edge4852 vertices
vertex4460 vertex4463
face link face1008 face1018 edges edge4852 edge4855 vertices
vertex4463 vertex4466
face link face1018 face1028 edges edge4855 edge4858 vertices
vertex4466 vertex4469
face link face1028 face1038 edges edge4858 edge4861 vertices
vertex4469 vertex4472
face link face1038 face1048 edges edge4861 edge4864 vertices
vertex4472 vertex4475
face link face1048 face1058 edges edge4864 edge4867 vertices
vertex4475 vertex4478
face link face911 face920 edges edge108 edge118 vertices
vertex88 vertex94
face link face920 face930 edges edge118 edge128 vertices
vertex94 vertex100
face link face930 face940 edges edge4783 edge4785 vertices
vertex4409 vertex4411
face link face940 face950 edges edge4785 edge4787 vertices
vertex4411 vertex4413
face link face950 face960 edges edge4787 edge4789 vertices
vertex4413 vertex4415
face link face960 face970 edges edge4789 edge4791 vertices
vertex4415 vertex4417
face link face970 face980 edges edge4791 edge4793 vertices
vertex4417 vertex4419
face link face980 face990 edges edge4793 edge4795 vertices
vertex4419 vertex4421
face link face990 face1000 edges edge4795 edge4797 vertices
vertex4421 vertex4423
face link face1000 face1010 edges edge4797 edge4799 vertices
vertex4423 vertex4425
face link face1010 face1020 edges edge4799 edge4801 vertices
vertex4425 vertex4427
face link face1020 face1030 edges edge4801 edge4803 vertices
vertex4427 vertex4429
face link face1030 face1040 edges edge4803 edge4805 vertices
vertex4429 vertex4431
face link face1040 face1050 edges edge4805 edge4807 vertices
vertex4431 vertex4433
LINKING THE TOP OF THE CHANEL OUTBOXES
face modify face1256 side vertex6322 vertex6321
face modify face1263 side vertex6322 vertex6321
face modify face1260 side vertex6397 vertex6396
92
face link face1256 face1260 edges edge6803 edge6923 vertices
vertex6322 vertex6397
face link face1256 face371 edges edge6774 edge2053 vertices
vertex6292 vertex1955 reverse
face link face371 face375 edges edge2053 edge2336 vertices
vertex1955 vertex2135
face link face1263 face378 edges edge6820 edge2228 vertices
vertex6322 vertex2071 reverse
face link face1263 face1273 edges edge6820 edge6823 vertices
vertex6322 vertex6324
face link face1273 face1283 edges edge6823 edge6826 vertices
vertex6324 vertex6326
face link face1283 face1293 edges edge6826 edge6829 vertices
vertex6326 vertex6328
face link face1293 face1303 edges edge6829 edge6832 vertices
vertex6328 vertex6330
face link face1303 face1313 edges edge6832 edge6835 vertices
vertex6330 vertex6332
face link face1313 face1323 edges edge6835 edge6838 vertices
vertex6332 vertex6334
face link face1323 face1333 edges edge6838 edge6841 vertices
vertex6334 vertex6336
face link face1333 face1343 edges edge6841 edge6844 vertices
vertex6336 vertex6338
face link face1343 face1353 edges edge6844 edge6847 vertices
vertex6338 vertex6340
face link face1353 face1363 edges edge6847 edge6850 vertices
vertex6340 vertex6342
face link face1363 face1373 edges edge6850 edge6853 vertices
vertex6342 vertex6344
face link face1373 face1383 edges edge6853 edge6856 vertices
vertex6344 vertex6346
face link face1383 face1393 edges edge6856 edge6859 vertices
vertex6346 vertex6348
face link face1393 face1403 edges edge6859 edge6862 vertices
vertex6348 vertex6350
face link face1256 face1265 edges edge6774 edge6776 vertices
vertex6292 vertex6294
face link face1265 face1275 edges edge6776 edge6778 vertices
vertex6294 vertex6296
face link face1275 face1285 edges edge6778 edge6780 vertices
vertex6296 vertex6298
face link face1285 face1295 edges edge6780 edge6782 vertices
vertex6298 vertex6300
face link face1295 face1305 edges edge6782 edge6784 vertices
vertex6300 vertex6302
face link face1305 face1315 edges edge6784 edge6786 vertices
vertex6302 vertex6304
face link face1315 face1325 edges edge6786 edge6788 vertices
vertex6304 vertex6306
face link face1325 face1335 edges edge6788 edge6790 vertices
vertex6306 vertex6308
face link face1335 face1345 edges edge6790 edge6792 vertices
vertex6308 vertex6310
face link face1345 face1355 edges edge6792 edge6794 vertices
vertex6310 vertex6312
93
face link face1355 face1365 edges edge6794 edge6796 vertices
vertex6312 vertex6314
face link face1365 face1375 edges edge6796 edge6798 vertices
vertex6314 vertex6316
face link face1375 face1385 edges edge6798 edge6800 vertices
vertex6316 vertex6318
face link face1385 face1395 edges edge6800 edge6802 vertices
vertex6318 vertex6320
face link face1260 face1270 edges edge6894 edge6896 vertices
vertex6353 vertex6356
face link face1270 face1280 edges edge6896 edge6898 vertices
vertex6356 vertex6359
face link face1280 face1290 edges edge6898 edge6900 vertices
vertex6359 vertex6362
face link face1290 face1300 edges edge6900 edge6902 vertices
vertex6362 vertex6365
face link face1300 face1310 edges edge6902 edge6904 vertices
vertex6365 vertex6368
face link face1310 face1320 edges edge6904 edge6906 vertices
vertex6368 vertex6371
face link face1320 face1330 edges edge6906 edge6908 vertices
vertex6371 vertex6374
face link face1330 face1340 edges edge6908 edge6910 vertices
vertex6374 vertex6377
face link face1340 face1350 edges edge6910 edge6912 vertices
vertex6377 vertex6380
face link face1350 face1360 edges edge6912 edge6914 vertices
vertex6380 vertex6383
face link face1360 face1370 edges edge6914 edge6916 vertices
vertex6383 vertex6386
face link face1370 face1380 edges edge6916 edge6918 vertices
vertex6386 vertex6389
face link face1380 face1390 edges edge6918 edge6920 vertices
vertex6389 vertex6392
face link face1390 face1400 edges edge6920 edge6922 vertices
vertex6392 vertex6395
LINKING THE BOTTOM OF THE CHANEL OUTBOXES
face link face375 face385 edges edge2440 edge2443 vertices
vertex2251 vertex2253
face link face385 face395 edges edge2443 edge2446 vertices
vertex2253 vertex2255
face link face395 face405 edges edge2446 edge2449 vertices
vertex2255 vertex2257
face link face405 face415 edges edge2449 edge2452 vertices
vertex2257 vertex2259
face link face415 face425 edges edge2452 edge2455 vertices
vertex2259 vertex2261
face link face425 face435 edges edge2455 edge2458 vertices
vertex2261 vertex2263
face link face435 face445 edges edge2458 edge2461 vertices
vertex2263 vertex2265
face link face445 face455 edges edge2461 edge2464 vertices
vertex2265 vertex2267
face link face455 face465 edges edge2464 edge2467 vertices
94
vertex2267 vertex2269
face link face465 face475 edges edge2467 edge2470 vertices
vertex2269 vertex2271
face link face475 face485 edges edge2470 edge2473 vertices
vertex2271 vertex2273
face link face485 face495 edges edge2473 edge2476 vertices
vertex2273 vertex2275
face link face495 face505 edges edge2476 edge2479 vertices
vertex2275 vertex2277
face link face505 face515 edges edge2479 edge2482 vertices
vertex2277 vertex2279
face link face378 face388 edges edge2245 edge2248 vertices
vertex2135 vertex2141
face link face388 face398 edges edge2248 edge2251 vertices
vertex2141 vertex2147
face link face398 face408 edges edge2251 edge2254 vertices
vertex2147 vertex2153
face link face408 face418 edges edge2254 edge2257 vertices
vertex2153 vertex2159
face link face418 face428 edges edge2257 edge2260 vertices
vertex2159 vertex2165
face link face428 face438 edges edge2260 edge2263 vertices
vertex2165 vertex2171
face link face438 face448 edges edge2263 edge2266 vertices
vertex2171 vertex2177
face link face448 face458 edges edge2266 edge2269 vertices
vertex2177 vertex2183
face link face458 face468 edges edge2269 edge2272 vertices
vertex2183 vertex2189
face link face468 face478 edges edge2272 edge2275 vertices
vertex2189 vertex2195
face link face478 face488 edges edge2275 edge2278 vertices
vertex2195 vertex2201
face link face488 face498 edges edge2278 edge2281 vertices
vertex2201 vertex2207
face link face498 face508 edges edge2281 edge2284 vertices
vertex2207 vertex2213
face link face508 face518 edges edge2284 edge2287 vertices
vertex2213 vertex2219
face link face371 face380 edges edge2185 edge2188 vertices
vertex2071 vertex2073
face link face380 face390 edges edge2188 edge2191 vertices
vertex2073 vertex2075
face link face390 face400 edges edge2191 edge2194 vertices
vertex2075 vertex2077
face link face400 face410 edges edge2194 edge2197 vertices
vertex2077 vertex2079
face link face410 face420 edges edge2197 edge2200 vertices
vertex2079 vertex2081
face link face420 face430 edges edge2200 edge2203 vertices
vertex2081 vertex2083
face link face430 face440 edges edge2203 edge2206 vertices
vertex2083 vertex2085
face link face440 face450 edges edge2206 edge2209 vertices
vertex2085 vertex2087
face link face450 face460 edges edge2209 edge2212 vertices
95
vertex2087 vertex2089
face link face460 face470 edges edge2212 edge2215 vertices
vertex2089 vertex2091
face link face470 face480 edges edge2215 edge2218 vertices
vertex2091 vertex2093
face link face480 face490 edges edge2218 edge2221 vertices
vertex2093 vertex2095
face link face490 face500 edges edge2221 edge2224 vertices
vertex2095 vertex2097
face link face500 face510 edges edge2224 edge2227 vertices
vertex2097 vertex2099
TOP SIDE BOX beginning of channel
face link face1649 face1633 edges edge97 edge3533 vertices
vertex4374 vertex3162 reverse
TOP SIDE BOXES
face link face1650 face1651 edges edge4749 edge4751 vertices
vertex4376 vertex4378
face link face1652 face1653 edges edge4753 edge4755 vertices
vertex4380 vertex4382
face link face1653 face1654 edges edge4755 edge4757 vertices
vertex4382 vertex4384
face link face1654 face1655 edges edge4757 edge4759 vertices
vertex4384 vertex4386
face link face1655 face1656 edges edge4759 edge4761 vertices
vertex4386 vertex4388
face link face1656 face114 edges edge4761 edge4763 vertices
vertex4388 vertex4390
face link face114 face1657 edges edge4763 edge4765 vertices
vertex4390 vertex4392
face link face1657 face1658 edges edge4765 edge4767 vertices
vertex4392 vertex4394
face link face1658 face1659 edges edge4767 edge4769 vertices
vertex4394 vertex4396
face link face1659 face1660 edges edge4769 edge4771 vertices
vertex4396 vertex4398
face link face1660 face1661 edges edge4771 edge4773 vertices
vertex4398 vertex4400
face link face1661 face1662 edges edge4773 edge4775 vertices
vertex4400 vertex4402
face link face1650 face1634 edges edge4900 edge8036 vertices
vertex4481 vertex3464 reverse
face link face1634 face1635 edges edge8036 edge8037 vertices
vertex3464 vertex3466
face link face1635 face1636 edges edge8037 edge8038 vertices
vertex3466 vertex3468
face link face1636 face1637 edges edge8038 edge8039 vertices
vertex3468 vertex3470
face link face1637 face1638 edges edge8039 edge8040 vertices
vertex3470 vertex3472
face link face1638 face1639 edges edge8040 edge8041 vertices
vertex3472 vertex3474
face link face1639 face6 edges edge8041 edge8042 vertices
96
vertex3474 vertex3476
face link face6 face1640 edges edge8042 edge8043 vertices
vertex3476 vertex3478
face link face1640 face1641 edges edge8043 edge8044 vertices
vertex3478 vertex3480
face link face1641 face1642 edges edge8044 edge8045 vertices
vertex3480 vertex3482
face link face1642 face1643 edges edge8045 edge8046 vertices
vertex3482 vertex3484
face link face1643 face1644 edges edge8046 edge8047 vertices
vertex3484 vertex3486
face link face1644 face1645 edges edge8047 edge8048 vertices
vertex3486 vertex3488
face link face1645 face1646 edges edge8048 edge8049 vertices
vertex3488 vertex3490
face link face1651 face1652 edges edge4751 edge4753 vertices
vertex4378 vertex4380
TOP SIDE BOX END OF CHANNEL
face link face1647 face1663 edges edge8050 edge99 vertices
vertex7433 vertex7435 reverse
TOP SIDE BOX BACK OF CHANNEL
face link face1648 face1664 edges edge12 edge8069 vertices
vertex8 vertex84 reverse
BOTTOM SIDE BOX
face link face1665 face1681 edges edge6773 edge2048 vertices
vertex6291 vertex1950 reverse
face link face1680 face1696 edges edge8071 edge8105 vertices
vertex7436 vertex7438 reverse
face link face1666 face1667 edges edge6894 edge6896 vertices
vertex6397 vertex6399
face link face1667 face1668 edges edge6896 edge6898 vertices
vertex6399 vertex6401
face link face1668 face1669 edges edge6898 edge6900 vertices
vertex6401 vertex6403
face link face1669 face1670 edges edge6900 edge6902 vertices
vertex6403 vertex6405
face link face1670 face1671 edges edge6902 edge6904 vertices
vertex6405 vertex6407
face link face1671 face209 edges edge6904 edge6906 vertices
vertex6407 vertex6409
face link face209 face1672 edges edge6906 edge6908 vertices
vertex6409 vertex6411
face link face1672 face1673 edges edge6908 edge6910 vertices
vertex6411 vertex6413
face link face1673 face1674 edges edge6910 edge6912 vertices
vertex6413 vertex6415
face link face1674 face1675 edges edge6912 edge6914 vertices
vertex6415 vertex6417
face link face1675 face1676 edges edge6914 edge6916 vertices
vertex6417 vertex6419
97
face link face1676 face1677 edges edge6916 edge6918 vertices
vertex6419 vertex6421
face link face1677 face1678 edges edge6918 edge6920 vertices
vertex6421 vertex6423
face link face1666 face1682 edges edge6894 edge8090 vertices
vertex6397 vertex2251 reverse
face link face1682 face1683 edges edge8090 edge8091 vertices
vertex2251 vertex2253
face link face1683 face1684 edges edge8091 edge8092 vertices
vertex2253 vertex2255
face link face1684 face1685 edges edge8092 edge8093 vertices
vertex2255 vertex2257
face link face1685 face1686 edges edge8093 edge8094 vertices
vertex2257 vertex2259
face link face1686 face1687 edges edge8094 edge8095 vertices
vertex2259 vertex2261
face link face1687 face1688 edges edge8095 edge8096 vertices
vertex2261 vertex2263
face link face1688 face1 edges edge8096 edge8097 vertices
vertex2263 vertex2265
face link face1 face1689 edges edge8097 edge8098 vertices
vertex2265 vertex2267
face link face1689 face1690 edges edge8098 edge8099 vertices
vertex2267 vertex2269
face link face1690 face1691 edges edge8099 edge8100 vertices
vertex2269 vertex2271
face link face1691 face1692 edges edge8100 edge8101 vertices
vertex2271 vertex2273
face link face1692 face1693 edges edge8101 edge8102 vertices
vertex2273 vertex2275
face link face1693 face1694 edges edge8102 edge8103 vertices
vertex2275 vertex2277
face link face1679 face1695 edges edge89 edge2227 vertices
vertex6320 vertex2039 reverse
MESHING BEGINS HERE
BOUNDARY LAYERS BEGINS HERE
BOUNDARY LAYER FOR THE bottom of plenum
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer1 face face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
98
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 edge edge97
edge4748 edge106 edge6946 edge6947 edge107 edge4749
edge4750 edge116 edge6972 edge6973 edge117 edge4751
edge4752 edge126 edge6998 edge6999 edge127 edge4753
edge4754 edge136 edge7024 edge7025 edge137 edge4755
edge4756 edge146 edge7050 edge7051 edge147 edge4757
edge4758 edge156 edge7076 edge7077 edge157 edge4759
edge4760 edge166 edge7102 edge7103 edge167 edge4761
edge4762 edge176 edge7128 edge7129 edge177 edge4763
edge4764 edge186 edge7154 edge7155 edge187 edge4765
edge4766 edge196 edge7180 edge7181 edge197 edge4767
edge4768 edge206 edge7206 edge7207 edge207 edge4769
edge4770 edge216 edge7232 edge7233 edge217 edge4771
edge4772 edge226 edge7258 edge7259 edge227 edge4773
edge4774 edge236 edge7284 edge7285 edge237 edge4775
edge4776 edge246 edge7310 edge7311 edge247 edge4777 add
MESHING THE PLENUM
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer2 face face4 face4 face5 face110
face110 edge edge99 edge8069 edge100 edge8052 edge98 add
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer4 face face1649 face1664 face1664
face1664 face1663 edge edge8052 edge98 edge100 edge8069
edge99 add
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer4 face face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face4 face2 face2 face2 face2 face2 face4
face5 face110 face110 edge edge9 edge3398 edge3399
edge3400 edge3401 edge3402 edge3403 edge3404 edge3406
edge3405 edge3407 edge3408 edge3409 edge3415 edge3410
edge3411 edge3412 edge3413 edge3414 edge3416 edge3417
edge3418 edge3419 edge3420 edge3421 edge3422 edge3423
edge3424 edge3425 edge3426 edge3427 edge3428 edge3429
edge3430 edge3431 edge3432 edge3433 edge3434 edge3435
edge3436 edge3437 edge3438 edge3439 edge3440 edge3441
edge3442 edge3443 edge3444 edge3445 edge3446 edge3447
99
edge3448 edge3449 edge3450 edge3451 edge3457 edge3452
edge3453 edge3454 edge3455 edge3456 edge3458 edge3459
edge3460 edge3461 edge3462 edge3463 edge3464 edge3465
edge3466 edge3467 edge3468 edge3469 edge3475 edge3481
edge3470 edge3471 edge3472 edge3473 edge3474 edge3476
edge3477 edge3478 edge3479 edge3480 edge3487 edge11
edge3482 edge3483 edge3484 edge3485 edge3486 edge8051
edge12 edge10 edge8034 add
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer5 face face1663 face1664 face1664
face1664 face1649 edge edge99 edge8069 edge100 edge98
edge8052 add
BOUNDARY LAYER OF THE HOLES
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer1 face face642 edge edge3534 add
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer7 face face117 face1600 edge edge4824
edge110 add
BONDARY LAYER OF THE CHANNEL
TARGET WALL BOUNDARY LAYER
BBBL
BBL
BBL
BBBL
BBL
BBL
BBBLLLLL
blayer create first $firstch growth $growthch rows $rowsch transition 1 trows 0
uniform
blayer attach b_layer8 face face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
100
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face105 face105 face106
face104 face104 edge edge2048 edge2049 edge2050 edge2051
edge2052 edge2053 edge2054 edge2055 edge2056 edge2057
edge2058 edge2059 edge2060 edge2061 edge2062 edge2063
edge2064 edge2065 edge2066 edge2072 edge2067 edge2068
edge2069 edge2070 edge2071 edge2084 edge2078 edge2073
edge2074 edge2075 edge2076 edge2077 edge2079 edge2080
edge2081 edge2082 edge2083 edge2090 edge2096 edge2085
edge2086 edge2087 edge2088 edge2089 edge2091 edge2092
edge2093 edge2094 edge2095 edge2102 edge2108 edge2097
edge2098 edge2099 edge2100 edge2101 edge2103 edge2104
edge2105 edge2106 edge2107 edge2114 edge2120 edge2109
edge2110 edge2111 edge2112 edge2113 edge2115 edge2116
edge2117 edge2118 edge2119 edge2126 edge2132 edge2121
edge2122 edge2123 edge2124 edge2125 edge2127 edge2128
edge2129 edge2130 edge2131 edge2133 edge2134 edge2136
edge2137 edge1 edge2135 edge8088 edge3 edge4 edge8105
edge2 add
blayer create first $firstch growth $growthch rows $rowsch transition 1 trows 0
uniform
blayer attach b_layer9 face face1681 face1696 face1696
face1696 face1695 edge edge2 edge8105 edge4 edge3
edge8088 add
blayer create first $firstch growth $growthch rows $rowsch transition 1 trows 0
uniform
blayer attach b_layer10 face face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face105 face105
face106 face104 face104 edge edge6743 edge101
edge7336 edge7337 edge102 edge6744 edge6745 edge111
edge7373 edge7374 edge112 edge6746 edge6747 edge121
edge7410 edge7411 edge122 edge6748 edge6749 edge131
edge7447 edge7448 edge132 edge6750 edge6751 edge141
edge7484 edge7485 edge142 edge6752 edge6755 edge6753
edge151 edge6754 edge7521 edge7522 edge152 edge161
101
edge6756 edge6757 edge7558 edge7559 edge162 edge171
edge7595 edge7596 edge172 edge6758 edge6759 edge181
edge7632 edge7633 edge182 edge6760 edge6761 edge191
edge7669 edge7670 edge192 edge6762 edge6763 edge6767
edge6765 edge201 edge7706 edge7707 edge202 edge6764
edge211 edge6766 edge7743 edge7744 edge212 edge6769
edge221 edge6768 edge7780 edge7781 edge222 edge6771
edge231 edge6770 edge7817 edge7818 edge232 edge241
edge7854 edge7855 edge242 edge6772 edge89 edge8070
edge91 edge92 edge8087 edge90 add
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer11 face face4 face5 face2 face5
face110 face2 edge edge8 edge8 edge6 edge7 edge7
edge5 add
blayer create first $firstch growth $growthch rows $rowsch transition 1 trows 0
uniform
blayer attach b_layer12 face face106 face104 face103 face105
edge edge87 edge87 edge85 edge88 add
BOUNDARY LAYERS ENDS HERE
edge picklink edge6948 edge6949
edge mesh edge6949 edge6948 successive ratio1 1 intervals $NumbNodes
edge picklink edge6950
edge mesh edge6950 successive ratio1 1 intervals ($NumbNodes2)
face mesh face1450 map
edge picklink edge6963 edge6947
edge mesh edge6947 edge6963 successive ratio1 1 intervals ($Numbtelnodes+$rows)
face mesh face912 map
edge picklink edge6961 edge6960 edge7889 edge7890
edge mesh edge7890 edge7889 edge6960 edge6961 successive ratio1 1
intervals ($NumbNodes)
edge picklink edge6959 edge7891
edge mesh edge7891 edge6959 successive ratio1 1 intervals ($NumbNodes2)
face mesh face1452 map
face mesh face1600 face117 map
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer12 face face2 face110 face5 face110
face2 face4 face5 face4 edge edge5 edge5 edge7
edge7 edge6 edge6 edge8 edge8 add
Meshing constants
$NumbNodes=5
$Numbtelnodes=6
$PLobnodes=5
$Chobnodes=5
$Plbenodes=($NumbNodes(4)+$rows)
$plsqnodes=($NumbNodes(3))
102
$Pllsnodes=($NumbNodes+$rows)
$Nojetcells=10
edge picklink edge3686 edge3402
edge mesh edge3686 edge3402 successive ratio1 1 intervals ($PLobnodes)
edge picklink edge6744 edge6864
edge mesh edge6864 edge6744 successive ratio1 1 intervals 5
face link face1260 face375 edges edge6923 edge2440 vertices
vertex6397 vertex2251 reverse
face modify face915 side vertex4479 vertex4480
face mesh face915 face918 face911 map size 1
face mesh face1260 face1263 face1256 map size 1
edge picklink edge8068 edge8053
edge mesh edge8068 edge8053 successive ratio1 1 intervals ($Plbenodes)
edge picklink edge8086 edge8071
edge mesh edge8071 edge8086 successive ratio1 1 intervals ($CHbenodes)
edge delete edge8053 edge8068 keepsettings onlymesh
edge mesh edge8053 edge8068 successive ratio1 1 intervals ($Plbenodes)
edge delete edge8090 keepsettings onlymesh
edge picklink edge8090
edge mesh edge8090 successive ratio1 1 intervals ($plsqnodes)
edge delete edge8054 keepsettings onlymesh
edge picklink edge8054
edge mesh edge8054 successive ratio1 1 intervals ($plsqnodes)
face mesh face1647 face1679 face1678 face1646 face1633
face1665 map
edge delete edge98 edge8087 keepsettings onlymesh
edge picklink edge8087 edge98
edge mesh edge98 successive ratio1 1 intervals ($Pllsnodes)
edge mesh edge8087 successive ratio1 1 intervals ($CHlsnodes)
face mesh face1648 face1680 map
COOPERING ALL THE JETS
volume mesh volume3 cooper source face1600 face1452 face117
face1514 face1512 face115 intervals ($Nojetcells)
volume mesh volume5 cooper source face1456 face1602 face124
face1518 face1520 face122 intervals ($Nojetcells)
volume mesh volume7 cooper source face1460 face1604 face131
face1526 face1524 face129 intervals ($Nojetcells)
volume mesh volume9 cooper source face1464 face1606 face138
face1532 face1530 face136 intervals ($Nojetcells)
volume mesh volume11 cooper source face1468 face1608 face145
face1538 face143 face1536 intervals ($Nojetcells)
volume mesh volume13 cooper source face1472 face1610 face152
face1544 face1542 face150 intervals ($Nojetcells)
volume mesh volume15 cooper source face1476 face1612 face159
face1550 face1548 face157 intervals ($Nojetcells)
volume mesh volume17 cooper source face1480 face1614 face166
face1556 face1554 face164 intervals ($Nojetcells)
volume mesh volume19 cooper source face1484 face1616 face173
face1562 face171 face1560 intervals ($Nojetcells)
volume mesh volume21 cooper source face1488 face1618 face180
face1568 face1566 face178 intervals ($Nojetcells)
103
volume mesh volume23 cooper source face1492 face1620 face187
face1574 face1572 face185 intervals ($Nojetcells)
volume mesh volume25 cooper source face1496 face1622 face194
face1578 face1580 face192 intervals ($Nojetcells)
volume mesh volume27 cooper source face1624 face1500 face201
face1586 face1584 face199 intervals ($Nojetcells)
volume mesh volume29 cooper source face1504 face1626 face208
face1592 face1590 face206 intervals ($Nojetcells)
volume mesh volume31 cooper source face1628 face1508 face215
face1596 face1598 face213 intervals ($Nojetcells)
volume mesh volume30 cooper source face1506 face1052 face1594
face1397 intervals ($Nojetcells)
volume mesh volume28 cooper source face1502 face1042 face1588
face1387 intervals ($Nojetcells)
volume mesh volume26 cooper source face1498 face1032 face1582
face1377 intervals ($Nojetcells)
volume mesh volume24 cooper source face1494 face1022 face1576
face1367 intervals ($Nojetcells)
volume mesh volume22 cooper source face1490 face1012 face1570
face1357 intervals ($Nojetcells)
volume mesh volume20 cooper source face1486 face1002 face1564
face1347 intervals ($Nojetcells)
volume mesh volume18 cooper source face1482 face992 face1558
face1337 intervals ($Nojetcells)
volume mesh volume16 cooper source face1478 face982 face1552
face1327 intervals ($Nojetcells)
volume mesh volume14 cooper source face1474 face972 face1546
face1317 intervals ($Nojetcells)
volume mesh volume12 cooper source face1470 face962 face1540
face1307 intervals ($Nojetcells)
volume mesh volume10 cooper source face1466 face952 face1534
face1297 intervals ($Nojetcells)
volume mesh volume8 cooper source face1462 face942 face1528
face1287 intervals ($Nojetcells)
volume mesh volume6 cooper source face1458 face932 face1522
face1277 intervals ($Nojetcells)
volume mesh volume4 cooper source face1454 face922 face1516
face1267 intervals ($Nojetcells)
volume mesh cylinder cooper source face1450 face912 face1510
face1257 intervals ($Nojetcells)
window modify invisible mesh
volume mesh volume34 cooper source face1649 face1650 face1651
face1652 face1653 face1654 face1655 face1664 face1639
face1638 face1637 face1636 face1635 face1634 face1633
face1648 face1610 face1608 face1606 face1604 face1602
face1600 face1472 face962 face1468 face952 face1464
face942 face1460 face932 face1456 face922 face1452
face912 face915 face918 face911 face925 face928
face920 face935 face938 face930 face945 face948
face940 face955 face958 face950 face965 face968
face960 face694 face689 face684 face679 face674
face669 face664 face659 face654 face649 face644
face640 face697 face696 face692 face687 face686
face682 face677 face676 face672 face667 face666
104
face662 face657 face656 face652 face647 face646
face642 face695 face698 face690 face685 face688
face680 face675 face678 face670 face665 face668
face660 face655 face658 face650 face645 face648
face641 face152 face1470 face145 face1466 face138
face1462 face131 face1458 face124 face1454 face117
face1450 face1657 face1658 face1659 face1660 face1661
face1662 face1663 face788 face1656 face1474 face159
face1647 face1646 face1645 face1644 face1643 face1642
face1641 face1640 face1478 face1628 face1626 face1624
face1622 face1620 face1618 face1616 face1614 face1612
face1508 face1052 face1504 face1042 face1500 face1032
face1496 face1022 face1492 face1012 face1488 face1002
face1484 face992 face1480 face982 face1476 face972
face975 face978 face970 face985 face988 face980
face995 face998 face990 face1005 face1008 face1000
face1015 face1018 face1010 face1025 face1028 face1020
face1035 face1038 face1030 face1045 face1048 face1040
face1050 face114 face1058 face774 face769 face764
face759 face754 face749 face744 face739 face734
face729 face724 face719 face714 face709 face704
face699 face777 face776 face772 face767 face766
face762 face757 face756 face752 face747 face746
face742 face737 face736 face732 face727 face726
face722 face717 face716 face712 face707 face706
face702 face779 face784 face787 face775 face778
face770 face765 face768 face760 face755 face758
face750 face745 face748 face740 face735 face738
face730 face725 face728 face720 face715 face718
face710 face705 face708 face700 face782 face786
face785 face6 face780 face1055 face215 face1506
face208 face1502 face201 face1498 face194 face1494
face187 face1490 face180 face1486 face173 face1482
face166 intervals ($Plzdnodes)
volume delete body onlymesh
volume mesh body cooper source face1689 face1690 face1691
face1692 face1693 face1681 face1682 face1683 face1684
face1685 face1686 face1687 face1688 face1696 face1671
face1670 face1669 face1668 face1667 face1666 face1665
face1677 face1676 face1675 face1674 face1673 face1672
face1680 face199 face1584 face1377 face192 face1578
face1367 face185 face1572 face1357 face178 face1566
face1347 face171 face1560 face1337 face164 face1554
face1327 face157 face1548 face1317 face150 face1542
face1307 face143 face1536 face1297 face136 face1530
face1287 face129 face1524 face1277 face122 face1518
face1267 face115 face1512 face1257 face1380 face1383
face1375 face1370 face1373 face1365 face1360 face1363
face1355 face1350 face1353 face1345 face1340 face1343
face1335 face1330 face1333 face1325 face1320 face1323
face1315 face1310 face1313 face1305 face1300 face1303
face1295 face1290 face1293 face1285 face1280 face1283
face1275 face1270 face1273 face1265 face1260 face1263
face1256 face209 face374 face370 face384 face379
face394 face389 face404 face399 face414 face409
105
face424 face419 face434 face429 face444 face439
face454 face449 face464 face459 face474 face469
face484 face479 face494 face489 face377 face376
face372 face387 face386 face382 face397 face396
face392 face407 face406 face402 face417 face416
face412 face427 face426 face422 face437 face436
face432 face447 face446 face442 face457 face456
face452 face467 face466 face462 face477 face476
face472 face487 face486 face482 face497 face496
face492 face375 face378 face371 face385 face388
face380 face395 face398 face390 face405 face408
face400 face415 face418 face410 face425 face428
face420 face435 face438 face430 face445 face448
face440 face455 face458 face450 face465 face468
face460 face475 face478 face470 face485 face488
face480 face495 face498 face490 face1 face1586
face1582 face1580 face1576 face1574 face1570 face1568
face1564 face1562 face1558 face1556 face1552 face1550
face1546 face1544 face1540 face1538 face1534 face1532
face1528 face1526 face1522 face1520 face1516 face1514
face1510 face1403 face518 face1588 face1592 face1594
face1694 face1695 face1598 face1679 face1678 face515
face516 face510 face500 face508 face505 face213
face1596 face1397 face206 face1590 face1387 face517
face514 face512 face502 face506 face507 face509
face499 face504 face1400 face1395 face1385 face1390
face1393 intervals ($Chzdnodes)
BOUNDARY CONDITIONS
physics create Symmetry btype SYMMETRY face face2 face103
face211 face204 face197 face190 face183 face176
face169 face162 face155 face148 face141 face134
face127 face120 face112
physics create Wall btype SYMMETRY face face110 face5 face1649
face1664 face918 face915 face911 face925 face1650
face928 face920 face935 face938 face930 face1652
face1651 face948 face945 face940 face1653 face1654
face958 face955 face950 face1655 face965 face968
face960 face978 face975 face970 face1656 face114
face985 face988 face980 face995 face998 face990
face1657 face1005 face1008 face1000 face1658 face1015
face1018 face1010 face1659 face1028 face1025 face1020
face1035 face1660 face1038 face1030 face1045 face1661
face1048 face1040 face1055 face1662 face1058 face1050
face1663 face4 face1395 face1679 face1403 face1400
face1680 face1385 face1678 face1393 face1390 face1375
face1677 face1383 face1380 face1676 face1365 face1373
face1370 face1675 face1355 face1363 face1360 face1674
face1345 face1353 face1350 face1673 face1335 face1343
face1340 face1672 face1325 face1333 face1330 face209
face1315 face1323 face1320 face1671 face1305 face1313
face1310 face1670 face1295 face1303 face1300 face1669
106
face1285 face1293 face1290 face1668 face1275 face1283
face1280 face1667 face1265 face1273 face1270 face1666
face1256 face1263 face1260 face1665 face214 face91
face207 face85 face200 face79 face193 face73 face186
face67 face179 face61 face172 face55 face165 face49
face158 face43 face151 face37 face144 face31 face137
face25 face130 face19 face123 face13 face116 face8
physics modify Wall btype WALL face face110 face5 face1649
face1664 face918 face915 face911 face925 face1650
face928 face920 face935 face938 face930 face1652
face1651 face948 face945 face940 face1653 face1654
face958 face955 face950 face1655 face965 face968
face960 face978 face975 face970 face1656 face114
face985 face988 face980 face995 face998 face990
face1657 face1005 face1008 face1000 face1658 face1015
face1018 face1010 face1659 face1028 face1025 face1020
face1035 face1660 face1038 face1030 face1045 face1661
face1048 face1040 face1055 face1662 face1058 face1050
face1663 face4 face1395 face1679 face1403 face1400
face1680 face1385 face1678 face1393 face1390 face1375
face1677 face1383 face1380 face1676 face1365 face1373
face1370 face1675 face1355 face1363 face1360 face1674
face1345 face1353 face1350 face1673 face1335 face1343
face1340 face1672 face1325 face1333 face1330 face209
face1315 face1323 face1320 face1671 face1305 face1313
face1310 face1670 face1295 face1303 face1300 face1669
face1285 face1293 face1290 face1668 face1275 face1283
face1280 face1667 face1265 face1273 face1270 face1666
face1256 face1263 face1260 face1665 face214 face91
face207 face85 face200 face79 face193 face73 face186
face67 face179 face61 face172 face55 face165 face49
face158 face43 face151 face37 face144 face31 face137
face25 face130 face19 face123 face13 face116 face8
physics create Heat Fluxes btype WALL face face104 face106
face370 face379 face389 face372 face382 face392
face371 face380 face390 face378 face388 face398
face376 face386 face396 face374 face384 face394
face377 face387 face397 face375 face385 face395
face1681 face1682 face1683 face1684 face1696 face402
face412 face422 face432 face442 face400 face410
face420 face430 face440 face408 face418 face428
face438 face448 face406 face416 face426 face436
face446 face404 face414 face424 face434 face444
face407 face417 face427 face437 face447 face405
face415 face425 face435 face445 face1688 face1685
face1686 face1687 face452 face462 face472 face482
face492 face1693 face450 face460 face470 face480
face490 face1692 face458 face468 face478 face488
face498 face1 face456 face466 face476 face486 face496
face454 face464 face474 face484 face494 face457
face467 face477 face487 face497 face1691 face455
face465 face475 face485 face495 face1689 face1690
face518 face502 face512 face1695 face500 face510
face1694 face508 face506 face516 face504 face514
face507 face517 face515 face505
physics create Mass flow inlet btype SYMMETRY face face640 face649
107
face659 face642 face652 face662 face672 face641
face650 face660 face670 face648 face658 face668
face678 face646 face656 face666 face676 face644
face654 face664 face674 face647 face657 face667
face677 face645 face655 face665 face675 face1633
face1634 face1635 face1636 face1637 face1648 face679
face689 face699 face682 face692 face702 face712
face680 face690 face700 face710 face688 face698
face708 face718 face6 face686 face696 face706 face716
face684 face694 face704 face714 face687 face697
face707 face717 face685 face695 face705 face715
face1640 face1638 face1639 face719 face729 face739
face749 face722 face732 face742 face752 face762
face720 face730 face740 face750 face760 face728
face738 face748 face758 face768 face726 face736
face746 face756 face766 face724 face734 face744
face754 face764 face727 face737 face747 face757
face767 face725 face735 face745 face755 face765
face1645 face1641 face1642 face1643 face1644 face788
face769 face779 face772 face782 face770 face780
face778 face776 face786 face774 face784 face777
face787 face775 face785 face1647 face1646
physics create Outflow btype OUTFLOW face face105
108
REFERENCES
Al-Aqal O M A 2003 ldquoHeat transfer distributions on the walls of a narrow channel
with jet impingement and cross flowrdquo PhD Thesis University of Pittsburgh
Bunker Ronald S 2007 Gas Turbine Heat Transfer Ten Remaining Hot Gas Path
Challengesrdquo Journal of Turbomachinery April Vol 129 pp 193-201
Downs James P Landis Kenneth K 2009 ldquoTurbine Cooling Systems Design- Past
Present and Futurerdquo Proceedings of ASME Turbo Expo 2009 June 8-12 2009
GT2009-59991
Florschuetz LW Berry R A Metzger D E 1980 ldquoPeriodic streamswise variations of
heat transfer coefficients for inline and staggered arrays of circular jets with cross
flow of spent airrdquo ASME J of Heat Transfer 102 p 132-137
Florschuetz L W Truman C R Metzger D E 1981 ldquoStreamwise Flow and Heat
Transfer Distributions for Jet Array Impingement with Cross flowrdquo Journal of
Heat Transfer Vol 103 pp 337
Florschuetz L W Isoda Y 1983 ldquoFlow Distributions and Discharge Coefficient for
Jet Array Impingement With Initial Cross flowrdquo Journal of Engineering for
Power Vol 105 pp 296
Incropera Frank P DeWitt D P 2002 Fundamentals of Heat and Mass Transfer John
Wiley amp Sons Inc New Jersey pp 491-493
Liu Quan Kapat J May 2006 ldquoStudy of Heat Transfer Characteristics of Impinging
Air Jet Using Pressure and Temperature Sensitive Luminescent Paintrdquo UCF
Dissertation
109
Martin H 1977 ldquoImpinging jet flow heat and mass transferrdquo Advances in heat transfer
Vol 13
Ricklick Mark Kapat J December 2009 ldquoCharacterization of an Inline Row
Impingement Channel for Turbine Blade Cooling Applicationsrdquo UCF
Dissertation
Zuckerman N Lior N 2005 ldquoImpingement Heat transfer Correlations and Numerical
Modelingrdquo Journal of Heat Transfer Vol 127 pp 544
vi
41 Heat Transfer Validation 32
42 Heat Transfer Results 33
43 XD Comparisons 40
44 3D Comparison of the Heat Transfer Profiles 45
45 Thermal Performance Calculations 48
CHAPTER FIVE COMPUTATIONAL FLUID DYNAMICS 52
51 Problem Setup 52
52 CFD Results 58
CHAPTER SIX CONCLUSIONS 63
APPENDICES 64
Appendix A 64
Appendix B 66
REFERENCES 108
vii
LIST OF FIGURES
Figure 1 Brayton Cycle Flow Path and T-s Diagram (Adapted from UPTB Website) 1
Figure 2 Thermal Loading Throughout a Turbine Blade (Daniels 1982) 3
Figure 3 Allowable Turbine Inlet Temperature vs Cooling Techniques over the Years
(Clifford 1985) 4
Figure 4 Turbine Inlet Temperature Increase with the help of TBC New Super Alloys
and Cooling Technologies (Kapat and Kiesow Lectures 2010) 4
Figure 5 Turbine Stator Cooled with Impingement Coupled with Film Cooling
(Florschuetz 1980) 5
Figure 6 Rotor Blade Cooling Configuration (Gladden 1988) 6
Figure 7 Cross-section of Turbine Airfoil with Cooling Channels (Han et al 1984) 6
Figure 8 Relative Temperatures for Hot Gas Metal Temperature and Coolant
Temperature (Cardwell 2005) 7
Figure 9 (a) The Development of the Wall Jet (b) Jet Diffusion to Surroundings (Liu
2006) 8
Figure 10 Simplified Jablonski Diagram (Adapted from ISSI Website) 17
Figure 11 Heater Strips Painted with TSP Too Closely 21
Figure 12 Flow Loop of Impingement Channel 22
Figure 13 Top View of Jet Plate 22
Figure 14 Front View of Impingement Channel 23
Figure 15 Target Wall Test Section with Heater Leads 23
Figure 16 Heat Transfer Coefficient Uncertainty Tree 27
viii
Figure 17 Temperature Profile of First Five Impingement Rows 29
Figure 18 Detailed View of First Heat Transfer Peak with a Polynomial Curve Fit 30
Figure 19 Control Volume Heat Transfer Analysis 30
Figure 20 Heat Loss through Convection and Lateral Conduction 31
Figure 21 Validation Spanwise Averaged Results 32
Figure 22 Target Wall Heat Transfer Coefficient Distributions 34
Figure 23 Span-averaged Target Wall Heat Transfer Distribution 35
Figure 24 Side Wall Heat Transfer Coefficient Distributions 36
Figure 25 Span-averaged Side wall Heat Transfer Distribution 37
Figure 26 XD=15 Target Wall Heat Transfer Profile 41
Figure 27 XD=15 Span-averaged Target Wall Heat Transfer Distribution 42
Figure 28 Target Wall Span-average Comparison of XD=5 and 15 at High Re 43
Figure 29 Side Wall Heat transfer Coefficient Profile 44
Figure 30 XD=15 Side Wall Span-averaged Heat Transfer Coefficients 45
Figure 31 3D Heat Transfer Profile for ZD=6 XD=5 46
Figure 32 3D Heat Transfer Profile for ZD=8 XD=5 47
Figure 33 3D Heat Transfer Profile for ZD=6 XD=15 48
Figure 34 Pressure Drop Ratio with Respect to Smooth Channel 49
Figure 35 Heat Transfer Enhancement 50
Figure 36 Thermal Performance at Constant Pressure Drop 50
Figure 37 Thermal Performance at Constant Pumping Power 51
Figure 38 Horizontal Plane of Impingement Channel Geometry 53
Figure 39 Target Side and Front End Wall y+ Values 54
ix
Figure 40 Finished Mesh with Boundary Conditions 55
Figure 41 Grid Independence Study 57
Figure 42 Residual Plots for the 26M Cell Run 57
Figure 43 Total Pressure Contours 58
Figure 44 Velocity Magnitude Contours 59
Figure 45 Turbulent Kinetic Energy Contours 60
Figure 46 Static Temperature Contours 60
Figure 47 Target and Side Wall Heat Transfer Coefficient Contours 61
Figure 48 Closer View of First few Rows of Impingement HTC Contours 61
Figure 49 Pathlines Generating from the First Row of Jets 62
NOMENCLATURE
Cross Sectional Area
Heater Surface Area (m2)
Specific Heat at Constant Pressure (kJkgK)
D Jet Diameter (m)
Channel Hydraulic Diameter (m)
Friction Factor
Heat Transfer Coefficient (HTC) (Wm2K)
Average Heat Transfer Coefficient (Wm2K)
Channel Length (m)
Mass Flow Rate (kgs)
Static Pressure (kPa)
x
Total Pressure (kPa)
Pr Prandtl Number
Heat Flux (Wm2)
Total Heat Input (W)
Heater Resistance (ohm)
Re Reynolds Number
SW Side Wall
Temperature (K)
TW Target Wall
Voltage Potential
Streamwise Location
y Spanwise Location
z Height from Target Wall
X Streamwise Distance (m)
Y Spanwise Distance (m)
Z Impingement Height (m)
Thermal Performance Parameter
Ratio of Specific Heats
Air Density (kgm3)
Subscripts
C Cold
H Hot
xi
Carnot Describing a Carnot cycle
Exit
Effective
Quantity Lost to the Environment
Reference Value
Wall Value
Base Line Value
1
CHAPTER ONE INTRODUCTION
11 Gas Turbine as a Heat Engine
Gas turbine is a form of heat engine where the hot reservoir is created by the
combustion of fuel and the cold reservoir is the open atmosphere It is well known that
the maximum efficiency of any heat engine is denoted as the Carnot efficiency
A more accurate cycle is used to describe the processes inside a gas turbine ndash the
Brayton Cycle The Brayton cycle as seen in Figure 1 is composed of four processes In
a gas turbine air is drawn in at state 1 it is compressed until it reaches state 2 The
compressed air is mixed with fuel and ignited as it passes through the combustor The hot
air then passes through the turbines where work is extracted The process from state 4 to
state 1 happens throughout the atmosphere therefore the Brayton cycle is an open loop
cycle as the same air is not continuously being fed through the motor
Figure 1 Brayton Cycle Flow Path and T-s Diagram (Adapted from UPTB Website)
The Brayton cycle has an isentropic efficiency similar to the carnot the Brayton
cycle efficiency is defined as
2
It can be seen that increasing the temperature at which air enters the first turbine
stage T3 increases the overall efficiency of the turbine Moreover increasing the
pressure ratio Pr also aids in the increase of the efficiency One of the hurdles of
increasing T3 is the fact that the post combustion gas is a few hundred degrees Celsius
above the melting point of the super alloys used to make the turbine stator vanes and
rotor blades For this reason it is important to cool the hot components of the gas turbine
in order to assure a reasonable life for the machine
12 Cooling of Hot Components
The transition duct that connects the combustor to the first stage turbine as well
as the first stage of the turbine are the parts that are subject to the harshest thermal
loadings and must therefore be cooled aggressively to maintain them in working
conditions for a long period of time Since the first stage guide vanes and rotor extrude
into the flow they are subject to the highest convection coefficients These heat transfer
coefficients can reach up to 4000 Wm2K (Downs 2009) Figure 2 shows the different
magnitudes of convection coefficient around the blade High heat transfer coefficients
occur where the air stagnates into the leading edge of the airfoil This high heat transfer
region is not only caused by the lack of a thermal boundary layer to protect the airfoil but
also because the effective heat transfer driving temperature is the recovery temperature
At the high Mach numbers that occur in turbines the ratio of total to static temperatures
is significant causing the leading edge to have the highest effective heat load Another
3
peak occurs on the suction side of the blade as the boundary layer created by the airfoil
switches from being a laminar boundary layer into a turbulent one Due to the nozzling
effect of the turbine rotor and stators the flow gathers speed toward the trailing edge of
the airfoil leading to higher convection coefficients on the pressure side of the airfoil
Figure 2 Thermal Loading Throughout a Turbine Blade (Daniels 1982)
Simple convection channels were implemented in the early nineteen sixties as
years passed the cooling techniques became more and more sophisticated allowing the
free stream temperature to increase to previously impossible levels Currently the use of
film cooling coupled with backside impingement leads the turbine cooling technology
The trend of allowable turbine inlet temperature is shown in Figure 3 from this figure it
can be seen that the allowable free stream temperature has increased around 600 degrees
in the past 50 years The addition of thermal barrier coatings also helps in the increase in
allowable combustion temperatures by creating an extra resistance that the heat needs to
move through as it moves from the combustion gasses into the coolant air It is impotatnt
to notice that as seen in Figure 4 the increase in turbine inlet temperatures is done with
the combined benefits of new alloys TBC and cooling technologies
4
Figure 3 Allowable Turbine Inlet Temperature vs Cooling Techniques over the Years (Clifford 1985)
Figure 4 Turbine Inlet Temperature Increase with the help of TBC New Super Alloys and Cooling
Technologies (Kapat and Kiesow Lectures 2010)
The cooling of inlet guide vanes can be done with the use of impingement inserts
inside the airfoils As air passes through the miniscule holes in the inserts a jet is formed
which then impinges on the wall of the airfoil producing one of the largest single phase
heat transfer coefficients This already impinged coolant air is then bled out as film
5
cooling as well as bled out through the trailing edge Figure 5 shows a stator vane with
the impingement insert in black the film cooling extraction as well as the trailing edge
bleed
Figure 5 Turbine Stator Cooled with Impingement Coupled with Film Cooling (Florschuetz 1980)
The cooling of turbine airfoils with the use of an impingement insert is only
possible in stationary components as the rotating ones are subject to centrifugal loadings
making it unfeasible to cool them with this setup Rotor blades are typically cooled with
serpentine passages that have heat transfer enhancing features such as ribs dimples and
other turbulators these serpentine passages are located in the mid chord of the blade On
the trailing edge a bank of pins are used to obtain high convective coefficients in the thin
region the coolant is the bled out to compensate for the boundary layer created around
the airfoil Rows of impingement holes cool the leading edge The spent air is then bled
out through showerhead cooling Figure 6 and Figure 7 show in detail the cooling
channels around two similar airfoils airfoils
6
Figure 6 Rotor Blade Cooling Configuration (Gladden 1988)
Figure 7 Cross-section of Turbine Airfoil with Cooling Channels (Han et al 1984)
7
The coolant air is bled out from the later stages of the compressor This air is
expensive as it has been compressed and not under gown the heat addition by
combustion It is imperative that the minimum amount of coolant is used in these cooling
configurations The cooling must also be as uniform as possible to reduce thermal
stresses within the blades leading to a higher component life Figure 8 shows freestream
metal and coolant temperatures of the flow blade and coolant air It can be seen that a
decrease of 25degrees in the surface temperature of the blade can provide an airfoil with
twice the working life Impingement cooling has great potential to provide high heat
transfer coefficients at a small flow rate Impingement of a jet onto a surface provides
high heat transfer coefficients due to a starting boundary layer as well as its high
turbulence When the jet is located around 3 diameters from the target surface the heat
transfer profile has two peaks one located at the stagnation region and the other located
between one and 3 diameters from the stagnation region As the jet is moved away from
the target wall the secondary peak diminishes leaving a profile with a maximum at the
stagnation region decreasing radialy
Figure 8 Relative Temperatures for Hot Gas Metal Temperature and Coolant Temperature (Cardwell 2005)
Cardwell N D 2005
8
Figure 9 shows a diagram of a jet impinging on a target surface The potential
core is the part of the jet that has not been affected by the surrounding stagnant fluid As
the jet moves towards the target wall its momentum diffuses into the surrounding fluid
decreasing the velocity at which it reaches the target wall and potentially decreasing the
corresponding heat transfer coefficient Studies have shown (Martin 1973 for example)
that the potential core may last anywhere between 7 to 10 diameters The successful
impingement of the potential core yields significantly higher heat transfer coefficients
than a fully diffused jet this comes however at a cost of higher pressure drop across the
jet plate as well as a highly non uniform heat transfer profile
Figure 9 (a) The Development of the Wall Jet (b) Jet Diffusion to Surroundings (Liu 2006)
9
CHAPTER TWO LITERATURE REVIEW
21 Impingement Literature Cornerstone
From the early days of simple convective cooling channels in turbine airfoils
studies have been done on modes of enhancing heat transfer coefficients while
maintaining a low pressure drop and minimum mass flow rate Heat transfer
characteristics of single round nozzle impingement were studied in the late 1960rsquos and
early 1970rsquos The collected works of many authors is combined into ldquoHeat and Mass
Transfer between Impinging Gas Jets and Solid Surfacesrdquo by Holger Martin 1977 The
paper collects works from multiple authors who studied single round nozzle impingement
effects on heat and mass transfer coefficients In this compilation non dimensional jet to
target spacing was studied they ranged from ZD=12-10 providing plots of Sherwood
number as a function of radius for four different jet to target spacings The local
Sherwood number was also given for a slot jet for HS ranging from 5 to 20 Studies on
impingement jet arrays were also gathered alongside an array of slot jets Correlations
were given for multiple setups present in the paper Circular jet arrays and slot arrays are
studied in detail with both analytical and experimental approaches The paper also
combines studies done on swirling jets turbulence enhancers on the target surface
impingement on concave surfaces and angle of attack variations Optimization studies
were also done to find the optimal spacing for round and slot jet arrays
Florschuetz studied the heat transfer characteristics of an array of jets impinging
on a flat surface This study was guided towards finding an optimal spacing for an array
for jets used to cool the midchord of turbine airfoils similar to that found in Figure 5 His
main contributions include a Nusselt number correlation as a function of jet to target
10
spacing jet Reynolds number and other flow and geometric parameters He found that an
increase in hole spacing and channel height resulted in a decrease of heat transfer He
also provided a one dimensional jet mass flux and channel mass flux correlations
His Nusselt number correlation takes the form of
Where A B and n are dependent by the two different types of arrays inline or staggered
Liu studied new techniques in temperature and pressure measurements of a single
slot jet with the use of temperature sensitive paint or TSP and pressure sensitive paint or
PSP In his work both measurement techniques are explained in detail Since TSP is the
only tool from that study currently used in this work it will be explained further in the
experimental setup section
11
22 Relevant Impingement Channel Studies
Al-Aqal 2003 studied three different types of impingement channels The use of
TLC was implemented in this work to obtain heat transfer distributions for the target
wall The three different configurations varied the number of holes in the streamwise and
spanwise directions The first channel had a single row of 6 streamwise jets the second
consisted of 2 rows of 12 streamwise holes summing up to a total of 24 holes The last
channel is a triple spanwise row with 18 streamwise jets This last geometry is the most
similar to the one present in the current study The third geometry will be used to
compare results There are differences however the total width of the channel is of 16
diameters as opposed to 8 in this study The streamwise jet spacing is also different Al-
Aqal used an XD of 65 compared to XD = 5 in this study The jet to target plate
spacings are similar on two occasions as he studied a ZD=4 6 and 8 while this work
uses a ZD = 6 8 and 10 Average jet Reynolds numbers also fall within the range of this
study as they range between 5000 and 33000 The author provides span averaged plots
for all cases and Reynolds numbers convenient when comparing the results
Ricklick 2009 studied a channel similar to the one found in this study His
channel was composed of a single row of 15 jets with a YcD = 4 XD = 5 and 15 and
ZD = 1 3 and 5 Two channels were tested one was pressure fed while the other was fed
by suction TSP was used to gather temperature data of all four wetted surfaces on the
pressure channel and two surfaces on the suction channel Since the maximum jet Mach
number was less than 03 the flow was assumed to be incompressible leading to the
conclusion that both channels contain identical flow patterns Thin foil heaters were used
to create the required heat flux for the channel Besides channel geometry Reynolds
12
numbers and heater geometry Ricklicksrsquo experimental setup is identical to the one
presented in this work The author also provided an ample comparison of his results to
literature He provided thermal performances of the entire channel at different Reynolds
numbers and channel heights
A small CFD study was also done A paved mesh was created on the target wall
with finer mesh near the impingement locations The resulting y+ at the wall was higher
than one yielding potentially faulty heat transfer values however this is acceptable since
the CFD was used as a tool to better understand the flow physics and help understand the
experimental heat transfer profiles
23 Computational Studies on Impingement Channels
El-Gabry did a numerical study of jet impingement with cross flow Two different
turbulence models were compared in their ability to predict surface Nusselt number The
Yang-Shih and standard k-ε models were used to compute the flow generated by jets
angled at 30 60 and 90 degrees with cross flow The computational results were
compared to previous experimental work by El-Gabry Comparisons to experimental
results at ZD = 1 and 2 90deg injection angle between Yang-Shih and standard k-ε The
error in the average Nu from the experimental results and both turbulence models were
calculated It was found that the Yang-Shih model behaved well at low Reynolds
numbers with the average Nusselt number being 5 off from the experimental value
while the standard k-ε was off my 94 As jet Reynolds number was increased the error
of the standard k-ε model dropped to as low as 39 while the error from the Yang-shih
model increased to -76 The span average plots show the experimental data Nusselt
number alongside the span averages of the results acquired by the Yang-Shih and
13
standard k-ε models High Nusselt numbers occur at the impingement location decreasing
thereafter after another impingement location is found The frequencies of these
variations are all the same for the experimental and the two numerical solutions The
amplitude of fluctuations between the impingement locations and the areas in between
are much larger for both of the numerical results however the Yang-Shih model over
predicts at the high Reynolds number for the ZD=2 case Since the amplitude of
fluctuations is greater for the CFD solutions it is important to note that even though the
error in average Nusselt number is not great the actual differences in the profile are much
greater upwards of 20 difference of heat transfer coefficients between the experimental
and numerical heat transfer peaks Other variations were studied (Injection angles for
example) but will not be discussed as their importance to the current study is minimal
Zuckerman compared a much wider set of turbulence models in their ability to
successfully predict Nusselt numbers caused by jet impingement The models tested were
k ndash ε k-ω Reynolds Stress Model algebraic stress models shear stress transport and
lastly the υ2f turbulence model DNS runs are extremely time consuming to run
therefore LES was run on its behalf to provide results for the unsteady turbulence
models The paper summarizes all the different models used their computational cost
impingement heat transfer coefficient and their ability to predict the second peak in heat
transfer As expected DNSLES provide the best prediction of both stagnation and
secondary peak heat transfer coefficient however this comes at a large computational
cost The k ndash ε and k-ω provide poor heat transfer results for the stagnation region where
they can have 30 error from the correct value The Realizable k ndash ε model provides
14
better heat transfer results while still maintaining a low computational cost The highest
accuracy to cost ratio was achieved by the υ2f model where it predicts the heat transfer
coefficient for the surface with a minimum of 2 error while not being as expensive as
the other unsteady models such as DNS and LES Ideally the CFD portion of this work
would be run with the υ2f model however since the code used to run the simulation
FLUENT does not have the υ2f model a realizable k ndash ε model will be used with
enhanced wall functions for both thermal and velocity gradients
15
CHAPTER THREE EXPERIMENTAL SETUP AND TECHNIQUES
31 Temperature Measurements with TSP
Temperature sensitive paint or TSP provides the capability of measuring
temperatures over the painted area This measurement technique supersedes the
advantages of other temperature measurement devices such as thermocouples because it
provides the user with data over a large area rather than point temperatures given by
thermocouples
Uni-Coat TSP is purchased from ISSI It is very robust to different working
conditions Calibration done on one batch of paint can be used for multiple cans as the
product is highly consistent The paint is calibrated in a dark booth a painted coupon is
placed on the hot side of a thermoelectric heat pump working on the Peltier effect
thermal paste is used to minimize contact resistance between the hot side and the TSP
coupon Calibrated thermocouples are placed in between the TSP and the thermoelectric
heat pump A reference temperature and picture are taken and the calibration commences
At least 5 or 6 data points should be taken to form the calibration Intensity ratios are
taken between the hot and cold pictures They are then plotted versus their corresponding
temperature
The paint consists of fluorescent molecules suspended in a binder These
molecules with a certain wavelength of light will be exited to a higher energy level The
molecules then can dissipate some of the energy by transferring it vibrationally to its
neighboring binder particles and dissipate the remainder of the energy by radiating it as a
photon as the molecule comes down to its original ground state Since the amount of
16
energy that the particle can transmit to others through vibration is directly proportional on
temperature and the total initial energy is fixed by measuring the ratio of the intensity at
a known temperature (reference picture) and intensity of the unknown temperature
feeding it through the correlation the unknown temperature can be found to an
uncertainty of 1 K Figure 10 shows a simplified Jablonski diagram adapted from the
suppliers website The blue arrows signify the blue light used to excite the luminescent
molecule Tris(22rsquo-bipyridyl) Ruthenium(II) Chloride Hexahydrate with a shellac binder
in our case The shellac binder is impermeable to oxygen opposite of that found in PSP
due to PSP relying on the presence of oxygen for it to function Once the particle is
excited it can give off the energy in two different ways one is by emitting it back out as
another photon of the same energy and therefore wavelength The second mode of the
particle to lose its energy is through vibrational relaxation This second process is directly
dependent on the temperature ie the higher the temperature the higher the probability
for it to lose energy to its surroundings Once it loses some energy to the surrounding
particles it releases the remainder of the energy as a photon of less energy of that which
excited it originally hence why a long pass filter is installed in the CCD camera For a
more descriptive explanation of the way TSP works refer to Liu 2006
17
Figure 10 Simplified Jablonski Diagram (Adapted from ISSI Website)
Throughout the past two years there have been numerous projects at CATER that
have used TSP Painting surfaces with TSP should be done carefully by someone who
has experience with spray painting since every single can costs $500 A single can should
be able to paint an area the size of an acrylic plate that is 36rdquo wide and 24rdquotallThe
sidewalls and the target wall of the impingement channel were painted with the use of
less than one can Painting on different surfaces is difficult for example when painting
Rohacell the paint canister can be held very close to the surface while spraying due to
the surface being somewhat porous and rough however when painting straight onto
metal heater strips the can should be placed as far back as possible for the first run
Ideally for the first pass through only a slight mist should be applied If the can is being
held too close to the surface the paint will run Figure 11 shows a set of heater strips that
has been painted too closely leading the paint to drip down Ideally the paint would be
applied to the surface in as many coats as possible Of course this would be time
18
demanding and impractical therefore with the knowledge that I have gained through the
multiple TSP paintings on different surfaces I have compiled a list of TSP dos and
donrsquots
Dos
Clean the surface to be painted with acetone or break parts cleaner Break
parts cleaner is preferable over acetone as it does not leave an oily residual
after cleaning
Paint the first coat as thin as possible Most of the surface should not be
covered There should be an even mist of miniscule TSP circles This will
give the later coats something to attach to
When positioning the test section to paint make sure to wipe it one last
time as small dust particles may have attached to the surface
Stop if you see small bumps in the paint This is caused by dust particles
collecting all the paint around it while it is still wet due to surface tension
Clean the surface and repaint This should be noticeable in the first few
coats If you see this pattern happening do not continue thinking it will be
covered by future coats What will happen is the problem will get worse
and worse ultimately the surface will have to be cleaned again and
repainted
When painting test sections try to paint the smallest section as possible
This will not only save paint but will make it very simple for the post
processing code to crop out the unpainted areas
19
Let the finished painted surface to sit at least for 90 minutes after the last
coat before baking There have been problems when baking steel and
acrylic test sections with the paint cracking while baking right after the
last coat Normally the finished surface is left to dry overnight and baked
first thing in the morning
For test sections that are too large to be baked in the oven the heat gun
may be used Carefully place a thermocouple in a central location with
blue painters tape The heating should be uniform and should not take
more than 20 minutes of continuous blowing When the thermocouple
reaches 80-90 C the plate can be assumed to be baked To introduce a
factor of safety in the baking it does not hurt to bake it longer than it
normally takes
Once the test section is mounted and ready to run cover it with cloth that
does not let any light through This will protect the paint for further uses
This is especially important on test sections that can be used multiple
times like the ones found in this study
When the test is running turn off the LED lights This light is the most
damaging to the TSP as it degrades the quality of the fluorescent
molecules
If there is a particular head of the TSP can that you prefer over others you
can remove it once the can is empty It is difficult to get used to a single
kind of nozzle being able to transfer it from can to can is a must if
painting consistency is to be kept
20
Donrsquots
Do not clean a test section that has already been used with too much
acetone The acetone is volatile evaporating quickly cooling the test
section rapidly If this test section has had heaters attached to it and run
previously the acrylic will crack due to uneven stresses inside of it
If paint is dripping stop painting immediately Clean the surface and start
over Hold the can far from the surface in order for it not to drip
Do not use TSP to teach new apprentices undergrads or graduate students
how to paint Regular spray paint is two orders of magnitude lower in cost
while the painting process is exactly the same
Do not paint with the doors closed The paint contains carcinogens that
can harm the lungs Always use a respirator and keep the room well
ventilated In-situ painting and baking has not been tried however it may
be a real option if the test section is difficult to disassemble and easily
accessible to painting and baking
If there is a can of paint that contains too little paint for the test section
that needs to be painted try to find a new can The mixing of two different
cans of TSP can be dangerous at times however it has been noticed over
the years that ISSI provides a very robust and dependable product that
does not vary significantly from batch to batch
21
Figure 11 Heater Strips Painted with TSP Too Closely
32 Experimental Setup of Suction Channel
The impingement channel is fed under suction As seen in Figure 12 air enters
through the plenum it crosses the jet plate as it gains speed to form the jets
which then impinge on the target wall The flow then passes through a venturi
flow meter and finally through the blower into the atmosphere A bypass valve is
used to control the flow rate of the impingement channel
22
Figure 12 Flow Loop of Impingement Channel
The impingement channel consists of 15 streamwise rows of 3 spanwise jets each The
total width of the channel YcD is of 8 diameters while the streamwise spacing between
the rows is XD=5 the spanwise distance between the holes is of YD=2 Figure 13shows
the top view of the jet plate The plate is counter bored to ensure that a nearly flat
velocity profile of the jet is achieved Figure 14 shows the front view of the channel Z is
denoted as the distance between the jet and target plates Side walls are interchangeable
to change the height of the channel to 6 8 and 10 diameters Two thirds of the
streamwise rows can be covered to change the XD from 5 to 15
Figure 13 Top View of Jet Plate
23
Figure 14 Front View of Impingement Channel
The target and sidewalls had heaters made specifically for them in a serpentine
style This was necessary to increase the resistance as the VARIACs used to power them
only had a maximum current output of 20 amps The heater strips are two diameters
wide at each end copper tape with conductive adhesive was used to connect the leads to
the power supply The heater consists of 50 micron thick steel sheet sandwiched between
two pieces of Kapton tape The heater is attached to the painted surface with the use of
double sided Kapton tape The target test section can be seen in Figure 15 also seen in
this figure are the two Teflon gaskets lined on the sides of the target plate With the target
wall bolted onto the sidewall the gasket is compressed generating a strong seal
Figure 15 Target Wall Test Section with Heater Leads
24
For this study the test matrix shown in Table 1 will be run Target and side wall
data will be taken at three different impingement heights at two different Reynolds
numbers of 7500 and 15000 denoted by A and B respectively A streamwise jet spacing
study is also done by testing the target and side wall heat transfer at an XD=15 for the
low impingement height channel
Table 1 Test Matrix
XD ZD Wall Re
5
10 TW
7500
15000
SW 7500
15000
8 TW
7500
15000
SW 7500
15000
6 TW
7500
15000
SW 7500
15000
15 6 TW
7500
15000
SW 7500
15000
33 Data Processing and Reduction
As described previously when taking temperature measurements with the use of TSP
reference temperatures are noted and a reference picture is taken The experiment is the
run once the experiment reaches steady state a new set of 4 pictures is taken Given the
calibration curve temperatures are backed out
25
Given the amount of heat generated inside the heater
Dividing by the heated area to get heat flux
Heat loss tests were run to consider how much of the heat flux generated by the heaters
goes through the backside instead of into the flow It was found that 25 of the heat flux
leaks out to the atmosphere through the acrylic In order to account for this heat leakage
it must be subtracted from the calculated value to become
Where Ah is the effective heated area given by
Where Aunheated is an estimate of how much unheated area is between the heater strips (~
3 of the total area)
To obtain heat transfer coefficient
Where Tref is the reference temperature Typically set in literature to be the jet
temperature
To obtain the average Reynolds number for the jets the total mass flow rate is used
Where Dj is the jet diameter and μ is dynamic viscosity (1983kgm s at 300K)
26
Pressure measurements were taken at the sidewall after the last jet entered the channel
These pressure measurements were used to determine the thermal performance of the
tallest two channels (ZD = 8 and 10)
The thermal performance at constant pumping power is found by using the equation
Where h is the average heat transfer coefficient for the target wall of them impingement
channel and ho is the heat transfer coefficient obtained by passing the same amount of
flow through a smooth duct ie the Dittus-Boelter correlation The friction factor f is
found with the use of
Where Ppl is the plenum static pressure assumed to be atmospheric and Plast jet is
the pressure read after the last jet V is the volumetric flow rate divided by the cross-
sectional area of the duct after the last impingement row The hydraulic diameter of the
channel is set to be
The baseline friction factor was calculated with the use of the Moody chart the hydraulic
diameter and the total mass flow rate though the channel Thermal performance at
constant pressure drop was also calculated with
27
34 Uncertainty Analysis
A simple uncertainty analysis was done to estimate the error in calculation of the
heat transfer coefficient from the given outputs of the test data From the bare basic
measurements for voltage area current temperature of thermocouples and temperature
profiles of paint a simple uncertainty analysis can be done to estimate the error for the
calculated heat transfer coefficient Figure 16 shows the different sources of error in the
calculation of heat transfer coefficient The effective uncertainty was calculated by taking
the root of the sum of the squares of all the individual percentage errors The
experimental uncertainty for heat transfer coefficient was of 703 This error may be
reduced by acquiring higher temperatures of the TSP reading current with a more
accurate ammeter or reading reference temperatures with the use of a thermopile instead
of a single thermocouple
Figure 16 Heat Transfer Coefficient Uncertainty Tree
28
35 Lateral Conduction Analysis
To take into account the lateral conduction occurring inside the heater foil while
the test is running two simple 1D conduction and convection equations were used to
quantify the amount of heat moving through the heater laterally and the amount of heat
convecting into the air The lateral conduction is expected to be at a maximum at the
places where there are large spatial variations of surface temperature which is why the
ZD = 6 XD = 5 case at high Re is chosen to be studied Figure 17 shows the
temperature distribution of the aforementioned case Four cold spots can be seen by their
distinct blue and yellow color located at the stagnation regions The maximum
temperature gradient occurs between the third jet impingement and the middle region
between jets The temperature difference was seen to be of 13degC The distance in between
these two temperatures is of 25D=01875m The corresponding heat flux between these
two points was calculated to be 13000Wm2 with ksteel~20Wm K A region of 1cm by
1cm was then created and the amount of heat calculated through conduction and
convection were compared To acquire the amount of heat removed through conduction
a heat flux of 13000Wm2 was imposed through an area of 01m by 00005m this
equaled to 00277 W The amount of heat moved through convection was calculated by
multiplying the heat flux used during the test by the area of the square 0001m2 the
resulting heat moving through the heater onto the air is 6 W Since the heat moving
through to the air is two orders of magnitudes larger than the heat moving laterally the
effective lateral conduction can be neglected
29
Figure 17 Temperature Profile of First Five Impingement Rows
A second order approach was also taken to quantify the amount of lateral
conduction in the heater The temperature gradient was taken from high peaks in heat
transfer caused by the second row of impingement of the same ZD=6 XD=5 channel at
high Re Figure 18 shows the high heat transfer coefficients created by the second row of
jets A quadratic curve fit was obtained by for this small region so that a continuous
equation of heat transfer coefficients as a function of streamwise distance was quantified
30
Figure 18 Detailed View of First Heat Transfer Peak with a Polynomial Curve Fit
The net heat gained by a differential volume from lateral conduction is the
difference in the temperature gradient at the entrance and the exit multiplied by the
thermal conductivity and cross sectional area Using this method shown in Figure 19 the
net change in convective heat transfer due to lateral conduction can be studied
Figure 19 Control Volume Heat Transfer Analysis
By taking the difference between the out flowing heat trough the right side and
the inflowing heat from the left side a net gain or loss can be found Figure 20 shows the
y = -470630x2 + 31244x - 14842Rsup2 = 09934
300
310
320
330
340
350
360
370
380
0 001 002 003 004 005
HTC
(W
m2K
)
x (m)
Heat Transfer Peak
Poly (Heat Transfer Peak)
31
difference in magnitude between the out flowing heat through convection seen in red and
the net inflow of heat from lateral conduction in blue From these calculations it was also
found that the amount of heat moving through lateral conduction is tow orders of
magnitude smaller than the amount of heat moving out through convection leading to the
belief that even at high temperature gradients lateral conduction does not play an
important role in the ongoing heat transfer processes in the impingement channel A more
detailed calculation of this work can be seen in appendix A
Figure 20 Heat Loss through Convection and Lateral Conduction
002 003 004 0051 10
5
1 104
1 103
001
qconv x( )
qnet x( )
x x
32
CHAPTER FOUR HEAT TRANSFER RESULTS
41 Heat Transfer Validation
In order to obtain confidence in our experimental setup an experiment was made
to test something that has already been published in literature A smooth channel was the
obvious choice as it was easy to setup by taking off the end cap and blocking all the holes
with smooth blue painters tape on the flow side and metal tape on the plenum side to
ensure no leaks into the channel from the jet plate The smooth channel has been studied
widely and multiple correlations exist one of these equations is the Dittus-Boelter
correlation (Incropera 2007) The test was run using the ZD=6 side wall so that the
hydraulic diameter was a minimum Figure 21 shows the span averaged results versus
non dimensional distance into the channel
Figure 21 Validation Spanwise Averaged Results
0
10
20
30
40
50
60
0 1 2 3 4 5 6 7 8 9
HTC
(W
m2K
)
XDc
Span Avg
Dittus Boelter
33
The plot shows decreasing heat transfer coefficient with increasing XDc due to
the developing thermal boundary layer The span average does not reach the Dittus-
Boelter due to it not being fully developed in the limited space it is given Typical flows
can take up to 60 diameters to achieve a fully developed profile with the current setup
the maximum length of the channel was of 9 diameters The profile however seems to
have an asymptote at the Dittus-Boelter correlation value leading to the belief that if the
channel was longer that value given by the correlation would be reached One important
factor to take into account in determining whether the experimental setup is validated is
the fact that the Dittus-Boelter correlation has an uncertainty near 30 Since the span
average at high XDc is well within 30 from the calculated value it is safe to assume
that the current experimental setup is validated
42 Heat Transfer Results
Heat transfer results are compared based on variations in channel height and
average jet Reynolds number As discussed earlier there are numerous other parameters
also affecting the heat transfer in these channels As these parameters are changed flow
structures within the channel are expected to be altered as well as discussed in the
literature Two of the major contributors to heat transfer in these channels are the
successful jet impingement and the resulting cross flow The same domain is captured in
both the local and averaged results
Figure 22 through Figure 25 highlights the heat transfer distribution for the cases
with a jet to jet spacing of 5 diameters in the streamwise direction and of 2 in the
spanwise direction It is evident that the smallest channel height (ZD=6) performs the
best at all Reynolds numbers on all surfaces It is also interesting to note the similarity
34
in the target wall profiles between case 528A and B where the curves are very similar
other than the obvious offset due to the change of the Reynolds number At this large
spacing we also see the degradation of the jets a few diameters downstream of each
impingement location The downstream shifts of the peaks are evident after the second
and third row of jets Also evident in these plots is the deflection of the impinging jet and
the wall jets from the cross flow The cross flow is forced to flow around the jet
deflecting the spread of the wall jet in the downstream direction Impingement locations
are also very evident at low XD however as XD and therefore the cross flow increase
the magnitude of the peaks start decreasing and eventually level out to pure internal flow
Figure 22 Target Wall Heat Transfer Coefficient Distributions
35
Figure 23 Span-averaged Target Wall Heat Transfer Distribution
36
Figure 24 Side Wall Heat Transfer Coefficient Distributions
37
Figure 25 Span-averaged Side wall Heat Transfer Distribution
Figure 23 and Figure 25 show similar details with impingement peaks clearly
diminishing and shifting in the downstream direction The cross flow clearly has some
negative influence on these geometries when compared to the more traditional
impingement highest on the order of 1 to 5 jet diameters The heat transfer profiles of the
target wall for all heights seen in Figure 22 and Figure 24 show the rapid decay in heat
transfer after the third jet This can be explained by understanding that the first jet does
not have any cross flow to deflect it the second jet only has the first jet worth of
momentum deflecting it downstream however since the channel is so tall the
momentum of the cross flow after the first and second jet are not enough to greatly
disturb the incoming jets After the third jet however the cross flow builds up enough
momentum to greatly affect the integrity of the jets downstream causing the span-
0
20
40
60
80
100
120
140
160
2 12 22 32 42 52 62 72
HTC
(W
m2K
)
XD
5210B_SW 528A_SW Jet Location
526A_TW 526B_TW
38
averaged heat transfer to rapidly drop The point at which the crossflow starts taking a
considerable effect occurs around XD =35 The target wall profile of the ZD=10
channel shows the outside jets on the second row of jet deflecting downstream It can be
conjectured that the bending of the outside jets downstream is caused by the wall jet
created by the first row of jets separating from the side wall and deflecting the outside
jets of the following rows of jets The heat transfer profile for the ZD case excludes the
first jet due to shadows being present when the data was taken
Also evident from this spanwise averaged data is the increase in heat transfer
with increases in Reynolds numbers and decreases in impingement height Results tend
to be the closest from case to case at the first impingement jet This is a reasonable
result as the effects of cross flow have little to no effect at the first few impingement
locations The impact of the jet would then be the driving force at these locations and
would be similar between cases except if the potential core is not reaching the target
surface The potential core of a jet tends to last between 6 and 10 diameters from its
origin It can be seen that the difference in heat transfer coefficient in the first two jets for
the ZD=8 and ZD=10 channel is much different than the corresponding difference
between the ZD=6 and ZD=8 heights This decreased difference between the heights of
the peaks may be attributed to the potential core reaching the target wall at the heights of
6 and 8 diameters leading to similar profiles and may not be reaching the surface at the
height of 10 diameters The heat transfer values of the peaks diminish in the downstream
direction The range of fluctuation also drops that is the profile becomes more uniform
at large XD This drop in fluctuation is more visible at the tallest channel height
(ZD=10) and less pronounced at the smallest channel This is due to the jet in the small
39
channel having to travel a shorter distance to impinge on the target plate leaving the
crossflow less time for it to deflect the jet as opposed to the tall channel where the jet has
to travel almost twice the distance as the ZD=6 channel for it to impinge on the target
wall This effect cannot be solely explained by the built up cross flow in the channel
Mixing loses also take part in the degradation of the stagnation size of the downstream
jets The mixing losses have much greater effect on the taller channels due to the same
reason that the cross flow has a higher impact on them too the jets have to travel a large
distance before hitting the target plate leading the stagnant or moving surrounding air to
be a sink of its downward momentum for a longer time and distance than the respective
smaller channels The heat transfer coefficient of the side wall was also analyzed
Similar effects are expected on the side wall due to the expected impact of the wall jet
As expected the strength of the cross flow is not enough to prevent wall jets from
successfully impacting the side wall at small XD jet locations however the crossflow
takes dominance at around XD=25 Also evident in these plots is the concentration of the
wall jet impact to the bottom of the channel on the order of 1-2 diameters in height It is
interesting to note that for the 5210B case in Figure 24 as the first jet diffuses outward
it impacts the sidewall at a height of ZD=6 The height at which the diffused jet affects
the sidewall heat transfer coefficient decreases as the crossflow increases The stagnation
regions are also deflected in the downstream direction similar to the target surface
results These effects are most evident in the 5210B Similar characteristics can be
explained from the spanwise-averaged plots shown in Figure 25 These results again
clearly show the effects of increasing the impingement height and increases in Reynolds
number As the height is increased the effect of the wall jet is significantly reduced
40
partially due to the increased surface area much of which is not affected by the wall jet
The diminishing effect of the cross flow accumulation is also evident in these plots as the
heat transfer peaks decrease in the downstream direction
43 XD Comparisons
The streamwise jet spacing was changed from XD=5 to 15 by covering two out
of three rows of jets This was done by covering the impingement holes inside the
channel with smooth blue painters tape and sealing the plenum side of the jet plate with
metal tape to ensure no leakage The profile is expected to be less uniform than the case
where XD=5 due to the large spreading of the high heat transfer peaks Due to the large
separation between the rows of jets there is a lower amount of downward momentum
than the equivalent XD=5 geometry for this reason it is expected to see a lower heat
transfer peak due to the jets momentum diffusing out faster to the stagnant air decreasing
the effective impingement velocity Figure 26 shows the target wall heat transfer
distribution Similar to the XD=5 profile it can be seen that the heat transfer due to the
jet impingement drastically reduces after the third jet This phenomenon leads us to
believe that at both Reynolds numbers the cross flow generated by the first three jets is
powerful enough to effectively deflect the fourth jet downstream diminishing its heat
transfer performance The similarity seen in Figure 26 between high and low Reynolds
number implies that the downstream deflection of the jets is not dependent on the jet
Reynolds numbers
41
Figure 26 XD=15 Target Wall Heat Transfer Profile
42
Figure 27 XD=15 Span-averaged Target Wall Heat Transfer Distribution
On the span averaged plots seen in Figure 27 the downstream deflection of the
jets is evident however as described previously the shifts in the peaks of heat transfer
occur at the same xD for both Reynolds numbers The amplitude of fluctuation of heat
transfer coefficients for the high Reynolds number case is larger than that of the low
Reynolds number Both profiles seem to start to level off at the end of the impingement
channel with the lowest span average being located just before the fourth jet at both
Reynolds numbers
A comparison of target wall heat transfer coefficients between XD =15 and 5 is
shown in Figure 28 At first glance it is clearly visible that the XD=15 average heat
transfer coefficient is smaller than its XD=5 counterpart This is also noticed by Ricklick
where he showed average HTC profiles for larger XD to be smaller than those at lower
XD (Ricklick 2009) This may occur due to there not being as high downward
0
50
100
150
200
250
300
350
0 20 40 60 80
HTC
(W
m2
K)
XD
Low Re
High Re
Impingement Location
43
momentum for the XD=15 case as compared to the XD=5 due to the lack of close jets
The stagnant air around the spaced out jets is taking away more of its momentum
decreasing the effective impingement Reynolds number Also important to notice is the
fact that since the XD=5 case has three times the flow impinged into it the cross flow
velocity and therefore Reynolds number will be three times as large increasing the heat
transfer coefficient
Figure 28 Target Wall Span-average Comparison of XD=5 and 15 at High Re
The side walls also show similar patterns to their XD=15 counterparts Strong
wall jet impingement can be seen on the side wall at low xD and zD Figure 29 shows
areas where the wall jet generated by the target wall impinges on the sidewall Similar to
the profile seen in Figure 24 the high heat transfer region reaches upward in the z
direction up to a height of 4-5 diameters for the first jet This high heat transfer stagnation
region decreases as xD increases to the point where the wall jet created by the last jet is
negligible when coupled with pure channel flow
0
50
100
150
200
250
300
350
400
0 10 20 30 40 50 60 70 80
HTC
(W
m2K
)
XD
XD = 5 XD = 15 Jet Location
- Blocked for XD =15
44
Figure 29 Side Wall Heat transfer Coefficient Profile
The span averaged plot seen in Figure 30 shows a nearly flat profile with peaks
located at the stagnation regions of the wall jets Thw downstream deflection for the
XD=15 case is much more pronounced than the one for the XD=5 case This is due to
the jet not being constrained by the wall jets generated by the previous and latter
impingement locations In the XD=15 case the wall jet is free to move downstream
more so than the XD=5 due to it not being disturbed by anything other than the cross
flow
45
Figure 30 XD=15 Side Wall Span-averaged Heat Transfer Coefficients
44 3D Comparison of the Heat Transfer Profiles
In order to further understand the targetsidewall interactions both heat transfer profiles
were positioned in an isometric view representative of the channel One important thing
to note is that both target and side wall profiles are not on the same scale This form of
data display is only qualitative way to describe the heat transfer profiles Figure 31 shows
the 3D profile of the XD=5 ZD=6 case The both stagnation regions of the jet onto the
target wall and the wall jet into the sidewall can be seen to occur at the same location for
the first three streamwise rows After the fourth and fifth row the wall jet diminishes in
magnitude Also visible in this view is the increasing heat transfer at low zD towards the
end of the channel of the side wall The constant input of mass and downward momentum
into the channel causes the cross flow generated by the previous jets to be squeezed into
the lower third of the channel increasing the velocity and the heat transfer of the target
wall
0
20
40
60
80
100
120
0 20 40 60 80
HTC
(W
m2K
)
XD
Low Re High Re Jet Locations
46
Figure 31 3D Heat Transfer Profile for ZD=6 XD=5
Similar patterns are seen in the taller ZD=8 channel seen in Figure 32 The wall jet
generate by the third streamwise row of jets is been deflected downward more than its
ZD=6 counterpart This can be attributed to the fact that the jet located at the ZD=8
channel has lost much of its momentum and is more easily bent downstream by the cross
flow generated by the first two jets The ZD=8 sidewall shows similar increasing heat
transfer at high xD however the increase is not as drastic as the one found in the ZD=6
channel This is caused due to the extra two diameters the jets have to cover to impinge
on the surface since the ZD=8 channel is one third larger than the ZD=6 one the flow
has to have more area to flow through The last few jets only deflect the cross flow
downward about 4 diameters this leaves two diameters for the flow to pass through on
the ZD=6 channel causing the velocity to increase rapidly and therefore increasing the
heat transfer coefficient at the low zD Since the ZD=8 channel has four remaining
47
diameters for the flow to move through it does not deflect it as much as the ZD=6
channel does only increasing the cross flow velocity and resulting heat transfer
coefficient slightly over the area at low zD and high xD
Figure 32 3D Heat Transfer Profile for ZD=8 XD=5
The 3D heat transfer profile for ZD=6 and xD=15 channel seen in Figure 33 shows
similar details to those seen in the XD=5 channels The stagnation regions of the jet and
wall jet occur at the same x location for the first three rows of jets the wall jet generated
by the fourth row of jets is deflected downstream only generating as small region of high
convective coefficients at the side wall The region located at the top right corner of the
side wall is colored red signifying high heat transfer however this area is generated by
the heaters providing non uniform heat flux at this location This region of high heat
transfer coefficients also occur at xD=0-4 of the target wall where the heater coil bends
48
Figure 33 3D Heat Transfer Profile for ZD=6 XD=15
45 Thermal Performance Calculations
Thermal performance calculations were done on the two tallest channels (ZD=8 and 10)
The pumping power was calculated for both channels at two Reynolds numbers Figure
34 shows the ratio of pressures required to pull the same amount of flow through as
smooth duct as opposed to through the jet plate The ZD=10 channel at high Reynolds
number requires the largest pressure as seen in the Figure however in order to pull the
same amount of flow rate through it requires a smaller pressure difference due to the
large cross section
49
Figure 34 Pressure Drop Ratio with Respect to Smooth Channel
Next the heat transfer enhancement was calculated A total area averaged heat
transfer coefficient was taken for the target wall and compared to the smooth channel
Dittus-Boelter value while using the same total mass flow rate Figure 35 shows an
average heat transfer enhancement of four times that of a smooth channel Similar trends
were noticed in the literature (Ricklick 2009) of decreasing heat transfer enhancement
with an increase of jet Reynolds number Ricklick also showed an increase in heat
transfer enhancement with an increase of jet to target spacing similar to the one seen in
Figure 35
0
10
20
30
40
50
60
528A_TW 528B_TW 5210A_TW 5210B_TW
PP
o
50
Figure 35 Heat Transfer Enhancement
Thermal performances at constant pressure drop were then calculated by dividing
the heat transfer enhancement by the pressure increase As seen in Figure 36 all the
values fall well below 1 making the impingement channel an unfeasible mode of heat
transfer enhancement when a constant pressure is supplied
Figure 36 Thermal Performance at Constant Pressure Drop
0
05
1
15
2
25
3
35
4
45
528A_TW 528B_TW 5210A_TW 5210B_TW
hh
o
0
002
004
006
008
01
012
014
528A_TW 528B_TW 5210A_TW 5210B_TW
(hh
o)
(PP
o)
51
The thermal performance at constant pumping drop was calculated in the same
way that the constant pressure drop was calculated the only difference being the pressure
ratio term was raised to the one third power As seen in Figure 37 the thermal
performances at constant pumping power are all higher than unity this signifies that if a
surface needs to be cooled with the supply of a constant pumping power the
impingement channel is a feasible option Similar to the figure literature (Ricklick 2009)
showed a decrease of thermal performance with an increase of channel height and
Reynolds number
Figure 37 Thermal Performance at Constant Pumping Power
0
02
04
06
08
1
12
14
528A_TW 528B_TW 5210A_TW 5210B_TW
(hh
o)
(PP
o)1
3
52
CHAPTER FIVE COMPUTATIONAL FLUID DYNAMICS
51 Problem Setup
In order to further enhance the understanding of the heat transfer profiles showed
previously a computational study was performed Even though CFD does not yield
accurate quantitative results it produces good qualitative data that can be used to explain
the flow physics in the channel and therefore increase the understanding of the patterns
seen previously The channel was meshed with the use of GAMBIT Due to the
symmetry the channel was split in half in the streamwise direction All horizontal
surfaces (parallel to the target wall) were divided into 6 different regions that are later on
going to be meshed individually The six regions are seen in Figure 38 section 1 is
located at the center of every jet also referred to as ldquojet centerrdquo This region was created
to reduce the squewness of the elements near the center of the jet by allowing the mesh to
be completely linear with a squewness of zero Section two complements section 1 to
complete the impingement hole The half impingement hole located at the symmetry wall
contains the same exact region 2 however it only has one half of the jet center Section 3
was made in order to bring the polar geometry of the holes to match the cartesian aspect
of the remainder of the channel With the addition of section 3 to the channel the only
remaining sections are square or rectangular regions Region 4 lies in between
streamwise rows of jets Section 5 is located at the entrance and the exit of the channel
These sections are not square in contrast with section 4 The last remaining section is
located near the side wall of the channel extending from the beginning to the exit of the
channel
53
Figure 38 Horizontal Plane of Impingement Channel Geometry
All the faces of sections 1 and 2 are linked throughout the channel and the
plenum however in order to have greater control of the mesh in the plenum and the
channel the remaining sections 3 4 5 and 6 are not linked to every single similar face
instead they are only linked to similar faces in either the plenum or the channel
Boundary layer spacing number of rows and growth factor are placed around the
channel In order to maintain a y+ of less than unity the first cell spacing of the boundary
layer inside the channel was set to be 000001 m (01mm) This first cell spacing yielded
y+
values varying between zero and 9 at the target side and front end wall Figure 39
shows a contour of y+ values on the heated walls The maximum values occur near the
impingement locations as expected due to large shear caused by the steep velocity
gradient normal to the wall On the downstream direction the y+ also increases due to the
increase of flow rate and therefore the increased skin friction on the wall At the
impingement location of the first jet the y+ is close to zero due to the velocity having its
direction mostly normal to the surface yielding no shear
54
Figure 39 Target Side and Front End Wall y+ Values
Once the faces were linked edge meshes were created on the sides of the jet center
Section 2rsquos inner edge was also meshed using a different parameter than the one used for
the jet center in order to allow for more freedom when trying to refine the mesh These
two edge meshes is followed by meshing all of section 2 faces alongside all the jet
centers Once these were complete section 3rsquos inner edge was meshed with different
parameters for the channel and plenum Sections 4 and 5 sides that connected with the
face made by section 6 were meshed so that their spacing was similar again the plenum
and channel were meshed separately for increased control of mesh density in both of
these areas The upstream-most edge of section 6 was meshed so that the spacing is
similar to the edge mesh in sections 4 and 5 this was done in order to have aspect ratios
of the wall be as close as possible to unity Sections 3 4 5 and 6 were meshed on both
the channel and the plenum With the entire target wall plane meshed these surface
meshes are coopered upwards to connect to the opposite wall The vertical spacing has
55
also been set up differently between the channel and the plenum The holes and the
plenum were also coopered The finished mesh was then exported as a msh file
Boundary conditions were set in GAMBIT once the mesh was imported into
Fluent values were set to every face depending on their location and purpose Figure 40
shows the four different boundary conditions Face 1 (blue) was set to be a mass flow
inlet The flow rate is half of the total flow rate at a given jet Reynolds number due to it
being only half of the entire domain Face 2 (yellow) is a symmetry plane face 3 (red) is
a pressure outlet at zero gauge pressure The rest of the faces in the channel denoted by
the number 4 (white) are set to walls The target side and front end wall had a heat flux
applied to them equal to 10000Wm2
Figure 40 Finished Mesh with Boundary Conditions
The model was imported into Fluent It was scaled down by a factor of 1000 due to it
being made in GAMBIT in millimeters The energy model was turned on The Realizable
k-ε model was used with enhanced wall functions on both the pressure and thermal
gradients The boundary conditions were set as discussed previously the mass flow inlet
was set to the specific flow rate normal to the surface the heat fluxes were set on the
56
heated walls the outflow gauge pressure was set to zero Two important reference values
characteristic length and reference temperature were set to be the diameter of the jet
(0075m) and 300K respectively The spatial discretization parameters were set to second
order upwind for momentum turbulent kinetic energy turbulent dissipation rate and
energy The under-relaxation factors were set to default Four monitors were created to
aid in the determination of convergence two of them read Nusselt numbers at the
stagnation region of the first and last jet the remaining two read the exit velocity at the
first and last jet The continuity x y and x velocities and energy equations residuals
were set to be 1E-6 while k and ε residuals were set to 1E-4 The solution was initialized
on the all zones at 1ms in the positive x direction The solution was set to autosave every
100 iterations while keeping only the two newest dat files The calculation was then run
for a maximum of 7000 iterations
A grid independence study was done on the domain to find the optimal size of
mesh that provides the correct solution while minimizing the compute time Two
monitors were set to check for grid independence both of them were vertex maximum
One of them read the Nusselt number at the impingement location of the first center jet
while the second one measures the velocity at the exit of the last jet Four different mesh
sizes were run to the convergence criterion explained before their sizes were 900000
15 million 28 million and 43 million cells
57
Figure 41 Grid Independence Study
It can be seen in Figure 41 that the difference between the 28 and 43 million cell
meshes are very small a difference of under 006 for velocity and 7 for Nusselt
number It can be safe to assume that the 28 million cell mesh is large enough to provide
a mesh independent solution The GAMBIT journal file used to create this mesh is
attached to the appendix The results shown hereafter are the ones obtained by the 28
million cell mesh
Figure 42 Residual Plots for the 26M Cell Run
67
69
71
73
75
77
79
81
83
85
485
4855
486
4865
487
4875
488
4885
489
0 1 2 3 4 5
Nu
sse
lt N
um
be
r
Cell Ammount (Millions)
Grid Independence Study
Velocity
Nusselt Number
58
For future reference Figure 42 shows the residuals of the 26M cell calculation
Up until around 4400 iterations the residuals were increasing shortly thereafter the
residuals started decreasing until it converged just after 5500 iterations All runs for the
differently sized meshes had the same residual patters with the peak of residuals and
point of convergence happening at different iterations
52 CFD Results
As describe previously all the results shown here are for the mesh containing 28 million
elements Figure 43 shows the total pressure contours It can be seen that the plenum
portion is at a constant total pressure Once the jets form since there are very small losses
in the jets due to the wall friction the total pressure still remains constant Only when the
jets enter the channel and start mixing with the cross flow is that they start losing the total
pressure head It is important to notice how the first two jets have the total pressure close
to the plenum arriving at the target wall This implies a successful impingement of the
undisturbed potential core As we move downstream the total pressure is lost quite
rapidly as the jets interact with the cross flow
Figure 43 Total Pressure Contours
59
Similar details can be drawn out from Figure 44 it can be seen that the first three
jets successfully impinge on the target wall while the rest of the downstream ones are
deflected by the cross flow As mentioned by Ricklick the velocity magnitude of the last
jet is larger than that of the first jet due to there being a lower static pressure at the end of
the channel providing it with a steeper pressure gradient hence higher velocity
Figure 44 Velocity Magnitude Contours
Turbulent kinetic energy was plotted in Figure 45 it is expected to have the
highest turbulent kinetic energy near the exit of the holes where the stagnant air is in
contact with the fast moving jet The mixing between the two regimes causes very
energetic eddies to form potentially enhancing the target and side wall heat transfer
coefficient As cross flow builds up towards the end of the channel the turbulent kinetic
energy increases due to larger overall velocities and fluctuations between the cross flow
and jets
60
Figure 45 Turbulent Kinetic Energy Contours
As Ricklick showed in his work the static temperature rise is quite small for such a small
channel It can be seen in Figure 46 that the driving temperature for heat transfer is that of
the plenum It is important to notice that a wall heat flux of 10000 Wm2 was used as the
boundary condition Not even in the most powerful tests would we ever use heat fluxes
that high they normally range between 2500 to a maximum of 7000 Wm2 A heat flux of
10000 Wm2 will increase the temperature at a faster rate than what it is normally used in
experimental testing
Figure 46 Static Temperature Contours
61
Figure 47 Target and Side Wall Heat Transfer Coefficient Contours
Figure 47 shows the target and sidewall heat transfer profiles Peaks can be seen at the
first three locations similar to that seen in Figure 22 The trend decreases rapidly to
eventually become a slowly increasing heat transfer profile due to the increase of mass
flow through the channel The sidewall provides the same results clear peaks in heat
transfer where the wall jets impinge on the sidewall seen in Figure 48 in more detail The
sidewall also shows a recirculation zone in between the first row of jets and the end wall
This is caused by the wall jet from the first row hitting the back wall moving upwards in
a circular pattern and coming back down when it encounters the first impingement row
Figure 48 Closer View of First few Rows of Impingement HTC Contours
62
Figure 49 Pathlines Generating from the First Row of Jets
Figure 49 helps explain the low heat transfer region between the first row of jets and
the end wall Pathlines are generated at the exit of each hole in the first row As the
air impinges on the surface half of it moves downstream and the other half movers
upstream to this recirculation zone where it circulates for a period of time before
reuniting with the remainder of the flow to move downstream The wall jet that
moves towards the second row of jets encounters the wall jet created by the second
row of jets causing the pathlines to drastically move upwards On the side of the
channel the pathlines behave erratically with no clear pattern clearly signifying the
highly turbulent and chaotic flow structure of this impingement channel
63
CHAPTER SIX CONCLUSIONS
It has been seen from this analysis that the side walls provide significant heat
transfer in an impingement channel especially at the relatively smaller channel
height This is primarily the result of successful impact of the wall jet with the side
walls It was shown that the tallest channel (ZD=10) has the most uniform profile with
low heat transfer coefficients when compared to the other channels The peaks of the
ZD=6 and 8 channels have a very similar profile which may indicate the successful
impingement of the potential core of the jet on the target surface As XD increases the
peaks diminish and a positive slope profile is attained by the increase of cross flow
velocity as more and more jets are introduced Tall impingement channels provide the
user with a heat transfer profile that is more uniform than those provided with the use of a
smaller channel while still maintaining higher convective coefficients when compared to
a smooth flow scenario The downstream shift of the wall jets is found to be independent
of Reynolds number and heavily dependent on streamwise position It was also found that
at XD=15 the wall jets decay faster than their XD=5 counterparts From the 3D heat
transfer profiles it was seen that the cross flow generated by multiple upstream jets is
deflected downward decreasing its effective flow area increasing its velocity hence
providing higher convective coefficients at the side wall at high xD and low zD
64
APPENDICES
Appendix A
Lateral Conduction Consideration
Thickness of foil heater Heat flux
Sample volume width
Volumetric heat generation
Volume of sample volume
Temperature profile from the first row of impingement ONLY valid for 02ltxlt045
t 50m k 20W
m K qflux 6000
W
m2
1mm
V 2
t qvol
qflux
t
T x( ) 298Kqflux
470630 x2
31244x 14842 W
m2K
N 15
x 02045 02
N 102 047
002 003 004 005314
315
316
317
318
319
320
T x( )
x
A t
qnet x( ) A kxT x
m
d
d xT x( )
d
d
1
m
002 003 004 0050
5 105
1 104
15 104
2 104
qnet x( )
x
65
Now comparing the net heat gained by lateral conduction to heat generated and convected out
It can be seen that the lateral conduction into the sample volume is two orders of magnitude smaller than the heat removed by convection
qgen qvol V 6 103
W
qconv x( ) 2
qflux qnet x( )
002 003 004 0051 10
5
1 104
1 103
001
qconv x( )
qnet x( )
x x
66
Appendix B
This is the journal file run on gambit to generate the geometry faces links
boundary layer face and volume meshes as well as the boundary conditions
set diameter
$d=75
$zc=6($d)
$xc=80($d)
$yc=4($d)
$y=2($d)
$x=5($d)
$zp=5($d)
$ztot=($zc)+($d)+($zp)
$jcf=(13)
$ocf=2
Boundary layer constants
$first=01
$growth=12
$rows=4
Meshing constants
$NumbNodes=5
$Numbtelnodes=6
$PLobnodes=5
$Chobnodes=5
$Plbenodes=($NumbNodes(4)+$rows)
$plsqnodes=($NumbNodes(3))
$Pllsnodes=($NumbNodes+$rows)
$Nojetcells=10
$Chzdnodes=($zc$Nojetcells)($d)
$Plzdnodes=($zp$Nojetcells)($d)
Boundary layer constants for channel
$firstch=001
$growthch=12
$rowsch=8
$CHbenodes=($NumbNodes(4)+$rowsch)
$CHlsnodes=($NumbNodes+$rowsch)
volume create body width ($xc) depth ($yc) height ($ztot) offset ($xc2) ($yc2) ($ztot2) brick
volume create cylinder height ($ztot) radius1 ($d2) radius3 ($d2) offset ($x) 0 ($ztot2) zaxis frustum
volume cmove cylinder multiple 1 offset 0 ($y) 0
volume cmove cylinder volume3 multiple 14 offset ($x) 0 0
volume create jetplate width ($xc) depth ($yc) height ($d)offset ($xc2) ($yc2) ($d2+$zc) brick
volume split body volumes jetplate connected
volume split jetplate volumes cylinder volume3 volume4 volume5
volume6 volume7 volume8 volume9 volume10 volume11
volume12 volume13 volume14 volume15 volume16 volume17
67
volume18 volume19 volume20 volume21 volume22 volume23
volume24 volume25 volume26 volume27 volume28 volume29
volume30 volume31 connected
face create jetcenter width ($jcf$d) height ($jcf$d) offset ($x) 0 0 xyplane rectangle
face create jetcircle radius ($d2) xyplane circle
face move jetcircle offset ($x) 0 0
face create outbox width ($ocf$d) height ($ocf$d) offset ($x) 0 0 xyplane rectangle
face split outbox connected faces jetcircle jetcenter
face split jetcircle connected faces face1
face split outbox connected faces face1
face cmove jetcenter outbox jetcircle face222 face223 multiple 1 offset 0 ($y) 0
face cmove jetcenter outbox jetcircle face222 face223 face224 face225 face226
face227 face228 multiple 14 offset ($x) 0 0
volume delete jetplate lowertopology
face split face1 connected keeptool faces jetcircle jetcenter outbox
face222 face223 face224 face225 face226 face227
face228 face229 face230 face231 face232 face233
face234 face235 face236 face237 face238 face239
face240 face241 face242 face243 face244 face245
face246 face247 face248 face249 face250 face251
face252 face253 face254 face255 face256 face257
face258 face259 face260 face261 face262 face263
face264 face265 face266 face267 face268 face269
face270 face271 face272 face273 face274 face275
face276 face277 face278 face279 face280 face281
face282 face283 face284 face285 face286 face287
face288 face289 face290 face291 face292 face293
face294 face295 face296 face297 face298 face299
face300 face301 face302 face303 face304 face305
face306 face307 face308 face309 face310 face311
face312 face313 face314 face315 face316 face317
face318 face319 face320 face321 face322 face323
face324 face325 face326 face327 face328 face329
face330 face331 face332 face333 face334 face335
face336 face337 face338 face339 face340 face341
face342 face343 face344 face345 face346 face347
face348 face349 face350 face351 face352 face353
face354 face355 face356 face357 face358 face359
face360 face361 face362 face363 face364 face365
face366 face367 face368
face move jetcircle jetcenter outbox face222 face223 face224
face225 face226 face227 face228 face229 face230
face231 face232 face233 face234 face235 face236
face237 face238 face239 face240 face241 face242
face243 face244 face245 face246 face247 face248
face249 face250 face251 face252 face253 face254
face255 face256 face257 face258 face259 face260
face261 face262 face263 face264 face265 face266
face267 face268 face269 face270 face271 face272
face273 face274 face275 face276 face277 face278
face279 face280 face281 face282 face283 face284
face285 face286 face287 face288 face289 face290
face291 face292 face293 face294 face295 face296
face297 face298 face299 face300 face301 face302
face303 face304 face305 face306 face307 face308
face309 face310 face311 face312 face313 face314
68
face315 face316 face317 face318 face319 face320
face321 face322 face323 face324 face325 face326
face327 face328 face329 face330 face331 face332
face333 face334 face335 face336 face337 face338
face339 face340 face341 face342 face343 face344
face345 face346 face347 face348 face349 face350
face351 face352 face353 face354 face355 face356
face357 face358 face359 face360 face361 face362
face363 face364 face365 face366 face367 face368 offset 0
0 $ztot
THIS SPLITS THE TOP PLENUM FACE WITH THE FACES CREATED IN THE BOTTOM
face split face6 connected keeptool faces jetcircle jetcenter outbox
face222 face223 face224 face225 face226 face227
face228 face229 face230 face231 face232 face233
face234 face235 face236 face237 face238 face239
face240 face241 face242 face243 face244 face245
face246 face247 face248 face249 face250 face251
face252 face253 face254 face255 face256 face257
face258 face259 face260 face261 face262 face263
face264 face265 face266 face267 face268 face269
face270 face271 face272 face273 face274 face275
face276 face277 face278 face279 face280 face281
face282 face283 face284 face285 face286 face287
face288 face289 face290 face291 face292 face293
face294 face295 face296 face297 face298 face299
face300 face301 face302 face303 face304 face305
face306 face307 face308 face309 face310 face311
face312 face313 face314 face315 face316 face317
face318 face319 face320 face321 face322 face323
face324 face325 face326 face327 face328 face329
face330 face331 face332 face333 face334 face335
face336 face337 face338 face339 face340 face341
face342 face343 face344 face345 face346 face347
face348 face349 face350 face351 face352 face353
face354 face355 face356 face357 face358 face359
face360 face361 face362 face363 face364 face365
face366 face367 face368
THIS MOVES THE FACES THAT WE ARE USING TO PLIT THE BOTTOM PLENUM SURFACE
face move jetcircle jetcenter outbox face222 face223 face224
face225 face226 face227 face228 face229 face230
face231 face232 face233 face234 face235 face236
face237 face238 face239 face240 face241 face242
face243 face244 face245 face246 face247 face248
face249 face250 face251 face252 face253 face254
face255 face256 face257 face258 face259 face260
face261 face262 face263 face264 face265 face266
face267 face268 face269 face270 face271 face272
face273 face274 face275 face276 face277 face278
face279 face280 face281 face282 face283 face284
face285 face286 face287 face288 face289 face290
face291 face292 face293 face294 face295 face296
face297 face298 face299 face300 face301 face302
69
face303 face304 face305 face306 face307 face308
face309 face310 face311 face312 face313 face314
face315 face316 face317 face318 face319 face320
face321 face322 face323 face324 face325 face326
face327 face328 face329 face330 face331 face332
face333 face334 face335 face336 face337 face338
face339 face340 face341 face342 face343 face344
face345 face346 face347 face348 face349 face350
face351 face352 face353 face354 face355 face356
face357 face358 face359 face360 face361 face362
face363 face364 face365 face366 face367 face368 offset 0
0 -$zp
SPLITS THE BOTTOM FACE OF THE PLENUM WITH THE FACES THAT ARE USED TO SPLIT
face split face114 connected keeptool faces jetcircle jetcenter
outbox face222 face223 face224 face225 face226 face227
face228 face229 face230 face231 face232 face233
face234 face235 face236 face237 face238 face239
face240 face241 face242 face243 face244 face245
face246 face247 face248 face249 face250 face251
face252 face253 face254 face255 face256 face257
face258 face259 face260 face261 face262 face263
face264 face265 face266 face267 face268 face269
face270 face271 face272 face273 face274 face275
face276 face277 face278 face279 face280 face281
face282 face283 face284 face285 face286 face287
face288 face289 face290 face291 face292 face293
face294 face295 face296 face297 face298 face299
face300 face301 face302 face303 face304 face305
face306 face307 face308 face309 face310 face311
face312 face313 face314 face315 face316 face317
face318 face319 face320 face321 face322 face323
face324 face325 face326 face327 face328 face329
face330 face331 face332 face333 face334 face335
face336 face337 face338 face339 face340 face341
face342 face343 face344 face345 face346 face347
face348 face349 face350 face351 face352 face353
face354 face355 face356 face357 face358 face359
face360 face361 face362 face363 face364 face365
face366 face367 face368
COPIES THE FACES THAT WE USED TO SPLIT TO BOTTOM OF THE PLENUM TO THE TOP OF
THE CHANNEL
face cmove jetcircle jetcenter outbox face222 face223 face224
face225 face226 face227 face228 face229 face230
face231 face232 face233 face234 face235 face236
face237 face238 face239 face240 face241 face242
face243 face244 face245 face246 face247 face248
face249 face250 face251 face252 face253 face254
face255 face256 face257 face258 face259 face260
face261 face262 face263 face264 face265 face266
face267 face268 face269 face270 face271 face272
face273 face274 face275 face276 face277 face278
face279 face280 face281 face282 face283 face284
70
face285 face286 face287 face288 face289 face290
face291 face292 face293 face294 face295 face296
face297 face298 face299 face300 face301 face302
face303 face304 face305 face306 face307 face308
face309 face310 face311 face312 face313 face314
face315 face316 face317 face318 face319 face320
face321 face322 face323 face324 face325 face326
face327 face328 face329 face330 face331 face332
face333 face334 face335 face336 face337 face338
face339 face340 face341 face342 face343 face344
face345 face346 face347 face348 face349 face350
face351 face352 face353 face354 face355 face356
face357 face358 face359 face360 face361 face362
face363 face364 face365 face366 face367 face368 multiple 1 offset 0
0 -$d
NAME OF COPIED NEW FACES
face1104 face1105 face1106 face1107 face1108 face1109 face1110 face1111
face1112 face1113 face1114 face1115 face1116 face1117 face1118 face1119
face1120 face1121 face1122 face1123 face1124 face1125 face1126 face1127
face1128 face1129 face1130 face1131 face1132 face1133 face1134 face1135
face1136 face1137 face1138 face1139 face1140 face1141 face1142 face1143
face1144 face1145 face1146 face1147 face1148 face1149 face1150 face1151
face1152 face1153 face1154 face1155 face1156 face1157 face1158 face1159
face1160 face1161 face1162 face1163 face1164 face1165 face1166 face1167
face1168 face1169 face1170 face1171 face1172 face1173 face1174 face1175
face1176 face1177 face1178 face1179 face1180 face1181 face1182 face1183
face1184 face1185 face1186 face1187 face1188 face1189 face1190 face1191
face1192 face1193 face1194 face1195 face1196 face1197 face1198 face1199
face1200 face1201 face1202 face1203 face1204 face1205 face1206 face1207
face1208 face1209 face1210 face1211 face1212 face1213 face1214 face1215
face1216 face1217 face1218 face1219 face1220 face1221 face1222 face1223
face1224 face1225 face1226 face1227 face1228 face1229 face1230 face1231
face1232 face1233 face1234 face1235 face1236 face1237 face1238 face1239
face1240 face1241 face1242 face1243 face1244 face1245 face1246 face1247
face1248 face1249 face1250 face1251 face1252 face1253
THIS SPLITS THE TOP OF THE CHANNEL WITH THE NEW COPIED FACES
face split face209 connected keeptool faces face1104 face1105 face1106 face1107
face1108 face1109 face1110 face1111 face1112 face1113 face1114 face1115
face1116 face1117 face1118 face1119 face1120 face1121 face1122 face1123
face1124 face1125 face1126 face1127 face1128 face1129 face1130 face1131
face1132 face1133 face1134 face1135 face1136 face1137 face1138 face1139
face1140 face1141 face1142 face1143 face1144 face1145 face1146 face1147
face1148 face1149 face1150 face1151 face1152 face1153 face1154 face1155
face1156 face1157 face1158 face1159 face1160 face1161 face1162 face1163
face1164 face1165 face1166 face1167 face1168 face1169 face1170 face1171
face1172 face1173 face1174 face1175 face1176 face1177 face1178 face1179
face1180 face1181 face1182 face1183 face1184 face1185 face1186 face1187
face1188 face1189 face1190 face1191 face1192 face1193 face1194 face1195
face1196 face1197 face1198 face1199 face1200 face1201 face1202 face1203
face1204 face1205 face1206 face1207 face1208 face1209 face1210 face1211
face1212 face1213 face1214 face1215 face1216 face1217 face1218 face1219
face1220 face1221 face1222 face1223 face1224 face1225 face1226 face1227
71
face1228 face1229 face1230 face1231 face1232 face1233 face1234 face1235
face1236 face1237 face1238 face1239 face1240 face1241 face1242 face1243
face1244 face1245 face1246 face1247 face1248 face1249 face1250 face1251
face1252 face1253
THIS UNITES THE RECTANGLE OUTSIDE FACES AND THE SEMICIRCLE SO THAT IT MAKES
A RECTANGLE WIHOUT THE CENTERJET
face unite faces jetcircle face223 real
face unite faces face222 outbox real
face unite faces face228 face226 real
face unite faces face225 face227 real
face unite faces face231 face233 real
face unite faces face232 face230 real
face unite faces face236 face238 real
face unite faces face237 face235 real
face unite faces face241 face243 real
face unite faces face242 face240 real
face unite faces face248 face246 real
face unite faces face245 face247 real
face unite faces face253 face251 real
face unite faces face252 face250 real
face unite faces face256 face258 real
face unite faces face257 face255 real
face unite faces face263 face261 real
face unite faces face260 face262 real
face unite faces face268 face266 real
face unite faces face265 face264 real
face unite faces face265 face267 real
face unite faces face273 face271 real
face unite faces face272 face270 real
face unite faces face276 face278 real
face unite faces face277 face275 real
face unite faces face281 face283 real
face unite faces face282 face280 real
face unite faces face286 face288 real
face unite faces face287 face285 real
face unite faces face291 face293 real
face unite faces face292 face290 real
face unite faces face296 face298 real
face unite faces face297 face295 real
face unite faces face301 face303 real
face unite faces face302 face300 real
face unite faces face306 face308 real
face unite faces face307 face305 real
face unite faces face316 face318 real
face unite faces face312 face310 real
face unite faces face311 face313 real
face unite faces face315 face317 real
face unite faces face321 face323 real
face unite faces face322 face320 real
face unite faces face326 face328 real
face unite faces face327 face325 real
face unite faces face331 face333 real
face unite faces face332 face330 real
face unite faces face336 face338 real
72
face unite faces face337 face335 real
face unite faces face347 face345 real
face unite faces face346 face348 real
face unite faces face342 face340 real
face unite faces face341 face343 real
face unite faces face356 face358 real
face unite faces face357 face355 real
face unite faces face352 face350 real
face unite faces face351 face353 real
face unite faces face361 face363 real
face unite faces face366 face368 real
face unite faces face360 face362 real
face unite faces face365 face367 real
SPLITTING ALL THE FACES OF THE CIRCLES IN THE BOTTOM OF THE PLENUM
face split face912 connected keeptool faces face222
face split face117 connected keeptool faces face228
face split face117 connected keeptool faces face225
face split face922 connected keeptool faces face232
face split face124 connected keeptool faces face236
face split face124 connected keeptool faces face237
face split face932 connected keeptool faces face242
face split face131 connected keeptool faces face248
face split face131 connected keeptool faces face245
face split face942 connected keeptool faces face252
face split face138 connected keeptool faces face256
face split face138 connected keeptool faces face257
face split face952 connected keeptool faces face260
face split face145 connected keeptool faces face268
face split face145 connected keeptool faces face265
face split face962 connected keeptool faces face272
face split face152 connected keeptool faces face276
face split face152 connected keeptool faces face277
face split face972 connected keeptool faces face282
face split face159 connected keeptool faces face286
face split face159 connected keeptool faces face287
face split face982 connected keeptool faces face292
face split face166 connected keeptool faces face296
face split face166 connected keeptool faces face297
face split face992 connected keeptool faces face302
face split face173 connected keeptool faces face306
face split face173 connected keeptool faces face307
face split face1002 connected keeptool faces face312
face split face180 connected keeptool faces face316
face split face180 connected keeptool faces face315
73
face split face1012 connected keeptool faces face322
face split face187 connected keeptool faces face326
face split face187 connected keeptool faces face327
face split face1022 connected keeptool faces face332
face split face194 connected keeptool faces face336
face split face194 connected keeptool faces face337
face split face1032 connected keeptool faces face342
face split face201 connected keeptool faces face346
face split face201 connected keeptool faces face347
face split face1042 connected keeptool faces face352
face split face208 connected keeptool faces face356
face split face208 connected keeptool faces face357
face split face1052 connected keeptool faces face360
face split face215 connected keeptool faces face366
face split face215 connected keeptool faces face365
THIS UNITES THE RECTANGLE OUTSIDE FACES AND THE SEMICIRCLE SO THAT IT MAKES
A RECTANGLE WIHOUT THE CENTERJET
face unite faces face1104 face1108 real
face unite faces face1107 face1106 real
face unite faces face1113 face1111 real
face unite faces face1112 face1110 real
face unite faces face1118 face1116 real
face unite faces face1117 face1115 real
face unite faces face1123 face1121 real
face unite faces face1122 face1120 real
face unite faces face1128 face1126 real
face unite faces face1127 face1125 real
face unite faces face1133 face1131 real
face unite faces face1132 face1130 real
face unite faces face1138 face1136 real
face unite faces face1137 face1135 real
face unite faces face1143 face1141 real
face unite faces face1142 face1140 real
face unite faces face1148 face1146 real
face unite faces face1147 face1145 real
face unite faces face1153 face1151 real
face unite faces face1152 face1150 real
face unite faces face1158 face1156 real
face unite faces face1157 face1155 real
face unite faces face1163 face1161 real
face unite faces face1162 face1160 real
face unite faces face1168 face1166 real
face unite faces face1167 face1165 real
face unite faces face1173 face1171 real
face unite faces face1172 face1170 real
face unite faces face1178 face1176 real
face unite faces face1177 face1175 real
face unite faces face1183 face1181 real
74
face unite faces face1182 face1180 real
face unite faces face1186 face1188 real
face unite faces face1187 face1185 real
face unite faces face1193 face1191 real
face unite faces face1192 face1190 real
face unite faces face1198 face1196 real
face unite faces face1197 face1195 real
face unite faces face1203 face1201 real
face unite faces face1202 face1200 real
face unite faces face1206 face1208 real
face unite faces face1207 face1205 real
face unite faces face1213 face1211 real
face unite faces face1212 face1210 real
face unite faces face1216 face1218 real
face unite faces face1217 face1215 real
face unite faces face1221 face1223 real
face unite faces face1222 face1220 real
face unite faces face1228 face1226 real
face unite faces face1227 face1225 real
face unite faces face1233 face1231 real
face unite faces face1232 face1230 real
face unite faces face1238 face1236 real
face unite faces face1237 face1235 real
face unite faces face1243 face1241 real
face unite faces face1242 face1240 real
face unite faces face1248 face1246 real
face unite faces face1247 face1245 real
face unite faces face1253 face1251 real
face unite faces face1252 face1250 real
SPLITTING ALL THE FACES OF THE CIRCLES IN THE TOP OF THE CHANNEL
face split face1257 connected keeptool faces face1107
face split face115 connected keeptool faces face1113
face split face115 connected keeptool faces face1112
face split face1267 connected keeptool faces face1117
face split face122 connected keeptool faces face1123
face split face122 connected keeptool faces face1122
face split face1277 connected keeptool faces face1127
face split face129 connected keeptool faces face1133
face split face129 connected keeptool faces face1132
face split face1287 connected keeptool faces face1137
face split face136 connected keeptool faces face1143
face split face136 connected keeptool faces face1142
face split face1297 connected keeptool faces face1147
face split face143 connected keeptool faces face1153
face split face143 connected keeptool faces face1152
face split face1307 connected keeptool faces face1157
face split face150 connected keeptool faces face1163
face split face150 connected keeptool faces face1162
75
face split face1317 connected keeptool faces face1167
face split face157 connected keeptool faces face1173
face split face157 connected keeptool faces face1172
face split face1327 connected keeptool faces face1177
face split face164 connected keeptool faces face1183
face split face164 connected keeptool faces face1182
face split face1337 connected keeptool faces face1187
face split face171 connected keeptool faces face1193
face split face171 connected keeptool faces face1192
face split face1347 connected keeptool faces face1197
face split face178 connected keeptool faces face1203
face split face178 connected keeptool faces face1202
face split face1357 connected keeptool faces face1207
face split face185 connected keeptool faces face1213
face split face185 connected keeptool faces face1212
face split face1367 connected keeptool faces face1217
face split face192 connected keeptool faces face1221
face split face192 connected keeptool faces face1222
face split face1377 connected keeptool faces face1227
face split face199 connected keeptool faces face1233
face split face199 connected keeptool faces face1232
face split face1387 connected keeptool faces face1237
face split face206 connected keeptool faces face1243
face split face206 connected keeptool faces face1242
face split face1397 connected keeptool faces face1247
face split face213 connected keeptool faces face1253
face split face213 connected keeptool faces face1252
face split face1452 connected keeptool faces face224
face split face1456 connected keeptool faces face234
face split face1460 connected keeptool faces face244
face split face1464 connected keeptool faces face254
face split face1468 connected keeptool faces face264
face split face1472 connected keeptool faces face274
face split face1476 connected keeptool faces face284
face split face1480 connected keeptool faces face294
face split face1484 connected keeptool faces face304
face split face1488 connected keeptool faces face314
face split face1492 connected keeptool faces face324
face split face1496 connected keeptool faces face334
face split face1500 connected keeptool faces face344
face split face1504 connected keeptool faces face354
face split face1508 connected keeptool faces face364
DELETING ALL THE FACES USED TO MAKE THE CUTS
face delete jetcircle face222 face228 face225 jetcenter
76
face224 face231 face232 face236 face237 face229
face1456 face241 face242 face239 face248 face244
face245 face253 face249 face252 face254 face256
face257 face263 face259 face260 face268 face264
face265 face273 face272 face269 face276 face277
face274 face281 face282 face286 face279 face287
face284 face291 face292 face296 face297 face289
face294 face301 face299 face302 face306 face307
face304 face311 face312 face316 face315 face309
face314 face321 face322 face326 face327 face319
face324 face331 face332 face329 face336 face334
face337 face341 face342 face339 face346 face344
face347 face351 face352 face349 face356 face354
face357 face361 face359 face360 face366 face364
face365 lowertopology
face delete face1104 face1105 face1107 face1113 face1112
face115 face234 face1118 face1114 face1117 face1123
face1122 face122 face1138 face1128 face1127 face1124
face1133 face1132 face129 face1134 face1137 face1143
face136 face1142 face1148 face1144 face1147 face1153
face143 face1152 face1158 face1154 face1157 face1163
face150 face1162 face1168 face1164 face1167 face1173
face157 face1172 face1178 face1174 face1177 face1183
face164 face1182 face1186 face1184 face1187 face1193
face171 face1192 face1198 face1194 face1197 face1203
face178 face1202 face1206 face1204 face1207 face1213
face185 face1212 face1216 face1214 face1217 face1221
face192 face1222 face1228 face1224 face1227 face1233
face199 face1232 face1238 face1234 face1237 face1243
face206 face1242 face1248 face1244 face1247 face1253
face213 face1252 lowertopology
face delete face1109 face1119 face1129 face1139 face1149 face1159
face1169 face1179 face1189 face1199 face1209 face1219
face1229 face1239 face1249 lowertopology
face create CP1 width 600 height 75 offset 300 (225+($d)2) 0 xyplane rectangle
face create CP2 width 600 height 75 offset 300 (225+($d)2) ($zc) xyplane rectangle
face create CP3 width 600 height 75 offset 300 (225+($d)2) ($zc+$d) xyplane rectangle
face create CP4 width 600 height 75 offset 300 (225+($d)2) ($zc+$d+$zp) xyplane rectangle
face split face6 connected faces CP4
face split face114 connected faces CP3
face split face209 connected faces CP2
face split face1 connected faces CP1
GEOMETRY IS FINISHED
face modify face912 side vertex6437 vertex6436
77
face modify face1600 side vertex7302 vertex7303
face modify face117 side vertex6446 vertex6447
face modify face646 side vertex3312
face modify face646 side vertex3313
face modify face647 side vertex3432 vertex3433
face modify face372 side vertex2040 vertex2041
face modify face376 side vertex2100 vertex2101
face modify face377 side vertex2221 vertex2220
LINKING ALL THE JET CENTERS
face link face1450 face640 edges edge6949 edge3518 vertices
vertex6437 vertex3253 reverse
face link face1450 face1257 edges edge6949 edge7340 vertices
vertex6437 vertex6797 reverse
face link face1257 face370 edges edge7340 edge2139 vertices
vertex6797 vertex2041 reverse
face link face1257 face1454 edges edge7340 edge6975 vertices
vertex6797 vertex6461 reverse
face link face1454 face649 edges edge6975 edge3519 vertices
vertex6461 vertex3255 reverse
face link face1454 face1267 edges edge6975 edge7377 vertices
vertex6461 vertex6831 reverse
face link face1267 face379 edges edge7377 edge2141 vertices
vertex6831 vertex2043 reverse
face link face1267 face1458 edges edge7377 edge7001 vertices
vertex6831 vertex6485 reverse
face link face1458 face659 edges edge7001 edge3520 vertices
vertex6485 vertex3257 reverse
face link face1458 face1277 edges edge7001 edge7414 vertices
vertex6485 vertex6865 reverse
face link face1277 face389 edges edge7414 edge2143 vertices
vertex6865 vertex2045 reverse
face link face1277 face1462 edges edge7414 edge7027 vertices
vertex6865 vertex6509 reverse
face link face1462 face669 edges edge7027 edge3521 vertices
vertex6509 vertex3259 reverse
face link face1462 face1287 edges edge7027 edge7451 vertices
vertex6509 vertex6899 reverse
face link face1287 face399 edges edge7451 edge2145 vertices
vertex6899 vertex2047 reverse
face link face1287 face1466 edges edge7451 edge7053 vertices
vertex6899 vertex6533 reverse
face link face1466 face679 edges edge7053 edge3522 vertices
vertex6533 vertex3261 reverse
face link face1466 face1297 edges edge7053 edge7488 vertices
vertex6533 vertex6933 reverse
face link face1297 face409 edges edge7488 edge2147 vertices
vertex6933 vertex2049 reverse
face link face1297 face1470 edges edge7488 edge7079 vertices
vertex6933 vertex6557 reverse
face link face1470 face689 edges edge7079 edge3523 vertices
vertex6557 vertex3263 reverse
face link face1470 face1307 edges edge7079 edge7525 vertices
vertex6557 vertex6967 reverse
face link face1307 face419 edges edge7525 edge2149 vertices
78
vertex6967 vertex2051 reverse
face link face1307 face1474 edges edge7525 edge7105 vertices
vertex6967 vertex6581 reverse
face link face1474 face1317 edges edge7105 edge7562 vertices
vertex6581 vertex7001 reverse
face link face1474 face699 edges edge7105 edge3524 vertices
vertex6581 vertex3265 reverse
face link face1317 face429 edges edge7562 edge2151 vertices
vertex7001 vertex2053 reverse
face link face1317 face1478 edges edge7562 edge7131 vertices
vertex7001 vertex6605 reverse
face link face1478 face1327 edges edge7131 edge7599 vertices
vertex6605 vertex7035 reverse
face link face1478 face709 edges edge7131 edge3525 vertices
vertex6605 vertex3267 reverse
face link face1327 face439 edges edge7599 edge2153 vertices
vertex7035 vertex2055 reverse
face link face1327 face1482 edges edge7599 edge7157 vertices
vertex7035 vertex6629 reverse
face link face1482 face719 edges edge7157 edge3526 vertices
vertex6629 vertex3269 reverse
face link face1482 face1337 edges edge7157 edge7636 vertices
vertex6629 vertex7069 reverse
face link face1337 face449 edges edge7636 edge2155 vertices
vertex7069 vertex2057 reverse
face link face1337 face1486 edges edge7636 edge7183 vertices
vertex7069 vertex6653 reverse
face link face1486 face1347 edges edge7183 edge7673 vertices
vertex6653 vertex7103 reverse
face link face1347 face459 edges edge7673 edge2157 vertices
vertex7103 vertex2059 reverse
face link face1486 face729 edges edge7183 edge3527 vertices
vertex6653 vertex3271 reverse
face link face1347 face1490 edges edge7673 edge7209 vertices
vertex7103 vertex6677 reverse
face link face1490 face1357 edges edge7209 edge7710 vertices
vertex6677 vertex7137 reverse
face link face1490 face739 edges edge7209 edge3528 vertices
vertex6677 vertex3273 reverse
face link face1357 face469 edges edge7710 edge2159 vertices
vertex7137 vertex2061 reverse
face link face1357 face1494 edges edge7710 edge7235 vertices
vertex7137 vertex6701 reverse
face link face1494 face1367 edges edge7235 edge7747 vertices
vertex6701 vertex7171 reverse
face link face1494 face749 edges edge7235 edge3529 vertices
vertex6701 vertex3275 reverse
face link face1367 face479 edges edge7747 edge2161 vertices
vertex7171 vertex2063 reverse
face link face1367 face1498 edges edge7747 edge7261 vertices
vertex7171 vertex6725 reverse
face link face1498 face1377 edges edge7261 edge7784 vertices
vertex6725 vertex7205 reverse
face link face1377 face489 edges edge7784 edge2163 vertices
vertex7205 vertex2065 reverse
face link face1498 face759 edges edge7261 edge3530 vertices
79
vertex6725 vertex3277 reverse
face link face1377 face1502 edges edge7784 edge7287 vertices
vertex7205 vertex6749 reverse
face link face1502 face1387 edges edge7287 edge7821 vertices
vertex6749 vertex7239 reverse
face link face1387 face499 edges edge7821 edge2165 vertices
vertex7239 vertex2067 reverse
face link face1387 face1506 edges edge7821 edge7313 vertices
vertex7239 vertex6773 reverse
face link face1502 face769 edges edge7287 edge3531 vertices
vertex6749 vertex3279 reverse
face link face1506 face1397 edges edge7313 edge7858 vertices
vertex6773 vertex7273 reverse
face link face1506 face779 edges edge7313 edge3532 vertices
vertex6773 vertex3281 reverse
face link face1397 face509 edges edge7858 edge2167 vertices
vertex7273 vertex2069 reverse
LINKING ALL THE COMPLETE JETCENTERS
face link face1452 face644 edges edge7891 edge3773 vertices
vertex7303 vertex3433
face link face1452 face115 edges edge7891 edge7364 vertices
vertex7303 vertex6819
face link face1452 face1456 edges edge7891 edge7900 vertices
vertex7303 vertex7311
face link face1456 face654 edges edge7900 edge3774 vertices
vertex7311 vertex3435
face link face1456 face122 edges edge7900 edge7401 vertices
vertex7311 vertex6853
face link face1456 face1460 edges edge7900 edge7909 vertices
vertex7311 vertex7319
face link face1460 face1464 edges edge7909 edge7918 vertices
vertex7319 vertex7327
face link face1460 face129 edges edge7909 edge7438 vertices
vertex7319 vertex6887
face link face1460 face664 edges edge7909 edge3775 vertices
vertex7319 vertex3437
face link face1464 face674 edges edge7918 edge3776 vertices
vertex7327 vertex3439
face link face1464 face136 edges edge7918 edge7475 vertices
vertex7327 vertex6921
face link face1464 face1468 edges edge7918 edge7927 vertices
vertex7327 vertex7335
face link face1472 face1468 edges edge7936 edge7927 vertices
vertex7343 vertex7335
face link face1468 face143 edges edge7927 edge7512 vertices
vertex7335 vertex6955
face link face1468 face684 edges edge7927 edge3777 vertices
vertex7335 vertex3441
face link face1472 face694 edges edge7936 edge3778 vertices
vertex7343 vertex3443
face link face1472 face150 edges edge7936 edge7549 vertices
vertex7343 vertex6989
face link face1472 face1476 edges edge7936 edge7945 vertices
80
vertex7343 vertex7351
face link face1476 face1480 edges edge7945 edge7954 vertices
vertex7351 vertex7359
face link face1476 face157 edges edge7945 edge7586 vertices
vertex7351 vertex7023
face link face1476 face704 edges edge7945 edge3779 vertices
vertex7351 vertex3445
face link face1480 face714 edges edge7954 edge3780 vertices
vertex7359 vertex3447
face link face1480 face164 edges edge7954 edge7623 vertices
vertex7359 vertex7057
face link face1480 face1484 edges edge7954 edge7963 vertices
vertex7359 vertex7367
face link face1484 face171 edges edge7963 edge7660 vertices
vertex7367 vertex7091
face link face1484 face724 edges edge7963 edge3781 vertices
vertex7367 vertex3449
face link face1480 face1488 edges edge7954 edge7972 vertices
vertex7359 vertex7375
face link face1488 face178 edges edge7972 edge7697 vertices
vertex7375 vertex7125
face link face1488 face734 edges edge7972 edge3782 vertices
vertex7375 vertex3451
face link face1488 face1492 edges edge7972 edge7981 vertices
vertex7375 vertex7383
face link face1492 face744 edges edge7981 edge3783 vertices
vertex7383 vertex3453
face link face1492 face185 edges edge7981 edge7734 vertices
vertex7383 vertex7159
face link face1492 face1496 edges edge7981 edge7990 vertices
vertex7383 vertex7391
face link face1496 face754 edges edge7990 edge3784 vertices
vertex7391 vertex3455
face link face1496 face192 edges edge7990 edge7771 vertices
vertex7391 vertex7193
face link face1496 face1500 edges edge7990 edge7999 vertices
vertex7391 vertex7399
face link face1500 face1504 edges edge7999 edge8008 vertices
vertex7399 vertex7407
face link face1504 face1508 edges edge8008 edge8017 vertices
vertex7407 vertex7415
face link face1500 face199 edges edge7999 edge7808 vertices
vertex7399 vertex7227
face link face1500 face764 edges edge7999 edge3785 vertices
vertex7399 vertex3457
face link face1504 face774 edges edge8008 edge3786 vertices
vertex7407 vertex3459
face link face1508 face784 edges edge8017 edge3787 vertices
vertex7415 vertex3461
face link face1504 face206 edges edge8008 edge7845 vertices
vertex7407 vertex7261
face link face1508 face213 edges edge8017 edge7882 vertices
vertex7415 vertex7295
linking the jetcenters of the bottom of the channel one of them has to be reversed but the otherones are not
81
face link face115 face374 edges edge7364 edge2394 vertices
vertex6819 vertex2221 reverse
face link face374 face384 edges edge2394 edge2396 vertices
vertex2221 vertex2223
face link face384 face394 edges edge2396 edge2398 vertices
vertex2223 vertex2225
face link face394 face404 edges edge2398 edge2400 vertices
vertex2225 vertex2227
face link face404 face414 edges edge2400 edge2402 vertices
vertex2227 vertex2229
face link face414 face424 edges edge2402 edge2404 vertices
vertex2229 vertex2231
face link face424 face434 edges edge2404 edge2406 vertices
vertex2231 vertex2233
face link face434 face444 edges edge2406 edge2408 vertices
vertex2233 vertex2235
face link face444 face454 edges edge2408 edge2410 vertices
vertex2235 vertex2237
face link face454 face464 edges edge2410 edge2412 vertices
vertex2237 vertex2239
face link face464 face474 edges edge2412 edge2414 vertices
vertex2239 vertex2241
face link face474 face484 edges edge2414 edge2416 vertices
vertex2241 vertex2243
face link face484 face494 edges edge2416 edge2418 vertices
vertex2243 vertex2245
face link face494 face504 edges edge2418 edge2420 vertices
vertex2245 vertex2247
face link face504 face514 edges edge2420 edge2422 vertices
vertex2247 vertex2249
UP TO THIS POINT ALL THE FACES ARE CONNCTED SUCCESSFULLY
LINKING THE FIRST THREE JET TELEPHONES
face link face912 face117 edges edge6950 edge6960 vertices
vertex6437 vertex6446 reverse
face link face912 face1600 edges edge6950 edge7890 vertices
vertex6437 vertex7303 reverse
face link face912 face372 edges edge6950 edge2168 vertices
vertex6437 vertex2041
face link face117 face376 edges edge6959 edge2304 vertices
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vertex2103 vertex2105
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face link face382 face392 edges edge2169 edge2170 vertices
vertex2043 vertex2045
face link face382 face392 edges edge2169 edge2170 vertices
vertex2043 vertex2045
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face link face487 face487 edges edge2434 edge2434 vertices
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face link face487 face487 edges edge2434 edge2434 vertices
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face link face487 face497 edges edge2434 edge2435 vertices
vertex2243 vertex2245
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vertex2245 vertex2247
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83
vertex2118 vertex2120
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LINKING THE TELEPHONES OF THE BOTTOM OF THE PLENUM
face link face912 face922 edges edge6950 edge6976 vertices
vertex6437 vertex6461
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vertex6509 vertex6533
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vertex6557 vertex6581
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vertex6581 vertex6605
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vertex6605 vertex6629
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vertex6629 vertex6653
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vertex6653 vertex6677
84
face link face1012 face1022 edges edge7210 edge7236 vertices
vertex6677 vertex6701
face link face1032 face1042 edges edge7262 edge7288 vertices
vertex6725 vertex6749
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vertex6749 vertex6773
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vertex6518 vertex6542
face link face145 face152 edges edge7064 edge7090 vertices
vertex6542 vertex6566
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vertex6566 vertex6590
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vertex6590 vertex6614
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vertex6638 vertex6662
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vertex6662 vertex6686
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vertex6710 vertex6734
face link face1022 face1032 edges edge7236 edge7262 vertices
vertex6701 vertex6725
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vertex6725 vertex6749
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vertex6759 vertex6783
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vertex7303 vertex7311
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vertex7311 vertex7319
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face link face1608 face1610 edges edge7926 edge7935 vertices
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face link face1610 face1612 edges edge7935 edge7944 vertices
vertex7343 vertex7351
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face link face1614 face1616 edges edge7953 edge7962 vertices
vertex7359 vertex7367
face link face1616 face1618 edges edge7962 edge7971 vertices
vertex7367 vertex7375
85
face link face1618 face1620 edges edge7971 edge7980 vertices
vertex7375 vertex7383
face link face1620 face1622 edges edge7980 edge7989 vertices
vertex7383 vertex7391
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vertex7391 vertex7399
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LINKING ALL THE TELEPHONES OF THE TOP OF THE CHANNEL
face link face912 face1510 edges edge6950 edge7339 vertices
vertex6437 vertex6797 reverse
face link face117 face1512 edges edge6959 edge7349 vertices
vertex6447 vertex6807
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vertex6865 vertex6899
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vertex6899 vertex6933
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face link face1540 face1546 edges edge7524 edge7561 vertices
vertex6967 vertex7001
face link face1546 face1552 edges edge7561 edge7598 vertices
vertex7001 vertex7035
face link face1552 face1558 edges edge7598 edge7635 vertices
vertex7035 vertex7069
face link face1558 face1564 edges edge7635 edge7672 vertices
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face link face1570 face1576 edges edge7709 edge7746 vertices
vertex7137 vertex7171
face link face1576 face1582 edges edge7746 edge7783 vertices
vertex7171 vertex7205
face link face1582 face1588 edges edge7783 edge7820 vertices
vertex7205 vertex7239
face link face1588 face1594 edges edge7820 edge7857 vertices
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face link face1512 face1518 edges edge7350 edge7387 vertices
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face link face1518 face1524 edges edge7387 edge7424 vertices
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vertex6874 vertex6908
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vertex6908 vertex6942
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86
vertex6942 vertex6976
face link face1542 face1548 edges edge7535 edge7572 vertices
vertex6976 vertex7010
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vertex7010 vertex7044
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face link face1544 face1550 edges edge7548 edge7585 vertices
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LINKING ALL THE TELEPHONES OF THE TOP OF THE PLENUM
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vertex6437 vertex3253 reverse
face link face642 face647 edges edge3489 edge3744 vertices
vertex3253 vertex3433
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87
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vertex3324 vertex3326
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vertex3326 vertex3328
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vertex3328 vertex3330
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vertex3330 vertex3332
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vertex3332 vertex3334
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vertex3336 vertex3338
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88
vertex3338 vertex3340
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LINKING OUTBOXES ON THE PLENUM
face modify face911 side vertex4404 vertex4405
face modify face918 side vertex4405 vertex4404
face link face911 face915 edges edge4778 edge4898 vertices
vertex4374 vertex4434
face link face915 face645 edges edge4899 edge3833 vertices
vertex4480 vertex3463 reverse
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vertex3463 vertex3465
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vertex3465 vertex3467
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vertex3467 vertex3469
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vertex3469 vertex3471
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89
vertex3471 vertex3473
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vertex3473 vertex3475
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vertex3475 vertex3477
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vertex3479 vertex3481
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vertex3481 vertex3483
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vertex3483 vertex3485
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vertex3485 vertex3487
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vertex3487 vertex3489
face link face775 face785 edges edge3846 edge3847 vertices
vertex3489 vertex3491
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vertex3347 vertex3353
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vertex3353 vertex3359
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vertex3359 vertex3365
face link face678 face688 edges edge3698 edge3702 vertices
vertex3365 vertex3371
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vertex3371 vertex3377
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vertex3377 vertex3383
face link face708 face718 edges edge3710 edge3714 vertices
vertex3383 vertex3389
face link face718 face728 edges edge3714 edge3718 vertices
vertex3389 vertex3395
face link face728 face738 edges edge3718 edge3722 vertices
vertex3395 vertex3401
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vertex3401 vertex3407
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vertex3407 vertex3413
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vertex3413 vertex3419
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vertex3419 vertex3425
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vertex3425 vertex3431
face link face641 face650 edges edge3578 edge3579 vertices
vertex3283 vertex3285
face link face650 face660 edges edge3579 edge3580 vertices
vertex3285 vertex3287
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vertex3287 vertex3289
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vertex3289 vertex3291
face link face680 face690 edges edge3582 edge3583 vertices
90
vertex3291 vertex3293
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vertex3293 vertex3295
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vertex3295 vertex3297
face link face710 face720 edges edge3585 edge3586 vertices
vertex3297 vertex3299
face link face720 face730 edges edge3586 edge3587 vertices
vertex3299 vertex3301
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vertex3301 vertex3303
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vertex3303 vertex3305
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vertex3305 vertex3307
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vertex3307 vertex3309
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vertex3309 vertex3311
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vertex4480 vertex4482
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vertex4482 vertex4484
face link face935 face945 edges edge4903 edge4905 vertices
vertex4484 vertex4486
face link face945 face955 edges edge4905 edge4907 vertices
vertex4486 vertex4488
face link face955 face965 edges edge4907 edge4909 vertices
vertex4488 vertex4490
face link face965 face975 edges edge4909 edge4911 vertices
vertex4490 vertex4492
face link face975 face985 edges edge4911 edge4913 vertices
vertex4492 vertex4494
face link face985 face995 edges edge4913 edge4915 vertices
vertex4494 vertex4496
face link face995 face1005 edges edge4915 edge4917 vertices
vertex4496 vertex4498
face link face1005 face1015 edges edge4917 edge4919 vertices
vertex4498 vertex4500
face link face1015 face1025 edges edge4919 edge4921 vertices
vertex4500 vertex4502
face link face1025 face1035 edges edge4921 edge4923 vertices
vertex4502 vertex4504
face link face1035 face1045 edges edge4923 edge4925 vertices
vertex4504 vertex4506
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vertex4506 vertex4508
face link face918 face928 edges edge4825 edge4828 vertices
vertex4436 vertex4439
face link face928 face938 edges edge4828 edge4831 vertices
vertex4439 vertex4442
face link face938 face948 edges edge4831 edge4834 vertices
vertex4442 vertex4445
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vertex4445 vertex4448
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91
vertex4448 vertex4451
face link face968 face978 edges edge4840 edge4843 vertices
vertex4451 vertex4454
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vertex4454 vertex4457
face link face988 face998 edges edge4846 edge4849 vertices
vertex4457 vertex4460
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vertex4460 vertex4463
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vertex4463 vertex4466
face link face1018 face1028 edges edge4855 edge4858 vertices
vertex4466 vertex4469
face link face1028 face1038 edges edge4858 edge4861 vertices
vertex4469 vertex4472
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vertex4472 vertex4475
face link face1048 face1058 edges edge4864 edge4867 vertices
vertex4475 vertex4478
face link face911 face920 edges edge108 edge118 vertices
vertex88 vertex94
face link face920 face930 edges edge118 edge128 vertices
vertex94 vertex100
face link face930 face940 edges edge4783 edge4785 vertices
vertex4409 vertex4411
face link face940 face950 edges edge4785 edge4787 vertices
vertex4411 vertex4413
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vertex4413 vertex4415
face link face960 face970 edges edge4789 edge4791 vertices
vertex4415 vertex4417
face link face970 face980 edges edge4791 edge4793 vertices
vertex4417 vertex4419
face link face980 face990 edges edge4793 edge4795 vertices
vertex4419 vertex4421
face link face990 face1000 edges edge4795 edge4797 vertices
vertex4421 vertex4423
face link face1000 face1010 edges edge4797 edge4799 vertices
vertex4423 vertex4425
face link face1010 face1020 edges edge4799 edge4801 vertices
vertex4425 vertex4427
face link face1020 face1030 edges edge4801 edge4803 vertices
vertex4427 vertex4429
face link face1030 face1040 edges edge4803 edge4805 vertices
vertex4429 vertex4431
face link face1040 face1050 edges edge4805 edge4807 vertices
vertex4431 vertex4433
LINKING THE TOP OF THE CHANEL OUTBOXES
face modify face1256 side vertex6322 vertex6321
face modify face1263 side vertex6322 vertex6321
face modify face1260 side vertex6397 vertex6396
92
face link face1256 face1260 edges edge6803 edge6923 vertices
vertex6322 vertex6397
face link face1256 face371 edges edge6774 edge2053 vertices
vertex6292 vertex1955 reverse
face link face371 face375 edges edge2053 edge2336 vertices
vertex1955 vertex2135
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vertex6322 vertex2071 reverse
face link face1263 face1273 edges edge6820 edge6823 vertices
vertex6322 vertex6324
face link face1273 face1283 edges edge6823 edge6826 vertices
vertex6324 vertex6326
face link face1283 face1293 edges edge6826 edge6829 vertices
vertex6326 vertex6328
face link face1293 face1303 edges edge6829 edge6832 vertices
vertex6328 vertex6330
face link face1303 face1313 edges edge6832 edge6835 vertices
vertex6330 vertex6332
face link face1313 face1323 edges edge6835 edge6838 vertices
vertex6332 vertex6334
face link face1323 face1333 edges edge6838 edge6841 vertices
vertex6334 vertex6336
face link face1333 face1343 edges edge6841 edge6844 vertices
vertex6336 vertex6338
face link face1343 face1353 edges edge6844 edge6847 vertices
vertex6338 vertex6340
face link face1353 face1363 edges edge6847 edge6850 vertices
vertex6340 vertex6342
face link face1363 face1373 edges edge6850 edge6853 vertices
vertex6342 vertex6344
face link face1373 face1383 edges edge6853 edge6856 vertices
vertex6344 vertex6346
face link face1383 face1393 edges edge6856 edge6859 vertices
vertex6346 vertex6348
face link face1393 face1403 edges edge6859 edge6862 vertices
vertex6348 vertex6350
face link face1256 face1265 edges edge6774 edge6776 vertices
vertex6292 vertex6294
face link face1265 face1275 edges edge6776 edge6778 vertices
vertex6294 vertex6296
face link face1275 face1285 edges edge6778 edge6780 vertices
vertex6296 vertex6298
face link face1285 face1295 edges edge6780 edge6782 vertices
vertex6298 vertex6300
face link face1295 face1305 edges edge6782 edge6784 vertices
vertex6300 vertex6302
face link face1305 face1315 edges edge6784 edge6786 vertices
vertex6302 vertex6304
face link face1315 face1325 edges edge6786 edge6788 vertices
vertex6304 vertex6306
face link face1325 face1335 edges edge6788 edge6790 vertices
vertex6306 vertex6308
face link face1335 face1345 edges edge6790 edge6792 vertices
vertex6308 vertex6310
face link face1345 face1355 edges edge6792 edge6794 vertices
vertex6310 vertex6312
93
face link face1355 face1365 edges edge6794 edge6796 vertices
vertex6312 vertex6314
face link face1365 face1375 edges edge6796 edge6798 vertices
vertex6314 vertex6316
face link face1375 face1385 edges edge6798 edge6800 vertices
vertex6316 vertex6318
face link face1385 face1395 edges edge6800 edge6802 vertices
vertex6318 vertex6320
face link face1260 face1270 edges edge6894 edge6896 vertices
vertex6353 vertex6356
face link face1270 face1280 edges edge6896 edge6898 vertices
vertex6356 vertex6359
face link face1280 face1290 edges edge6898 edge6900 vertices
vertex6359 vertex6362
face link face1290 face1300 edges edge6900 edge6902 vertices
vertex6362 vertex6365
face link face1300 face1310 edges edge6902 edge6904 vertices
vertex6365 vertex6368
face link face1310 face1320 edges edge6904 edge6906 vertices
vertex6368 vertex6371
face link face1320 face1330 edges edge6906 edge6908 vertices
vertex6371 vertex6374
face link face1330 face1340 edges edge6908 edge6910 vertices
vertex6374 vertex6377
face link face1340 face1350 edges edge6910 edge6912 vertices
vertex6377 vertex6380
face link face1350 face1360 edges edge6912 edge6914 vertices
vertex6380 vertex6383
face link face1360 face1370 edges edge6914 edge6916 vertices
vertex6383 vertex6386
face link face1370 face1380 edges edge6916 edge6918 vertices
vertex6386 vertex6389
face link face1380 face1390 edges edge6918 edge6920 vertices
vertex6389 vertex6392
face link face1390 face1400 edges edge6920 edge6922 vertices
vertex6392 vertex6395
LINKING THE BOTTOM OF THE CHANEL OUTBOXES
face link face375 face385 edges edge2440 edge2443 vertices
vertex2251 vertex2253
face link face385 face395 edges edge2443 edge2446 vertices
vertex2253 vertex2255
face link face395 face405 edges edge2446 edge2449 vertices
vertex2255 vertex2257
face link face405 face415 edges edge2449 edge2452 vertices
vertex2257 vertex2259
face link face415 face425 edges edge2452 edge2455 vertices
vertex2259 vertex2261
face link face425 face435 edges edge2455 edge2458 vertices
vertex2261 vertex2263
face link face435 face445 edges edge2458 edge2461 vertices
vertex2263 vertex2265
face link face445 face455 edges edge2461 edge2464 vertices
vertex2265 vertex2267
face link face455 face465 edges edge2464 edge2467 vertices
94
vertex2267 vertex2269
face link face465 face475 edges edge2467 edge2470 vertices
vertex2269 vertex2271
face link face475 face485 edges edge2470 edge2473 vertices
vertex2271 vertex2273
face link face485 face495 edges edge2473 edge2476 vertices
vertex2273 vertex2275
face link face495 face505 edges edge2476 edge2479 vertices
vertex2275 vertex2277
face link face505 face515 edges edge2479 edge2482 vertices
vertex2277 vertex2279
face link face378 face388 edges edge2245 edge2248 vertices
vertex2135 vertex2141
face link face388 face398 edges edge2248 edge2251 vertices
vertex2141 vertex2147
face link face398 face408 edges edge2251 edge2254 vertices
vertex2147 vertex2153
face link face408 face418 edges edge2254 edge2257 vertices
vertex2153 vertex2159
face link face418 face428 edges edge2257 edge2260 vertices
vertex2159 vertex2165
face link face428 face438 edges edge2260 edge2263 vertices
vertex2165 vertex2171
face link face438 face448 edges edge2263 edge2266 vertices
vertex2171 vertex2177
face link face448 face458 edges edge2266 edge2269 vertices
vertex2177 vertex2183
face link face458 face468 edges edge2269 edge2272 vertices
vertex2183 vertex2189
face link face468 face478 edges edge2272 edge2275 vertices
vertex2189 vertex2195
face link face478 face488 edges edge2275 edge2278 vertices
vertex2195 vertex2201
face link face488 face498 edges edge2278 edge2281 vertices
vertex2201 vertex2207
face link face498 face508 edges edge2281 edge2284 vertices
vertex2207 vertex2213
face link face508 face518 edges edge2284 edge2287 vertices
vertex2213 vertex2219
face link face371 face380 edges edge2185 edge2188 vertices
vertex2071 vertex2073
face link face380 face390 edges edge2188 edge2191 vertices
vertex2073 vertex2075
face link face390 face400 edges edge2191 edge2194 vertices
vertex2075 vertex2077
face link face400 face410 edges edge2194 edge2197 vertices
vertex2077 vertex2079
face link face410 face420 edges edge2197 edge2200 vertices
vertex2079 vertex2081
face link face420 face430 edges edge2200 edge2203 vertices
vertex2081 vertex2083
face link face430 face440 edges edge2203 edge2206 vertices
vertex2083 vertex2085
face link face440 face450 edges edge2206 edge2209 vertices
vertex2085 vertex2087
face link face450 face460 edges edge2209 edge2212 vertices
95
vertex2087 vertex2089
face link face460 face470 edges edge2212 edge2215 vertices
vertex2089 vertex2091
face link face470 face480 edges edge2215 edge2218 vertices
vertex2091 vertex2093
face link face480 face490 edges edge2218 edge2221 vertices
vertex2093 vertex2095
face link face490 face500 edges edge2221 edge2224 vertices
vertex2095 vertex2097
face link face500 face510 edges edge2224 edge2227 vertices
vertex2097 vertex2099
TOP SIDE BOX beginning of channel
face link face1649 face1633 edges edge97 edge3533 vertices
vertex4374 vertex3162 reverse
TOP SIDE BOXES
face link face1650 face1651 edges edge4749 edge4751 vertices
vertex4376 vertex4378
face link face1652 face1653 edges edge4753 edge4755 vertices
vertex4380 vertex4382
face link face1653 face1654 edges edge4755 edge4757 vertices
vertex4382 vertex4384
face link face1654 face1655 edges edge4757 edge4759 vertices
vertex4384 vertex4386
face link face1655 face1656 edges edge4759 edge4761 vertices
vertex4386 vertex4388
face link face1656 face114 edges edge4761 edge4763 vertices
vertex4388 vertex4390
face link face114 face1657 edges edge4763 edge4765 vertices
vertex4390 vertex4392
face link face1657 face1658 edges edge4765 edge4767 vertices
vertex4392 vertex4394
face link face1658 face1659 edges edge4767 edge4769 vertices
vertex4394 vertex4396
face link face1659 face1660 edges edge4769 edge4771 vertices
vertex4396 vertex4398
face link face1660 face1661 edges edge4771 edge4773 vertices
vertex4398 vertex4400
face link face1661 face1662 edges edge4773 edge4775 vertices
vertex4400 vertex4402
face link face1650 face1634 edges edge4900 edge8036 vertices
vertex4481 vertex3464 reverse
face link face1634 face1635 edges edge8036 edge8037 vertices
vertex3464 vertex3466
face link face1635 face1636 edges edge8037 edge8038 vertices
vertex3466 vertex3468
face link face1636 face1637 edges edge8038 edge8039 vertices
vertex3468 vertex3470
face link face1637 face1638 edges edge8039 edge8040 vertices
vertex3470 vertex3472
face link face1638 face1639 edges edge8040 edge8041 vertices
vertex3472 vertex3474
face link face1639 face6 edges edge8041 edge8042 vertices
96
vertex3474 vertex3476
face link face6 face1640 edges edge8042 edge8043 vertices
vertex3476 vertex3478
face link face1640 face1641 edges edge8043 edge8044 vertices
vertex3478 vertex3480
face link face1641 face1642 edges edge8044 edge8045 vertices
vertex3480 vertex3482
face link face1642 face1643 edges edge8045 edge8046 vertices
vertex3482 vertex3484
face link face1643 face1644 edges edge8046 edge8047 vertices
vertex3484 vertex3486
face link face1644 face1645 edges edge8047 edge8048 vertices
vertex3486 vertex3488
face link face1645 face1646 edges edge8048 edge8049 vertices
vertex3488 vertex3490
face link face1651 face1652 edges edge4751 edge4753 vertices
vertex4378 vertex4380
TOP SIDE BOX END OF CHANNEL
face link face1647 face1663 edges edge8050 edge99 vertices
vertex7433 vertex7435 reverse
TOP SIDE BOX BACK OF CHANNEL
face link face1648 face1664 edges edge12 edge8069 vertices
vertex8 vertex84 reverse
BOTTOM SIDE BOX
face link face1665 face1681 edges edge6773 edge2048 vertices
vertex6291 vertex1950 reverse
face link face1680 face1696 edges edge8071 edge8105 vertices
vertex7436 vertex7438 reverse
face link face1666 face1667 edges edge6894 edge6896 vertices
vertex6397 vertex6399
face link face1667 face1668 edges edge6896 edge6898 vertices
vertex6399 vertex6401
face link face1668 face1669 edges edge6898 edge6900 vertices
vertex6401 vertex6403
face link face1669 face1670 edges edge6900 edge6902 vertices
vertex6403 vertex6405
face link face1670 face1671 edges edge6902 edge6904 vertices
vertex6405 vertex6407
face link face1671 face209 edges edge6904 edge6906 vertices
vertex6407 vertex6409
face link face209 face1672 edges edge6906 edge6908 vertices
vertex6409 vertex6411
face link face1672 face1673 edges edge6908 edge6910 vertices
vertex6411 vertex6413
face link face1673 face1674 edges edge6910 edge6912 vertices
vertex6413 vertex6415
face link face1674 face1675 edges edge6912 edge6914 vertices
vertex6415 vertex6417
face link face1675 face1676 edges edge6914 edge6916 vertices
vertex6417 vertex6419
97
face link face1676 face1677 edges edge6916 edge6918 vertices
vertex6419 vertex6421
face link face1677 face1678 edges edge6918 edge6920 vertices
vertex6421 vertex6423
face link face1666 face1682 edges edge6894 edge8090 vertices
vertex6397 vertex2251 reverse
face link face1682 face1683 edges edge8090 edge8091 vertices
vertex2251 vertex2253
face link face1683 face1684 edges edge8091 edge8092 vertices
vertex2253 vertex2255
face link face1684 face1685 edges edge8092 edge8093 vertices
vertex2255 vertex2257
face link face1685 face1686 edges edge8093 edge8094 vertices
vertex2257 vertex2259
face link face1686 face1687 edges edge8094 edge8095 vertices
vertex2259 vertex2261
face link face1687 face1688 edges edge8095 edge8096 vertices
vertex2261 vertex2263
face link face1688 face1 edges edge8096 edge8097 vertices
vertex2263 vertex2265
face link face1 face1689 edges edge8097 edge8098 vertices
vertex2265 vertex2267
face link face1689 face1690 edges edge8098 edge8099 vertices
vertex2267 vertex2269
face link face1690 face1691 edges edge8099 edge8100 vertices
vertex2269 vertex2271
face link face1691 face1692 edges edge8100 edge8101 vertices
vertex2271 vertex2273
face link face1692 face1693 edges edge8101 edge8102 vertices
vertex2273 vertex2275
face link face1693 face1694 edges edge8102 edge8103 vertices
vertex2275 vertex2277
face link face1679 face1695 edges edge89 edge2227 vertices
vertex6320 vertex2039 reverse
MESHING BEGINS HERE
BOUNDARY LAYERS BEGINS HERE
BOUNDARY LAYER FOR THE bottom of plenum
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer1 face face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
98
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 edge edge97
edge4748 edge106 edge6946 edge6947 edge107 edge4749
edge4750 edge116 edge6972 edge6973 edge117 edge4751
edge4752 edge126 edge6998 edge6999 edge127 edge4753
edge4754 edge136 edge7024 edge7025 edge137 edge4755
edge4756 edge146 edge7050 edge7051 edge147 edge4757
edge4758 edge156 edge7076 edge7077 edge157 edge4759
edge4760 edge166 edge7102 edge7103 edge167 edge4761
edge4762 edge176 edge7128 edge7129 edge177 edge4763
edge4764 edge186 edge7154 edge7155 edge187 edge4765
edge4766 edge196 edge7180 edge7181 edge197 edge4767
edge4768 edge206 edge7206 edge7207 edge207 edge4769
edge4770 edge216 edge7232 edge7233 edge217 edge4771
edge4772 edge226 edge7258 edge7259 edge227 edge4773
edge4774 edge236 edge7284 edge7285 edge237 edge4775
edge4776 edge246 edge7310 edge7311 edge247 edge4777 add
MESHING THE PLENUM
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer2 face face4 face4 face5 face110
face110 edge edge99 edge8069 edge100 edge8052 edge98 add
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer4 face face1649 face1664 face1664
face1664 face1663 edge edge8052 edge98 edge100 edge8069
edge99 add
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer4 face face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face4 face2 face2 face2 face2 face2 face4
face5 face110 face110 edge edge9 edge3398 edge3399
edge3400 edge3401 edge3402 edge3403 edge3404 edge3406
edge3405 edge3407 edge3408 edge3409 edge3415 edge3410
edge3411 edge3412 edge3413 edge3414 edge3416 edge3417
edge3418 edge3419 edge3420 edge3421 edge3422 edge3423
edge3424 edge3425 edge3426 edge3427 edge3428 edge3429
edge3430 edge3431 edge3432 edge3433 edge3434 edge3435
edge3436 edge3437 edge3438 edge3439 edge3440 edge3441
edge3442 edge3443 edge3444 edge3445 edge3446 edge3447
99
edge3448 edge3449 edge3450 edge3451 edge3457 edge3452
edge3453 edge3454 edge3455 edge3456 edge3458 edge3459
edge3460 edge3461 edge3462 edge3463 edge3464 edge3465
edge3466 edge3467 edge3468 edge3469 edge3475 edge3481
edge3470 edge3471 edge3472 edge3473 edge3474 edge3476
edge3477 edge3478 edge3479 edge3480 edge3487 edge11
edge3482 edge3483 edge3484 edge3485 edge3486 edge8051
edge12 edge10 edge8034 add
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer5 face face1663 face1664 face1664
face1664 face1649 edge edge99 edge8069 edge100 edge98
edge8052 add
BOUNDARY LAYER OF THE HOLES
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer1 face face642 edge edge3534 add
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer7 face face117 face1600 edge edge4824
edge110 add
BONDARY LAYER OF THE CHANNEL
TARGET WALL BOUNDARY LAYER
BBBL
BBL
BBL
BBBL
BBL
BBL
BBBLLLLL
blayer create first $firstch growth $growthch rows $rowsch transition 1 trows 0
uniform
blayer attach b_layer8 face face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
100
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face105 face105 face106
face104 face104 edge edge2048 edge2049 edge2050 edge2051
edge2052 edge2053 edge2054 edge2055 edge2056 edge2057
edge2058 edge2059 edge2060 edge2061 edge2062 edge2063
edge2064 edge2065 edge2066 edge2072 edge2067 edge2068
edge2069 edge2070 edge2071 edge2084 edge2078 edge2073
edge2074 edge2075 edge2076 edge2077 edge2079 edge2080
edge2081 edge2082 edge2083 edge2090 edge2096 edge2085
edge2086 edge2087 edge2088 edge2089 edge2091 edge2092
edge2093 edge2094 edge2095 edge2102 edge2108 edge2097
edge2098 edge2099 edge2100 edge2101 edge2103 edge2104
edge2105 edge2106 edge2107 edge2114 edge2120 edge2109
edge2110 edge2111 edge2112 edge2113 edge2115 edge2116
edge2117 edge2118 edge2119 edge2126 edge2132 edge2121
edge2122 edge2123 edge2124 edge2125 edge2127 edge2128
edge2129 edge2130 edge2131 edge2133 edge2134 edge2136
edge2137 edge1 edge2135 edge8088 edge3 edge4 edge8105
edge2 add
blayer create first $firstch growth $growthch rows $rowsch transition 1 trows 0
uniform
blayer attach b_layer9 face face1681 face1696 face1696
face1696 face1695 edge edge2 edge8105 edge4 edge3
edge8088 add
blayer create first $firstch growth $growthch rows $rowsch transition 1 trows 0
uniform
blayer attach b_layer10 face face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face105 face105
face106 face104 face104 edge edge6743 edge101
edge7336 edge7337 edge102 edge6744 edge6745 edge111
edge7373 edge7374 edge112 edge6746 edge6747 edge121
edge7410 edge7411 edge122 edge6748 edge6749 edge131
edge7447 edge7448 edge132 edge6750 edge6751 edge141
edge7484 edge7485 edge142 edge6752 edge6755 edge6753
edge151 edge6754 edge7521 edge7522 edge152 edge161
101
edge6756 edge6757 edge7558 edge7559 edge162 edge171
edge7595 edge7596 edge172 edge6758 edge6759 edge181
edge7632 edge7633 edge182 edge6760 edge6761 edge191
edge7669 edge7670 edge192 edge6762 edge6763 edge6767
edge6765 edge201 edge7706 edge7707 edge202 edge6764
edge211 edge6766 edge7743 edge7744 edge212 edge6769
edge221 edge6768 edge7780 edge7781 edge222 edge6771
edge231 edge6770 edge7817 edge7818 edge232 edge241
edge7854 edge7855 edge242 edge6772 edge89 edge8070
edge91 edge92 edge8087 edge90 add
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer11 face face4 face5 face2 face5
face110 face2 edge edge8 edge8 edge6 edge7 edge7
edge5 add
blayer create first $firstch growth $growthch rows $rowsch transition 1 trows 0
uniform
blayer attach b_layer12 face face106 face104 face103 face105
edge edge87 edge87 edge85 edge88 add
BOUNDARY LAYERS ENDS HERE
edge picklink edge6948 edge6949
edge mesh edge6949 edge6948 successive ratio1 1 intervals $NumbNodes
edge picklink edge6950
edge mesh edge6950 successive ratio1 1 intervals ($NumbNodes2)
face mesh face1450 map
edge picklink edge6963 edge6947
edge mesh edge6947 edge6963 successive ratio1 1 intervals ($Numbtelnodes+$rows)
face mesh face912 map
edge picklink edge6961 edge6960 edge7889 edge7890
edge mesh edge7890 edge7889 edge6960 edge6961 successive ratio1 1
intervals ($NumbNodes)
edge picklink edge6959 edge7891
edge mesh edge7891 edge6959 successive ratio1 1 intervals ($NumbNodes2)
face mesh face1452 map
face mesh face1600 face117 map
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer12 face face2 face110 face5 face110
face2 face4 face5 face4 edge edge5 edge5 edge7
edge7 edge6 edge6 edge8 edge8 add
Meshing constants
$NumbNodes=5
$Numbtelnodes=6
$PLobnodes=5
$Chobnodes=5
$Plbenodes=($NumbNodes(4)+$rows)
$plsqnodes=($NumbNodes(3))
102
$Pllsnodes=($NumbNodes+$rows)
$Nojetcells=10
edge picklink edge3686 edge3402
edge mesh edge3686 edge3402 successive ratio1 1 intervals ($PLobnodes)
edge picklink edge6744 edge6864
edge mesh edge6864 edge6744 successive ratio1 1 intervals 5
face link face1260 face375 edges edge6923 edge2440 vertices
vertex6397 vertex2251 reverse
face modify face915 side vertex4479 vertex4480
face mesh face915 face918 face911 map size 1
face mesh face1260 face1263 face1256 map size 1
edge picklink edge8068 edge8053
edge mesh edge8068 edge8053 successive ratio1 1 intervals ($Plbenodes)
edge picklink edge8086 edge8071
edge mesh edge8071 edge8086 successive ratio1 1 intervals ($CHbenodes)
edge delete edge8053 edge8068 keepsettings onlymesh
edge mesh edge8053 edge8068 successive ratio1 1 intervals ($Plbenodes)
edge delete edge8090 keepsettings onlymesh
edge picklink edge8090
edge mesh edge8090 successive ratio1 1 intervals ($plsqnodes)
edge delete edge8054 keepsettings onlymesh
edge picklink edge8054
edge mesh edge8054 successive ratio1 1 intervals ($plsqnodes)
face mesh face1647 face1679 face1678 face1646 face1633
face1665 map
edge delete edge98 edge8087 keepsettings onlymesh
edge picklink edge8087 edge98
edge mesh edge98 successive ratio1 1 intervals ($Pllsnodes)
edge mesh edge8087 successive ratio1 1 intervals ($CHlsnodes)
face mesh face1648 face1680 map
COOPERING ALL THE JETS
volume mesh volume3 cooper source face1600 face1452 face117
face1514 face1512 face115 intervals ($Nojetcells)
volume mesh volume5 cooper source face1456 face1602 face124
face1518 face1520 face122 intervals ($Nojetcells)
volume mesh volume7 cooper source face1460 face1604 face131
face1526 face1524 face129 intervals ($Nojetcells)
volume mesh volume9 cooper source face1464 face1606 face138
face1532 face1530 face136 intervals ($Nojetcells)
volume mesh volume11 cooper source face1468 face1608 face145
face1538 face143 face1536 intervals ($Nojetcells)
volume mesh volume13 cooper source face1472 face1610 face152
face1544 face1542 face150 intervals ($Nojetcells)
volume mesh volume15 cooper source face1476 face1612 face159
face1550 face1548 face157 intervals ($Nojetcells)
volume mesh volume17 cooper source face1480 face1614 face166
face1556 face1554 face164 intervals ($Nojetcells)
volume mesh volume19 cooper source face1484 face1616 face173
face1562 face171 face1560 intervals ($Nojetcells)
volume mesh volume21 cooper source face1488 face1618 face180
face1568 face1566 face178 intervals ($Nojetcells)
103
volume mesh volume23 cooper source face1492 face1620 face187
face1574 face1572 face185 intervals ($Nojetcells)
volume mesh volume25 cooper source face1496 face1622 face194
face1578 face1580 face192 intervals ($Nojetcells)
volume mesh volume27 cooper source face1624 face1500 face201
face1586 face1584 face199 intervals ($Nojetcells)
volume mesh volume29 cooper source face1504 face1626 face208
face1592 face1590 face206 intervals ($Nojetcells)
volume mesh volume31 cooper source face1628 face1508 face215
face1596 face1598 face213 intervals ($Nojetcells)
volume mesh volume30 cooper source face1506 face1052 face1594
face1397 intervals ($Nojetcells)
volume mesh volume28 cooper source face1502 face1042 face1588
face1387 intervals ($Nojetcells)
volume mesh volume26 cooper source face1498 face1032 face1582
face1377 intervals ($Nojetcells)
volume mesh volume24 cooper source face1494 face1022 face1576
face1367 intervals ($Nojetcells)
volume mesh volume22 cooper source face1490 face1012 face1570
face1357 intervals ($Nojetcells)
volume mesh volume20 cooper source face1486 face1002 face1564
face1347 intervals ($Nojetcells)
volume mesh volume18 cooper source face1482 face992 face1558
face1337 intervals ($Nojetcells)
volume mesh volume16 cooper source face1478 face982 face1552
face1327 intervals ($Nojetcells)
volume mesh volume14 cooper source face1474 face972 face1546
face1317 intervals ($Nojetcells)
volume mesh volume12 cooper source face1470 face962 face1540
face1307 intervals ($Nojetcells)
volume mesh volume10 cooper source face1466 face952 face1534
face1297 intervals ($Nojetcells)
volume mesh volume8 cooper source face1462 face942 face1528
face1287 intervals ($Nojetcells)
volume mesh volume6 cooper source face1458 face932 face1522
face1277 intervals ($Nojetcells)
volume mesh volume4 cooper source face1454 face922 face1516
face1267 intervals ($Nojetcells)
volume mesh cylinder cooper source face1450 face912 face1510
face1257 intervals ($Nojetcells)
window modify invisible mesh
volume mesh volume34 cooper source face1649 face1650 face1651
face1652 face1653 face1654 face1655 face1664 face1639
face1638 face1637 face1636 face1635 face1634 face1633
face1648 face1610 face1608 face1606 face1604 face1602
face1600 face1472 face962 face1468 face952 face1464
face942 face1460 face932 face1456 face922 face1452
face912 face915 face918 face911 face925 face928
face920 face935 face938 face930 face945 face948
face940 face955 face958 face950 face965 face968
face960 face694 face689 face684 face679 face674
face669 face664 face659 face654 face649 face644
face640 face697 face696 face692 face687 face686
face682 face677 face676 face672 face667 face666
104
face662 face657 face656 face652 face647 face646
face642 face695 face698 face690 face685 face688
face680 face675 face678 face670 face665 face668
face660 face655 face658 face650 face645 face648
face641 face152 face1470 face145 face1466 face138
face1462 face131 face1458 face124 face1454 face117
face1450 face1657 face1658 face1659 face1660 face1661
face1662 face1663 face788 face1656 face1474 face159
face1647 face1646 face1645 face1644 face1643 face1642
face1641 face1640 face1478 face1628 face1626 face1624
face1622 face1620 face1618 face1616 face1614 face1612
face1508 face1052 face1504 face1042 face1500 face1032
face1496 face1022 face1492 face1012 face1488 face1002
face1484 face992 face1480 face982 face1476 face972
face975 face978 face970 face985 face988 face980
face995 face998 face990 face1005 face1008 face1000
face1015 face1018 face1010 face1025 face1028 face1020
face1035 face1038 face1030 face1045 face1048 face1040
face1050 face114 face1058 face774 face769 face764
face759 face754 face749 face744 face739 face734
face729 face724 face719 face714 face709 face704
face699 face777 face776 face772 face767 face766
face762 face757 face756 face752 face747 face746
face742 face737 face736 face732 face727 face726
face722 face717 face716 face712 face707 face706
face702 face779 face784 face787 face775 face778
face770 face765 face768 face760 face755 face758
face750 face745 face748 face740 face735 face738
face730 face725 face728 face720 face715 face718
face710 face705 face708 face700 face782 face786
face785 face6 face780 face1055 face215 face1506
face208 face1502 face201 face1498 face194 face1494
face187 face1490 face180 face1486 face173 face1482
face166 intervals ($Plzdnodes)
volume delete body onlymesh
volume mesh body cooper source face1689 face1690 face1691
face1692 face1693 face1681 face1682 face1683 face1684
face1685 face1686 face1687 face1688 face1696 face1671
face1670 face1669 face1668 face1667 face1666 face1665
face1677 face1676 face1675 face1674 face1673 face1672
face1680 face199 face1584 face1377 face192 face1578
face1367 face185 face1572 face1357 face178 face1566
face1347 face171 face1560 face1337 face164 face1554
face1327 face157 face1548 face1317 face150 face1542
face1307 face143 face1536 face1297 face136 face1530
face1287 face129 face1524 face1277 face122 face1518
face1267 face115 face1512 face1257 face1380 face1383
face1375 face1370 face1373 face1365 face1360 face1363
face1355 face1350 face1353 face1345 face1340 face1343
face1335 face1330 face1333 face1325 face1320 face1323
face1315 face1310 face1313 face1305 face1300 face1303
face1295 face1290 face1293 face1285 face1280 face1283
face1275 face1270 face1273 face1265 face1260 face1263
face1256 face209 face374 face370 face384 face379
face394 face389 face404 face399 face414 face409
105
face424 face419 face434 face429 face444 face439
face454 face449 face464 face459 face474 face469
face484 face479 face494 face489 face377 face376
face372 face387 face386 face382 face397 face396
face392 face407 face406 face402 face417 face416
face412 face427 face426 face422 face437 face436
face432 face447 face446 face442 face457 face456
face452 face467 face466 face462 face477 face476
face472 face487 face486 face482 face497 face496
face492 face375 face378 face371 face385 face388
face380 face395 face398 face390 face405 face408
face400 face415 face418 face410 face425 face428
face420 face435 face438 face430 face445 face448
face440 face455 face458 face450 face465 face468
face460 face475 face478 face470 face485 face488
face480 face495 face498 face490 face1 face1586
face1582 face1580 face1576 face1574 face1570 face1568
face1564 face1562 face1558 face1556 face1552 face1550
face1546 face1544 face1540 face1538 face1534 face1532
face1528 face1526 face1522 face1520 face1516 face1514
face1510 face1403 face518 face1588 face1592 face1594
face1694 face1695 face1598 face1679 face1678 face515
face516 face510 face500 face508 face505 face213
face1596 face1397 face206 face1590 face1387 face517
face514 face512 face502 face506 face507 face509
face499 face504 face1400 face1395 face1385 face1390
face1393 intervals ($Chzdnodes)
BOUNDARY CONDITIONS
physics create Symmetry btype SYMMETRY face face2 face103
face211 face204 face197 face190 face183 face176
face169 face162 face155 face148 face141 face134
face127 face120 face112
physics create Wall btype SYMMETRY face face110 face5 face1649
face1664 face918 face915 face911 face925 face1650
face928 face920 face935 face938 face930 face1652
face1651 face948 face945 face940 face1653 face1654
face958 face955 face950 face1655 face965 face968
face960 face978 face975 face970 face1656 face114
face985 face988 face980 face995 face998 face990
face1657 face1005 face1008 face1000 face1658 face1015
face1018 face1010 face1659 face1028 face1025 face1020
face1035 face1660 face1038 face1030 face1045 face1661
face1048 face1040 face1055 face1662 face1058 face1050
face1663 face4 face1395 face1679 face1403 face1400
face1680 face1385 face1678 face1393 face1390 face1375
face1677 face1383 face1380 face1676 face1365 face1373
face1370 face1675 face1355 face1363 face1360 face1674
face1345 face1353 face1350 face1673 face1335 face1343
face1340 face1672 face1325 face1333 face1330 face209
face1315 face1323 face1320 face1671 face1305 face1313
face1310 face1670 face1295 face1303 face1300 face1669
106
face1285 face1293 face1290 face1668 face1275 face1283
face1280 face1667 face1265 face1273 face1270 face1666
face1256 face1263 face1260 face1665 face214 face91
face207 face85 face200 face79 face193 face73 face186
face67 face179 face61 face172 face55 face165 face49
face158 face43 face151 face37 face144 face31 face137
face25 face130 face19 face123 face13 face116 face8
physics modify Wall btype WALL face face110 face5 face1649
face1664 face918 face915 face911 face925 face1650
face928 face920 face935 face938 face930 face1652
face1651 face948 face945 face940 face1653 face1654
face958 face955 face950 face1655 face965 face968
face960 face978 face975 face970 face1656 face114
face985 face988 face980 face995 face998 face990
face1657 face1005 face1008 face1000 face1658 face1015
face1018 face1010 face1659 face1028 face1025 face1020
face1035 face1660 face1038 face1030 face1045 face1661
face1048 face1040 face1055 face1662 face1058 face1050
face1663 face4 face1395 face1679 face1403 face1400
face1680 face1385 face1678 face1393 face1390 face1375
face1677 face1383 face1380 face1676 face1365 face1373
face1370 face1675 face1355 face1363 face1360 face1674
face1345 face1353 face1350 face1673 face1335 face1343
face1340 face1672 face1325 face1333 face1330 face209
face1315 face1323 face1320 face1671 face1305 face1313
face1310 face1670 face1295 face1303 face1300 face1669
face1285 face1293 face1290 face1668 face1275 face1283
face1280 face1667 face1265 face1273 face1270 face1666
face1256 face1263 face1260 face1665 face214 face91
face207 face85 face200 face79 face193 face73 face186
face67 face179 face61 face172 face55 face165 face49
face158 face43 face151 face37 face144 face31 face137
face25 face130 face19 face123 face13 face116 face8
physics create Heat Fluxes btype WALL face face104 face106
face370 face379 face389 face372 face382 face392
face371 face380 face390 face378 face388 face398
face376 face386 face396 face374 face384 face394
face377 face387 face397 face375 face385 face395
face1681 face1682 face1683 face1684 face1696 face402
face412 face422 face432 face442 face400 face410
face420 face430 face440 face408 face418 face428
face438 face448 face406 face416 face426 face436
face446 face404 face414 face424 face434 face444
face407 face417 face427 face437 face447 face405
face415 face425 face435 face445 face1688 face1685
face1686 face1687 face452 face462 face472 face482
face492 face1693 face450 face460 face470 face480
face490 face1692 face458 face468 face478 face488
face498 face1 face456 face466 face476 face486 face496
face454 face464 face474 face484 face494 face457
face467 face477 face487 face497 face1691 face455
face465 face475 face485 face495 face1689 face1690
face518 face502 face512 face1695 face500 face510
face1694 face508 face506 face516 face504 face514
face507 face517 face515 face505
physics create Mass flow inlet btype SYMMETRY face face640 face649
107
face659 face642 face652 face662 face672 face641
face650 face660 face670 face648 face658 face668
face678 face646 face656 face666 face676 face644
face654 face664 face674 face647 face657 face667
face677 face645 face655 face665 face675 face1633
face1634 face1635 face1636 face1637 face1648 face679
face689 face699 face682 face692 face702 face712
face680 face690 face700 face710 face688 face698
face708 face718 face6 face686 face696 face706 face716
face684 face694 face704 face714 face687 face697
face707 face717 face685 face695 face705 face715
face1640 face1638 face1639 face719 face729 face739
face749 face722 face732 face742 face752 face762
face720 face730 face740 face750 face760 face728
face738 face748 face758 face768 face726 face736
face746 face756 face766 face724 face734 face744
face754 face764 face727 face737 face747 face757
face767 face725 face735 face745 face755 face765
face1645 face1641 face1642 face1643 face1644 face788
face769 face779 face772 face782 face770 face780
face778 face776 face786 face774 face784 face777
face787 face775 face785 face1647 face1646
physics create Outflow btype OUTFLOW face face105
108
REFERENCES
Al-Aqal O M A 2003 ldquoHeat transfer distributions on the walls of a narrow channel
with jet impingement and cross flowrdquo PhD Thesis University of Pittsburgh
Bunker Ronald S 2007 Gas Turbine Heat Transfer Ten Remaining Hot Gas Path
Challengesrdquo Journal of Turbomachinery April Vol 129 pp 193-201
Downs James P Landis Kenneth K 2009 ldquoTurbine Cooling Systems Design- Past
Present and Futurerdquo Proceedings of ASME Turbo Expo 2009 June 8-12 2009
GT2009-59991
Florschuetz LW Berry R A Metzger D E 1980 ldquoPeriodic streamswise variations of
heat transfer coefficients for inline and staggered arrays of circular jets with cross
flow of spent airrdquo ASME J of Heat Transfer 102 p 132-137
Florschuetz L W Truman C R Metzger D E 1981 ldquoStreamwise Flow and Heat
Transfer Distributions for Jet Array Impingement with Cross flowrdquo Journal of
Heat Transfer Vol 103 pp 337
Florschuetz L W Isoda Y 1983 ldquoFlow Distributions and Discharge Coefficient for
Jet Array Impingement With Initial Cross flowrdquo Journal of Engineering for
Power Vol 105 pp 296
Incropera Frank P DeWitt D P 2002 Fundamentals of Heat and Mass Transfer John
Wiley amp Sons Inc New Jersey pp 491-493
Liu Quan Kapat J May 2006 ldquoStudy of Heat Transfer Characteristics of Impinging
Air Jet Using Pressure and Temperature Sensitive Luminescent Paintrdquo UCF
Dissertation
109
Martin H 1977 ldquoImpinging jet flow heat and mass transferrdquo Advances in heat transfer
Vol 13
Ricklick Mark Kapat J December 2009 ldquoCharacterization of an Inline Row
Impingement Channel for Turbine Blade Cooling Applicationsrdquo UCF
Dissertation
Zuckerman N Lior N 2005 ldquoImpingement Heat transfer Correlations and Numerical
Modelingrdquo Journal of Heat Transfer Vol 127 pp 544
vii
LIST OF FIGURES
Figure 1 Brayton Cycle Flow Path and T-s Diagram (Adapted from UPTB Website) 1
Figure 2 Thermal Loading Throughout a Turbine Blade (Daniels 1982) 3
Figure 3 Allowable Turbine Inlet Temperature vs Cooling Techniques over the Years
(Clifford 1985) 4
Figure 4 Turbine Inlet Temperature Increase with the help of TBC New Super Alloys
and Cooling Technologies (Kapat and Kiesow Lectures 2010) 4
Figure 5 Turbine Stator Cooled with Impingement Coupled with Film Cooling
(Florschuetz 1980) 5
Figure 6 Rotor Blade Cooling Configuration (Gladden 1988) 6
Figure 7 Cross-section of Turbine Airfoil with Cooling Channels (Han et al 1984) 6
Figure 8 Relative Temperatures for Hot Gas Metal Temperature and Coolant
Temperature (Cardwell 2005) 7
Figure 9 (a) The Development of the Wall Jet (b) Jet Diffusion to Surroundings (Liu
2006) 8
Figure 10 Simplified Jablonski Diagram (Adapted from ISSI Website) 17
Figure 11 Heater Strips Painted with TSP Too Closely 21
Figure 12 Flow Loop of Impingement Channel 22
Figure 13 Top View of Jet Plate 22
Figure 14 Front View of Impingement Channel 23
Figure 15 Target Wall Test Section with Heater Leads 23
Figure 16 Heat Transfer Coefficient Uncertainty Tree 27
viii
Figure 17 Temperature Profile of First Five Impingement Rows 29
Figure 18 Detailed View of First Heat Transfer Peak with a Polynomial Curve Fit 30
Figure 19 Control Volume Heat Transfer Analysis 30
Figure 20 Heat Loss through Convection and Lateral Conduction 31
Figure 21 Validation Spanwise Averaged Results 32
Figure 22 Target Wall Heat Transfer Coefficient Distributions 34
Figure 23 Span-averaged Target Wall Heat Transfer Distribution 35
Figure 24 Side Wall Heat Transfer Coefficient Distributions 36
Figure 25 Span-averaged Side wall Heat Transfer Distribution 37
Figure 26 XD=15 Target Wall Heat Transfer Profile 41
Figure 27 XD=15 Span-averaged Target Wall Heat Transfer Distribution 42
Figure 28 Target Wall Span-average Comparison of XD=5 and 15 at High Re 43
Figure 29 Side Wall Heat transfer Coefficient Profile 44
Figure 30 XD=15 Side Wall Span-averaged Heat Transfer Coefficients 45
Figure 31 3D Heat Transfer Profile for ZD=6 XD=5 46
Figure 32 3D Heat Transfer Profile for ZD=8 XD=5 47
Figure 33 3D Heat Transfer Profile for ZD=6 XD=15 48
Figure 34 Pressure Drop Ratio with Respect to Smooth Channel 49
Figure 35 Heat Transfer Enhancement 50
Figure 36 Thermal Performance at Constant Pressure Drop 50
Figure 37 Thermal Performance at Constant Pumping Power 51
Figure 38 Horizontal Plane of Impingement Channel Geometry 53
Figure 39 Target Side and Front End Wall y+ Values 54
ix
Figure 40 Finished Mesh with Boundary Conditions 55
Figure 41 Grid Independence Study 57
Figure 42 Residual Plots for the 26M Cell Run 57
Figure 43 Total Pressure Contours 58
Figure 44 Velocity Magnitude Contours 59
Figure 45 Turbulent Kinetic Energy Contours 60
Figure 46 Static Temperature Contours 60
Figure 47 Target and Side Wall Heat Transfer Coefficient Contours 61
Figure 48 Closer View of First few Rows of Impingement HTC Contours 61
Figure 49 Pathlines Generating from the First Row of Jets 62
NOMENCLATURE
Cross Sectional Area
Heater Surface Area (m2)
Specific Heat at Constant Pressure (kJkgK)
D Jet Diameter (m)
Channel Hydraulic Diameter (m)
Friction Factor
Heat Transfer Coefficient (HTC) (Wm2K)
Average Heat Transfer Coefficient (Wm2K)
Channel Length (m)
Mass Flow Rate (kgs)
Static Pressure (kPa)
x
Total Pressure (kPa)
Pr Prandtl Number
Heat Flux (Wm2)
Total Heat Input (W)
Heater Resistance (ohm)
Re Reynolds Number
SW Side Wall
Temperature (K)
TW Target Wall
Voltage Potential
Streamwise Location
y Spanwise Location
z Height from Target Wall
X Streamwise Distance (m)
Y Spanwise Distance (m)
Z Impingement Height (m)
Thermal Performance Parameter
Ratio of Specific Heats
Air Density (kgm3)
Subscripts
C Cold
H Hot
xi
Carnot Describing a Carnot cycle
Exit
Effective
Quantity Lost to the Environment
Reference Value
Wall Value
Base Line Value
1
CHAPTER ONE INTRODUCTION
11 Gas Turbine as a Heat Engine
Gas turbine is a form of heat engine where the hot reservoir is created by the
combustion of fuel and the cold reservoir is the open atmosphere It is well known that
the maximum efficiency of any heat engine is denoted as the Carnot efficiency
A more accurate cycle is used to describe the processes inside a gas turbine ndash the
Brayton Cycle The Brayton cycle as seen in Figure 1 is composed of four processes In
a gas turbine air is drawn in at state 1 it is compressed until it reaches state 2 The
compressed air is mixed with fuel and ignited as it passes through the combustor The hot
air then passes through the turbines where work is extracted The process from state 4 to
state 1 happens throughout the atmosphere therefore the Brayton cycle is an open loop
cycle as the same air is not continuously being fed through the motor
Figure 1 Brayton Cycle Flow Path and T-s Diagram (Adapted from UPTB Website)
The Brayton cycle has an isentropic efficiency similar to the carnot the Brayton
cycle efficiency is defined as
2
It can be seen that increasing the temperature at which air enters the first turbine
stage T3 increases the overall efficiency of the turbine Moreover increasing the
pressure ratio Pr also aids in the increase of the efficiency One of the hurdles of
increasing T3 is the fact that the post combustion gas is a few hundred degrees Celsius
above the melting point of the super alloys used to make the turbine stator vanes and
rotor blades For this reason it is important to cool the hot components of the gas turbine
in order to assure a reasonable life for the machine
12 Cooling of Hot Components
The transition duct that connects the combustor to the first stage turbine as well
as the first stage of the turbine are the parts that are subject to the harshest thermal
loadings and must therefore be cooled aggressively to maintain them in working
conditions for a long period of time Since the first stage guide vanes and rotor extrude
into the flow they are subject to the highest convection coefficients These heat transfer
coefficients can reach up to 4000 Wm2K (Downs 2009) Figure 2 shows the different
magnitudes of convection coefficient around the blade High heat transfer coefficients
occur where the air stagnates into the leading edge of the airfoil This high heat transfer
region is not only caused by the lack of a thermal boundary layer to protect the airfoil but
also because the effective heat transfer driving temperature is the recovery temperature
At the high Mach numbers that occur in turbines the ratio of total to static temperatures
is significant causing the leading edge to have the highest effective heat load Another
3
peak occurs on the suction side of the blade as the boundary layer created by the airfoil
switches from being a laminar boundary layer into a turbulent one Due to the nozzling
effect of the turbine rotor and stators the flow gathers speed toward the trailing edge of
the airfoil leading to higher convection coefficients on the pressure side of the airfoil
Figure 2 Thermal Loading Throughout a Turbine Blade (Daniels 1982)
Simple convection channels were implemented in the early nineteen sixties as
years passed the cooling techniques became more and more sophisticated allowing the
free stream temperature to increase to previously impossible levels Currently the use of
film cooling coupled with backside impingement leads the turbine cooling technology
The trend of allowable turbine inlet temperature is shown in Figure 3 from this figure it
can be seen that the allowable free stream temperature has increased around 600 degrees
in the past 50 years The addition of thermal barrier coatings also helps in the increase in
allowable combustion temperatures by creating an extra resistance that the heat needs to
move through as it moves from the combustion gasses into the coolant air It is impotatnt
to notice that as seen in Figure 4 the increase in turbine inlet temperatures is done with
the combined benefits of new alloys TBC and cooling technologies
4
Figure 3 Allowable Turbine Inlet Temperature vs Cooling Techniques over the Years (Clifford 1985)
Figure 4 Turbine Inlet Temperature Increase with the help of TBC New Super Alloys and Cooling
Technologies (Kapat and Kiesow Lectures 2010)
The cooling of inlet guide vanes can be done with the use of impingement inserts
inside the airfoils As air passes through the miniscule holes in the inserts a jet is formed
which then impinges on the wall of the airfoil producing one of the largest single phase
heat transfer coefficients This already impinged coolant air is then bled out as film
5
cooling as well as bled out through the trailing edge Figure 5 shows a stator vane with
the impingement insert in black the film cooling extraction as well as the trailing edge
bleed
Figure 5 Turbine Stator Cooled with Impingement Coupled with Film Cooling (Florschuetz 1980)
The cooling of turbine airfoils with the use of an impingement insert is only
possible in stationary components as the rotating ones are subject to centrifugal loadings
making it unfeasible to cool them with this setup Rotor blades are typically cooled with
serpentine passages that have heat transfer enhancing features such as ribs dimples and
other turbulators these serpentine passages are located in the mid chord of the blade On
the trailing edge a bank of pins are used to obtain high convective coefficients in the thin
region the coolant is the bled out to compensate for the boundary layer created around
the airfoil Rows of impingement holes cool the leading edge The spent air is then bled
out through showerhead cooling Figure 6 and Figure 7 show in detail the cooling
channels around two similar airfoils airfoils
6
Figure 6 Rotor Blade Cooling Configuration (Gladden 1988)
Figure 7 Cross-section of Turbine Airfoil with Cooling Channels (Han et al 1984)
7
The coolant air is bled out from the later stages of the compressor This air is
expensive as it has been compressed and not under gown the heat addition by
combustion It is imperative that the minimum amount of coolant is used in these cooling
configurations The cooling must also be as uniform as possible to reduce thermal
stresses within the blades leading to a higher component life Figure 8 shows freestream
metal and coolant temperatures of the flow blade and coolant air It can be seen that a
decrease of 25degrees in the surface temperature of the blade can provide an airfoil with
twice the working life Impingement cooling has great potential to provide high heat
transfer coefficients at a small flow rate Impingement of a jet onto a surface provides
high heat transfer coefficients due to a starting boundary layer as well as its high
turbulence When the jet is located around 3 diameters from the target surface the heat
transfer profile has two peaks one located at the stagnation region and the other located
between one and 3 diameters from the stagnation region As the jet is moved away from
the target wall the secondary peak diminishes leaving a profile with a maximum at the
stagnation region decreasing radialy
Figure 8 Relative Temperatures for Hot Gas Metal Temperature and Coolant Temperature (Cardwell 2005)
Cardwell N D 2005
8
Figure 9 shows a diagram of a jet impinging on a target surface The potential
core is the part of the jet that has not been affected by the surrounding stagnant fluid As
the jet moves towards the target wall its momentum diffuses into the surrounding fluid
decreasing the velocity at which it reaches the target wall and potentially decreasing the
corresponding heat transfer coefficient Studies have shown (Martin 1973 for example)
that the potential core may last anywhere between 7 to 10 diameters The successful
impingement of the potential core yields significantly higher heat transfer coefficients
than a fully diffused jet this comes however at a cost of higher pressure drop across the
jet plate as well as a highly non uniform heat transfer profile
Figure 9 (a) The Development of the Wall Jet (b) Jet Diffusion to Surroundings (Liu 2006)
9
CHAPTER TWO LITERATURE REVIEW
21 Impingement Literature Cornerstone
From the early days of simple convective cooling channels in turbine airfoils
studies have been done on modes of enhancing heat transfer coefficients while
maintaining a low pressure drop and minimum mass flow rate Heat transfer
characteristics of single round nozzle impingement were studied in the late 1960rsquos and
early 1970rsquos The collected works of many authors is combined into ldquoHeat and Mass
Transfer between Impinging Gas Jets and Solid Surfacesrdquo by Holger Martin 1977 The
paper collects works from multiple authors who studied single round nozzle impingement
effects on heat and mass transfer coefficients In this compilation non dimensional jet to
target spacing was studied they ranged from ZD=12-10 providing plots of Sherwood
number as a function of radius for four different jet to target spacings The local
Sherwood number was also given for a slot jet for HS ranging from 5 to 20 Studies on
impingement jet arrays were also gathered alongside an array of slot jets Correlations
were given for multiple setups present in the paper Circular jet arrays and slot arrays are
studied in detail with both analytical and experimental approaches The paper also
combines studies done on swirling jets turbulence enhancers on the target surface
impingement on concave surfaces and angle of attack variations Optimization studies
were also done to find the optimal spacing for round and slot jet arrays
Florschuetz studied the heat transfer characteristics of an array of jets impinging
on a flat surface This study was guided towards finding an optimal spacing for an array
for jets used to cool the midchord of turbine airfoils similar to that found in Figure 5 His
main contributions include a Nusselt number correlation as a function of jet to target
10
spacing jet Reynolds number and other flow and geometric parameters He found that an
increase in hole spacing and channel height resulted in a decrease of heat transfer He
also provided a one dimensional jet mass flux and channel mass flux correlations
His Nusselt number correlation takes the form of
Where A B and n are dependent by the two different types of arrays inline or staggered
Liu studied new techniques in temperature and pressure measurements of a single
slot jet with the use of temperature sensitive paint or TSP and pressure sensitive paint or
PSP In his work both measurement techniques are explained in detail Since TSP is the
only tool from that study currently used in this work it will be explained further in the
experimental setup section
11
22 Relevant Impingement Channel Studies
Al-Aqal 2003 studied three different types of impingement channels The use of
TLC was implemented in this work to obtain heat transfer distributions for the target
wall The three different configurations varied the number of holes in the streamwise and
spanwise directions The first channel had a single row of 6 streamwise jets the second
consisted of 2 rows of 12 streamwise holes summing up to a total of 24 holes The last
channel is a triple spanwise row with 18 streamwise jets This last geometry is the most
similar to the one present in the current study The third geometry will be used to
compare results There are differences however the total width of the channel is of 16
diameters as opposed to 8 in this study The streamwise jet spacing is also different Al-
Aqal used an XD of 65 compared to XD = 5 in this study The jet to target plate
spacings are similar on two occasions as he studied a ZD=4 6 and 8 while this work
uses a ZD = 6 8 and 10 Average jet Reynolds numbers also fall within the range of this
study as they range between 5000 and 33000 The author provides span averaged plots
for all cases and Reynolds numbers convenient when comparing the results
Ricklick 2009 studied a channel similar to the one found in this study His
channel was composed of a single row of 15 jets with a YcD = 4 XD = 5 and 15 and
ZD = 1 3 and 5 Two channels were tested one was pressure fed while the other was fed
by suction TSP was used to gather temperature data of all four wetted surfaces on the
pressure channel and two surfaces on the suction channel Since the maximum jet Mach
number was less than 03 the flow was assumed to be incompressible leading to the
conclusion that both channels contain identical flow patterns Thin foil heaters were used
to create the required heat flux for the channel Besides channel geometry Reynolds
12
numbers and heater geometry Ricklicksrsquo experimental setup is identical to the one
presented in this work The author also provided an ample comparison of his results to
literature He provided thermal performances of the entire channel at different Reynolds
numbers and channel heights
A small CFD study was also done A paved mesh was created on the target wall
with finer mesh near the impingement locations The resulting y+ at the wall was higher
than one yielding potentially faulty heat transfer values however this is acceptable since
the CFD was used as a tool to better understand the flow physics and help understand the
experimental heat transfer profiles
23 Computational Studies on Impingement Channels
El-Gabry did a numerical study of jet impingement with cross flow Two different
turbulence models were compared in their ability to predict surface Nusselt number The
Yang-Shih and standard k-ε models were used to compute the flow generated by jets
angled at 30 60 and 90 degrees with cross flow The computational results were
compared to previous experimental work by El-Gabry Comparisons to experimental
results at ZD = 1 and 2 90deg injection angle between Yang-Shih and standard k-ε The
error in the average Nu from the experimental results and both turbulence models were
calculated It was found that the Yang-Shih model behaved well at low Reynolds
numbers with the average Nusselt number being 5 off from the experimental value
while the standard k-ε was off my 94 As jet Reynolds number was increased the error
of the standard k-ε model dropped to as low as 39 while the error from the Yang-shih
model increased to -76 The span average plots show the experimental data Nusselt
number alongside the span averages of the results acquired by the Yang-Shih and
13
standard k-ε models High Nusselt numbers occur at the impingement location decreasing
thereafter after another impingement location is found The frequencies of these
variations are all the same for the experimental and the two numerical solutions The
amplitude of fluctuations between the impingement locations and the areas in between
are much larger for both of the numerical results however the Yang-Shih model over
predicts at the high Reynolds number for the ZD=2 case Since the amplitude of
fluctuations is greater for the CFD solutions it is important to note that even though the
error in average Nusselt number is not great the actual differences in the profile are much
greater upwards of 20 difference of heat transfer coefficients between the experimental
and numerical heat transfer peaks Other variations were studied (Injection angles for
example) but will not be discussed as their importance to the current study is minimal
Zuckerman compared a much wider set of turbulence models in their ability to
successfully predict Nusselt numbers caused by jet impingement The models tested were
k ndash ε k-ω Reynolds Stress Model algebraic stress models shear stress transport and
lastly the υ2f turbulence model DNS runs are extremely time consuming to run
therefore LES was run on its behalf to provide results for the unsteady turbulence
models The paper summarizes all the different models used their computational cost
impingement heat transfer coefficient and their ability to predict the second peak in heat
transfer As expected DNSLES provide the best prediction of both stagnation and
secondary peak heat transfer coefficient however this comes at a large computational
cost The k ndash ε and k-ω provide poor heat transfer results for the stagnation region where
they can have 30 error from the correct value The Realizable k ndash ε model provides
14
better heat transfer results while still maintaining a low computational cost The highest
accuracy to cost ratio was achieved by the υ2f model where it predicts the heat transfer
coefficient for the surface with a minimum of 2 error while not being as expensive as
the other unsteady models such as DNS and LES Ideally the CFD portion of this work
would be run with the υ2f model however since the code used to run the simulation
FLUENT does not have the υ2f model a realizable k ndash ε model will be used with
enhanced wall functions for both thermal and velocity gradients
15
CHAPTER THREE EXPERIMENTAL SETUP AND TECHNIQUES
31 Temperature Measurements with TSP
Temperature sensitive paint or TSP provides the capability of measuring
temperatures over the painted area This measurement technique supersedes the
advantages of other temperature measurement devices such as thermocouples because it
provides the user with data over a large area rather than point temperatures given by
thermocouples
Uni-Coat TSP is purchased from ISSI It is very robust to different working
conditions Calibration done on one batch of paint can be used for multiple cans as the
product is highly consistent The paint is calibrated in a dark booth a painted coupon is
placed on the hot side of a thermoelectric heat pump working on the Peltier effect
thermal paste is used to minimize contact resistance between the hot side and the TSP
coupon Calibrated thermocouples are placed in between the TSP and the thermoelectric
heat pump A reference temperature and picture are taken and the calibration commences
At least 5 or 6 data points should be taken to form the calibration Intensity ratios are
taken between the hot and cold pictures They are then plotted versus their corresponding
temperature
The paint consists of fluorescent molecules suspended in a binder These
molecules with a certain wavelength of light will be exited to a higher energy level The
molecules then can dissipate some of the energy by transferring it vibrationally to its
neighboring binder particles and dissipate the remainder of the energy by radiating it as a
photon as the molecule comes down to its original ground state Since the amount of
16
energy that the particle can transmit to others through vibration is directly proportional on
temperature and the total initial energy is fixed by measuring the ratio of the intensity at
a known temperature (reference picture) and intensity of the unknown temperature
feeding it through the correlation the unknown temperature can be found to an
uncertainty of 1 K Figure 10 shows a simplified Jablonski diagram adapted from the
suppliers website The blue arrows signify the blue light used to excite the luminescent
molecule Tris(22rsquo-bipyridyl) Ruthenium(II) Chloride Hexahydrate with a shellac binder
in our case The shellac binder is impermeable to oxygen opposite of that found in PSP
due to PSP relying on the presence of oxygen for it to function Once the particle is
excited it can give off the energy in two different ways one is by emitting it back out as
another photon of the same energy and therefore wavelength The second mode of the
particle to lose its energy is through vibrational relaxation This second process is directly
dependent on the temperature ie the higher the temperature the higher the probability
for it to lose energy to its surroundings Once it loses some energy to the surrounding
particles it releases the remainder of the energy as a photon of less energy of that which
excited it originally hence why a long pass filter is installed in the CCD camera For a
more descriptive explanation of the way TSP works refer to Liu 2006
17
Figure 10 Simplified Jablonski Diagram (Adapted from ISSI Website)
Throughout the past two years there have been numerous projects at CATER that
have used TSP Painting surfaces with TSP should be done carefully by someone who
has experience with spray painting since every single can costs $500 A single can should
be able to paint an area the size of an acrylic plate that is 36rdquo wide and 24rdquotallThe
sidewalls and the target wall of the impingement channel were painted with the use of
less than one can Painting on different surfaces is difficult for example when painting
Rohacell the paint canister can be held very close to the surface while spraying due to
the surface being somewhat porous and rough however when painting straight onto
metal heater strips the can should be placed as far back as possible for the first run
Ideally for the first pass through only a slight mist should be applied If the can is being
held too close to the surface the paint will run Figure 11 shows a set of heater strips that
has been painted too closely leading the paint to drip down Ideally the paint would be
applied to the surface in as many coats as possible Of course this would be time
18
demanding and impractical therefore with the knowledge that I have gained through the
multiple TSP paintings on different surfaces I have compiled a list of TSP dos and
donrsquots
Dos
Clean the surface to be painted with acetone or break parts cleaner Break
parts cleaner is preferable over acetone as it does not leave an oily residual
after cleaning
Paint the first coat as thin as possible Most of the surface should not be
covered There should be an even mist of miniscule TSP circles This will
give the later coats something to attach to
When positioning the test section to paint make sure to wipe it one last
time as small dust particles may have attached to the surface
Stop if you see small bumps in the paint This is caused by dust particles
collecting all the paint around it while it is still wet due to surface tension
Clean the surface and repaint This should be noticeable in the first few
coats If you see this pattern happening do not continue thinking it will be
covered by future coats What will happen is the problem will get worse
and worse ultimately the surface will have to be cleaned again and
repainted
When painting test sections try to paint the smallest section as possible
This will not only save paint but will make it very simple for the post
processing code to crop out the unpainted areas
19
Let the finished painted surface to sit at least for 90 minutes after the last
coat before baking There have been problems when baking steel and
acrylic test sections with the paint cracking while baking right after the
last coat Normally the finished surface is left to dry overnight and baked
first thing in the morning
For test sections that are too large to be baked in the oven the heat gun
may be used Carefully place a thermocouple in a central location with
blue painters tape The heating should be uniform and should not take
more than 20 minutes of continuous blowing When the thermocouple
reaches 80-90 C the plate can be assumed to be baked To introduce a
factor of safety in the baking it does not hurt to bake it longer than it
normally takes
Once the test section is mounted and ready to run cover it with cloth that
does not let any light through This will protect the paint for further uses
This is especially important on test sections that can be used multiple
times like the ones found in this study
When the test is running turn off the LED lights This light is the most
damaging to the TSP as it degrades the quality of the fluorescent
molecules
If there is a particular head of the TSP can that you prefer over others you
can remove it once the can is empty It is difficult to get used to a single
kind of nozzle being able to transfer it from can to can is a must if
painting consistency is to be kept
20
Donrsquots
Do not clean a test section that has already been used with too much
acetone The acetone is volatile evaporating quickly cooling the test
section rapidly If this test section has had heaters attached to it and run
previously the acrylic will crack due to uneven stresses inside of it
If paint is dripping stop painting immediately Clean the surface and start
over Hold the can far from the surface in order for it not to drip
Do not use TSP to teach new apprentices undergrads or graduate students
how to paint Regular spray paint is two orders of magnitude lower in cost
while the painting process is exactly the same
Do not paint with the doors closed The paint contains carcinogens that
can harm the lungs Always use a respirator and keep the room well
ventilated In-situ painting and baking has not been tried however it may
be a real option if the test section is difficult to disassemble and easily
accessible to painting and baking
If there is a can of paint that contains too little paint for the test section
that needs to be painted try to find a new can The mixing of two different
cans of TSP can be dangerous at times however it has been noticed over
the years that ISSI provides a very robust and dependable product that
does not vary significantly from batch to batch
21
Figure 11 Heater Strips Painted with TSP Too Closely
32 Experimental Setup of Suction Channel
The impingement channel is fed under suction As seen in Figure 12 air enters
through the plenum it crosses the jet plate as it gains speed to form the jets
which then impinge on the target wall The flow then passes through a venturi
flow meter and finally through the blower into the atmosphere A bypass valve is
used to control the flow rate of the impingement channel
22
Figure 12 Flow Loop of Impingement Channel
The impingement channel consists of 15 streamwise rows of 3 spanwise jets each The
total width of the channel YcD is of 8 diameters while the streamwise spacing between
the rows is XD=5 the spanwise distance between the holes is of YD=2 Figure 13shows
the top view of the jet plate The plate is counter bored to ensure that a nearly flat
velocity profile of the jet is achieved Figure 14 shows the front view of the channel Z is
denoted as the distance between the jet and target plates Side walls are interchangeable
to change the height of the channel to 6 8 and 10 diameters Two thirds of the
streamwise rows can be covered to change the XD from 5 to 15
Figure 13 Top View of Jet Plate
23
Figure 14 Front View of Impingement Channel
The target and sidewalls had heaters made specifically for them in a serpentine
style This was necessary to increase the resistance as the VARIACs used to power them
only had a maximum current output of 20 amps The heater strips are two diameters
wide at each end copper tape with conductive adhesive was used to connect the leads to
the power supply The heater consists of 50 micron thick steel sheet sandwiched between
two pieces of Kapton tape The heater is attached to the painted surface with the use of
double sided Kapton tape The target test section can be seen in Figure 15 also seen in
this figure are the two Teflon gaskets lined on the sides of the target plate With the target
wall bolted onto the sidewall the gasket is compressed generating a strong seal
Figure 15 Target Wall Test Section with Heater Leads
24
For this study the test matrix shown in Table 1 will be run Target and side wall
data will be taken at three different impingement heights at two different Reynolds
numbers of 7500 and 15000 denoted by A and B respectively A streamwise jet spacing
study is also done by testing the target and side wall heat transfer at an XD=15 for the
low impingement height channel
Table 1 Test Matrix
XD ZD Wall Re
5
10 TW
7500
15000
SW 7500
15000
8 TW
7500
15000
SW 7500
15000
6 TW
7500
15000
SW 7500
15000
15 6 TW
7500
15000
SW 7500
15000
33 Data Processing and Reduction
As described previously when taking temperature measurements with the use of TSP
reference temperatures are noted and a reference picture is taken The experiment is the
run once the experiment reaches steady state a new set of 4 pictures is taken Given the
calibration curve temperatures are backed out
25
Given the amount of heat generated inside the heater
Dividing by the heated area to get heat flux
Heat loss tests were run to consider how much of the heat flux generated by the heaters
goes through the backside instead of into the flow It was found that 25 of the heat flux
leaks out to the atmosphere through the acrylic In order to account for this heat leakage
it must be subtracted from the calculated value to become
Where Ah is the effective heated area given by
Where Aunheated is an estimate of how much unheated area is between the heater strips (~
3 of the total area)
To obtain heat transfer coefficient
Where Tref is the reference temperature Typically set in literature to be the jet
temperature
To obtain the average Reynolds number for the jets the total mass flow rate is used
Where Dj is the jet diameter and μ is dynamic viscosity (1983kgm s at 300K)
26
Pressure measurements were taken at the sidewall after the last jet entered the channel
These pressure measurements were used to determine the thermal performance of the
tallest two channels (ZD = 8 and 10)
The thermal performance at constant pumping power is found by using the equation
Where h is the average heat transfer coefficient for the target wall of them impingement
channel and ho is the heat transfer coefficient obtained by passing the same amount of
flow through a smooth duct ie the Dittus-Boelter correlation The friction factor f is
found with the use of
Where Ppl is the plenum static pressure assumed to be atmospheric and Plast jet is
the pressure read after the last jet V is the volumetric flow rate divided by the cross-
sectional area of the duct after the last impingement row The hydraulic diameter of the
channel is set to be
The baseline friction factor was calculated with the use of the Moody chart the hydraulic
diameter and the total mass flow rate though the channel Thermal performance at
constant pressure drop was also calculated with
27
34 Uncertainty Analysis
A simple uncertainty analysis was done to estimate the error in calculation of the
heat transfer coefficient from the given outputs of the test data From the bare basic
measurements for voltage area current temperature of thermocouples and temperature
profiles of paint a simple uncertainty analysis can be done to estimate the error for the
calculated heat transfer coefficient Figure 16 shows the different sources of error in the
calculation of heat transfer coefficient The effective uncertainty was calculated by taking
the root of the sum of the squares of all the individual percentage errors The
experimental uncertainty for heat transfer coefficient was of 703 This error may be
reduced by acquiring higher temperatures of the TSP reading current with a more
accurate ammeter or reading reference temperatures with the use of a thermopile instead
of a single thermocouple
Figure 16 Heat Transfer Coefficient Uncertainty Tree
28
35 Lateral Conduction Analysis
To take into account the lateral conduction occurring inside the heater foil while
the test is running two simple 1D conduction and convection equations were used to
quantify the amount of heat moving through the heater laterally and the amount of heat
convecting into the air The lateral conduction is expected to be at a maximum at the
places where there are large spatial variations of surface temperature which is why the
ZD = 6 XD = 5 case at high Re is chosen to be studied Figure 17 shows the
temperature distribution of the aforementioned case Four cold spots can be seen by their
distinct blue and yellow color located at the stagnation regions The maximum
temperature gradient occurs between the third jet impingement and the middle region
between jets The temperature difference was seen to be of 13degC The distance in between
these two temperatures is of 25D=01875m The corresponding heat flux between these
two points was calculated to be 13000Wm2 with ksteel~20Wm K A region of 1cm by
1cm was then created and the amount of heat calculated through conduction and
convection were compared To acquire the amount of heat removed through conduction
a heat flux of 13000Wm2 was imposed through an area of 01m by 00005m this
equaled to 00277 W The amount of heat moved through convection was calculated by
multiplying the heat flux used during the test by the area of the square 0001m2 the
resulting heat moving through the heater onto the air is 6 W Since the heat moving
through to the air is two orders of magnitudes larger than the heat moving laterally the
effective lateral conduction can be neglected
29
Figure 17 Temperature Profile of First Five Impingement Rows
A second order approach was also taken to quantify the amount of lateral
conduction in the heater The temperature gradient was taken from high peaks in heat
transfer caused by the second row of impingement of the same ZD=6 XD=5 channel at
high Re Figure 18 shows the high heat transfer coefficients created by the second row of
jets A quadratic curve fit was obtained by for this small region so that a continuous
equation of heat transfer coefficients as a function of streamwise distance was quantified
30
Figure 18 Detailed View of First Heat Transfer Peak with a Polynomial Curve Fit
The net heat gained by a differential volume from lateral conduction is the
difference in the temperature gradient at the entrance and the exit multiplied by the
thermal conductivity and cross sectional area Using this method shown in Figure 19 the
net change in convective heat transfer due to lateral conduction can be studied
Figure 19 Control Volume Heat Transfer Analysis
By taking the difference between the out flowing heat trough the right side and
the inflowing heat from the left side a net gain or loss can be found Figure 20 shows the
y = -470630x2 + 31244x - 14842Rsup2 = 09934
300
310
320
330
340
350
360
370
380
0 001 002 003 004 005
HTC
(W
m2K
)
x (m)
Heat Transfer Peak
Poly (Heat Transfer Peak)
31
difference in magnitude between the out flowing heat through convection seen in red and
the net inflow of heat from lateral conduction in blue From these calculations it was also
found that the amount of heat moving through lateral conduction is tow orders of
magnitude smaller than the amount of heat moving out through convection leading to the
belief that even at high temperature gradients lateral conduction does not play an
important role in the ongoing heat transfer processes in the impingement channel A more
detailed calculation of this work can be seen in appendix A
Figure 20 Heat Loss through Convection and Lateral Conduction
002 003 004 0051 10
5
1 104
1 103
001
qconv x( )
qnet x( )
x x
32
CHAPTER FOUR HEAT TRANSFER RESULTS
41 Heat Transfer Validation
In order to obtain confidence in our experimental setup an experiment was made
to test something that has already been published in literature A smooth channel was the
obvious choice as it was easy to setup by taking off the end cap and blocking all the holes
with smooth blue painters tape on the flow side and metal tape on the plenum side to
ensure no leaks into the channel from the jet plate The smooth channel has been studied
widely and multiple correlations exist one of these equations is the Dittus-Boelter
correlation (Incropera 2007) The test was run using the ZD=6 side wall so that the
hydraulic diameter was a minimum Figure 21 shows the span averaged results versus
non dimensional distance into the channel
Figure 21 Validation Spanwise Averaged Results
0
10
20
30
40
50
60
0 1 2 3 4 5 6 7 8 9
HTC
(W
m2K
)
XDc
Span Avg
Dittus Boelter
33
The plot shows decreasing heat transfer coefficient with increasing XDc due to
the developing thermal boundary layer The span average does not reach the Dittus-
Boelter due to it not being fully developed in the limited space it is given Typical flows
can take up to 60 diameters to achieve a fully developed profile with the current setup
the maximum length of the channel was of 9 diameters The profile however seems to
have an asymptote at the Dittus-Boelter correlation value leading to the belief that if the
channel was longer that value given by the correlation would be reached One important
factor to take into account in determining whether the experimental setup is validated is
the fact that the Dittus-Boelter correlation has an uncertainty near 30 Since the span
average at high XDc is well within 30 from the calculated value it is safe to assume
that the current experimental setup is validated
42 Heat Transfer Results
Heat transfer results are compared based on variations in channel height and
average jet Reynolds number As discussed earlier there are numerous other parameters
also affecting the heat transfer in these channels As these parameters are changed flow
structures within the channel are expected to be altered as well as discussed in the
literature Two of the major contributors to heat transfer in these channels are the
successful jet impingement and the resulting cross flow The same domain is captured in
both the local and averaged results
Figure 22 through Figure 25 highlights the heat transfer distribution for the cases
with a jet to jet spacing of 5 diameters in the streamwise direction and of 2 in the
spanwise direction It is evident that the smallest channel height (ZD=6) performs the
best at all Reynolds numbers on all surfaces It is also interesting to note the similarity
34
in the target wall profiles between case 528A and B where the curves are very similar
other than the obvious offset due to the change of the Reynolds number At this large
spacing we also see the degradation of the jets a few diameters downstream of each
impingement location The downstream shifts of the peaks are evident after the second
and third row of jets Also evident in these plots is the deflection of the impinging jet and
the wall jets from the cross flow The cross flow is forced to flow around the jet
deflecting the spread of the wall jet in the downstream direction Impingement locations
are also very evident at low XD however as XD and therefore the cross flow increase
the magnitude of the peaks start decreasing and eventually level out to pure internal flow
Figure 22 Target Wall Heat Transfer Coefficient Distributions
35
Figure 23 Span-averaged Target Wall Heat Transfer Distribution
36
Figure 24 Side Wall Heat Transfer Coefficient Distributions
37
Figure 25 Span-averaged Side wall Heat Transfer Distribution
Figure 23 and Figure 25 show similar details with impingement peaks clearly
diminishing and shifting in the downstream direction The cross flow clearly has some
negative influence on these geometries when compared to the more traditional
impingement highest on the order of 1 to 5 jet diameters The heat transfer profiles of the
target wall for all heights seen in Figure 22 and Figure 24 show the rapid decay in heat
transfer after the third jet This can be explained by understanding that the first jet does
not have any cross flow to deflect it the second jet only has the first jet worth of
momentum deflecting it downstream however since the channel is so tall the
momentum of the cross flow after the first and second jet are not enough to greatly
disturb the incoming jets After the third jet however the cross flow builds up enough
momentum to greatly affect the integrity of the jets downstream causing the span-
0
20
40
60
80
100
120
140
160
2 12 22 32 42 52 62 72
HTC
(W
m2K
)
XD
5210B_SW 528A_SW Jet Location
526A_TW 526B_TW
38
averaged heat transfer to rapidly drop The point at which the crossflow starts taking a
considerable effect occurs around XD =35 The target wall profile of the ZD=10
channel shows the outside jets on the second row of jet deflecting downstream It can be
conjectured that the bending of the outside jets downstream is caused by the wall jet
created by the first row of jets separating from the side wall and deflecting the outside
jets of the following rows of jets The heat transfer profile for the ZD case excludes the
first jet due to shadows being present when the data was taken
Also evident from this spanwise averaged data is the increase in heat transfer
with increases in Reynolds numbers and decreases in impingement height Results tend
to be the closest from case to case at the first impingement jet This is a reasonable
result as the effects of cross flow have little to no effect at the first few impingement
locations The impact of the jet would then be the driving force at these locations and
would be similar between cases except if the potential core is not reaching the target
surface The potential core of a jet tends to last between 6 and 10 diameters from its
origin It can be seen that the difference in heat transfer coefficient in the first two jets for
the ZD=8 and ZD=10 channel is much different than the corresponding difference
between the ZD=6 and ZD=8 heights This decreased difference between the heights of
the peaks may be attributed to the potential core reaching the target wall at the heights of
6 and 8 diameters leading to similar profiles and may not be reaching the surface at the
height of 10 diameters The heat transfer values of the peaks diminish in the downstream
direction The range of fluctuation also drops that is the profile becomes more uniform
at large XD This drop in fluctuation is more visible at the tallest channel height
(ZD=10) and less pronounced at the smallest channel This is due to the jet in the small
39
channel having to travel a shorter distance to impinge on the target plate leaving the
crossflow less time for it to deflect the jet as opposed to the tall channel where the jet has
to travel almost twice the distance as the ZD=6 channel for it to impinge on the target
wall This effect cannot be solely explained by the built up cross flow in the channel
Mixing loses also take part in the degradation of the stagnation size of the downstream
jets The mixing losses have much greater effect on the taller channels due to the same
reason that the cross flow has a higher impact on them too the jets have to travel a large
distance before hitting the target plate leading the stagnant or moving surrounding air to
be a sink of its downward momentum for a longer time and distance than the respective
smaller channels The heat transfer coefficient of the side wall was also analyzed
Similar effects are expected on the side wall due to the expected impact of the wall jet
As expected the strength of the cross flow is not enough to prevent wall jets from
successfully impacting the side wall at small XD jet locations however the crossflow
takes dominance at around XD=25 Also evident in these plots is the concentration of the
wall jet impact to the bottom of the channel on the order of 1-2 diameters in height It is
interesting to note that for the 5210B case in Figure 24 as the first jet diffuses outward
it impacts the sidewall at a height of ZD=6 The height at which the diffused jet affects
the sidewall heat transfer coefficient decreases as the crossflow increases The stagnation
regions are also deflected in the downstream direction similar to the target surface
results These effects are most evident in the 5210B Similar characteristics can be
explained from the spanwise-averaged plots shown in Figure 25 These results again
clearly show the effects of increasing the impingement height and increases in Reynolds
number As the height is increased the effect of the wall jet is significantly reduced
40
partially due to the increased surface area much of which is not affected by the wall jet
The diminishing effect of the cross flow accumulation is also evident in these plots as the
heat transfer peaks decrease in the downstream direction
43 XD Comparisons
The streamwise jet spacing was changed from XD=5 to 15 by covering two out
of three rows of jets This was done by covering the impingement holes inside the
channel with smooth blue painters tape and sealing the plenum side of the jet plate with
metal tape to ensure no leakage The profile is expected to be less uniform than the case
where XD=5 due to the large spreading of the high heat transfer peaks Due to the large
separation between the rows of jets there is a lower amount of downward momentum
than the equivalent XD=5 geometry for this reason it is expected to see a lower heat
transfer peak due to the jets momentum diffusing out faster to the stagnant air decreasing
the effective impingement velocity Figure 26 shows the target wall heat transfer
distribution Similar to the XD=5 profile it can be seen that the heat transfer due to the
jet impingement drastically reduces after the third jet This phenomenon leads us to
believe that at both Reynolds numbers the cross flow generated by the first three jets is
powerful enough to effectively deflect the fourth jet downstream diminishing its heat
transfer performance The similarity seen in Figure 26 between high and low Reynolds
number implies that the downstream deflection of the jets is not dependent on the jet
Reynolds numbers
41
Figure 26 XD=15 Target Wall Heat Transfer Profile
42
Figure 27 XD=15 Span-averaged Target Wall Heat Transfer Distribution
On the span averaged plots seen in Figure 27 the downstream deflection of the
jets is evident however as described previously the shifts in the peaks of heat transfer
occur at the same xD for both Reynolds numbers The amplitude of fluctuation of heat
transfer coefficients for the high Reynolds number case is larger than that of the low
Reynolds number Both profiles seem to start to level off at the end of the impingement
channel with the lowest span average being located just before the fourth jet at both
Reynolds numbers
A comparison of target wall heat transfer coefficients between XD =15 and 5 is
shown in Figure 28 At first glance it is clearly visible that the XD=15 average heat
transfer coefficient is smaller than its XD=5 counterpart This is also noticed by Ricklick
where he showed average HTC profiles for larger XD to be smaller than those at lower
XD (Ricklick 2009) This may occur due to there not being as high downward
0
50
100
150
200
250
300
350
0 20 40 60 80
HTC
(W
m2
K)
XD
Low Re
High Re
Impingement Location
43
momentum for the XD=15 case as compared to the XD=5 due to the lack of close jets
The stagnant air around the spaced out jets is taking away more of its momentum
decreasing the effective impingement Reynolds number Also important to notice is the
fact that since the XD=5 case has three times the flow impinged into it the cross flow
velocity and therefore Reynolds number will be three times as large increasing the heat
transfer coefficient
Figure 28 Target Wall Span-average Comparison of XD=5 and 15 at High Re
The side walls also show similar patterns to their XD=15 counterparts Strong
wall jet impingement can be seen on the side wall at low xD and zD Figure 29 shows
areas where the wall jet generated by the target wall impinges on the sidewall Similar to
the profile seen in Figure 24 the high heat transfer region reaches upward in the z
direction up to a height of 4-5 diameters for the first jet This high heat transfer stagnation
region decreases as xD increases to the point where the wall jet created by the last jet is
negligible when coupled with pure channel flow
0
50
100
150
200
250
300
350
400
0 10 20 30 40 50 60 70 80
HTC
(W
m2K
)
XD
XD = 5 XD = 15 Jet Location
- Blocked for XD =15
44
Figure 29 Side Wall Heat transfer Coefficient Profile
The span averaged plot seen in Figure 30 shows a nearly flat profile with peaks
located at the stagnation regions of the wall jets Thw downstream deflection for the
XD=15 case is much more pronounced than the one for the XD=5 case This is due to
the jet not being constrained by the wall jets generated by the previous and latter
impingement locations In the XD=15 case the wall jet is free to move downstream
more so than the XD=5 due to it not being disturbed by anything other than the cross
flow
45
Figure 30 XD=15 Side Wall Span-averaged Heat Transfer Coefficients
44 3D Comparison of the Heat Transfer Profiles
In order to further understand the targetsidewall interactions both heat transfer profiles
were positioned in an isometric view representative of the channel One important thing
to note is that both target and side wall profiles are not on the same scale This form of
data display is only qualitative way to describe the heat transfer profiles Figure 31 shows
the 3D profile of the XD=5 ZD=6 case The both stagnation regions of the jet onto the
target wall and the wall jet into the sidewall can be seen to occur at the same location for
the first three streamwise rows After the fourth and fifth row the wall jet diminishes in
magnitude Also visible in this view is the increasing heat transfer at low zD towards the
end of the channel of the side wall The constant input of mass and downward momentum
into the channel causes the cross flow generated by the previous jets to be squeezed into
the lower third of the channel increasing the velocity and the heat transfer of the target
wall
0
20
40
60
80
100
120
0 20 40 60 80
HTC
(W
m2K
)
XD
Low Re High Re Jet Locations
46
Figure 31 3D Heat Transfer Profile for ZD=6 XD=5
Similar patterns are seen in the taller ZD=8 channel seen in Figure 32 The wall jet
generate by the third streamwise row of jets is been deflected downward more than its
ZD=6 counterpart This can be attributed to the fact that the jet located at the ZD=8
channel has lost much of its momentum and is more easily bent downstream by the cross
flow generated by the first two jets The ZD=8 sidewall shows similar increasing heat
transfer at high xD however the increase is not as drastic as the one found in the ZD=6
channel This is caused due to the extra two diameters the jets have to cover to impinge
on the surface since the ZD=8 channel is one third larger than the ZD=6 one the flow
has to have more area to flow through The last few jets only deflect the cross flow
downward about 4 diameters this leaves two diameters for the flow to pass through on
the ZD=6 channel causing the velocity to increase rapidly and therefore increasing the
heat transfer coefficient at the low zD Since the ZD=8 channel has four remaining
47
diameters for the flow to move through it does not deflect it as much as the ZD=6
channel does only increasing the cross flow velocity and resulting heat transfer
coefficient slightly over the area at low zD and high xD
Figure 32 3D Heat Transfer Profile for ZD=8 XD=5
The 3D heat transfer profile for ZD=6 and xD=15 channel seen in Figure 33 shows
similar details to those seen in the XD=5 channels The stagnation regions of the jet and
wall jet occur at the same x location for the first three rows of jets the wall jet generated
by the fourth row of jets is deflected downstream only generating as small region of high
convective coefficients at the side wall The region located at the top right corner of the
side wall is colored red signifying high heat transfer however this area is generated by
the heaters providing non uniform heat flux at this location This region of high heat
transfer coefficients also occur at xD=0-4 of the target wall where the heater coil bends
48
Figure 33 3D Heat Transfer Profile for ZD=6 XD=15
45 Thermal Performance Calculations
Thermal performance calculations were done on the two tallest channels (ZD=8 and 10)
The pumping power was calculated for both channels at two Reynolds numbers Figure
34 shows the ratio of pressures required to pull the same amount of flow through as
smooth duct as opposed to through the jet plate The ZD=10 channel at high Reynolds
number requires the largest pressure as seen in the Figure however in order to pull the
same amount of flow rate through it requires a smaller pressure difference due to the
large cross section
49
Figure 34 Pressure Drop Ratio with Respect to Smooth Channel
Next the heat transfer enhancement was calculated A total area averaged heat
transfer coefficient was taken for the target wall and compared to the smooth channel
Dittus-Boelter value while using the same total mass flow rate Figure 35 shows an
average heat transfer enhancement of four times that of a smooth channel Similar trends
were noticed in the literature (Ricklick 2009) of decreasing heat transfer enhancement
with an increase of jet Reynolds number Ricklick also showed an increase in heat
transfer enhancement with an increase of jet to target spacing similar to the one seen in
Figure 35
0
10
20
30
40
50
60
528A_TW 528B_TW 5210A_TW 5210B_TW
PP
o
50
Figure 35 Heat Transfer Enhancement
Thermal performances at constant pressure drop were then calculated by dividing
the heat transfer enhancement by the pressure increase As seen in Figure 36 all the
values fall well below 1 making the impingement channel an unfeasible mode of heat
transfer enhancement when a constant pressure is supplied
Figure 36 Thermal Performance at Constant Pressure Drop
0
05
1
15
2
25
3
35
4
45
528A_TW 528B_TW 5210A_TW 5210B_TW
hh
o
0
002
004
006
008
01
012
014
528A_TW 528B_TW 5210A_TW 5210B_TW
(hh
o)
(PP
o)
51
The thermal performance at constant pumping drop was calculated in the same
way that the constant pressure drop was calculated the only difference being the pressure
ratio term was raised to the one third power As seen in Figure 37 the thermal
performances at constant pumping power are all higher than unity this signifies that if a
surface needs to be cooled with the supply of a constant pumping power the
impingement channel is a feasible option Similar to the figure literature (Ricklick 2009)
showed a decrease of thermal performance with an increase of channel height and
Reynolds number
Figure 37 Thermal Performance at Constant Pumping Power
0
02
04
06
08
1
12
14
528A_TW 528B_TW 5210A_TW 5210B_TW
(hh
o)
(PP
o)1
3
52
CHAPTER FIVE COMPUTATIONAL FLUID DYNAMICS
51 Problem Setup
In order to further enhance the understanding of the heat transfer profiles showed
previously a computational study was performed Even though CFD does not yield
accurate quantitative results it produces good qualitative data that can be used to explain
the flow physics in the channel and therefore increase the understanding of the patterns
seen previously The channel was meshed with the use of GAMBIT Due to the
symmetry the channel was split in half in the streamwise direction All horizontal
surfaces (parallel to the target wall) were divided into 6 different regions that are later on
going to be meshed individually The six regions are seen in Figure 38 section 1 is
located at the center of every jet also referred to as ldquojet centerrdquo This region was created
to reduce the squewness of the elements near the center of the jet by allowing the mesh to
be completely linear with a squewness of zero Section two complements section 1 to
complete the impingement hole The half impingement hole located at the symmetry wall
contains the same exact region 2 however it only has one half of the jet center Section 3
was made in order to bring the polar geometry of the holes to match the cartesian aspect
of the remainder of the channel With the addition of section 3 to the channel the only
remaining sections are square or rectangular regions Region 4 lies in between
streamwise rows of jets Section 5 is located at the entrance and the exit of the channel
These sections are not square in contrast with section 4 The last remaining section is
located near the side wall of the channel extending from the beginning to the exit of the
channel
53
Figure 38 Horizontal Plane of Impingement Channel Geometry
All the faces of sections 1 and 2 are linked throughout the channel and the
plenum however in order to have greater control of the mesh in the plenum and the
channel the remaining sections 3 4 5 and 6 are not linked to every single similar face
instead they are only linked to similar faces in either the plenum or the channel
Boundary layer spacing number of rows and growth factor are placed around the
channel In order to maintain a y+ of less than unity the first cell spacing of the boundary
layer inside the channel was set to be 000001 m (01mm) This first cell spacing yielded
y+
values varying between zero and 9 at the target side and front end wall Figure 39
shows a contour of y+ values on the heated walls The maximum values occur near the
impingement locations as expected due to large shear caused by the steep velocity
gradient normal to the wall On the downstream direction the y+ also increases due to the
increase of flow rate and therefore the increased skin friction on the wall At the
impingement location of the first jet the y+ is close to zero due to the velocity having its
direction mostly normal to the surface yielding no shear
54
Figure 39 Target Side and Front End Wall y+ Values
Once the faces were linked edge meshes were created on the sides of the jet center
Section 2rsquos inner edge was also meshed using a different parameter than the one used for
the jet center in order to allow for more freedom when trying to refine the mesh These
two edge meshes is followed by meshing all of section 2 faces alongside all the jet
centers Once these were complete section 3rsquos inner edge was meshed with different
parameters for the channel and plenum Sections 4 and 5 sides that connected with the
face made by section 6 were meshed so that their spacing was similar again the plenum
and channel were meshed separately for increased control of mesh density in both of
these areas The upstream-most edge of section 6 was meshed so that the spacing is
similar to the edge mesh in sections 4 and 5 this was done in order to have aspect ratios
of the wall be as close as possible to unity Sections 3 4 5 and 6 were meshed on both
the channel and the plenum With the entire target wall plane meshed these surface
meshes are coopered upwards to connect to the opposite wall The vertical spacing has
55
also been set up differently between the channel and the plenum The holes and the
plenum were also coopered The finished mesh was then exported as a msh file
Boundary conditions were set in GAMBIT once the mesh was imported into
Fluent values were set to every face depending on their location and purpose Figure 40
shows the four different boundary conditions Face 1 (blue) was set to be a mass flow
inlet The flow rate is half of the total flow rate at a given jet Reynolds number due to it
being only half of the entire domain Face 2 (yellow) is a symmetry plane face 3 (red) is
a pressure outlet at zero gauge pressure The rest of the faces in the channel denoted by
the number 4 (white) are set to walls The target side and front end wall had a heat flux
applied to them equal to 10000Wm2
Figure 40 Finished Mesh with Boundary Conditions
The model was imported into Fluent It was scaled down by a factor of 1000 due to it
being made in GAMBIT in millimeters The energy model was turned on The Realizable
k-ε model was used with enhanced wall functions on both the pressure and thermal
gradients The boundary conditions were set as discussed previously the mass flow inlet
was set to the specific flow rate normal to the surface the heat fluxes were set on the
56
heated walls the outflow gauge pressure was set to zero Two important reference values
characteristic length and reference temperature were set to be the diameter of the jet
(0075m) and 300K respectively The spatial discretization parameters were set to second
order upwind for momentum turbulent kinetic energy turbulent dissipation rate and
energy The under-relaxation factors were set to default Four monitors were created to
aid in the determination of convergence two of them read Nusselt numbers at the
stagnation region of the first and last jet the remaining two read the exit velocity at the
first and last jet The continuity x y and x velocities and energy equations residuals
were set to be 1E-6 while k and ε residuals were set to 1E-4 The solution was initialized
on the all zones at 1ms in the positive x direction The solution was set to autosave every
100 iterations while keeping only the two newest dat files The calculation was then run
for a maximum of 7000 iterations
A grid independence study was done on the domain to find the optimal size of
mesh that provides the correct solution while minimizing the compute time Two
monitors were set to check for grid independence both of them were vertex maximum
One of them read the Nusselt number at the impingement location of the first center jet
while the second one measures the velocity at the exit of the last jet Four different mesh
sizes were run to the convergence criterion explained before their sizes were 900000
15 million 28 million and 43 million cells
57
Figure 41 Grid Independence Study
It can be seen in Figure 41 that the difference between the 28 and 43 million cell
meshes are very small a difference of under 006 for velocity and 7 for Nusselt
number It can be safe to assume that the 28 million cell mesh is large enough to provide
a mesh independent solution The GAMBIT journal file used to create this mesh is
attached to the appendix The results shown hereafter are the ones obtained by the 28
million cell mesh
Figure 42 Residual Plots for the 26M Cell Run
67
69
71
73
75
77
79
81
83
85
485
4855
486
4865
487
4875
488
4885
489
0 1 2 3 4 5
Nu
sse
lt N
um
be
r
Cell Ammount (Millions)
Grid Independence Study
Velocity
Nusselt Number
58
For future reference Figure 42 shows the residuals of the 26M cell calculation
Up until around 4400 iterations the residuals were increasing shortly thereafter the
residuals started decreasing until it converged just after 5500 iterations All runs for the
differently sized meshes had the same residual patters with the peak of residuals and
point of convergence happening at different iterations
52 CFD Results
As describe previously all the results shown here are for the mesh containing 28 million
elements Figure 43 shows the total pressure contours It can be seen that the plenum
portion is at a constant total pressure Once the jets form since there are very small losses
in the jets due to the wall friction the total pressure still remains constant Only when the
jets enter the channel and start mixing with the cross flow is that they start losing the total
pressure head It is important to notice how the first two jets have the total pressure close
to the plenum arriving at the target wall This implies a successful impingement of the
undisturbed potential core As we move downstream the total pressure is lost quite
rapidly as the jets interact with the cross flow
Figure 43 Total Pressure Contours
59
Similar details can be drawn out from Figure 44 it can be seen that the first three
jets successfully impinge on the target wall while the rest of the downstream ones are
deflected by the cross flow As mentioned by Ricklick the velocity magnitude of the last
jet is larger than that of the first jet due to there being a lower static pressure at the end of
the channel providing it with a steeper pressure gradient hence higher velocity
Figure 44 Velocity Magnitude Contours
Turbulent kinetic energy was plotted in Figure 45 it is expected to have the
highest turbulent kinetic energy near the exit of the holes where the stagnant air is in
contact with the fast moving jet The mixing between the two regimes causes very
energetic eddies to form potentially enhancing the target and side wall heat transfer
coefficient As cross flow builds up towards the end of the channel the turbulent kinetic
energy increases due to larger overall velocities and fluctuations between the cross flow
and jets
60
Figure 45 Turbulent Kinetic Energy Contours
As Ricklick showed in his work the static temperature rise is quite small for such a small
channel It can be seen in Figure 46 that the driving temperature for heat transfer is that of
the plenum It is important to notice that a wall heat flux of 10000 Wm2 was used as the
boundary condition Not even in the most powerful tests would we ever use heat fluxes
that high they normally range between 2500 to a maximum of 7000 Wm2 A heat flux of
10000 Wm2 will increase the temperature at a faster rate than what it is normally used in
experimental testing
Figure 46 Static Temperature Contours
61
Figure 47 Target and Side Wall Heat Transfer Coefficient Contours
Figure 47 shows the target and sidewall heat transfer profiles Peaks can be seen at the
first three locations similar to that seen in Figure 22 The trend decreases rapidly to
eventually become a slowly increasing heat transfer profile due to the increase of mass
flow through the channel The sidewall provides the same results clear peaks in heat
transfer where the wall jets impinge on the sidewall seen in Figure 48 in more detail The
sidewall also shows a recirculation zone in between the first row of jets and the end wall
This is caused by the wall jet from the first row hitting the back wall moving upwards in
a circular pattern and coming back down when it encounters the first impingement row
Figure 48 Closer View of First few Rows of Impingement HTC Contours
62
Figure 49 Pathlines Generating from the First Row of Jets
Figure 49 helps explain the low heat transfer region between the first row of jets and
the end wall Pathlines are generated at the exit of each hole in the first row As the
air impinges on the surface half of it moves downstream and the other half movers
upstream to this recirculation zone where it circulates for a period of time before
reuniting with the remainder of the flow to move downstream The wall jet that
moves towards the second row of jets encounters the wall jet created by the second
row of jets causing the pathlines to drastically move upwards On the side of the
channel the pathlines behave erratically with no clear pattern clearly signifying the
highly turbulent and chaotic flow structure of this impingement channel
63
CHAPTER SIX CONCLUSIONS
It has been seen from this analysis that the side walls provide significant heat
transfer in an impingement channel especially at the relatively smaller channel
height This is primarily the result of successful impact of the wall jet with the side
walls It was shown that the tallest channel (ZD=10) has the most uniform profile with
low heat transfer coefficients when compared to the other channels The peaks of the
ZD=6 and 8 channels have a very similar profile which may indicate the successful
impingement of the potential core of the jet on the target surface As XD increases the
peaks diminish and a positive slope profile is attained by the increase of cross flow
velocity as more and more jets are introduced Tall impingement channels provide the
user with a heat transfer profile that is more uniform than those provided with the use of a
smaller channel while still maintaining higher convective coefficients when compared to
a smooth flow scenario The downstream shift of the wall jets is found to be independent
of Reynolds number and heavily dependent on streamwise position It was also found that
at XD=15 the wall jets decay faster than their XD=5 counterparts From the 3D heat
transfer profiles it was seen that the cross flow generated by multiple upstream jets is
deflected downward decreasing its effective flow area increasing its velocity hence
providing higher convective coefficients at the side wall at high xD and low zD
64
APPENDICES
Appendix A
Lateral Conduction Consideration
Thickness of foil heater Heat flux
Sample volume width
Volumetric heat generation
Volume of sample volume
Temperature profile from the first row of impingement ONLY valid for 02ltxlt045
t 50m k 20W
m K qflux 6000
W
m2
1mm
V 2
t qvol
qflux
t
T x( ) 298Kqflux
470630 x2
31244x 14842 W
m2K
N 15
x 02045 02
N 102 047
002 003 004 005314
315
316
317
318
319
320
T x( )
x
A t
qnet x( ) A kxT x
m
d
d xT x( )
d
d
1
m
002 003 004 0050
5 105
1 104
15 104
2 104
qnet x( )
x
65
Now comparing the net heat gained by lateral conduction to heat generated and convected out
It can be seen that the lateral conduction into the sample volume is two orders of magnitude smaller than the heat removed by convection
qgen qvol V 6 103
W
qconv x( ) 2
qflux qnet x( )
002 003 004 0051 10
5
1 104
1 103
001
qconv x( )
qnet x( )
x x
66
Appendix B
This is the journal file run on gambit to generate the geometry faces links
boundary layer face and volume meshes as well as the boundary conditions
set diameter
$d=75
$zc=6($d)
$xc=80($d)
$yc=4($d)
$y=2($d)
$x=5($d)
$zp=5($d)
$ztot=($zc)+($d)+($zp)
$jcf=(13)
$ocf=2
Boundary layer constants
$first=01
$growth=12
$rows=4
Meshing constants
$NumbNodes=5
$Numbtelnodes=6
$PLobnodes=5
$Chobnodes=5
$Plbenodes=($NumbNodes(4)+$rows)
$plsqnodes=($NumbNodes(3))
$Pllsnodes=($NumbNodes+$rows)
$Nojetcells=10
$Chzdnodes=($zc$Nojetcells)($d)
$Plzdnodes=($zp$Nojetcells)($d)
Boundary layer constants for channel
$firstch=001
$growthch=12
$rowsch=8
$CHbenodes=($NumbNodes(4)+$rowsch)
$CHlsnodes=($NumbNodes+$rowsch)
volume create body width ($xc) depth ($yc) height ($ztot) offset ($xc2) ($yc2) ($ztot2) brick
volume create cylinder height ($ztot) radius1 ($d2) radius3 ($d2) offset ($x) 0 ($ztot2) zaxis frustum
volume cmove cylinder multiple 1 offset 0 ($y) 0
volume cmove cylinder volume3 multiple 14 offset ($x) 0 0
volume create jetplate width ($xc) depth ($yc) height ($d)offset ($xc2) ($yc2) ($d2+$zc) brick
volume split body volumes jetplate connected
volume split jetplate volumes cylinder volume3 volume4 volume5
volume6 volume7 volume8 volume9 volume10 volume11
volume12 volume13 volume14 volume15 volume16 volume17
67
volume18 volume19 volume20 volume21 volume22 volume23
volume24 volume25 volume26 volume27 volume28 volume29
volume30 volume31 connected
face create jetcenter width ($jcf$d) height ($jcf$d) offset ($x) 0 0 xyplane rectangle
face create jetcircle radius ($d2) xyplane circle
face move jetcircle offset ($x) 0 0
face create outbox width ($ocf$d) height ($ocf$d) offset ($x) 0 0 xyplane rectangle
face split outbox connected faces jetcircle jetcenter
face split jetcircle connected faces face1
face split outbox connected faces face1
face cmove jetcenter outbox jetcircle face222 face223 multiple 1 offset 0 ($y) 0
face cmove jetcenter outbox jetcircle face222 face223 face224 face225 face226
face227 face228 multiple 14 offset ($x) 0 0
volume delete jetplate lowertopology
face split face1 connected keeptool faces jetcircle jetcenter outbox
face222 face223 face224 face225 face226 face227
face228 face229 face230 face231 face232 face233
face234 face235 face236 face237 face238 face239
face240 face241 face242 face243 face244 face245
face246 face247 face248 face249 face250 face251
face252 face253 face254 face255 face256 face257
face258 face259 face260 face261 face262 face263
face264 face265 face266 face267 face268 face269
face270 face271 face272 face273 face274 face275
face276 face277 face278 face279 face280 face281
face282 face283 face284 face285 face286 face287
face288 face289 face290 face291 face292 face293
face294 face295 face296 face297 face298 face299
face300 face301 face302 face303 face304 face305
face306 face307 face308 face309 face310 face311
face312 face313 face314 face315 face316 face317
face318 face319 face320 face321 face322 face323
face324 face325 face326 face327 face328 face329
face330 face331 face332 face333 face334 face335
face336 face337 face338 face339 face340 face341
face342 face343 face344 face345 face346 face347
face348 face349 face350 face351 face352 face353
face354 face355 face356 face357 face358 face359
face360 face361 face362 face363 face364 face365
face366 face367 face368
face move jetcircle jetcenter outbox face222 face223 face224
face225 face226 face227 face228 face229 face230
face231 face232 face233 face234 face235 face236
face237 face238 face239 face240 face241 face242
face243 face244 face245 face246 face247 face248
face249 face250 face251 face252 face253 face254
face255 face256 face257 face258 face259 face260
face261 face262 face263 face264 face265 face266
face267 face268 face269 face270 face271 face272
face273 face274 face275 face276 face277 face278
face279 face280 face281 face282 face283 face284
face285 face286 face287 face288 face289 face290
face291 face292 face293 face294 face295 face296
face297 face298 face299 face300 face301 face302
face303 face304 face305 face306 face307 face308
face309 face310 face311 face312 face313 face314
68
face315 face316 face317 face318 face319 face320
face321 face322 face323 face324 face325 face326
face327 face328 face329 face330 face331 face332
face333 face334 face335 face336 face337 face338
face339 face340 face341 face342 face343 face344
face345 face346 face347 face348 face349 face350
face351 face352 face353 face354 face355 face356
face357 face358 face359 face360 face361 face362
face363 face364 face365 face366 face367 face368 offset 0
0 $ztot
THIS SPLITS THE TOP PLENUM FACE WITH THE FACES CREATED IN THE BOTTOM
face split face6 connected keeptool faces jetcircle jetcenter outbox
face222 face223 face224 face225 face226 face227
face228 face229 face230 face231 face232 face233
face234 face235 face236 face237 face238 face239
face240 face241 face242 face243 face244 face245
face246 face247 face248 face249 face250 face251
face252 face253 face254 face255 face256 face257
face258 face259 face260 face261 face262 face263
face264 face265 face266 face267 face268 face269
face270 face271 face272 face273 face274 face275
face276 face277 face278 face279 face280 face281
face282 face283 face284 face285 face286 face287
face288 face289 face290 face291 face292 face293
face294 face295 face296 face297 face298 face299
face300 face301 face302 face303 face304 face305
face306 face307 face308 face309 face310 face311
face312 face313 face314 face315 face316 face317
face318 face319 face320 face321 face322 face323
face324 face325 face326 face327 face328 face329
face330 face331 face332 face333 face334 face335
face336 face337 face338 face339 face340 face341
face342 face343 face344 face345 face346 face347
face348 face349 face350 face351 face352 face353
face354 face355 face356 face357 face358 face359
face360 face361 face362 face363 face364 face365
face366 face367 face368
THIS MOVES THE FACES THAT WE ARE USING TO PLIT THE BOTTOM PLENUM SURFACE
face move jetcircle jetcenter outbox face222 face223 face224
face225 face226 face227 face228 face229 face230
face231 face232 face233 face234 face235 face236
face237 face238 face239 face240 face241 face242
face243 face244 face245 face246 face247 face248
face249 face250 face251 face252 face253 face254
face255 face256 face257 face258 face259 face260
face261 face262 face263 face264 face265 face266
face267 face268 face269 face270 face271 face272
face273 face274 face275 face276 face277 face278
face279 face280 face281 face282 face283 face284
face285 face286 face287 face288 face289 face290
face291 face292 face293 face294 face295 face296
face297 face298 face299 face300 face301 face302
69
face303 face304 face305 face306 face307 face308
face309 face310 face311 face312 face313 face314
face315 face316 face317 face318 face319 face320
face321 face322 face323 face324 face325 face326
face327 face328 face329 face330 face331 face332
face333 face334 face335 face336 face337 face338
face339 face340 face341 face342 face343 face344
face345 face346 face347 face348 face349 face350
face351 face352 face353 face354 face355 face356
face357 face358 face359 face360 face361 face362
face363 face364 face365 face366 face367 face368 offset 0
0 -$zp
SPLITS THE BOTTOM FACE OF THE PLENUM WITH THE FACES THAT ARE USED TO SPLIT
face split face114 connected keeptool faces jetcircle jetcenter
outbox face222 face223 face224 face225 face226 face227
face228 face229 face230 face231 face232 face233
face234 face235 face236 face237 face238 face239
face240 face241 face242 face243 face244 face245
face246 face247 face248 face249 face250 face251
face252 face253 face254 face255 face256 face257
face258 face259 face260 face261 face262 face263
face264 face265 face266 face267 face268 face269
face270 face271 face272 face273 face274 face275
face276 face277 face278 face279 face280 face281
face282 face283 face284 face285 face286 face287
face288 face289 face290 face291 face292 face293
face294 face295 face296 face297 face298 face299
face300 face301 face302 face303 face304 face305
face306 face307 face308 face309 face310 face311
face312 face313 face314 face315 face316 face317
face318 face319 face320 face321 face322 face323
face324 face325 face326 face327 face328 face329
face330 face331 face332 face333 face334 face335
face336 face337 face338 face339 face340 face341
face342 face343 face344 face345 face346 face347
face348 face349 face350 face351 face352 face353
face354 face355 face356 face357 face358 face359
face360 face361 face362 face363 face364 face365
face366 face367 face368
COPIES THE FACES THAT WE USED TO SPLIT TO BOTTOM OF THE PLENUM TO THE TOP OF
THE CHANNEL
face cmove jetcircle jetcenter outbox face222 face223 face224
face225 face226 face227 face228 face229 face230
face231 face232 face233 face234 face235 face236
face237 face238 face239 face240 face241 face242
face243 face244 face245 face246 face247 face248
face249 face250 face251 face252 face253 face254
face255 face256 face257 face258 face259 face260
face261 face262 face263 face264 face265 face266
face267 face268 face269 face270 face271 face272
face273 face274 face275 face276 face277 face278
face279 face280 face281 face282 face283 face284
70
face285 face286 face287 face288 face289 face290
face291 face292 face293 face294 face295 face296
face297 face298 face299 face300 face301 face302
face303 face304 face305 face306 face307 face308
face309 face310 face311 face312 face313 face314
face315 face316 face317 face318 face319 face320
face321 face322 face323 face324 face325 face326
face327 face328 face329 face330 face331 face332
face333 face334 face335 face336 face337 face338
face339 face340 face341 face342 face343 face344
face345 face346 face347 face348 face349 face350
face351 face352 face353 face354 face355 face356
face357 face358 face359 face360 face361 face362
face363 face364 face365 face366 face367 face368 multiple 1 offset 0
0 -$d
NAME OF COPIED NEW FACES
face1104 face1105 face1106 face1107 face1108 face1109 face1110 face1111
face1112 face1113 face1114 face1115 face1116 face1117 face1118 face1119
face1120 face1121 face1122 face1123 face1124 face1125 face1126 face1127
face1128 face1129 face1130 face1131 face1132 face1133 face1134 face1135
face1136 face1137 face1138 face1139 face1140 face1141 face1142 face1143
face1144 face1145 face1146 face1147 face1148 face1149 face1150 face1151
face1152 face1153 face1154 face1155 face1156 face1157 face1158 face1159
face1160 face1161 face1162 face1163 face1164 face1165 face1166 face1167
face1168 face1169 face1170 face1171 face1172 face1173 face1174 face1175
face1176 face1177 face1178 face1179 face1180 face1181 face1182 face1183
face1184 face1185 face1186 face1187 face1188 face1189 face1190 face1191
face1192 face1193 face1194 face1195 face1196 face1197 face1198 face1199
face1200 face1201 face1202 face1203 face1204 face1205 face1206 face1207
face1208 face1209 face1210 face1211 face1212 face1213 face1214 face1215
face1216 face1217 face1218 face1219 face1220 face1221 face1222 face1223
face1224 face1225 face1226 face1227 face1228 face1229 face1230 face1231
face1232 face1233 face1234 face1235 face1236 face1237 face1238 face1239
face1240 face1241 face1242 face1243 face1244 face1245 face1246 face1247
face1248 face1249 face1250 face1251 face1252 face1253
THIS SPLITS THE TOP OF THE CHANNEL WITH THE NEW COPIED FACES
face split face209 connected keeptool faces face1104 face1105 face1106 face1107
face1108 face1109 face1110 face1111 face1112 face1113 face1114 face1115
face1116 face1117 face1118 face1119 face1120 face1121 face1122 face1123
face1124 face1125 face1126 face1127 face1128 face1129 face1130 face1131
face1132 face1133 face1134 face1135 face1136 face1137 face1138 face1139
face1140 face1141 face1142 face1143 face1144 face1145 face1146 face1147
face1148 face1149 face1150 face1151 face1152 face1153 face1154 face1155
face1156 face1157 face1158 face1159 face1160 face1161 face1162 face1163
face1164 face1165 face1166 face1167 face1168 face1169 face1170 face1171
face1172 face1173 face1174 face1175 face1176 face1177 face1178 face1179
face1180 face1181 face1182 face1183 face1184 face1185 face1186 face1187
face1188 face1189 face1190 face1191 face1192 face1193 face1194 face1195
face1196 face1197 face1198 face1199 face1200 face1201 face1202 face1203
face1204 face1205 face1206 face1207 face1208 face1209 face1210 face1211
face1212 face1213 face1214 face1215 face1216 face1217 face1218 face1219
face1220 face1221 face1222 face1223 face1224 face1225 face1226 face1227
71
face1228 face1229 face1230 face1231 face1232 face1233 face1234 face1235
face1236 face1237 face1238 face1239 face1240 face1241 face1242 face1243
face1244 face1245 face1246 face1247 face1248 face1249 face1250 face1251
face1252 face1253
THIS UNITES THE RECTANGLE OUTSIDE FACES AND THE SEMICIRCLE SO THAT IT MAKES
A RECTANGLE WIHOUT THE CENTERJET
face unite faces jetcircle face223 real
face unite faces face222 outbox real
face unite faces face228 face226 real
face unite faces face225 face227 real
face unite faces face231 face233 real
face unite faces face232 face230 real
face unite faces face236 face238 real
face unite faces face237 face235 real
face unite faces face241 face243 real
face unite faces face242 face240 real
face unite faces face248 face246 real
face unite faces face245 face247 real
face unite faces face253 face251 real
face unite faces face252 face250 real
face unite faces face256 face258 real
face unite faces face257 face255 real
face unite faces face263 face261 real
face unite faces face260 face262 real
face unite faces face268 face266 real
face unite faces face265 face264 real
face unite faces face265 face267 real
face unite faces face273 face271 real
face unite faces face272 face270 real
face unite faces face276 face278 real
face unite faces face277 face275 real
face unite faces face281 face283 real
face unite faces face282 face280 real
face unite faces face286 face288 real
face unite faces face287 face285 real
face unite faces face291 face293 real
face unite faces face292 face290 real
face unite faces face296 face298 real
face unite faces face297 face295 real
face unite faces face301 face303 real
face unite faces face302 face300 real
face unite faces face306 face308 real
face unite faces face307 face305 real
face unite faces face316 face318 real
face unite faces face312 face310 real
face unite faces face311 face313 real
face unite faces face315 face317 real
face unite faces face321 face323 real
face unite faces face322 face320 real
face unite faces face326 face328 real
face unite faces face327 face325 real
face unite faces face331 face333 real
face unite faces face332 face330 real
face unite faces face336 face338 real
72
face unite faces face337 face335 real
face unite faces face347 face345 real
face unite faces face346 face348 real
face unite faces face342 face340 real
face unite faces face341 face343 real
face unite faces face356 face358 real
face unite faces face357 face355 real
face unite faces face352 face350 real
face unite faces face351 face353 real
face unite faces face361 face363 real
face unite faces face366 face368 real
face unite faces face360 face362 real
face unite faces face365 face367 real
SPLITTING ALL THE FACES OF THE CIRCLES IN THE BOTTOM OF THE PLENUM
face split face912 connected keeptool faces face222
face split face117 connected keeptool faces face228
face split face117 connected keeptool faces face225
face split face922 connected keeptool faces face232
face split face124 connected keeptool faces face236
face split face124 connected keeptool faces face237
face split face932 connected keeptool faces face242
face split face131 connected keeptool faces face248
face split face131 connected keeptool faces face245
face split face942 connected keeptool faces face252
face split face138 connected keeptool faces face256
face split face138 connected keeptool faces face257
face split face952 connected keeptool faces face260
face split face145 connected keeptool faces face268
face split face145 connected keeptool faces face265
face split face962 connected keeptool faces face272
face split face152 connected keeptool faces face276
face split face152 connected keeptool faces face277
face split face972 connected keeptool faces face282
face split face159 connected keeptool faces face286
face split face159 connected keeptool faces face287
face split face982 connected keeptool faces face292
face split face166 connected keeptool faces face296
face split face166 connected keeptool faces face297
face split face992 connected keeptool faces face302
face split face173 connected keeptool faces face306
face split face173 connected keeptool faces face307
face split face1002 connected keeptool faces face312
face split face180 connected keeptool faces face316
face split face180 connected keeptool faces face315
73
face split face1012 connected keeptool faces face322
face split face187 connected keeptool faces face326
face split face187 connected keeptool faces face327
face split face1022 connected keeptool faces face332
face split face194 connected keeptool faces face336
face split face194 connected keeptool faces face337
face split face1032 connected keeptool faces face342
face split face201 connected keeptool faces face346
face split face201 connected keeptool faces face347
face split face1042 connected keeptool faces face352
face split face208 connected keeptool faces face356
face split face208 connected keeptool faces face357
face split face1052 connected keeptool faces face360
face split face215 connected keeptool faces face366
face split face215 connected keeptool faces face365
THIS UNITES THE RECTANGLE OUTSIDE FACES AND THE SEMICIRCLE SO THAT IT MAKES
A RECTANGLE WIHOUT THE CENTERJET
face unite faces face1104 face1108 real
face unite faces face1107 face1106 real
face unite faces face1113 face1111 real
face unite faces face1112 face1110 real
face unite faces face1118 face1116 real
face unite faces face1117 face1115 real
face unite faces face1123 face1121 real
face unite faces face1122 face1120 real
face unite faces face1128 face1126 real
face unite faces face1127 face1125 real
face unite faces face1133 face1131 real
face unite faces face1132 face1130 real
face unite faces face1138 face1136 real
face unite faces face1137 face1135 real
face unite faces face1143 face1141 real
face unite faces face1142 face1140 real
face unite faces face1148 face1146 real
face unite faces face1147 face1145 real
face unite faces face1153 face1151 real
face unite faces face1152 face1150 real
face unite faces face1158 face1156 real
face unite faces face1157 face1155 real
face unite faces face1163 face1161 real
face unite faces face1162 face1160 real
face unite faces face1168 face1166 real
face unite faces face1167 face1165 real
face unite faces face1173 face1171 real
face unite faces face1172 face1170 real
face unite faces face1178 face1176 real
face unite faces face1177 face1175 real
face unite faces face1183 face1181 real
74
face unite faces face1182 face1180 real
face unite faces face1186 face1188 real
face unite faces face1187 face1185 real
face unite faces face1193 face1191 real
face unite faces face1192 face1190 real
face unite faces face1198 face1196 real
face unite faces face1197 face1195 real
face unite faces face1203 face1201 real
face unite faces face1202 face1200 real
face unite faces face1206 face1208 real
face unite faces face1207 face1205 real
face unite faces face1213 face1211 real
face unite faces face1212 face1210 real
face unite faces face1216 face1218 real
face unite faces face1217 face1215 real
face unite faces face1221 face1223 real
face unite faces face1222 face1220 real
face unite faces face1228 face1226 real
face unite faces face1227 face1225 real
face unite faces face1233 face1231 real
face unite faces face1232 face1230 real
face unite faces face1238 face1236 real
face unite faces face1237 face1235 real
face unite faces face1243 face1241 real
face unite faces face1242 face1240 real
face unite faces face1248 face1246 real
face unite faces face1247 face1245 real
face unite faces face1253 face1251 real
face unite faces face1252 face1250 real
SPLITTING ALL THE FACES OF THE CIRCLES IN THE TOP OF THE CHANNEL
face split face1257 connected keeptool faces face1107
face split face115 connected keeptool faces face1113
face split face115 connected keeptool faces face1112
face split face1267 connected keeptool faces face1117
face split face122 connected keeptool faces face1123
face split face122 connected keeptool faces face1122
face split face1277 connected keeptool faces face1127
face split face129 connected keeptool faces face1133
face split face129 connected keeptool faces face1132
face split face1287 connected keeptool faces face1137
face split face136 connected keeptool faces face1143
face split face136 connected keeptool faces face1142
face split face1297 connected keeptool faces face1147
face split face143 connected keeptool faces face1153
face split face143 connected keeptool faces face1152
face split face1307 connected keeptool faces face1157
face split face150 connected keeptool faces face1163
face split face150 connected keeptool faces face1162
75
face split face1317 connected keeptool faces face1167
face split face157 connected keeptool faces face1173
face split face157 connected keeptool faces face1172
face split face1327 connected keeptool faces face1177
face split face164 connected keeptool faces face1183
face split face164 connected keeptool faces face1182
face split face1337 connected keeptool faces face1187
face split face171 connected keeptool faces face1193
face split face171 connected keeptool faces face1192
face split face1347 connected keeptool faces face1197
face split face178 connected keeptool faces face1203
face split face178 connected keeptool faces face1202
face split face1357 connected keeptool faces face1207
face split face185 connected keeptool faces face1213
face split face185 connected keeptool faces face1212
face split face1367 connected keeptool faces face1217
face split face192 connected keeptool faces face1221
face split face192 connected keeptool faces face1222
face split face1377 connected keeptool faces face1227
face split face199 connected keeptool faces face1233
face split face199 connected keeptool faces face1232
face split face1387 connected keeptool faces face1237
face split face206 connected keeptool faces face1243
face split face206 connected keeptool faces face1242
face split face1397 connected keeptool faces face1247
face split face213 connected keeptool faces face1253
face split face213 connected keeptool faces face1252
face split face1452 connected keeptool faces face224
face split face1456 connected keeptool faces face234
face split face1460 connected keeptool faces face244
face split face1464 connected keeptool faces face254
face split face1468 connected keeptool faces face264
face split face1472 connected keeptool faces face274
face split face1476 connected keeptool faces face284
face split face1480 connected keeptool faces face294
face split face1484 connected keeptool faces face304
face split face1488 connected keeptool faces face314
face split face1492 connected keeptool faces face324
face split face1496 connected keeptool faces face334
face split face1500 connected keeptool faces face344
face split face1504 connected keeptool faces face354
face split face1508 connected keeptool faces face364
DELETING ALL THE FACES USED TO MAKE THE CUTS
face delete jetcircle face222 face228 face225 jetcenter
76
face224 face231 face232 face236 face237 face229
face1456 face241 face242 face239 face248 face244
face245 face253 face249 face252 face254 face256
face257 face263 face259 face260 face268 face264
face265 face273 face272 face269 face276 face277
face274 face281 face282 face286 face279 face287
face284 face291 face292 face296 face297 face289
face294 face301 face299 face302 face306 face307
face304 face311 face312 face316 face315 face309
face314 face321 face322 face326 face327 face319
face324 face331 face332 face329 face336 face334
face337 face341 face342 face339 face346 face344
face347 face351 face352 face349 face356 face354
face357 face361 face359 face360 face366 face364
face365 lowertopology
face delete face1104 face1105 face1107 face1113 face1112
face115 face234 face1118 face1114 face1117 face1123
face1122 face122 face1138 face1128 face1127 face1124
face1133 face1132 face129 face1134 face1137 face1143
face136 face1142 face1148 face1144 face1147 face1153
face143 face1152 face1158 face1154 face1157 face1163
face150 face1162 face1168 face1164 face1167 face1173
face157 face1172 face1178 face1174 face1177 face1183
face164 face1182 face1186 face1184 face1187 face1193
face171 face1192 face1198 face1194 face1197 face1203
face178 face1202 face1206 face1204 face1207 face1213
face185 face1212 face1216 face1214 face1217 face1221
face192 face1222 face1228 face1224 face1227 face1233
face199 face1232 face1238 face1234 face1237 face1243
face206 face1242 face1248 face1244 face1247 face1253
face213 face1252 lowertopology
face delete face1109 face1119 face1129 face1139 face1149 face1159
face1169 face1179 face1189 face1199 face1209 face1219
face1229 face1239 face1249 lowertopology
face create CP1 width 600 height 75 offset 300 (225+($d)2) 0 xyplane rectangle
face create CP2 width 600 height 75 offset 300 (225+($d)2) ($zc) xyplane rectangle
face create CP3 width 600 height 75 offset 300 (225+($d)2) ($zc+$d) xyplane rectangle
face create CP4 width 600 height 75 offset 300 (225+($d)2) ($zc+$d+$zp) xyplane rectangle
face split face6 connected faces CP4
face split face114 connected faces CP3
face split face209 connected faces CP2
face split face1 connected faces CP1
GEOMETRY IS FINISHED
face modify face912 side vertex6437 vertex6436
77
face modify face1600 side vertex7302 vertex7303
face modify face117 side vertex6446 vertex6447
face modify face646 side vertex3312
face modify face646 side vertex3313
face modify face647 side vertex3432 vertex3433
face modify face372 side vertex2040 vertex2041
face modify face376 side vertex2100 vertex2101
face modify face377 side vertex2221 vertex2220
LINKING ALL THE JET CENTERS
face link face1450 face640 edges edge6949 edge3518 vertices
vertex6437 vertex3253 reverse
face link face1450 face1257 edges edge6949 edge7340 vertices
vertex6437 vertex6797 reverse
face link face1257 face370 edges edge7340 edge2139 vertices
vertex6797 vertex2041 reverse
face link face1257 face1454 edges edge7340 edge6975 vertices
vertex6797 vertex6461 reverse
face link face1454 face649 edges edge6975 edge3519 vertices
vertex6461 vertex3255 reverse
face link face1454 face1267 edges edge6975 edge7377 vertices
vertex6461 vertex6831 reverse
face link face1267 face379 edges edge7377 edge2141 vertices
vertex6831 vertex2043 reverse
face link face1267 face1458 edges edge7377 edge7001 vertices
vertex6831 vertex6485 reverse
face link face1458 face659 edges edge7001 edge3520 vertices
vertex6485 vertex3257 reverse
face link face1458 face1277 edges edge7001 edge7414 vertices
vertex6485 vertex6865 reverse
face link face1277 face389 edges edge7414 edge2143 vertices
vertex6865 vertex2045 reverse
face link face1277 face1462 edges edge7414 edge7027 vertices
vertex6865 vertex6509 reverse
face link face1462 face669 edges edge7027 edge3521 vertices
vertex6509 vertex3259 reverse
face link face1462 face1287 edges edge7027 edge7451 vertices
vertex6509 vertex6899 reverse
face link face1287 face399 edges edge7451 edge2145 vertices
vertex6899 vertex2047 reverse
face link face1287 face1466 edges edge7451 edge7053 vertices
vertex6899 vertex6533 reverse
face link face1466 face679 edges edge7053 edge3522 vertices
vertex6533 vertex3261 reverse
face link face1466 face1297 edges edge7053 edge7488 vertices
vertex6533 vertex6933 reverse
face link face1297 face409 edges edge7488 edge2147 vertices
vertex6933 vertex2049 reverse
face link face1297 face1470 edges edge7488 edge7079 vertices
vertex6933 vertex6557 reverse
face link face1470 face689 edges edge7079 edge3523 vertices
vertex6557 vertex3263 reverse
face link face1470 face1307 edges edge7079 edge7525 vertices
vertex6557 vertex6967 reverse
face link face1307 face419 edges edge7525 edge2149 vertices
78
vertex6967 vertex2051 reverse
face link face1307 face1474 edges edge7525 edge7105 vertices
vertex6967 vertex6581 reverse
face link face1474 face1317 edges edge7105 edge7562 vertices
vertex6581 vertex7001 reverse
face link face1474 face699 edges edge7105 edge3524 vertices
vertex6581 vertex3265 reverse
face link face1317 face429 edges edge7562 edge2151 vertices
vertex7001 vertex2053 reverse
face link face1317 face1478 edges edge7562 edge7131 vertices
vertex7001 vertex6605 reverse
face link face1478 face1327 edges edge7131 edge7599 vertices
vertex6605 vertex7035 reverse
face link face1478 face709 edges edge7131 edge3525 vertices
vertex6605 vertex3267 reverse
face link face1327 face439 edges edge7599 edge2153 vertices
vertex7035 vertex2055 reverse
face link face1327 face1482 edges edge7599 edge7157 vertices
vertex7035 vertex6629 reverse
face link face1482 face719 edges edge7157 edge3526 vertices
vertex6629 vertex3269 reverse
face link face1482 face1337 edges edge7157 edge7636 vertices
vertex6629 vertex7069 reverse
face link face1337 face449 edges edge7636 edge2155 vertices
vertex7069 vertex2057 reverse
face link face1337 face1486 edges edge7636 edge7183 vertices
vertex7069 vertex6653 reverse
face link face1486 face1347 edges edge7183 edge7673 vertices
vertex6653 vertex7103 reverse
face link face1347 face459 edges edge7673 edge2157 vertices
vertex7103 vertex2059 reverse
face link face1486 face729 edges edge7183 edge3527 vertices
vertex6653 vertex3271 reverse
face link face1347 face1490 edges edge7673 edge7209 vertices
vertex7103 vertex6677 reverse
face link face1490 face1357 edges edge7209 edge7710 vertices
vertex6677 vertex7137 reverse
face link face1490 face739 edges edge7209 edge3528 vertices
vertex6677 vertex3273 reverse
face link face1357 face469 edges edge7710 edge2159 vertices
vertex7137 vertex2061 reverse
face link face1357 face1494 edges edge7710 edge7235 vertices
vertex7137 vertex6701 reverse
face link face1494 face1367 edges edge7235 edge7747 vertices
vertex6701 vertex7171 reverse
face link face1494 face749 edges edge7235 edge3529 vertices
vertex6701 vertex3275 reverse
face link face1367 face479 edges edge7747 edge2161 vertices
vertex7171 vertex2063 reverse
face link face1367 face1498 edges edge7747 edge7261 vertices
vertex7171 vertex6725 reverse
face link face1498 face1377 edges edge7261 edge7784 vertices
vertex6725 vertex7205 reverse
face link face1377 face489 edges edge7784 edge2163 vertices
vertex7205 vertex2065 reverse
face link face1498 face759 edges edge7261 edge3530 vertices
79
vertex6725 vertex3277 reverse
face link face1377 face1502 edges edge7784 edge7287 vertices
vertex7205 vertex6749 reverse
face link face1502 face1387 edges edge7287 edge7821 vertices
vertex6749 vertex7239 reverse
face link face1387 face499 edges edge7821 edge2165 vertices
vertex7239 vertex2067 reverse
face link face1387 face1506 edges edge7821 edge7313 vertices
vertex7239 vertex6773 reverse
face link face1502 face769 edges edge7287 edge3531 vertices
vertex6749 vertex3279 reverse
face link face1506 face1397 edges edge7313 edge7858 vertices
vertex6773 vertex7273 reverse
face link face1506 face779 edges edge7313 edge3532 vertices
vertex6773 vertex3281 reverse
face link face1397 face509 edges edge7858 edge2167 vertices
vertex7273 vertex2069 reverse
LINKING ALL THE COMPLETE JETCENTERS
face link face1452 face644 edges edge7891 edge3773 vertices
vertex7303 vertex3433
face link face1452 face115 edges edge7891 edge7364 vertices
vertex7303 vertex6819
face link face1452 face1456 edges edge7891 edge7900 vertices
vertex7303 vertex7311
face link face1456 face654 edges edge7900 edge3774 vertices
vertex7311 vertex3435
face link face1456 face122 edges edge7900 edge7401 vertices
vertex7311 vertex6853
face link face1456 face1460 edges edge7900 edge7909 vertices
vertex7311 vertex7319
face link face1460 face1464 edges edge7909 edge7918 vertices
vertex7319 vertex7327
face link face1460 face129 edges edge7909 edge7438 vertices
vertex7319 vertex6887
face link face1460 face664 edges edge7909 edge3775 vertices
vertex7319 vertex3437
face link face1464 face674 edges edge7918 edge3776 vertices
vertex7327 vertex3439
face link face1464 face136 edges edge7918 edge7475 vertices
vertex7327 vertex6921
face link face1464 face1468 edges edge7918 edge7927 vertices
vertex7327 vertex7335
face link face1472 face1468 edges edge7936 edge7927 vertices
vertex7343 vertex7335
face link face1468 face143 edges edge7927 edge7512 vertices
vertex7335 vertex6955
face link face1468 face684 edges edge7927 edge3777 vertices
vertex7335 vertex3441
face link face1472 face694 edges edge7936 edge3778 vertices
vertex7343 vertex3443
face link face1472 face150 edges edge7936 edge7549 vertices
vertex7343 vertex6989
face link face1472 face1476 edges edge7936 edge7945 vertices
80
vertex7343 vertex7351
face link face1476 face1480 edges edge7945 edge7954 vertices
vertex7351 vertex7359
face link face1476 face157 edges edge7945 edge7586 vertices
vertex7351 vertex7023
face link face1476 face704 edges edge7945 edge3779 vertices
vertex7351 vertex3445
face link face1480 face714 edges edge7954 edge3780 vertices
vertex7359 vertex3447
face link face1480 face164 edges edge7954 edge7623 vertices
vertex7359 vertex7057
face link face1480 face1484 edges edge7954 edge7963 vertices
vertex7359 vertex7367
face link face1484 face171 edges edge7963 edge7660 vertices
vertex7367 vertex7091
face link face1484 face724 edges edge7963 edge3781 vertices
vertex7367 vertex3449
face link face1480 face1488 edges edge7954 edge7972 vertices
vertex7359 vertex7375
face link face1488 face178 edges edge7972 edge7697 vertices
vertex7375 vertex7125
face link face1488 face734 edges edge7972 edge3782 vertices
vertex7375 vertex3451
face link face1488 face1492 edges edge7972 edge7981 vertices
vertex7375 vertex7383
face link face1492 face744 edges edge7981 edge3783 vertices
vertex7383 vertex3453
face link face1492 face185 edges edge7981 edge7734 vertices
vertex7383 vertex7159
face link face1492 face1496 edges edge7981 edge7990 vertices
vertex7383 vertex7391
face link face1496 face754 edges edge7990 edge3784 vertices
vertex7391 vertex3455
face link face1496 face192 edges edge7990 edge7771 vertices
vertex7391 vertex7193
face link face1496 face1500 edges edge7990 edge7999 vertices
vertex7391 vertex7399
face link face1500 face1504 edges edge7999 edge8008 vertices
vertex7399 vertex7407
face link face1504 face1508 edges edge8008 edge8017 vertices
vertex7407 vertex7415
face link face1500 face199 edges edge7999 edge7808 vertices
vertex7399 vertex7227
face link face1500 face764 edges edge7999 edge3785 vertices
vertex7399 vertex3457
face link face1504 face774 edges edge8008 edge3786 vertices
vertex7407 vertex3459
face link face1508 face784 edges edge8017 edge3787 vertices
vertex7415 vertex3461
face link face1504 face206 edges edge8008 edge7845 vertices
vertex7407 vertex7261
face link face1508 face213 edges edge8017 edge7882 vertices
vertex7415 vertex7295
linking the jetcenters of the bottom of the channel one of them has to be reversed but the otherones are not
81
face link face115 face374 edges edge7364 edge2394 vertices
vertex6819 vertex2221 reverse
face link face374 face384 edges edge2394 edge2396 vertices
vertex2221 vertex2223
face link face384 face394 edges edge2396 edge2398 vertices
vertex2223 vertex2225
face link face394 face404 edges edge2398 edge2400 vertices
vertex2225 vertex2227
face link face404 face414 edges edge2400 edge2402 vertices
vertex2227 vertex2229
face link face414 face424 edges edge2402 edge2404 vertices
vertex2229 vertex2231
face link face424 face434 edges edge2404 edge2406 vertices
vertex2231 vertex2233
face link face434 face444 edges edge2406 edge2408 vertices
vertex2233 vertex2235
face link face444 face454 edges edge2408 edge2410 vertices
vertex2235 vertex2237
face link face454 face464 edges edge2410 edge2412 vertices
vertex2237 vertex2239
face link face464 face474 edges edge2412 edge2414 vertices
vertex2239 vertex2241
face link face474 face484 edges edge2414 edge2416 vertices
vertex2241 vertex2243
face link face484 face494 edges edge2416 edge2418 vertices
vertex2243 vertex2245
face link face494 face504 edges edge2418 edge2420 vertices
vertex2245 vertex2247
face link face504 face514 edges edge2420 edge2422 vertices
vertex2247 vertex2249
UP TO THIS POINT ALL THE FACES ARE CONNCTED SUCCESSFULLY
LINKING THE FIRST THREE JET TELEPHONES
face link face912 face117 edges edge6950 edge6960 vertices
vertex6437 vertex6446 reverse
face link face912 face1600 edges edge6950 edge7890 vertices
vertex6437 vertex7303 reverse
face link face912 face372 edges edge6950 edge2168 vertices
vertex6437 vertex2041
face link face117 face376 edges edge6959 edge2304 vertices
vertex6447 vertex2101 reverse
face link face1600 face377 edges edge7890 edge2423 vertices
vertex7303 vertex2221 reverse
face link face372 face382 edges edge2168 edge2169 vertices
vertex2041 vertex2043
face link face377 face387 edges edge2423 edge2424 vertices
vertex2221 vertex2223
face link face376 face386 edges edge2304 edge2306 vertices
vertex2101 vertex2103
face link face387 face397 edges edge2424 edge2425 vertices
vertex2223 vertex2225
face link face386 face396 edges edge2306 edge2308 vertices
82
vertex2103 vertex2105
face link face382 face392 edges edge2169 edge2170 vertices
vertex2043 vertex2045
face link face382 face392 edges edge2169 edge2170 vertices
vertex2043 vertex2045
face link face382 face392 edges edge2169 edge2170 vertices
vertex2043 vertex2045
face link face382 face392 edges edge2169 edge2170 vertices
vertex2043 vertex2045
face link face397 face407 edges edge2425 edge2426 vertices
vertex2225 vertex2227
face link face392 face402 edges edge2170 edge2171 vertices
vertex2045 vertex2047
face link face396 face406 edges edge2290 edge2291 vertices
vertex2104 vertex2106
face link face407 face417 edges edge2426 edge2427 vertices
vertex2227 vertex2229
face link face417 face427 edges edge2427 edge2428 vertices
vertex2229 vertex2231
face link face427 face437 edges edge2428 edge2429 vertices
vertex2231 vertex2233
face link face437 face447 edges edge2429 edge2430 vertices
vertex2233 vertex2235
face link face447 face457 edges edge2430 edge2431 vertices
vertex2235 vertex2237
face link face457 face467 edges edge2431 edge2432 vertices
vertex2237 vertex2239
face link face467 face477 edges edge2432 edge2433 vertices
vertex2239 vertex2241
face link face477 face487 edges edge2433 edge2434 vertices
vertex2241 vertex2243
face link face487 face487 edges edge2434 edge2434 vertices
vertex2243 vertex2243
face link face487 face487 edges edge2434 edge2434 vertices
vertex2243 vertex2243
face link face487 face487 edges edge2434 edge2434 vertices
vertex2243 vertex2243
face link face487 face497 edges edge2434 edge2435 vertices
vertex2243 vertex2245
face link face497 face507 edges edge2435 edge2436 vertices
vertex2245 vertex2247
face link face507 face517 edges edge2436 edge2437 vertices
vertex2247 vertex2249
face link face406 face416 edges edge2291 edge2292 vertices
vertex2106 vertex2108
face link face416 face426 edges edge2292 edge2293 vertices
vertex2108 vertex2110
face link face426 face436 edges edge2293 edge2294 vertices
vertex2110 vertex2112
face link face436 face446 edges edge2294 edge2295 vertices
vertex2112 vertex2114
face link face446 face456 edges edge2295 edge2296 vertices
vertex2114 vertex2116
face link face456 face466 edges edge2296 edge2297 vertices
vertex2116 vertex2118
face link face466 face476 edges edge2297 edge2298 vertices
83
vertex2118 vertex2120
face link face486 face496 edges edge2299 edge2300 vertices
vertex2122 vertex2124
face link face476 face486 edges edge2298 edge2299 vertices
vertex2120 vertex2122
face link face496 face506 edges edge2300 edge2301 vertices
vertex2124 vertex2126
face link face506 face516 edges edge2301 edge2302 vertices
vertex2126 vertex2128
face link face392 face402 edges edge2142 edge2144 vertices
vertex2044 vertex2046
face link face402 face412 edges edge2171 edge2172 vertices
vertex2047 vertex2049
face link face412 face422 edges edge2172 edge2173 vertices
vertex2049 vertex2051
face link face422 face432 edges edge2173 edge2174 vertices
vertex2051 vertex2053
face link face432 face442 edges edge2174 edge2175 vertices
vertex2053 vertex2055
face link face442 face452 edges edge2175 edge2176 vertices
vertex2055 vertex2057
face link face452 face462 edges edge2176 edge2177 vertices
vertex2057 vertex2059
face link face462 face472 edges edge2177 edge2178 vertices
vertex2059 vertex2061
face link face472 face482 edges edge2178 edge2179 vertices
vertex2061 vertex2063
face link face482 face492 edges edge2179 edge2180 vertices
vertex2063 vertex2065
face link face492 face502 edges edge2180 edge2181 vertices
vertex2065 vertex2067
face link face502 face512 edges edge2181 edge2182 vertices
vertex2067 vertex2069
LINKING THE TELEPHONES OF THE BOTTOM OF THE PLENUM
face link face912 face922 edges edge6950 edge6976 vertices
vertex6437 vertex6461
face link face922 face932 edges edge6976 edge7002 vertices
vertex6461 vertex6485
face link face932 face942 edges edge7002 edge7028 vertices
vertex6485 vertex6509
face link face942 face952 edges edge7028 edge7054 vertices
vertex6509 vertex6533
face link face952 face962 edges edge7054 edge7080 vertices
vertex6533 vertex6557
face link face962 face972 edges edge7080 edge7106 vertices
vertex6557 vertex6581
face link face972 face982 edges edge7106 edge7132 vertices
vertex6581 vertex6605
face link face982 face992 edges edge7132 edge7158 vertices
vertex6605 vertex6629
face link face992 face1002 edges edge7158 edge7184 vertices
vertex6629 vertex6653
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vertex6653 vertex6677
84
face link face1012 face1022 edges edge7210 edge7236 vertices
vertex6677 vertex6701
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vertex6518 vertex6542
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vertex6542 vertex6566
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vertex6566 vertex6590
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vertex6590 vertex6614
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vertex6614 vertex6638
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vertex6638 vertex6662
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vertex6662 vertex6686
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vertex6710 vertex6734
face link face1022 face1032 edges edge7236 edge7262 vertices
vertex6701 vertex6725
face link face1032 face1042 edges edge7262 edge7288 vertices
vertex6725 vertex6749
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vertex6735 vertex6759
face link face208 face215 edges edge7297 edge7323 vertices
vertex6759 vertex6783
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vertex7303 vertex7311
face link face1602 face1604 edges edge7899 edge7908 vertices
vertex7311 vertex7319
face link face1604 face1606 edges edge7908 edge7917 vertices
vertex7319 vertex7327
face link face1606 face1608 edges edge7917 edge7926 vertices
vertex7327 vertex7335
face link face1608 face1610 edges edge7926 edge7935 vertices
vertex7335 vertex7343
face link face1610 face1612 edges edge7935 edge7944 vertices
vertex7343 vertex7351
face link face1612 face1614 edges edge7944 edge7953 vertices
vertex7351 vertex7359
face link face1614 face1616 edges edge7953 edge7962 vertices
vertex7359 vertex7367
face link face1616 face1618 edges edge7962 edge7971 vertices
vertex7367 vertex7375
85
face link face1618 face1620 edges edge7971 edge7980 vertices
vertex7375 vertex7383
face link face1620 face1622 edges edge7980 edge7989 vertices
vertex7383 vertex7391
face link face1622 face1624 edges edge7989 edge7998 vertices
vertex7391 vertex7399
face link face1624 face1626 edges edge7998 edge8007 vertices
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face link face1626 face1628 edges edge8007 edge8016 vertices
vertex7407 vertex7415
LINKING ALL THE TELEPHONES OF THE TOP OF THE CHANNEL
face link face912 face1510 edges edge6950 edge7339 vertices
vertex6437 vertex6797 reverse
face link face117 face1512 edges edge6959 edge7349 vertices
vertex6447 vertex6807
face link face1600 face1514 edges edge7890 edge7363 vertices
vertex7303 vertex6819
face link face1510 face1516 edges edge7339 edge7376 vertices
vertex6797 vertex6831
face link face1516 face1522 edges edge7376 edge7413 vertices
vertex6831 vertex6865
face link face1522 face1528 edges edge7413 edge7450 vertices
vertex6865 vertex6899
face link face1528 face1534 edges edge7450 edge7487 vertices
vertex6899 vertex6933
face link face1534 face1540 edges edge7487 edge7524 vertices
vertex6933 vertex6967
face link face1540 face1546 edges edge7524 edge7561 vertices
vertex6967 vertex7001
face link face1546 face1552 edges edge7561 edge7598 vertices
vertex7001 vertex7035
face link face1552 face1558 edges edge7598 edge7635 vertices
vertex7035 vertex7069
face link face1558 face1564 edges edge7635 edge7672 vertices
vertex7069 vertex7103
face link face1564 face1570 edges edge7672 edge7709 vertices
vertex7103 vertex7137
face link face1570 face1576 edges edge7709 edge7746 vertices
vertex7137 vertex7171
face link face1576 face1582 edges edge7746 edge7783 vertices
vertex7171 vertex7205
face link face1582 face1588 edges edge7783 edge7820 vertices
vertex7205 vertex7239
face link face1588 face1594 edges edge7820 edge7857 vertices
vertex7239 vertex7273
face link face1512 face1518 edges edge7350 edge7387 vertices
vertex6806 vertex6840
face link face1518 face1524 edges edge7387 edge7424 vertices
vertex6840 vertex6874
face link face1524 face1530 edges edge7424 edge7461 vertices
vertex6874 vertex6908
face link face1530 face1536 edges edge7461 edge7498 vertices
vertex6908 vertex6942
face link face1536 face1542 edges edge7498 edge7535 vertices
86
vertex6942 vertex6976
face link face1542 face1548 edges edge7535 edge7572 vertices
vertex6976 vertex7010
face link face1548 face1554 edges edge7572 edge7609 vertices
vertex7010 vertex7044
face link face1554 face1560 edges edge7609 edge7646 vertices
vertex7044 vertex7078
face link face1560 face1566 edges edge7646 edge7683 vertices
vertex7078 vertex7112
face link face1566 face1572 edges edge7683 edge7720 vertices
vertex7112 vertex7146
face link face1572 face1578 edges edge7720 edge7757 vertices
vertex7146 vertex7180
face link face1578 face1584 edges edge7757 edge7794 vertices
vertex7180 vertex7214
face link face1584 face1590 edges edge7794 edge7831 vertices
vertex7214 vertex7248
face link face1590 face1596 edges edge7831 edge7868 vertices
vertex7248 vertex7282
face link face1514 face1520 edges edge7363 edge7400 vertices
vertex6819 vertex6853
face link face1520 face1526 edges edge7400 edge7437 vertices
vertex6853 vertex6887
face link face1526 face1532 edges edge7437 edge7474 vertices
vertex6887 vertex6921
face link face1532 face1538 edges edge7474 edge7511 vertices
vertex6921 vertex6955
face link face1538 face1544 edges edge7511 edge7548 vertices
vertex6955 vertex6989
face link face1544 face1550 edges edge7548 edge7585 vertices
vertex6989 vertex7023
face link face1550 face1556 edges edge7585 edge7622 vertices
vertex7023 vertex7057
face link face1556 face1562 edges edge7622 edge7659 vertices
vertex7057 vertex7091
face link face1562 face1568 edges edge7659 edge7696 vertices
vertex7091 vertex7125
face link face1568 face1574 edges edge7696 edge7733 vertices
vertex7125 vertex7159
face link face1574 face1580 edges edge7733 edge7770 vertices
vertex7159 vertex7193
face link face1580 face1586 edges edge7770 edge7807 vertices
vertex7193 vertex7227
face link face1586 face1592 edges edge7807 edge7844 vertices
vertex7227 vertex7261
face link face1592 face1598 edges edge7844 edge7881 vertices
vertex7261 vertex7295
LINKING ALL THE TELEPHONES OF THE TOP OF THE PLENUM
face link face912 face642 edges edge6950 edge3489 vertices
vertex6437 vertex3253 reverse
face link face642 face647 edges edge3489 edge3744 vertices
vertex3253 vertex3433
face link face117 face646 edges edge6959 edge3638 vertices
vertex6447 vertex3313
87
face link face642 face652 edges edge3489 edge3491 vertices
vertex3253 vertex3255
face link face652 face662 edges edge3491 edge3493 vertices
vertex3255 vertex3257
face link face662 face672 edges edge3493 edge3495 vertices
vertex3257 vertex3259
face link face672 face682 edges edge3495 edge3497 vertices
vertex3259 vertex3261
face link face682 face692 edges edge3497 edge3499 vertices
vertex3261 vertex3263
face link face692 face702 edges edge3499 edge3501 vertices
vertex3263 vertex3265
face link face702 face712 edges edge3501 edge3503 vertices
vertex3265 vertex3267
face link face712 face722 edges edge3503 edge3505 vertices
vertex3267 vertex3269
face link face722 face732 edges edge3505 edge3507 vertices
vertex3269 vertex3271
face link face732 face742 edges edge3507 edge3509 vertices
vertex3271 vertex3273
face link face742 face752 edges edge3509 edge3511 vertices
vertex3273 vertex3275
face link face752 face762 edges edge3511 edge3513 vertices
vertex3275 vertex3277
face link face762 face772 edges edge3513 edge3515 vertices
vertex3277 vertex3279
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vertex3314 vertex3316
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vertex3316 vertex3318
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vertex3318 vertex3320
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vertex3320 vertex3322
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vertex3322 vertex3324
face link face706 face716 edges edge3665 edge3667 vertices
vertex3324 vertex3326
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vertex3326 vertex3328
face link face726 face736 edges edge3669 edge3671 vertices
vertex3328 vertex3330
face link face736 face746 edges edge3671 edge3673 vertices
vertex3330 vertex3332
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vertex3332 vertex3334
face link face756 face766 edges edge3675 edge3677 vertices
vertex3334 vertex3336
face link face766 face776 edges edge3677 edge3679 vertices
vertex3336 vertex3338
face link face776 face786 edges edge3679 edge3681 vertices
88
vertex3338 vertex3340
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vertex3433 vertex3435
face link face657 face667 edges edge3746 edge3748 vertices
vertex3435 vertex3437
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vertex3437 vertex3439
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vertex3439 vertex3441
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vertex3441 vertex3443
face link face697 face707 edges edge3754 edge3756 vertices
vertex3443 vertex3445
face link face707 face717 edges edge3756 edge3758 vertices
vertex3445 vertex3447
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vertex3447 vertex3449
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vertex3449 vertex3451
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vertex3457 vertex3459
face link face777 face787 edges edge3770 edge3772 vertices
vertex3459 vertex3461
face link face647 face1600 edges edge3685 edge6963 vertices
vertex3345 vertex6449
LINKING OUTBOXES ON THE PLENUM
face modify face911 side vertex4404 vertex4405
face modify face918 side vertex4405 vertex4404
face link face911 face915 edges edge4778 edge4898 vertices
vertex4374 vertex4434
face link face915 face645 edges edge4899 edge3833 vertices
vertex4480 vertex3463 reverse
face link face911 face641 edges edge4779 edge3578 vertices
vertex4405 vertex3283 reverse
face link face918 face648 edges edge4825 edge3686 vertices
vertex4436 vertex3347 reverse
face link face645 face655 edges edge3833 edge3834 vertices
vertex3463 vertex3465
face link face655 face665 edges edge3834 edge3835 vertices
vertex3465 vertex3467
face link face665 face675 edges edge3835 edge3836 vertices
vertex3467 vertex3469
face link face675 face685 edges edge3836 edge3837 vertices
vertex3469 vertex3471
face link face685 face695 edges edge3837 edge3838 vertices
89
vertex3471 vertex3473
face link face695 face705 edges edge3838 edge3839 vertices
vertex3473 vertex3475
face link face705 face715 edges edge3839 edge3840 vertices
vertex3475 vertex3477
face link face715 face725 edges edge3840 edge3841 vertices
vertex3477 vertex3479
face link face725 face735 edges edge3841 edge3842 vertices
vertex3479 vertex3481
face link face735 face745 edges edge3842 edge3843 vertices
vertex3481 vertex3483
face link face745 face755 edges edge3843 edge3844 vertices
vertex3483 vertex3485
face link face755 face765 edges edge3844 edge3845 vertices
vertex3485 vertex3487
face link face765 face775 edges edge3845 edge3846 vertices
vertex3487 vertex3489
face link face775 face785 edges edge3846 edge3847 vertices
vertex3489 vertex3491
face link face648 face658 edges edge3686 edge3690 vertices
vertex3347 vertex3353
face link face658 face668 edges edge3690 edge3694 vertices
vertex3353 vertex3359
face link face668 face678 edges edge3694 edge3698 vertices
vertex3359 vertex3365
face link face678 face688 edges edge3698 edge3702 vertices
vertex3365 vertex3371
face link face688 face698 edges edge3702 edge3706 vertices
vertex3371 vertex3377
face link face698 face708 edges edge3706 edge3710 vertices
vertex3377 vertex3383
face link face708 face718 edges edge3710 edge3714 vertices
vertex3383 vertex3389
face link face718 face728 edges edge3714 edge3718 vertices
vertex3389 vertex3395
face link face728 face738 edges edge3718 edge3722 vertices
vertex3395 vertex3401
face link face738 face748 edges edge3722 edge3726 vertices
vertex3401 vertex3407
face link face748 face758 edges edge3726 edge3730 vertices
vertex3407 vertex3413
face link face758 face768 edges edge3730 edge3734 vertices
vertex3413 vertex3419
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vertex3419 vertex3425
face link face778 face788 edges edge3738 edge3742 vertices
vertex3425 vertex3431
face link face641 face650 edges edge3578 edge3579 vertices
vertex3283 vertex3285
face link face650 face660 edges edge3579 edge3580 vertices
vertex3285 vertex3287
face link face660 face670 edges edge3580 edge3581 vertices
vertex3287 vertex3289
face link face670 face680 edges edge3581 edge3582 vertices
vertex3289 vertex3291
face link face680 face690 edges edge3582 edge3583 vertices
90
vertex3291 vertex3293
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vertex3293 vertex3295
face link face700 face710 edges edge3584 edge3585 vertices
vertex3295 vertex3297
face link face710 face720 edges edge3585 edge3586 vertices
vertex3297 vertex3299
face link face720 face730 edges edge3586 edge3587 vertices
vertex3299 vertex3301
face link face730 face740 edges edge3587 edge3588 vertices
vertex3301 vertex3303
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vertex3303 vertex3305
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vertex3305 vertex3307
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vertex3307 vertex3309
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vertex3309 vertex3311
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vertex4480 vertex4482
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vertex4482 vertex4484
face link face935 face945 edges edge4903 edge4905 vertices
vertex4484 vertex4486
face link face945 face955 edges edge4905 edge4907 vertices
vertex4486 vertex4488
face link face955 face965 edges edge4907 edge4909 vertices
vertex4488 vertex4490
face link face965 face975 edges edge4909 edge4911 vertices
vertex4490 vertex4492
face link face975 face985 edges edge4911 edge4913 vertices
vertex4492 vertex4494
face link face985 face995 edges edge4913 edge4915 vertices
vertex4494 vertex4496
face link face995 face1005 edges edge4915 edge4917 vertices
vertex4496 vertex4498
face link face1005 face1015 edges edge4917 edge4919 vertices
vertex4498 vertex4500
face link face1015 face1025 edges edge4919 edge4921 vertices
vertex4500 vertex4502
face link face1025 face1035 edges edge4921 edge4923 vertices
vertex4502 vertex4504
face link face1035 face1045 edges edge4923 edge4925 vertices
vertex4504 vertex4506
face link face1045 face1055 edges edge4925 edge4927 vertices
vertex4506 vertex4508
face link face918 face928 edges edge4825 edge4828 vertices
vertex4436 vertex4439
face link face928 face938 edges edge4828 edge4831 vertices
vertex4439 vertex4442
face link face938 face948 edges edge4831 edge4834 vertices
vertex4442 vertex4445
face link face948 face958 edges edge4834 edge4837 vertices
vertex4445 vertex4448
face link face958 face968 edges edge4837 edge4840 vertices
91
vertex4448 vertex4451
face link face968 face978 edges edge4840 edge4843 vertices
vertex4451 vertex4454
face link face978 face988 edges edge4843 edge4846 vertices
vertex4454 vertex4457
face link face988 face998 edges edge4846 edge4849 vertices
vertex4457 vertex4460
face link face998 face1008 edges edge4849 edge4852 vertices
vertex4460 vertex4463
face link face1008 face1018 edges edge4852 edge4855 vertices
vertex4463 vertex4466
face link face1018 face1028 edges edge4855 edge4858 vertices
vertex4466 vertex4469
face link face1028 face1038 edges edge4858 edge4861 vertices
vertex4469 vertex4472
face link face1038 face1048 edges edge4861 edge4864 vertices
vertex4472 vertex4475
face link face1048 face1058 edges edge4864 edge4867 vertices
vertex4475 vertex4478
face link face911 face920 edges edge108 edge118 vertices
vertex88 vertex94
face link face920 face930 edges edge118 edge128 vertices
vertex94 vertex100
face link face930 face940 edges edge4783 edge4785 vertices
vertex4409 vertex4411
face link face940 face950 edges edge4785 edge4787 vertices
vertex4411 vertex4413
face link face950 face960 edges edge4787 edge4789 vertices
vertex4413 vertex4415
face link face960 face970 edges edge4789 edge4791 vertices
vertex4415 vertex4417
face link face970 face980 edges edge4791 edge4793 vertices
vertex4417 vertex4419
face link face980 face990 edges edge4793 edge4795 vertices
vertex4419 vertex4421
face link face990 face1000 edges edge4795 edge4797 vertices
vertex4421 vertex4423
face link face1000 face1010 edges edge4797 edge4799 vertices
vertex4423 vertex4425
face link face1010 face1020 edges edge4799 edge4801 vertices
vertex4425 vertex4427
face link face1020 face1030 edges edge4801 edge4803 vertices
vertex4427 vertex4429
face link face1030 face1040 edges edge4803 edge4805 vertices
vertex4429 vertex4431
face link face1040 face1050 edges edge4805 edge4807 vertices
vertex4431 vertex4433
LINKING THE TOP OF THE CHANEL OUTBOXES
face modify face1256 side vertex6322 vertex6321
face modify face1263 side vertex6322 vertex6321
face modify face1260 side vertex6397 vertex6396
92
face link face1256 face1260 edges edge6803 edge6923 vertices
vertex6322 vertex6397
face link face1256 face371 edges edge6774 edge2053 vertices
vertex6292 vertex1955 reverse
face link face371 face375 edges edge2053 edge2336 vertices
vertex1955 vertex2135
face link face1263 face378 edges edge6820 edge2228 vertices
vertex6322 vertex2071 reverse
face link face1263 face1273 edges edge6820 edge6823 vertices
vertex6322 vertex6324
face link face1273 face1283 edges edge6823 edge6826 vertices
vertex6324 vertex6326
face link face1283 face1293 edges edge6826 edge6829 vertices
vertex6326 vertex6328
face link face1293 face1303 edges edge6829 edge6832 vertices
vertex6328 vertex6330
face link face1303 face1313 edges edge6832 edge6835 vertices
vertex6330 vertex6332
face link face1313 face1323 edges edge6835 edge6838 vertices
vertex6332 vertex6334
face link face1323 face1333 edges edge6838 edge6841 vertices
vertex6334 vertex6336
face link face1333 face1343 edges edge6841 edge6844 vertices
vertex6336 vertex6338
face link face1343 face1353 edges edge6844 edge6847 vertices
vertex6338 vertex6340
face link face1353 face1363 edges edge6847 edge6850 vertices
vertex6340 vertex6342
face link face1363 face1373 edges edge6850 edge6853 vertices
vertex6342 vertex6344
face link face1373 face1383 edges edge6853 edge6856 vertices
vertex6344 vertex6346
face link face1383 face1393 edges edge6856 edge6859 vertices
vertex6346 vertex6348
face link face1393 face1403 edges edge6859 edge6862 vertices
vertex6348 vertex6350
face link face1256 face1265 edges edge6774 edge6776 vertices
vertex6292 vertex6294
face link face1265 face1275 edges edge6776 edge6778 vertices
vertex6294 vertex6296
face link face1275 face1285 edges edge6778 edge6780 vertices
vertex6296 vertex6298
face link face1285 face1295 edges edge6780 edge6782 vertices
vertex6298 vertex6300
face link face1295 face1305 edges edge6782 edge6784 vertices
vertex6300 vertex6302
face link face1305 face1315 edges edge6784 edge6786 vertices
vertex6302 vertex6304
face link face1315 face1325 edges edge6786 edge6788 vertices
vertex6304 vertex6306
face link face1325 face1335 edges edge6788 edge6790 vertices
vertex6306 vertex6308
face link face1335 face1345 edges edge6790 edge6792 vertices
vertex6308 vertex6310
face link face1345 face1355 edges edge6792 edge6794 vertices
vertex6310 vertex6312
93
face link face1355 face1365 edges edge6794 edge6796 vertices
vertex6312 vertex6314
face link face1365 face1375 edges edge6796 edge6798 vertices
vertex6314 vertex6316
face link face1375 face1385 edges edge6798 edge6800 vertices
vertex6316 vertex6318
face link face1385 face1395 edges edge6800 edge6802 vertices
vertex6318 vertex6320
face link face1260 face1270 edges edge6894 edge6896 vertices
vertex6353 vertex6356
face link face1270 face1280 edges edge6896 edge6898 vertices
vertex6356 vertex6359
face link face1280 face1290 edges edge6898 edge6900 vertices
vertex6359 vertex6362
face link face1290 face1300 edges edge6900 edge6902 vertices
vertex6362 vertex6365
face link face1300 face1310 edges edge6902 edge6904 vertices
vertex6365 vertex6368
face link face1310 face1320 edges edge6904 edge6906 vertices
vertex6368 vertex6371
face link face1320 face1330 edges edge6906 edge6908 vertices
vertex6371 vertex6374
face link face1330 face1340 edges edge6908 edge6910 vertices
vertex6374 vertex6377
face link face1340 face1350 edges edge6910 edge6912 vertices
vertex6377 vertex6380
face link face1350 face1360 edges edge6912 edge6914 vertices
vertex6380 vertex6383
face link face1360 face1370 edges edge6914 edge6916 vertices
vertex6383 vertex6386
face link face1370 face1380 edges edge6916 edge6918 vertices
vertex6386 vertex6389
face link face1380 face1390 edges edge6918 edge6920 vertices
vertex6389 vertex6392
face link face1390 face1400 edges edge6920 edge6922 vertices
vertex6392 vertex6395
LINKING THE BOTTOM OF THE CHANEL OUTBOXES
face link face375 face385 edges edge2440 edge2443 vertices
vertex2251 vertex2253
face link face385 face395 edges edge2443 edge2446 vertices
vertex2253 vertex2255
face link face395 face405 edges edge2446 edge2449 vertices
vertex2255 vertex2257
face link face405 face415 edges edge2449 edge2452 vertices
vertex2257 vertex2259
face link face415 face425 edges edge2452 edge2455 vertices
vertex2259 vertex2261
face link face425 face435 edges edge2455 edge2458 vertices
vertex2261 vertex2263
face link face435 face445 edges edge2458 edge2461 vertices
vertex2263 vertex2265
face link face445 face455 edges edge2461 edge2464 vertices
vertex2265 vertex2267
face link face455 face465 edges edge2464 edge2467 vertices
94
vertex2267 vertex2269
face link face465 face475 edges edge2467 edge2470 vertices
vertex2269 vertex2271
face link face475 face485 edges edge2470 edge2473 vertices
vertex2271 vertex2273
face link face485 face495 edges edge2473 edge2476 vertices
vertex2273 vertex2275
face link face495 face505 edges edge2476 edge2479 vertices
vertex2275 vertex2277
face link face505 face515 edges edge2479 edge2482 vertices
vertex2277 vertex2279
face link face378 face388 edges edge2245 edge2248 vertices
vertex2135 vertex2141
face link face388 face398 edges edge2248 edge2251 vertices
vertex2141 vertex2147
face link face398 face408 edges edge2251 edge2254 vertices
vertex2147 vertex2153
face link face408 face418 edges edge2254 edge2257 vertices
vertex2153 vertex2159
face link face418 face428 edges edge2257 edge2260 vertices
vertex2159 vertex2165
face link face428 face438 edges edge2260 edge2263 vertices
vertex2165 vertex2171
face link face438 face448 edges edge2263 edge2266 vertices
vertex2171 vertex2177
face link face448 face458 edges edge2266 edge2269 vertices
vertex2177 vertex2183
face link face458 face468 edges edge2269 edge2272 vertices
vertex2183 vertex2189
face link face468 face478 edges edge2272 edge2275 vertices
vertex2189 vertex2195
face link face478 face488 edges edge2275 edge2278 vertices
vertex2195 vertex2201
face link face488 face498 edges edge2278 edge2281 vertices
vertex2201 vertex2207
face link face498 face508 edges edge2281 edge2284 vertices
vertex2207 vertex2213
face link face508 face518 edges edge2284 edge2287 vertices
vertex2213 vertex2219
face link face371 face380 edges edge2185 edge2188 vertices
vertex2071 vertex2073
face link face380 face390 edges edge2188 edge2191 vertices
vertex2073 vertex2075
face link face390 face400 edges edge2191 edge2194 vertices
vertex2075 vertex2077
face link face400 face410 edges edge2194 edge2197 vertices
vertex2077 vertex2079
face link face410 face420 edges edge2197 edge2200 vertices
vertex2079 vertex2081
face link face420 face430 edges edge2200 edge2203 vertices
vertex2081 vertex2083
face link face430 face440 edges edge2203 edge2206 vertices
vertex2083 vertex2085
face link face440 face450 edges edge2206 edge2209 vertices
vertex2085 vertex2087
face link face450 face460 edges edge2209 edge2212 vertices
95
vertex2087 vertex2089
face link face460 face470 edges edge2212 edge2215 vertices
vertex2089 vertex2091
face link face470 face480 edges edge2215 edge2218 vertices
vertex2091 vertex2093
face link face480 face490 edges edge2218 edge2221 vertices
vertex2093 vertex2095
face link face490 face500 edges edge2221 edge2224 vertices
vertex2095 vertex2097
face link face500 face510 edges edge2224 edge2227 vertices
vertex2097 vertex2099
TOP SIDE BOX beginning of channel
face link face1649 face1633 edges edge97 edge3533 vertices
vertex4374 vertex3162 reverse
TOP SIDE BOXES
face link face1650 face1651 edges edge4749 edge4751 vertices
vertex4376 vertex4378
face link face1652 face1653 edges edge4753 edge4755 vertices
vertex4380 vertex4382
face link face1653 face1654 edges edge4755 edge4757 vertices
vertex4382 vertex4384
face link face1654 face1655 edges edge4757 edge4759 vertices
vertex4384 vertex4386
face link face1655 face1656 edges edge4759 edge4761 vertices
vertex4386 vertex4388
face link face1656 face114 edges edge4761 edge4763 vertices
vertex4388 vertex4390
face link face114 face1657 edges edge4763 edge4765 vertices
vertex4390 vertex4392
face link face1657 face1658 edges edge4765 edge4767 vertices
vertex4392 vertex4394
face link face1658 face1659 edges edge4767 edge4769 vertices
vertex4394 vertex4396
face link face1659 face1660 edges edge4769 edge4771 vertices
vertex4396 vertex4398
face link face1660 face1661 edges edge4771 edge4773 vertices
vertex4398 vertex4400
face link face1661 face1662 edges edge4773 edge4775 vertices
vertex4400 vertex4402
face link face1650 face1634 edges edge4900 edge8036 vertices
vertex4481 vertex3464 reverse
face link face1634 face1635 edges edge8036 edge8037 vertices
vertex3464 vertex3466
face link face1635 face1636 edges edge8037 edge8038 vertices
vertex3466 vertex3468
face link face1636 face1637 edges edge8038 edge8039 vertices
vertex3468 vertex3470
face link face1637 face1638 edges edge8039 edge8040 vertices
vertex3470 vertex3472
face link face1638 face1639 edges edge8040 edge8041 vertices
vertex3472 vertex3474
face link face1639 face6 edges edge8041 edge8042 vertices
96
vertex3474 vertex3476
face link face6 face1640 edges edge8042 edge8043 vertices
vertex3476 vertex3478
face link face1640 face1641 edges edge8043 edge8044 vertices
vertex3478 vertex3480
face link face1641 face1642 edges edge8044 edge8045 vertices
vertex3480 vertex3482
face link face1642 face1643 edges edge8045 edge8046 vertices
vertex3482 vertex3484
face link face1643 face1644 edges edge8046 edge8047 vertices
vertex3484 vertex3486
face link face1644 face1645 edges edge8047 edge8048 vertices
vertex3486 vertex3488
face link face1645 face1646 edges edge8048 edge8049 vertices
vertex3488 vertex3490
face link face1651 face1652 edges edge4751 edge4753 vertices
vertex4378 vertex4380
TOP SIDE BOX END OF CHANNEL
face link face1647 face1663 edges edge8050 edge99 vertices
vertex7433 vertex7435 reverse
TOP SIDE BOX BACK OF CHANNEL
face link face1648 face1664 edges edge12 edge8069 vertices
vertex8 vertex84 reverse
BOTTOM SIDE BOX
face link face1665 face1681 edges edge6773 edge2048 vertices
vertex6291 vertex1950 reverse
face link face1680 face1696 edges edge8071 edge8105 vertices
vertex7436 vertex7438 reverse
face link face1666 face1667 edges edge6894 edge6896 vertices
vertex6397 vertex6399
face link face1667 face1668 edges edge6896 edge6898 vertices
vertex6399 vertex6401
face link face1668 face1669 edges edge6898 edge6900 vertices
vertex6401 vertex6403
face link face1669 face1670 edges edge6900 edge6902 vertices
vertex6403 vertex6405
face link face1670 face1671 edges edge6902 edge6904 vertices
vertex6405 vertex6407
face link face1671 face209 edges edge6904 edge6906 vertices
vertex6407 vertex6409
face link face209 face1672 edges edge6906 edge6908 vertices
vertex6409 vertex6411
face link face1672 face1673 edges edge6908 edge6910 vertices
vertex6411 vertex6413
face link face1673 face1674 edges edge6910 edge6912 vertices
vertex6413 vertex6415
face link face1674 face1675 edges edge6912 edge6914 vertices
vertex6415 vertex6417
face link face1675 face1676 edges edge6914 edge6916 vertices
vertex6417 vertex6419
97
face link face1676 face1677 edges edge6916 edge6918 vertices
vertex6419 vertex6421
face link face1677 face1678 edges edge6918 edge6920 vertices
vertex6421 vertex6423
face link face1666 face1682 edges edge6894 edge8090 vertices
vertex6397 vertex2251 reverse
face link face1682 face1683 edges edge8090 edge8091 vertices
vertex2251 vertex2253
face link face1683 face1684 edges edge8091 edge8092 vertices
vertex2253 vertex2255
face link face1684 face1685 edges edge8092 edge8093 vertices
vertex2255 vertex2257
face link face1685 face1686 edges edge8093 edge8094 vertices
vertex2257 vertex2259
face link face1686 face1687 edges edge8094 edge8095 vertices
vertex2259 vertex2261
face link face1687 face1688 edges edge8095 edge8096 vertices
vertex2261 vertex2263
face link face1688 face1 edges edge8096 edge8097 vertices
vertex2263 vertex2265
face link face1 face1689 edges edge8097 edge8098 vertices
vertex2265 vertex2267
face link face1689 face1690 edges edge8098 edge8099 vertices
vertex2267 vertex2269
face link face1690 face1691 edges edge8099 edge8100 vertices
vertex2269 vertex2271
face link face1691 face1692 edges edge8100 edge8101 vertices
vertex2271 vertex2273
face link face1692 face1693 edges edge8101 edge8102 vertices
vertex2273 vertex2275
face link face1693 face1694 edges edge8102 edge8103 vertices
vertex2275 vertex2277
face link face1679 face1695 edges edge89 edge2227 vertices
vertex6320 vertex2039 reverse
MESHING BEGINS HERE
BOUNDARY LAYERS BEGINS HERE
BOUNDARY LAYER FOR THE bottom of plenum
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer1 face face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
98
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 edge edge97
edge4748 edge106 edge6946 edge6947 edge107 edge4749
edge4750 edge116 edge6972 edge6973 edge117 edge4751
edge4752 edge126 edge6998 edge6999 edge127 edge4753
edge4754 edge136 edge7024 edge7025 edge137 edge4755
edge4756 edge146 edge7050 edge7051 edge147 edge4757
edge4758 edge156 edge7076 edge7077 edge157 edge4759
edge4760 edge166 edge7102 edge7103 edge167 edge4761
edge4762 edge176 edge7128 edge7129 edge177 edge4763
edge4764 edge186 edge7154 edge7155 edge187 edge4765
edge4766 edge196 edge7180 edge7181 edge197 edge4767
edge4768 edge206 edge7206 edge7207 edge207 edge4769
edge4770 edge216 edge7232 edge7233 edge217 edge4771
edge4772 edge226 edge7258 edge7259 edge227 edge4773
edge4774 edge236 edge7284 edge7285 edge237 edge4775
edge4776 edge246 edge7310 edge7311 edge247 edge4777 add
MESHING THE PLENUM
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer2 face face4 face4 face5 face110
face110 edge edge99 edge8069 edge100 edge8052 edge98 add
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer4 face face1649 face1664 face1664
face1664 face1663 edge edge8052 edge98 edge100 edge8069
edge99 add
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer4 face face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face4 face2 face2 face2 face2 face2 face4
face5 face110 face110 edge edge9 edge3398 edge3399
edge3400 edge3401 edge3402 edge3403 edge3404 edge3406
edge3405 edge3407 edge3408 edge3409 edge3415 edge3410
edge3411 edge3412 edge3413 edge3414 edge3416 edge3417
edge3418 edge3419 edge3420 edge3421 edge3422 edge3423
edge3424 edge3425 edge3426 edge3427 edge3428 edge3429
edge3430 edge3431 edge3432 edge3433 edge3434 edge3435
edge3436 edge3437 edge3438 edge3439 edge3440 edge3441
edge3442 edge3443 edge3444 edge3445 edge3446 edge3447
99
edge3448 edge3449 edge3450 edge3451 edge3457 edge3452
edge3453 edge3454 edge3455 edge3456 edge3458 edge3459
edge3460 edge3461 edge3462 edge3463 edge3464 edge3465
edge3466 edge3467 edge3468 edge3469 edge3475 edge3481
edge3470 edge3471 edge3472 edge3473 edge3474 edge3476
edge3477 edge3478 edge3479 edge3480 edge3487 edge11
edge3482 edge3483 edge3484 edge3485 edge3486 edge8051
edge12 edge10 edge8034 add
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer5 face face1663 face1664 face1664
face1664 face1649 edge edge99 edge8069 edge100 edge98
edge8052 add
BOUNDARY LAYER OF THE HOLES
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer1 face face642 edge edge3534 add
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer7 face face117 face1600 edge edge4824
edge110 add
BONDARY LAYER OF THE CHANNEL
TARGET WALL BOUNDARY LAYER
BBBL
BBL
BBL
BBBL
BBL
BBL
BBBLLLLL
blayer create first $firstch growth $growthch rows $rowsch transition 1 trows 0
uniform
blayer attach b_layer8 face face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
100
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face105 face105 face106
face104 face104 edge edge2048 edge2049 edge2050 edge2051
edge2052 edge2053 edge2054 edge2055 edge2056 edge2057
edge2058 edge2059 edge2060 edge2061 edge2062 edge2063
edge2064 edge2065 edge2066 edge2072 edge2067 edge2068
edge2069 edge2070 edge2071 edge2084 edge2078 edge2073
edge2074 edge2075 edge2076 edge2077 edge2079 edge2080
edge2081 edge2082 edge2083 edge2090 edge2096 edge2085
edge2086 edge2087 edge2088 edge2089 edge2091 edge2092
edge2093 edge2094 edge2095 edge2102 edge2108 edge2097
edge2098 edge2099 edge2100 edge2101 edge2103 edge2104
edge2105 edge2106 edge2107 edge2114 edge2120 edge2109
edge2110 edge2111 edge2112 edge2113 edge2115 edge2116
edge2117 edge2118 edge2119 edge2126 edge2132 edge2121
edge2122 edge2123 edge2124 edge2125 edge2127 edge2128
edge2129 edge2130 edge2131 edge2133 edge2134 edge2136
edge2137 edge1 edge2135 edge8088 edge3 edge4 edge8105
edge2 add
blayer create first $firstch growth $growthch rows $rowsch transition 1 trows 0
uniform
blayer attach b_layer9 face face1681 face1696 face1696
face1696 face1695 edge edge2 edge8105 edge4 edge3
edge8088 add
blayer create first $firstch growth $growthch rows $rowsch transition 1 trows 0
uniform
blayer attach b_layer10 face face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face105 face105
face106 face104 face104 edge edge6743 edge101
edge7336 edge7337 edge102 edge6744 edge6745 edge111
edge7373 edge7374 edge112 edge6746 edge6747 edge121
edge7410 edge7411 edge122 edge6748 edge6749 edge131
edge7447 edge7448 edge132 edge6750 edge6751 edge141
edge7484 edge7485 edge142 edge6752 edge6755 edge6753
edge151 edge6754 edge7521 edge7522 edge152 edge161
101
edge6756 edge6757 edge7558 edge7559 edge162 edge171
edge7595 edge7596 edge172 edge6758 edge6759 edge181
edge7632 edge7633 edge182 edge6760 edge6761 edge191
edge7669 edge7670 edge192 edge6762 edge6763 edge6767
edge6765 edge201 edge7706 edge7707 edge202 edge6764
edge211 edge6766 edge7743 edge7744 edge212 edge6769
edge221 edge6768 edge7780 edge7781 edge222 edge6771
edge231 edge6770 edge7817 edge7818 edge232 edge241
edge7854 edge7855 edge242 edge6772 edge89 edge8070
edge91 edge92 edge8087 edge90 add
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer11 face face4 face5 face2 face5
face110 face2 edge edge8 edge8 edge6 edge7 edge7
edge5 add
blayer create first $firstch growth $growthch rows $rowsch transition 1 trows 0
uniform
blayer attach b_layer12 face face106 face104 face103 face105
edge edge87 edge87 edge85 edge88 add
BOUNDARY LAYERS ENDS HERE
edge picklink edge6948 edge6949
edge mesh edge6949 edge6948 successive ratio1 1 intervals $NumbNodes
edge picklink edge6950
edge mesh edge6950 successive ratio1 1 intervals ($NumbNodes2)
face mesh face1450 map
edge picklink edge6963 edge6947
edge mesh edge6947 edge6963 successive ratio1 1 intervals ($Numbtelnodes+$rows)
face mesh face912 map
edge picklink edge6961 edge6960 edge7889 edge7890
edge mesh edge7890 edge7889 edge6960 edge6961 successive ratio1 1
intervals ($NumbNodes)
edge picklink edge6959 edge7891
edge mesh edge7891 edge6959 successive ratio1 1 intervals ($NumbNodes2)
face mesh face1452 map
face mesh face1600 face117 map
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer12 face face2 face110 face5 face110
face2 face4 face5 face4 edge edge5 edge5 edge7
edge7 edge6 edge6 edge8 edge8 add
Meshing constants
$NumbNodes=5
$Numbtelnodes=6
$PLobnodes=5
$Chobnodes=5
$Plbenodes=($NumbNodes(4)+$rows)
$plsqnodes=($NumbNodes(3))
102
$Pllsnodes=($NumbNodes+$rows)
$Nojetcells=10
edge picklink edge3686 edge3402
edge mesh edge3686 edge3402 successive ratio1 1 intervals ($PLobnodes)
edge picklink edge6744 edge6864
edge mesh edge6864 edge6744 successive ratio1 1 intervals 5
face link face1260 face375 edges edge6923 edge2440 vertices
vertex6397 vertex2251 reverse
face modify face915 side vertex4479 vertex4480
face mesh face915 face918 face911 map size 1
face mesh face1260 face1263 face1256 map size 1
edge picklink edge8068 edge8053
edge mesh edge8068 edge8053 successive ratio1 1 intervals ($Plbenodes)
edge picklink edge8086 edge8071
edge mesh edge8071 edge8086 successive ratio1 1 intervals ($CHbenodes)
edge delete edge8053 edge8068 keepsettings onlymesh
edge mesh edge8053 edge8068 successive ratio1 1 intervals ($Plbenodes)
edge delete edge8090 keepsettings onlymesh
edge picklink edge8090
edge mesh edge8090 successive ratio1 1 intervals ($plsqnodes)
edge delete edge8054 keepsettings onlymesh
edge picklink edge8054
edge mesh edge8054 successive ratio1 1 intervals ($plsqnodes)
face mesh face1647 face1679 face1678 face1646 face1633
face1665 map
edge delete edge98 edge8087 keepsettings onlymesh
edge picklink edge8087 edge98
edge mesh edge98 successive ratio1 1 intervals ($Pllsnodes)
edge mesh edge8087 successive ratio1 1 intervals ($CHlsnodes)
face mesh face1648 face1680 map
COOPERING ALL THE JETS
volume mesh volume3 cooper source face1600 face1452 face117
face1514 face1512 face115 intervals ($Nojetcells)
volume mesh volume5 cooper source face1456 face1602 face124
face1518 face1520 face122 intervals ($Nojetcells)
volume mesh volume7 cooper source face1460 face1604 face131
face1526 face1524 face129 intervals ($Nojetcells)
volume mesh volume9 cooper source face1464 face1606 face138
face1532 face1530 face136 intervals ($Nojetcells)
volume mesh volume11 cooper source face1468 face1608 face145
face1538 face143 face1536 intervals ($Nojetcells)
volume mesh volume13 cooper source face1472 face1610 face152
face1544 face1542 face150 intervals ($Nojetcells)
volume mesh volume15 cooper source face1476 face1612 face159
face1550 face1548 face157 intervals ($Nojetcells)
volume mesh volume17 cooper source face1480 face1614 face166
face1556 face1554 face164 intervals ($Nojetcells)
volume mesh volume19 cooper source face1484 face1616 face173
face1562 face171 face1560 intervals ($Nojetcells)
volume mesh volume21 cooper source face1488 face1618 face180
face1568 face1566 face178 intervals ($Nojetcells)
103
volume mesh volume23 cooper source face1492 face1620 face187
face1574 face1572 face185 intervals ($Nojetcells)
volume mesh volume25 cooper source face1496 face1622 face194
face1578 face1580 face192 intervals ($Nojetcells)
volume mesh volume27 cooper source face1624 face1500 face201
face1586 face1584 face199 intervals ($Nojetcells)
volume mesh volume29 cooper source face1504 face1626 face208
face1592 face1590 face206 intervals ($Nojetcells)
volume mesh volume31 cooper source face1628 face1508 face215
face1596 face1598 face213 intervals ($Nojetcells)
volume mesh volume30 cooper source face1506 face1052 face1594
face1397 intervals ($Nojetcells)
volume mesh volume28 cooper source face1502 face1042 face1588
face1387 intervals ($Nojetcells)
volume mesh volume26 cooper source face1498 face1032 face1582
face1377 intervals ($Nojetcells)
volume mesh volume24 cooper source face1494 face1022 face1576
face1367 intervals ($Nojetcells)
volume mesh volume22 cooper source face1490 face1012 face1570
face1357 intervals ($Nojetcells)
volume mesh volume20 cooper source face1486 face1002 face1564
face1347 intervals ($Nojetcells)
volume mesh volume18 cooper source face1482 face992 face1558
face1337 intervals ($Nojetcells)
volume mesh volume16 cooper source face1478 face982 face1552
face1327 intervals ($Nojetcells)
volume mesh volume14 cooper source face1474 face972 face1546
face1317 intervals ($Nojetcells)
volume mesh volume12 cooper source face1470 face962 face1540
face1307 intervals ($Nojetcells)
volume mesh volume10 cooper source face1466 face952 face1534
face1297 intervals ($Nojetcells)
volume mesh volume8 cooper source face1462 face942 face1528
face1287 intervals ($Nojetcells)
volume mesh volume6 cooper source face1458 face932 face1522
face1277 intervals ($Nojetcells)
volume mesh volume4 cooper source face1454 face922 face1516
face1267 intervals ($Nojetcells)
volume mesh cylinder cooper source face1450 face912 face1510
face1257 intervals ($Nojetcells)
window modify invisible mesh
volume mesh volume34 cooper source face1649 face1650 face1651
face1652 face1653 face1654 face1655 face1664 face1639
face1638 face1637 face1636 face1635 face1634 face1633
face1648 face1610 face1608 face1606 face1604 face1602
face1600 face1472 face962 face1468 face952 face1464
face942 face1460 face932 face1456 face922 face1452
face912 face915 face918 face911 face925 face928
face920 face935 face938 face930 face945 face948
face940 face955 face958 face950 face965 face968
face960 face694 face689 face684 face679 face674
face669 face664 face659 face654 face649 face644
face640 face697 face696 face692 face687 face686
face682 face677 face676 face672 face667 face666
104
face662 face657 face656 face652 face647 face646
face642 face695 face698 face690 face685 face688
face680 face675 face678 face670 face665 face668
face660 face655 face658 face650 face645 face648
face641 face152 face1470 face145 face1466 face138
face1462 face131 face1458 face124 face1454 face117
face1450 face1657 face1658 face1659 face1660 face1661
face1662 face1663 face788 face1656 face1474 face159
face1647 face1646 face1645 face1644 face1643 face1642
face1641 face1640 face1478 face1628 face1626 face1624
face1622 face1620 face1618 face1616 face1614 face1612
face1508 face1052 face1504 face1042 face1500 face1032
face1496 face1022 face1492 face1012 face1488 face1002
face1484 face992 face1480 face982 face1476 face972
face975 face978 face970 face985 face988 face980
face995 face998 face990 face1005 face1008 face1000
face1015 face1018 face1010 face1025 face1028 face1020
face1035 face1038 face1030 face1045 face1048 face1040
face1050 face114 face1058 face774 face769 face764
face759 face754 face749 face744 face739 face734
face729 face724 face719 face714 face709 face704
face699 face777 face776 face772 face767 face766
face762 face757 face756 face752 face747 face746
face742 face737 face736 face732 face727 face726
face722 face717 face716 face712 face707 face706
face702 face779 face784 face787 face775 face778
face770 face765 face768 face760 face755 face758
face750 face745 face748 face740 face735 face738
face730 face725 face728 face720 face715 face718
face710 face705 face708 face700 face782 face786
face785 face6 face780 face1055 face215 face1506
face208 face1502 face201 face1498 face194 face1494
face187 face1490 face180 face1486 face173 face1482
face166 intervals ($Plzdnodes)
volume delete body onlymesh
volume mesh body cooper source face1689 face1690 face1691
face1692 face1693 face1681 face1682 face1683 face1684
face1685 face1686 face1687 face1688 face1696 face1671
face1670 face1669 face1668 face1667 face1666 face1665
face1677 face1676 face1675 face1674 face1673 face1672
face1680 face199 face1584 face1377 face192 face1578
face1367 face185 face1572 face1357 face178 face1566
face1347 face171 face1560 face1337 face164 face1554
face1327 face157 face1548 face1317 face150 face1542
face1307 face143 face1536 face1297 face136 face1530
face1287 face129 face1524 face1277 face122 face1518
face1267 face115 face1512 face1257 face1380 face1383
face1375 face1370 face1373 face1365 face1360 face1363
face1355 face1350 face1353 face1345 face1340 face1343
face1335 face1330 face1333 face1325 face1320 face1323
face1315 face1310 face1313 face1305 face1300 face1303
face1295 face1290 face1293 face1285 face1280 face1283
face1275 face1270 face1273 face1265 face1260 face1263
face1256 face209 face374 face370 face384 face379
face394 face389 face404 face399 face414 face409
105
face424 face419 face434 face429 face444 face439
face454 face449 face464 face459 face474 face469
face484 face479 face494 face489 face377 face376
face372 face387 face386 face382 face397 face396
face392 face407 face406 face402 face417 face416
face412 face427 face426 face422 face437 face436
face432 face447 face446 face442 face457 face456
face452 face467 face466 face462 face477 face476
face472 face487 face486 face482 face497 face496
face492 face375 face378 face371 face385 face388
face380 face395 face398 face390 face405 face408
face400 face415 face418 face410 face425 face428
face420 face435 face438 face430 face445 face448
face440 face455 face458 face450 face465 face468
face460 face475 face478 face470 face485 face488
face480 face495 face498 face490 face1 face1586
face1582 face1580 face1576 face1574 face1570 face1568
face1564 face1562 face1558 face1556 face1552 face1550
face1546 face1544 face1540 face1538 face1534 face1532
face1528 face1526 face1522 face1520 face1516 face1514
face1510 face1403 face518 face1588 face1592 face1594
face1694 face1695 face1598 face1679 face1678 face515
face516 face510 face500 face508 face505 face213
face1596 face1397 face206 face1590 face1387 face517
face514 face512 face502 face506 face507 face509
face499 face504 face1400 face1395 face1385 face1390
face1393 intervals ($Chzdnodes)
BOUNDARY CONDITIONS
physics create Symmetry btype SYMMETRY face face2 face103
face211 face204 face197 face190 face183 face176
face169 face162 face155 face148 face141 face134
face127 face120 face112
physics create Wall btype SYMMETRY face face110 face5 face1649
face1664 face918 face915 face911 face925 face1650
face928 face920 face935 face938 face930 face1652
face1651 face948 face945 face940 face1653 face1654
face958 face955 face950 face1655 face965 face968
face960 face978 face975 face970 face1656 face114
face985 face988 face980 face995 face998 face990
face1657 face1005 face1008 face1000 face1658 face1015
face1018 face1010 face1659 face1028 face1025 face1020
face1035 face1660 face1038 face1030 face1045 face1661
face1048 face1040 face1055 face1662 face1058 face1050
face1663 face4 face1395 face1679 face1403 face1400
face1680 face1385 face1678 face1393 face1390 face1375
face1677 face1383 face1380 face1676 face1365 face1373
face1370 face1675 face1355 face1363 face1360 face1674
face1345 face1353 face1350 face1673 face1335 face1343
face1340 face1672 face1325 face1333 face1330 face209
face1315 face1323 face1320 face1671 face1305 face1313
face1310 face1670 face1295 face1303 face1300 face1669
106
face1285 face1293 face1290 face1668 face1275 face1283
face1280 face1667 face1265 face1273 face1270 face1666
face1256 face1263 face1260 face1665 face214 face91
face207 face85 face200 face79 face193 face73 face186
face67 face179 face61 face172 face55 face165 face49
face158 face43 face151 face37 face144 face31 face137
face25 face130 face19 face123 face13 face116 face8
physics modify Wall btype WALL face face110 face5 face1649
face1664 face918 face915 face911 face925 face1650
face928 face920 face935 face938 face930 face1652
face1651 face948 face945 face940 face1653 face1654
face958 face955 face950 face1655 face965 face968
face960 face978 face975 face970 face1656 face114
face985 face988 face980 face995 face998 face990
face1657 face1005 face1008 face1000 face1658 face1015
face1018 face1010 face1659 face1028 face1025 face1020
face1035 face1660 face1038 face1030 face1045 face1661
face1048 face1040 face1055 face1662 face1058 face1050
face1663 face4 face1395 face1679 face1403 face1400
face1680 face1385 face1678 face1393 face1390 face1375
face1677 face1383 face1380 face1676 face1365 face1373
face1370 face1675 face1355 face1363 face1360 face1674
face1345 face1353 face1350 face1673 face1335 face1343
face1340 face1672 face1325 face1333 face1330 face209
face1315 face1323 face1320 face1671 face1305 face1313
face1310 face1670 face1295 face1303 face1300 face1669
face1285 face1293 face1290 face1668 face1275 face1283
face1280 face1667 face1265 face1273 face1270 face1666
face1256 face1263 face1260 face1665 face214 face91
face207 face85 face200 face79 face193 face73 face186
face67 face179 face61 face172 face55 face165 face49
face158 face43 face151 face37 face144 face31 face137
face25 face130 face19 face123 face13 face116 face8
physics create Heat Fluxes btype WALL face face104 face106
face370 face379 face389 face372 face382 face392
face371 face380 face390 face378 face388 face398
face376 face386 face396 face374 face384 face394
face377 face387 face397 face375 face385 face395
face1681 face1682 face1683 face1684 face1696 face402
face412 face422 face432 face442 face400 face410
face420 face430 face440 face408 face418 face428
face438 face448 face406 face416 face426 face436
face446 face404 face414 face424 face434 face444
face407 face417 face427 face437 face447 face405
face415 face425 face435 face445 face1688 face1685
face1686 face1687 face452 face462 face472 face482
face492 face1693 face450 face460 face470 face480
face490 face1692 face458 face468 face478 face488
face498 face1 face456 face466 face476 face486 face496
face454 face464 face474 face484 face494 face457
face467 face477 face487 face497 face1691 face455
face465 face475 face485 face495 face1689 face1690
face518 face502 face512 face1695 face500 face510
face1694 face508 face506 face516 face504 face514
face507 face517 face515 face505
physics create Mass flow inlet btype SYMMETRY face face640 face649
107
face659 face642 face652 face662 face672 face641
face650 face660 face670 face648 face658 face668
face678 face646 face656 face666 face676 face644
face654 face664 face674 face647 face657 face667
face677 face645 face655 face665 face675 face1633
face1634 face1635 face1636 face1637 face1648 face679
face689 face699 face682 face692 face702 face712
face680 face690 face700 face710 face688 face698
face708 face718 face6 face686 face696 face706 face716
face684 face694 face704 face714 face687 face697
face707 face717 face685 face695 face705 face715
face1640 face1638 face1639 face719 face729 face739
face749 face722 face732 face742 face752 face762
face720 face730 face740 face750 face760 face728
face738 face748 face758 face768 face726 face736
face746 face756 face766 face724 face734 face744
face754 face764 face727 face737 face747 face757
face767 face725 face735 face745 face755 face765
face1645 face1641 face1642 face1643 face1644 face788
face769 face779 face772 face782 face770 face780
face778 face776 face786 face774 face784 face777
face787 face775 face785 face1647 face1646
physics create Outflow btype OUTFLOW face face105
108
REFERENCES
Al-Aqal O M A 2003 ldquoHeat transfer distributions on the walls of a narrow channel
with jet impingement and cross flowrdquo PhD Thesis University of Pittsburgh
Bunker Ronald S 2007 Gas Turbine Heat Transfer Ten Remaining Hot Gas Path
Challengesrdquo Journal of Turbomachinery April Vol 129 pp 193-201
Downs James P Landis Kenneth K 2009 ldquoTurbine Cooling Systems Design- Past
Present and Futurerdquo Proceedings of ASME Turbo Expo 2009 June 8-12 2009
GT2009-59991
Florschuetz LW Berry R A Metzger D E 1980 ldquoPeriodic streamswise variations of
heat transfer coefficients for inline and staggered arrays of circular jets with cross
flow of spent airrdquo ASME J of Heat Transfer 102 p 132-137
Florschuetz L W Truman C R Metzger D E 1981 ldquoStreamwise Flow and Heat
Transfer Distributions for Jet Array Impingement with Cross flowrdquo Journal of
Heat Transfer Vol 103 pp 337
Florschuetz L W Isoda Y 1983 ldquoFlow Distributions and Discharge Coefficient for
Jet Array Impingement With Initial Cross flowrdquo Journal of Engineering for
Power Vol 105 pp 296
Incropera Frank P DeWitt D P 2002 Fundamentals of Heat and Mass Transfer John
Wiley amp Sons Inc New Jersey pp 491-493
Liu Quan Kapat J May 2006 ldquoStudy of Heat Transfer Characteristics of Impinging
Air Jet Using Pressure and Temperature Sensitive Luminescent Paintrdquo UCF
Dissertation
109
Martin H 1977 ldquoImpinging jet flow heat and mass transferrdquo Advances in heat transfer
Vol 13
Ricklick Mark Kapat J December 2009 ldquoCharacterization of an Inline Row
Impingement Channel for Turbine Blade Cooling Applicationsrdquo UCF
Dissertation
Zuckerman N Lior N 2005 ldquoImpingement Heat transfer Correlations and Numerical
Modelingrdquo Journal of Heat Transfer Vol 127 pp 544
viii
Figure 17 Temperature Profile of First Five Impingement Rows 29
Figure 18 Detailed View of First Heat Transfer Peak with a Polynomial Curve Fit 30
Figure 19 Control Volume Heat Transfer Analysis 30
Figure 20 Heat Loss through Convection and Lateral Conduction 31
Figure 21 Validation Spanwise Averaged Results 32
Figure 22 Target Wall Heat Transfer Coefficient Distributions 34
Figure 23 Span-averaged Target Wall Heat Transfer Distribution 35
Figure 24 Side Wall Heat Transfer Coefficient Distributions 36
Figure 25 Span-averaged Side wall Heat Transfer Distribution 37
Figure 26 XD=15 Target Wall Heat Transfer Profile 41
Figure 27 XD=15 Span-averaged Target Wall Heat Transfer Distribution 42
Figure 28 Target Wall Span-average Comparison of XD=5 and 15 at High Re 43
Figure 29 Side Wall Heat transfer Coefficient Profile 44
Figure 30 XD=15 Side Wall Span-averaged Heat Transfer Coefficients 45
Figure 31 3D Heat Transfer Profile for ZD=6 XD=5 46
Figure 32 3D Heat Transfer Profile for ZD=8 XD=5 47
Figure 33 3D Heat Transfer Profile for ZD=6 XD=15 48
Figure 34 Pressure Drop Ratio with Respect to Smooth Channel 49
Figure 35 Heat Transfer Enhancement 50
Figure 36 Thermal Performance at Constant Pressure Drop 50
Figure 37 Thermal Performance at Constant Pumping Power 51
Figure 38 Horizontal Plane of Impingement Channel Geometry 53
Figure 39 Target Side and Front End Wall y+ Values 54
ix
Figure 40 Finished Mesh with Boundary Conditions 55
Figure 41 Grid Independence Study 57
Figure 42 Residual Plots for the 26M Cell Run 57
Figure 43 Total Pressure Contours 58
Figure 44 Velocity Magnitude Contours 59
Figure 45 Turbulent Kinetic Energy Contours 60
Figure 46 Static Temperature Contours 60
Figure 47 Target and Side Wall Heat Transfer Coefficient Contours 61
Figure 48 Closer View of First few Rows of Impingement HTC Contours 61
Figure 49 Pathlines Generating from the First Row of Jets 62
NOMENCLATURE
Cross Sectional Area
Heater Surface Area (m2)
Specific Heat at Constant Pressure (kJkgK)
D Jet Diameter (m)
Channel Hydraulic Diameter (m)
Friction Factor
Heat Transfer Coefficient (HTC) (Wm2K)
Average Heat Transfer Coefficient (Wm2K)
Channel Length (m)
Mass Flow Rate (kgs)
Static Pressure (kPa)
x
Total Pressure (kPa)
Pr Prandtl Number
Heat Flux (Wm2)
Total Heat Input (W)
Heater Resistance (ohm)
Re Reynolds Number
SW Side Wall
Temperature (K)
TW Target Wall
Voltage Potential
Streamwise Location
y Spanwise Location
z Height from Target Wall
X Streamwise Distance (m)
Y Spanwise Distance (m)
Z Impingement Height (m)
Thermal Performance Parameter
Ratio of Specific Heats
Air Density (kgm3)
Subscripts
C Cold
H Hot
xi
Carnot Describing a Carnot cycle
Exit
Effective
Quantity Lost to the Environment
Reference Value
Wall Value
Base Line Value
1
CHAPTER ONE INTRODUCTION
11 Gas Turbine as a Heat Engine
Gas turbine is a form of heat engine where the hot reservoir is created by the
combustion of fuel and the cold reservoir is the open atmosphere It is well known that
the maximum efficiency of any heat engine is denoted as the Carnot efficiency
A more accurate cycle is used to describe the processes inside a gas turbine ndash the
Brayton Cycle The Brayton cycle as seen in Figure 1 is composed of four processes In
a gas turbine air is drawn in at state 1 it is compressed until it reaches state 2 The
compressed air is mixed with fuel and ignited as it passes through the combustor The hot
air then passes through the turbines where work is extracted The process from state 4 to
state 1 happens throughout the atmosphere therefore the Brayton cycle is an open loop
cycle as the same air is not continuously being fed through the motor
Figure 1 Brayton Cycle Flow Path and T-s Diagram (Adapted from UPTB Website)
The Brayton cycle has an isentropic efficiency similar to the carnot the Brayton
cycle efficiency is defined as
2
It can be seen that increasing the temperature at which air enters the first turbine
stage T3 increases the overall efficiency of the turbine Moreover increasing the
pressure ratio Pr also aids in the increase of the efficiency One of the hurdles of
increasing T3 is the fact that the post combustion gas is a few hundred degrees Celsius
above the melting point of the super alloys used to make the turbine stator vanes and
rotor blades For this reason it is important to cool the hot components of the gas turbine
in order to assure a reasonable life for the machine
12 Cooling of Hot Components
The transition duct that connects the combustor to the first stage turbine as well
as the first stage of the turbine are the parts that are subject to the harshest thermal
loadings and must therefore be cooled aggressively to maintain them in working
conditions for a long period of time Since the first stage guide vanes and rotor extrude
into the flow they are subject to the highest convection coefficients These heat transfer
coefficients can reach up to 4000 Wm2K (Downs 2009) Figure 2 shows the different
magnitudes of convection coefficient around the blade High heat transfer coefficients
occur where the air stagnates into the leading edge of the airfoil This high heat transfer
region is not only caused by the lack of a thermal boundary layer to protect the airfoil but
also because the effective heat transfer driving temperature is the recovery temperature
At the high Mach numbers that occur in turbines the ratio of total to static temperatures
is significant causing the leading edge to have the highest effective heat load Another
3
peak occurs on the suction side of the blade as the boundary layer created by the airfoil
switches from being a laminar boundary layer into a turbulent one Due to the nozzling
effect of the turbine rotor and stators the flow gathers speed toward the trailing edge of
the airfoil leading to higher convection coefficients on the pressure side of the airfoil
Figure 2 Thermal Loading Throughout a Turbine Blade (Daniels 1982)
Simple convection channels were implemented in the early nineteen sixties as
years passed the cooling techniques became more and more sophisticated allowing the
free stream temperature to increase to previously impossible levels Currently the use of
film cooling coupled with backside impingement leads the turbine cooling technology
The trend of allowable turbine inlet temperature is shown in Figure 3 from this figure it
can be seen that the allowable free stream temperature has increased around 600 degrees
in the past 50 years The addition of thermal barrier coatings also helps in the increase in
allowable combustion temperatures by creating an extra resistance that the heat needs to
move through as it moves from the combustion gasses into the coolant air It is impotatnt
to notice that as seen in Figure 4 the increase in turbine inlet temperatures is done with
the combined benefits of new alloys TBC and cooling technologies
4
Figure 3 Allowable Turbine Inlet Temperature vs Cooling Techniques over the Years (Clifford 1985)
Figure 4 Turbine Inlet Temperature Increase with the help of TBC New Super Alloys and Cooling
Technologies (Kapat and Kiesow Lectures 2010)
The cooling of inlet guide vanes can be done with the use of impingement inserts
inside the airfoils As air passes through the miniscule holes in the inserts a jet is formed
which then impinges on the wall of the airfoil producing one of the largest single phase
heat transfer coefficients This already impinged coolant air is then bled out as film
5
cooling as well as bled out through the trailing edge Figure 5 shows a stator vane with
the impingement insert in black the film cooling extraction as well as the trailing edge
bleed
Figure 5 Turbine Stator Cooled with Impingement Coupled with Film Cooling (Florschuetz 1980)
The cooling of turbine airfoils with the use of an impingement insert is only
possible in stationary components as the rotating ones are subject to centrifugal loadings
making it unfeasible to cool them with this setup Rotor blades are typically cooled with
serpentine passages that have heat transfer enhancing features such as ribs dimples and
other turbulators these serpentine passages are located in the mid chord of the blade On
the trailing edge a bank of pins are used to obtain high convective coefficients in the thin
region the coolant is the bled out to compensate for the boundary layer created around
the airfoil Rows of impingement holes cool the leading edge The spent air is then bled
out through showerhead cooling Figure 6 and Figure 7 show in detail the cooling
channels around two similar airfoils airfoils
6
Figure 6 Rotor Blade Cooling Configuration (Gladden 1988)
Figure 7 Cross-section of Turbine Airfoil with Cooling Channels (Han et al 1984)
7
The coolant air is bled out from the later stages of the compressor This air is
expensive as it has been compressed and not under gown the heat addition by
combustion It is imperative that the minimum amount of coolant is used in these cooling
configurations The cooling must also be as uniform as possible to reduce thermal
stresses within the blades leading to a higher component life Figure 8 shows freestream
metal and coolant temperatures of the flow blade and coolant air It can be seen that a
decrease of 25degrees in the surface temperature of the blade can provide an airfoil with
twice the working life Impingement cooling has great potential to provide high heat
transfer coefficients at a small flow rate Impingement of a jet onto a surface provides
high heat transfer coefficients due to a starting boundary layer as well as its high
turbulence When the jet is located around 3 diameters from the target surface the heat
transfer profile has two peaks one located at the stagnation region and the other located
between one and 3 diameters from the stagnation region As the jet is moved away from
the target wall the secondary peak diminishes leaving a profile with a maximum at the
stagnation region decreasing radialy
Figure 8 Relative Temperatures for Hot Gas Metal Temperature and Coolant Temperature (Cardwell 2005)
Cardwell N D 2005
8
Figure 9 shows a diagram of a jet impinging on a target surface The potential
core is the part of the jet that has not been affected by the surrounding stagnant fluid As
the jet moves towards the target wall its momentum diffuses into the surrounding fluid
decreasing the velocity at which it reaches the target wall and potentially decreasing the
corresponding heat transfer coefficient Studies have shown (Martin 1973 for example)
that the potential core may last anywhere between 7 to 10 diameters The successful
impingement of the potential core yields significantly higher heat transfer coefficients
than a fully diffused jet this comes however at a cost of higher pressure drop across the
jet plate as well as a highly non uniform heat transfer profile
Figure 9 (a) The Development of the Wall Jet (b) Jet Diffusion to Surroundings (Liu 2006)
9
CHAPTER TWO LITERATURE REVIEW
21 Impingement Literature Cornerstone
From the early days of simple convective cooling channels in turbine airfoils
studies have been done on modes of enhancing heat transfer coefficients while
maintaining a low pressure drop and minimum mass flow rate Heat transfer
characteristics of single round nozzle impingement were studied in the late 1960rsquos and
early 1970rsquos The collected works of many authors is combined into ldquoHeat and Mass
Transfer between Impinging Gas Jets and Solid Surfacesrdquo by Holger Martin 1977 The
paper collects works from multiple authors who studied single round nozzle impingement
effects on heat and mass transfer coefficients In this compilation non dimensional jet to
target spacing was studied they ranged from ZD=12-10 providing plots of Sherwood
number as a function of radius for four different jet to target spacings The local
Sherwood number was also given for a slot jet for HS ranging from 5 to 20 Studies on
impingement jet arrays were also gathered alongside an array of slot jets Correlations
were given for multiple setups present in the paper Circular jet arrays and slot arrays are
studied in detail with both analytical and experimental approaches The paper also
combines studies done on swirling jets turbulence enhancers on the target surface
impingement on concave surfaces and angle of attack variations Optimization studies
were also done to find the optimal spacing for round and slot jet arrays
Florschuetz studied the heat transfer characteristics of an array of jets impinging
on a flat surface This study was guided towards finding an optimal spacing for an array
for jets used to cool the midchord of turbine airfoils similar to that found in Figure 5 His
main contributions include a Nusselt number correlation as a function of jet to target
10
spacing jet Reynolds number and other flow and geometric parameters He found that an
increase in hole spacing and channel height resulted in a decrease of heat transfer He
also provided a one dimensional jet mass flux and channel mass flux correlations
His Nusselt number correlation takes the form of
Where A B and n are dependent by the two different types of arrays inline or staggered
Liu studied new techniques in temperature and pressure measurements of a single
slot jet with the use of temperature sensitive paint or TSP and pressure sensitive paint or
PSP In his work both measurement techniques are explained in detail Since TSP is the
only tool from that study currently used in this work it will be explained further in the
experimental setup section
11
22 Relevant Impingement Channel Studies
Al-Aqal 2003 studied three different types of impingement channels The use of
TLC was implemented in this work to obtain heat transfer distributions for the target
wall The three different configurations varied the number of holes in the streamwise and
spanwise directions The first channel had a single row of 6 streamwise jets the second
consisted of 2 rows of 12 streamwise holes summing up to a total of 24 holes The last
channel is a triple spanwise row with 18 streamwise jets This last geometry is the most
similar to the one present in the current study The third geometry will be used to
compare results There are differences however the total width of the channel is of 16
diameters as opposed to 8 in this study The streamwise jet spacing is also different Al-
Aqal used an XD of 65 compared to XD = 5 in this study The jet to target plate
spacings are similar on two occasions as he studied a ZD=4 6 and 8 while this work
uses a ZD = 6 8 and 10 Average jet Reynolds numbers also fall within the range of this
study as they range between 5000 and 33000 The author provides span averaged plots
for all cases and Reynolds numbers convenient when comparing the results
Ricklick 2009 studied a channel similar to the one found in this study His
channel was composed of a single row of 15 jets with a YcD = 4 XD = 5 and 15 and
ZD = 1 3 and 5 Two channels were tested one was pressure fed while the other was fed
by suction TSP was used to gather temperature data of all four wetted surfaces on the
pressure channel and two surfaces on the suction channel Since the maximum jet Mach
number was less than 03 the flow was assumed to be incompressible leading to the
conclusion that both channels contain identical flow patterns Thin foil heaters were used
to create the required heat flux for the channel Besides channel geometry Reynolds
12
numbers and heater geometry Ricklicksrsquo experimental setup is identical to the one
presented in this work The author also provided an ample comparison of his results to
literature He provided thermal performances of the entire channel at different Reynolds
numbers and channel heights
A small CFD study was also done A paved mesh was created on the target wall
with finer mesh near the impingement locations The resulting y+ at the wall was higher
than one yielding potentially faulty heat transfer values however this is acceptable since
the CFD was used as a tool to better understand the flow physics and help understand the
experimental heat transfer profiles
23 Computational Studies on Impingement Channels
El-Gabry did a numerical study of jet impingement with cross flow Two different
turbulence models were compared in their ability to predict surface Nusselt number The
Yang-Shih and standard k-ε models were used to compute the flow generated by jets
angled at 30 60 and 90 degrees with cross flow The computational results were
compared to previous experimental work by El-Gabry Comparisons to experimental
results at ZD = 1 and 2 90deg injection angle between Yang-Shih and standard k-ε The
error in the average Nu from the experimental results and both turbulence models were
calculated It was found that the Yang-Shih model behaved well at low Reynolds
numbers with the average Nusselt number being 5 off from the experimental value
while the standard k-ε was off my 94 As jet Reynolds number was increased the error
of the standard k-ε model dropped to as low as 39 while the error from the Yang-shih
model increased to -76 The span average plots show the experimental data Nusselt
number alongside the span averages of the results acquired by the Yang-Shih and
13
standard k-ε models High Nusselt numbers occur at the impingement location decreasing
thereafter after another impingement location is found The frequencies of these
variations are all the same for the experimental and the two numerical solutions The
amplitude of fluctuations between the impingement locations and the areas in between
are much larger for both of the numerical results however the Yang-Shih model over
predicts at the high Reynolds number for the ZD=2 case Since the amplitude of
fluctuations is greater for the CFD solutions it is important to note that even though the
error in average Nusselt number is not great the actual differences in the profile are much
greater upwards of 20 difference of heat transfer coefficients between the experimental
and numerical heat transfer peaks Other variations were studied (Injection angles for
example) but will not be discussed as their importance to the current study is minimal
Zuckerman compared a much wider set of turbulence models in their ability to
successfully predict Nusselt numbers caused by jet impingement The models tested were
k ndash ε k-ω Reynolds Stress Model algebraic stress models shear stress transport and
lastly the υ2f turbulence model DNS runs are extremely time consuming to run
therefore LES was run on its behalf to provide results for the unsteady turbulence
models The paper summarizes all the different models used their computational cost
impingement heat transfer coefficient and their ability to predict the second peak in heat
transfer As expected DNSLES provide the best prediction of both stagnation and
secondary peak heat transfer coefficient however this comes at a large computational
cost The k ndash ε and k-ω provide poor heat transfer results for the stagnation region where
they can have 30 error from the correct value The Realizable k ndash ε model provides
14
better heat transfer results while still maintaining a low computational cost The highest
accuracy to cost ratio was achieved by the υ2f model where it predicts the heat transfer
coefficient for the surface with a minimum of 2 error while not being as expensive as
the other unsteady models such as DNS and LES Ideally the CFD portion of this work
would be run with the υ2f model however since the code used to run the simulation
FLUENT does not have the υ2f model a realizable k ndash ε model will be used with
enhanced wall functions for both thermal and velocity gradients
15
CHAPTER THREE EXPERIMENTAL SETUP AND TECHNIQUES
31 Temperature Measurements with TSP
Temperature sensitive paint or TSP provides the capability of measuring
temperatures over the painted area This measurement technique supersedes the
advantages of other temperature measurement devices such as thermocouples because it
provides the user with data over a large area rather than point temperatures given by
thermocouples
Uni-Coat TSP is purchased from ISSI It is very robust to different working
conditions Calibration done on one batch of paint can be used for multiple cans as the
product is highly consistent The paint is calibrated in a dark booth a painted coupon is
placed on the hot side of a thermoelectric heat pump working on the Peltier effect
thermal paste is used to minimize contact resistance between the hot side and the TSP
coupon Calibrated thermocouples are placed in between the TSP and the thermoelectric
heat pump A reference temperature and picture are taken and the calibration commences
At least 5 or 6 data points should be taken to form the calibration Intensity ratios are
taken between the hot and cold pictures They are then plotted versus their corresponding
temperature
The paint consists of fluorescent molecules suspended in a binder These
molecules with a certain wavelength of light will be exited to a higher energy level The
molecules then can dissipate some of the energy by transferring it vibrationally to its
neighboring binder particles and dissipate the remainder of the energy by radiating it as a
photon as the molecule comes down to its original ground state Since the amount of
16
energy that the particle can transmit to others through vibration is directly proportional on
temperature and the total initial energy is fixed by measuring the ratio of the intensity at
a known temperature (reference picture) and intensity of the unknown temperature
feeding it through the correlation the unknown temperature can be found to an
uncertainty of 1 K Figure 10 shows a simplified Jablonski diagram adapted from the
suppliers website The blue arrows signify the blue light used to excite the luminescent
molecule Tris(22rsquo-bipyridyl) Ruthenium(II) Chloride Hexahydrate with a shellac binder
in our case The shellac binder is impermeable to oxygen opposite of that found in PSP
due to PSP relying on the presence of oxygen for it to function Once the particle is
excited it can give off the energy in two different ways one is by emitting it back out as
another photon of the same energy and therefore wavelength The second mode of the
particle to lose its energy is through vibrational relaxation This second process is directly
dependent on the temperature ie the higher the temperature the higher the probability
for it to lose energy to its surroundings Once it loses some energy to the surrounding
particles it releases the remainder of the energy as a photon of less energy of that which
excited it originally hence why a long pass filter is installed in the CCD camera For a
more descriptive explanation of the way TSP works refer to Liu 2006
17
Figure 10 Simplified Jablonski Diagram (Adapted from ISSI Website)
Throughout the past two years there have been numerous projects at CATER that
have used TSP Painting surfaces with TSP should be done carefully by someone who
has experience with spray painting since every single can costs $500 A single can should
be able to paint an area the size of an acrylic plate that is 36rdquo wide and 24rdquotallThe
sidewalls and the target wall of the impingement channel were painted with the use of
less than one can Painting on different surfaces is difficult for example when painting
Rohacell the paint canister can be held very close to the surface while spraying due to
the surface being somewhat porous and rough however when painting straight onto
metal heater strips the can should be placed as far back as possible for the first run
Ideally for the first pass through only a slight mist should be applied If the can is being
held too close to the surface the paint will run Figure 11 shows a set of heater strips that
has been painted too closely leading the paint to drip down Ideally the paint would be
applied to the surface in as many coats as possible Of course this would be time
18
demanding and impractical therefore with the knowledge that I have gained through the
multiple TSP paintings on different surfaces I have compiled a list of TSP dos and
donrsquots
Dos
Clean the surface to be painted with acetone or break parts cleaner Break
parts cleaner is preferable over acetone as it does not leave an oily residual
after cleaning
Paint the first coat as thin as possible Most of the surface should not be
covered There should be an even mist of miniscule TSP circles This will
give the later coats something to attach to
When positioning the test section to paint make sure to wipe it one last
time as small dust particles may have attached to the surface
Stop if you see small bumps in the paint This is caused by dust particles
collecting all the paint around it while it is still wet due to surface tension
Clean the surface and repaint This should be noticeable in the first few
coats If you see this pattern happening do not continue thinking it will be
covered by future coats What will happen is the problem will get worse
and worse ultimately the surface will have to be cleaned again and
repainted
When painting test sections try to paint the smallest section as possible
This will not only save paint but will make it very simple for the post
processing code to crop out the unpainted areas
19
Let the finished painted surface to sit at least for 90 minutes after the last
coat before baking There have been problems when baking steel and
acrylic test sections with the paint cracking while baking right after the
last coat Normally the finished surface is left to dry overnight and baked
first thing in the morning
For test sections that are too large to be baked in the oven the heat gun
may be used Carefully place a thermocouple in a central location with
blue painters tape The heating should be uniform and should not take
more than 20 minutes of continuous blowing When the thermocouple
reaches 80-90 C the plate can be assumed to be baked To introduce a
factor of safety in the baking it does not hurt to bake it longer than it
normally takes
Once the test section is mounted and ready to run cover it with cloth that
does not let any light through This will protect the paint for further uses
This is especially important on test sections that can be used multiple
times like the ones found in this study
When the test is running turn off the LED lights This light is the most
damaging to the TSP as it degrades the quality of the fluorescent
molecules
If there is a particular head of the TSP can that you prefer over others you
can remove it once the can is empty It is difficult to get used to a single
kind of nozzle being able to transfer it from can to can is a must if
painting consistency is to be kept
20
Donrsquots
Do not clean a test section that has already been used with too much
acetone The acetone is volatile evaporating quickly cooling the test
section rapidly If this test section has had heaters attached to it and run
previously the acrylic will crack due to uneven stresses inside of it
If paint is dripping stop painting immediately Clean the surface and start
over Hold the can far from the surface in order for it not to drip
Do not use TSP to teach new apprentices undergrads or graduate students
how to paint Regular spray paint is two orders of magnitude lower in cost
while the painting process is exactly the same
Do not paint with the doors closed The paint contains carcinogens that
can harm the lungs Always use a respirator and keep the room well
ventilated In-situ painting and baking has not been tried however it may
be a real option if the test section is difficult to disassemble and easily
accessible to painting and baking
If there is a can of paint that contains too little paint for the test section
that needs to be painted try to find a new can The mixing of two different
cans of TSP can be dangerous at times however it has been noticed over
the years that ISSI provides a very robust and dependable product that
does not vary significantly from batch to batch
21
Figure 11 Heater Strips Painted with TSP Too Closely
32 Experimental Setup of Suction Channel
The impingement channel is fed under suction As seen in Figure 12 air enters
through the plenum it crosses the jet plate as it gains speed to form the jets
which then impinge on the target wall The flow then passes through a venturi
flow meter and finally through the blower into the atmosphere A bypass valve is
used to control the flow rate of the impingement channel
22
Figure 12 Flow Loop of Impingement Channel
The impingement channel consists of 15 streamwise rows of 3 spanwise jets each The
total width of the channel YcD is of 8 diameters while the streamwise spacing between
the rows is XD=5 the spanwise distance between the holes is of YD=2 Figure 13shows
the top view of the jet plate The plate is counter bored to ensure that a nearly flat
velocity profile of the jet is achieved Figure 14 shows the front view of the channel Z is
denoted as the distance between the jet and target plates Side walls are interchangeable
to change the height of the channel to 6 8 and 10 diameters Two thirds of the
streamwise rows can be covered to change the XD from 5 to 15
Figure 13 Top View of Jet Plate
23
Figure 14 Front View of Impingement Channel
The target and sidewalls had heaters made specifically for them in a serpentine
style This was necessary to increase the resistance as the VARIACs used to power them
only had a maximum current output of 20 amps The heater strips are two diameters
wide at each end copper tape with conductive adhesive was used to connect the leads to
the power supply The heater consists of 50 micron thick steel sheet sandwiched between
two pieces of Kapton tape The heater is attached to the painted surface with the use of
double sided Kapton tape The target test section can be seen in Figure 15 also seen in
this figure are the two Teflon gaskets lined on the sides of the target plate With the target
wall bolted onto the sidewall the gasket is compressed generating a strong seal
Figure 15 Target Wall Test Section with Heater Leads
24
For this study the test matrix shown in Table 1 will be run Target and side wall
data will be taken at three different impingement heights at two different Reynolds
numbers of 7500 and 15000 denoted by A and B respectively A streamwise jet spacing
study is also done by testing the target and side wall heat transfer at an XD=15 for the
low impingement height channel
Table 1 Test Matrix
XD ZD Wall Re
5
10 TW
7500
15000
SW 7500
15000
8 TW
7500
15000
SW 7500
15000
6 TW
7500
15000
SW 7500
15000
15 6 TW
7500
15000
SW 7500
15000
33 Data Processing and Reduction
As described previously when taking temperature measurements with the use of TSP
reference temperatures are noted and a reference picture is taken The experiment is the
run once the experiment reaches steady state a new set of 4 pictures is taken Given the
calibration curve temperatures are backed out
25
Given the amount of heat generated inside the heater
Dividing by the heated area to get heat flux
Heat loss tests were run to consider how much of the heat flux generated by the heaters
goes through the backside instead of into the flow It was found that 25 of the heat flux
leaks out to the atmosphere through the acrylic In order to account for this heat leakage
it must be subtracted from the calculated value to become
Where Ah is the effective heated area given by
Where Aunheated is an estimate of how much unheated area is between the heater strips (~
3 of the total area)
To obtain heat transfer coefficient
Where Tref is the reference temperature Typically set in literature to be the jet
temperature
To obtain the average Reynolds number for the jets the total mass flow rate is used
Where Dj is the jet diameter and μ is dynamic viscosity (1983kgm s at 300K)
26
Pressure measurements were taken at the sidewall after the last jet entered the channel
These pressure measurements were used to determine the thermal performance of the
tallest two channels (ZD = 8 and 10)
The thermal performance at constant pumping power is found by using the equation
Where h is the average heat transfer coefficient for the target wall of them impingement
channel and ho is the heat transfer coefficient obtained by passing the same amount of
flow through a smooth duct ie the Dittus-Boelter correlation The friction factor f is
found with the use of
Where Ppl is the plenum static pressure assumed to be atmospheric and Plast jet is
the pressure read after the last jet V is the volumetric flow rate divided by the cross-
sectional area of the duct after the last impingement row The hydraulic diameter of the
channel is set to be
The baseline friction factor was calculated with the use of the Moody chart the hydraulic
diameter and the total mass flow rate though the channel Thermal performance at
constant pressure drop was also calculated with
27
34 Uncertainty Analysis
A simple uncertainty analysis was done to estimate the error in calculation of the
heat transfer coefficient from the given outputs of the test data From the bare basic
measurements for voltage area current temperature of thermocouples and temperature
profiles of paint a simple uncertainty analysis can be done to estimate the error for the
calculated heat transfer coefficient Figure 16 shows the different sources of error in the
calculation of heat transfer coefficient The effective uncertainty was calculated by taking
the root of the sum of the squares of all the individual percentage errors The
experimental uncertainty for heat transfer coefficient was of 703 This error may be
reduced by acquiring higher temperatures of the TSP reading current with a more
accurate ammeter or reading reference temperatures with the use of a thermopile instead
of a single thermocouple
Figure 16 Heat Transfer Coefficient Uncertainty Tree
28
35 Lateral Conduction Analysis
To take into account the lateral conduction occurring inside the heater foil while
the test is running two simple 1D conduction and convection equations were used to
quantify the amount of heat moving through the heater laterally and the amount of heat
convecting into the air The lateral conduction is expected to be at a maximum at the
places where there are large spatial variations of surface temperature which is why the
ZD = 6 XD = 5 case at high Re is chosen to be studied Figure 17 shows the
temperature distribution of the aforementioned case Four cold spots can be seen by their
distinct blue and yellow color located at the stagnation regions The maximum
temperature gradient occurs between the third jet impingement and the middle region
between jets The temperature difference was seen to be of 13degC The distance in between
these two temperatures is of 25D=01875m The corresponding heat flux between these
two points was calculated to be 13000Wm2 with ksteel~20Wm K A region of 1cm by
1cm was then created and the amount of heat calculated through conduction and
convection were compared To acquire the amount of heat removed through conduction
a heat flux of 13000Wm2 was imposed through an area of 01m by 00005m this
equaled to 00277 W The amount of heat moved through convection was calculated by
multiplying the heat flux used during the test by the area of the square 0001m2 the
resulting heat moving through the heater onto the air is 6 W Since the heat moving
through to the air is two orders of magnitudes larger than the heat moving laterally the
effective lateral conduction can be neglected
29
Figure 17 Temperature Profile of First Five Impingement Rows
A second order approach was also taken to quantify the amount of lateral
conduction in the heater The temperature gradient was taken from high peaks in heat
transfer caused by the second row of impingement of the same ZD=6 XD=5 channel at
high Re Figure 18 shows the high heat transfer coefficients created by the second row of
jets A quadratic curve fit was obtained by for this small region so that a continuous
equation of heat transfer coefficients as a function of streamwise distance was quantified
30
Figure 18 Detailed View of First Heat Transfer Peak with a Polynomial Curve Fit
The net heat gained by a differential volume from lateral conduction is the
difference in the temperature gradient at the entrance and the exit multiplied by the
thermal conductivity and cross sectional area Using this method shown in Figure 19 the
net change in convective heat transfer due to lateral conduction can be studied
Figure 19 Control Volume Heat Transfer Analysis
By taking the difference between the out flowing heat trough the right side and
the inflowing heat from the left side a net gain or loss can be found Figure 20 shows the
y = -470630x2 + 31244x - 14842Rsup2 = 09934
300
310
320
330
340
350
360
370
380
0 001 002 003 004 005
HTC
(W
m2K
)
x (m)
Heat Transfer Peak
Poly (Heat Transfer Peak)
31
difference in magnitude between the out flowing heat through convection seen in red and
the net inflow of heat from lateral conduction in blue From these calculations it was also
found that the amount of heat moving through lateral conduction is tow orders of
magnitude smaller than the amount of heat moving out through convection leading to the
belief that even at high temperature gradients lateral conduction does not play an
important role in the ongoing heat transfer processes in the impingement channel A more
detailed calculation of this work can be seen in appendix A
Figure 20 Heat Loss through Convection and Lateral Conduction
002 003 004 0051 10
5
1 104
1 103
001
qconv x( )
qnet x( )
x x
32
CHAPTER FOUR HEAT TRANSFER RESULTS
41 Heat Transfer Validation
In order to obtain confidence in our experimental setup an experiment was made
to test something that has already been published in literature A smooth channel was the
obvious choice as it was easy to setup by taking off the end cap and blocking all the holes
with smooth blue painters tape on the flow side and metal tape on the plenum side to
ensure no leaks into the channel from the jet plate The smooth channel has been studied
widely and multiple correlations exist one of these equations is the Dittus-Boelter
correlation (Incropera 2007) The test was run using the ZD=6 side wall so that the
hydraulic diameter was a minimum Figure 21 shows the span averaged results versus
non dimensional distance into the channel
Figure 21 Validation Spanwise Averaged Results
0
10
20
30
40
50
60
0 1 2 3 4 5 6 7 8 9
HTC
(W
m2K
)
XDc
Span Avg
Dittus Boelter
33
The plot shows decreasing heat transfer coefficient with increasing XDc due to
the developing thermal boundary layer The span average does not reach the Dittus-
Boelter due to it not being fully developed in the limited space it is given Typical flows
can take up to 60 diameters to achieve a fully developed profile with the current setup
the maximum length of the channel was of 9 diameters The profile however seems to
have an asymptote at the Dittus-Boelter correlation value leading to the belief that if the
channel was longer that value given by the correlation would be reached One important
factor to take into account in determining whether the experimental setup is validated is
the fact that the Dittus-Boelter correlation has an uncertainty near 30 Since the span
average at high XDc is well within 30 from the calculated value it is safe to assume
that the current experimental setup is validated
42 Heat Transfer Results
Heat transfer results are compared based on variations in channel height and
average jet Reynolds number As discussed earlier there are numerous other parameters
also affecting the heat transfer in these channels As these parameters are changed flow
structures within the channel are expected to be altered as well as discussed in the
literature Two of the major contributors to heat transfer in these channels are the
successful jet impingement and the resulting cross flow The same domain is captured in
both the local and averaged results
Figure 22 through Figure 25 highlights the heat transfer distribution for the cases
with a jet to jet spacing of 5 diameters in the streamwise direction and of 2 in the
spanwise direction It is evident that the smallest channel height (ZD=6) performs the
best at all Reynolds numbers on all surfaces It is also interesting to note the similarity
34
in the target wall profiles between case 528A and B where the curves are very similar
other than the obvious offset due to the change of the Reynolds number At this large
spacing we also see the degradation of the jets a few diameters downstream of each
impingement location The downstream shifts of the peaks are evident after the second
and third row of jets Also evident in these plots is the deflection of the impinging jet and
the wall jets from the cross flow The cross flow is forced to flow around the jet
deflecting the spread of the wall jet in the downstream direction Impingement locations
are also very evident at low XD however as XD and therefore the cross flow increase
the magnitude of the peaks start decreasing and eventually level out to pure internal flow
Figure 22 Target Wall Heat Transfer Coefficient Distributions
35
Figure 23 Span-averaged Target Wall Heat Transfer Distribution
36
Figure 24 Side Wall Heat Transfer Coefficient Distributions
37
Figure 25 Span-averaged Side wall Heat Transfer Distribution
Figure 23 and Figure 25 show similar details with impingement peaks clearly
diminishing and shifting in the downstream direction The cross flow clearly has some
negative influence on these geometries when compared to the more traditional
impingement highest on the order of 1 to 5 jet diameters The heat transfer profiles of the
target wall for all heights seen in Figure 22 and Figure 24 show the rapid decay in heat
transfer after the third jet This can be explained by understanding that the first jet does
not have any cross flow to deflect it the second jet only has the first jet worth of
momentum deflecting it downstream however since the channel is so tall the
momentum of the cross flow after the first and second jet are not enough to greatly
disturb the incoming jets After the third jet however the cross flow builds up enough
momentum to greatly affect the integrity of the jets downstream causing the span-
0
20
40
60
80
100
120
140
160
2 12 22 32 42 52 62 72
HTC
(W
m2K
)
XD
5210B_SW 528A_SW Jet Location
526A_TW 526B_TW
38
averaged heat transfer to rapidly drop The point at which the crossflow starts taking a
considerable effect occurs around XD =35 The target wall profile of the ZD=10
channel shows the outside jets on the second row of jet deflecting downstream It can be
conjectured that the bending of the outside jets downstream is caused by the wall jet
created by the first row of jets separating from the side wall and deflecting the outside
jets of the following rows of jets The heat transfer profile for the ZD case excludes the
first jet due to shadows being present when the data was taken
Also evident from this spanwise averaged data is the increase in heat transfer
with increases in Reynolds numbers and decreases in impingement height Results tend
to be the closest from case to case at the first impingement jet This is a reasonable
result as the effects of cross flow have little to no effect at the first few impingement
locations The impact of the jet would then be the driving force at these locations and
would be similar between cases except if the potential core is not reaching the target
surface The potential core of a jet tends to last between 6 and 10 diameters from its
origin It can be seen that the difference in heat transfer coefficient in the first two jets for
the ZD=8 and ZD=10 channel is much different than the corresponding difference
between the ZD=6 and ZD=8 heights This decreased difference between the heights of
the peaks may be attributed to the potential core reaching the target wall at the heights of
6 and 8 diameters leading to similar profiles and may not be reaching the surface at the
height of 10 diameters The heat transfer values of the peaks diminish in the downstream
direction The range of fluctuation also drops that is the profile becomes more uniform
at large XD This drop in fluctuation is more visible at the tallest channel height
(ZD=10) and less pronounced at the smallest channel This is due to the jet in the small
39
channel having to travel a shorter distance to impinge on the target plate leaving the
crossflow less time for it to deflect the jet as opposed to the tall channel where the jet has
to travel almost twice the distance as the ZD=6 channel for it to impinge on the target
wall This effect cannot be solely explained by the built up cross flow in the channel
Mixing loses also take part in the degradation of the stagnation size of the downstream
jets The mixing losses have much greater effect on the taller channels due to the same
reason that the cross flow has a higher impact on them too the jets have to travel a large
distance before hitting the target plate leading the stagnant or moving surrounding air to
be a sink of its downward momentum for a longer time and distance than the respective
smaller channels The heat transfer coefficient of the side wall was also analyzed
Similar effects are expected on the side wall due to the expected impact of the wall jet
As expected the strength of the cross flow is not enough to prevent wall jets from
successfully impacting the side wall at small XD jet locations however the crossflow
takes dominance at around XD=25 Also evident in these plots is the concentration of the
wall jet impact to the bottom of the channel on the order of 1-2 diameters in height It is
interesting to note that for the 5210B case in Figure 24 as the first jet diffuses outward
it impacts the sidewall at a height of ZD=6 The height at which the diffused jet affects
the sidewall heat transfer coefficient decreases as the crossflow increases The stagnation
regions are also deflected in the downstream direction similar to the target surface
results These effects are most evident in the 5210B Similar characteristics can be
explained from the spanwise-averaged plots shown in Figure 25 These results again
clearly show the effects of increasing the impingement height and increases in Reynolds
number As the height is increased the effect of the wall jet is significantly reduced
40
partially due to the increased surface area much of which is not affected by the wall jet
The diminishing effect of the cross flow accumulation is also evident in these plots as the
heat transfer peaks decrease in the downstream direction
43 XD Comparisons
The streamwise jet spacing was changed from XD=5 to 15 by covering two out
of three rows of jets This was done by covering the impingement holes inside the
channel with smooth blue painters tape and sealing the plenum side of the jet plate with
metal tape to ensure no leakage The profile is expected to be less uniform than the case
where XD=5 due to the large spreading of the high heat transfer peaks Due to the large
separation between the rows of jets there is a lower amount of downward momentum
than the equivalent XD=5 geometry for this reason it is expected to see a lower heat
transfer peak due to the jets momentum diffusing out faster to the stagnant air decreasing
the effective impingement velocity Figure 26 shows the target wall heat transfer
distribution Similar to the XD=5 profile it can be seen that the heat transfer due to the
jet impingement drastically reduces after the third jet This phenomenon leads us to
believe that at both Reynolds numbers the cross flow generated by the first three jets is
powerful enough to effectively deflect the fourth jet downstream diminishing its heat
transfer performance The similarity seen in Figure 26 between high and low Reynolds
number implies that the downstream deflection of the jets is not dependent on the jet
Reynolds numbers
41
Figure 26 XD=15 Target Wall Heat Transfer Profile
42
Figure 27 XD=15 Span-averaged Target Wall Heat Transfer Distribution
On the span averaged plots seen in Figure 27 the downstream deflection of the
jets is evident however as described previously the shifts in the peaks of heat transfer
occur at the same xD for both Reynolds numbers The amplitude of fluctuation of heat
transfer coefficients for the high Reynolds number case is larger than that of the low
Reynolds number Both profiles seem to start to level off at the end of the impingement
channel with the lowest span average being located just before the fourth jet at both
Reynolds numbers
A comparison of target wall heat transfer coefficients between XD =15 and 5 is
shown in Figure 28 At first glance it is clearly visible that the XD=15 average heat
transfer coefficient is smaller than its XD=5 counterpart This is also noticed by Ricklick
where he showed average HTC profiles for larger XD to be smaller than those at lower
XD (Ricklick 2009) This may occur due to there not being as high downward
0
50
100
150
200
250
300
350
0 20 40 60 80
HTC
(W
m2
K)
XD
Low Re
High Re
Impingement Location
43
momentum for the XD=15 case as compared to the XD=5 due to the lack of close jets
The stagnant air around the spaced out jets is taking away more of its momentum
decreasing the effective impingement Reynolds number Also important to notice is the
fact that since the XD=5 case has three times the flow impinged into it the cross flow
velocity and therefore Reynolds number will be three times as large increasing the heat
transfer coefficient
Figure 28 Target Wall Span-average Comparison of XD=5 and 15 at High Re
The side walls also show similar patterns to their XD=15 counterparts Strong
wall jet impingement can be seen on the side wall at low xD and zD Figure 29 shows
areas where the wall jet generated by the target wall impinges on the sidewall Similar to
the profile seen in Figure 24 the high heat transfer region reaches upward in the z
direction up to a height of 4-5 diameters for the first jet This high heat transfer stagnation
region decreases as xD increases to the point where the wall jet created by the last jet is
negligible when coupled with pure channel flow
0
50
100
150
200
250
300
350
400
0 10 20 30 40 50 60 70 80
HTC
(W
m2K
)
XD
XD = 5 XD = 15 Jet Location
- Blocked for XD =15
44
Figure 29 Side Wall Heat transfer Coefficient Profile
The span averaged plot seen in Figure 30 shows a nearly flat profile with peaks
located at the stagnation regions of the wall jets Thw downstream deflection for the
XD=15 case is much more pronounced than the one for the XD=5 case This is due to
the jet not being constrained by the wall jets generated by the previous and latter
impingement locations In the XD=15 case the wall jet is free to move downstream
more so than the XD=5 due to it not being disturbed by anything other than the cross
flow
45
Figure 30 XD=15 Side Wall Span-averaged Heat Transfer Coefficients
44 3D Comparison of the Heat Transfer Profiles
In order to further understand the targetsidewall interactions both heat transfer profiles
were positioned in an isometric view representative of the channel One important thing
to note is that both target and side wall profiles are not on the same scale This form of
data display is only qualitative way to describe the heat transfer profiles Figure 31 shows
the 3D profile of the XD=5 ZD=6 case The both stagnation regions of the jet onto the
target wall and the wall jet into the sidewall can be seen to occur at the same location for
the first three streamwise rows After the fourth and fifth row the wall jet diminishes in
magnitude Also visible in this view is the increasing heat transfer at low zD towards the
end of the channel of the side wall The constant input of mass and downward momentum
into the channel causes the cross flow generated by the previous jets to be squeezed into
the lower third of the channel increasing the velocity and the heat transfer of the target
wall
0
20
40
60
80
100
120
0 20 40 60 80
HTC
(W
m2K
)
XD
Low Re High Re Jet Locations
46
Figure 31 3D Heat Transfer Profile for ZD=6 XD=5
Similar patterns are seen in the taller ZD=8 channel seen in Figure 32 The wall jet
generate by the third streamwise row of jets is been deflected downward more than its
ZD=6 counterpart This can be attributed to the fact that the jet located at the ZD=8
channel has lost much of its momentum and is more easily bent downstream by the cross
flow generated by the first two jets The ZD=8 sidewall shows similar increasing heat
transfer at high xD however the increase is not as drastic as the one found in the ZD=6
channel This is caused due to the extra two diameters the jets have to cover to impinge
on the surface since the ZD=8 channel is one third larger than the ZD=6 one the flow
has to have more area to flow through The last few jets only deflect the cross flow
downward about 4 diameters this leaves two diameters for the flow to pass through on
the ZD=6 channel causing the velocity to increase rapidly and therefore increasing the
heat transfer coefficient at the low zD Since the ZD=8 channel has four remaining
47
diameters for the flow to move through it does not deflect it as much as the ZD=6
channel does only increasing the cross flow velocity and resulting heat transfer
coefficient slightly over the area at low zD and high xD
Figure 32 3D Heat Transfer Profile for ZD=8 XD=5
The 3D heat transfer profile for ZD=6 and xD=15 channel seen in Figure 33 shows
similar details to those seen in the XD=5 channels The stagnation regions of the jet and
wall jet occur at the same x location for the first three rows of jets the wall jet generated
by the fourth row of jets is deflected downstream only generating as small region of high
convective coefficients at the side wall The region located at the top right corner of the
side wall is colored red signifying high heat transfer however this area is generated by
the heaters providing non uniform heat flux at this location This region of high heat
transfer coefficients also occur at xD=0-4 of the target wall where the heater coil bends
48
Figure 33 3D Heat Transfer Profile for ZD=6 XD=15
45 Thermal Performance Calculations
Thermal performance calculations were done on the two tallest channels (ZD=8 and 10)
The pumping power was calculated for both channels at two Reynolds numbers Figure
34 shows the ratio of pressures required to pull the same amount of flow through as
smooth duct as opposed to through the jet plate The ZD=10 channel at high Reynolds
number requires the largest pressure as seen in the Figure however in order to pull the
same amount of flow rate through it requires a smaller pressure difference due to the
large cross section
49
Figure 34 Pressure Drop Ratio with Respect to Smooth Channel
Next the heat transfer enhancement was calculated A total area averaged heat
transfer coefficient was taken for the target wall and compared to the smooth channel
Dittus-Boelter value while using the same total mass flow rate Figure 35 shows an
average heat transfer enhancement of four times that of a smooth channel Similar trends
were noticed in the literature (Ricklick 2009) of decreasing heat transfer enhancement
with an increase of jet Reynolds number Ricklick also showed an increase in heat
transfer enhancement with an increase of jet to target spacing similar to the one seen in
Figure 35
0
10
20
30
40
50
60
528A_TW 528B_TW 5210A_TW 5210B_TW
PP
o
50
Figure 35 Heat Transfer Enhancement
Thermal performances at constant pressure drop were then calculated by dividing
the heat transfer enhancement by the pressure increase As seen in Figure 36 all the
values fall well below 1 making the impingement channel an unfeasible mode of heat
transfer enhancement when a constant pressure is supplied
Figure 36 Thermal Performance at Constant Pressure Drop
0
05
1
15
2
25
3
35
4
45
528A_TW 528B_TW 5210A_TW 5210B_TW
hh
o
0
002
004
006
008
01
012
014
528A_TW 528B_TW 5210A_TW 5210B_TW
(hh
o)
(PP
o)
51
The thermal performance at constant pumping drop was calculated in the same
way that the constant pressure drop was calculated the only difference being the pressure
ratio term was raised to the one third power As seen in Figure 37 the thermal
performances at constant pumping power are all higher than unity this signifies that if a
surface needs to be cooled with the supply of a constant pumping power the
impingement channel is a feasible option Similar to the figure literature (Ricklick 2009)
showed a decrease of thermal performance with an increase of channel height and
Reynolds number
Figure 37 Thermal Performance at Constant Pumping Power
0
02
04
06
08
1
12
14
528A_TW 528B_TW 5210A_TW 5210B_TW
(hh
o)
(PP
o)1
3
52
CHAPTER FIVE COMPUTATIONAL FLUID DYNAMICS
51 Problem Setup
In order to further enhance the understanding of the heat transfer profiles showed
previously a computational study was performed Even though CFD does not yield
accurate quantitative results it produces good qualitative data that can be used to explain
the flow physics in the channel and therefore increase the understanding of the patterns
seen previously The channel was meshed with the use of GAMBIT Due to the
symmetry the channel was split in half in the streamwise direction All horizontal
surfaces (parallel to the target wall) were divided into 6 different regions that are later on
going to be meshed individually The six regions are seen in Figure 38 section 1 is
located at the center of every jet also referred to as ldquojet centerrdquo This region was created
to reduce the squewness of the elements near the center of the jet by allowing the mesh to
be completely linear with a squewness of zero Section two complements section 1 to
complete the impingement hole The half impingement hole located at the symmetry wall
contains the same exact region 2 however it only has one half of the jet center Section 3
was made in order to bring the polar geometry of the holes to match the cartesian aspect
of the remainder of the channel With the addition of section 3 to the channel the only
remaining sections are square or rectangular regions Region 4 lies in between
streamwise rows of jets Section 5 is located at the entrance and the exit of the channel
These sections are not square in contrast with section 4 The last remaining section is
located near the side wall of the channel extending from the beginning to the exit of the
channel
53
Figure 38 Horizontal Plane of Impingement Channel Geometry
All the faces of sections 1 and 2 are linked throughout the channel and the
plenum however in order to have greater control of the mesh in the plenum and the
channel the remaining sections 3 4 5 and 6 are not linked to every single similar face
instead they are only linked to similar faces in either the plenum or the channel
Boundary layer spacing number of rows and growth factor are placed around the
channel In order to maintain a y+ of less than unity the first cell spacing of the boundary
layer inside the channel was set to be 000001 m (01mm) This first cell spacing yielded
y+
values varying between zero and 9 at the target side and front end wall Figure 39
shows a contour of y+ values on the heated walls The maximum values occur near the
impingement locations as expected due to large shear caused by the steep velocity
gradient normal to the wall On the downstream direction the y+ also increases due to the
increase of flow rate and therefore the increased skin friction on the wall At the
impingement location of the first jet the y+ is close to zero due to the velocity having its
direction mostly normal to the surface yielding no shear
54
Figure 39 Target Side and Front End Wall y+ Values
Once the faces were linked edge meshes were created on the sides of the jet center
Section 2rsquos inner edge was also meshed using a different parameter than the one used for
the jet center in order to allow for more freedom when trying to refine the mesh These
two edge meshes is followed by meshing all of section 2 faces alongside all the jet
centers Once these were complete section 3rsquos inner edge was meshed with different
parameters for the channel and plenum Sections 4 and 5 sides that connected with the
face made by section 6 were meshed so that their spacing was similar again the plenum
and channel were meshed separately for increased control of mesh density in both of
these areas The upstream-most edge of section 6 was meshed so that the spacing is
similar to the edge mesh in sections 4 and 5 this was done in order to have aspect ratios
of the wall be as close as possible to unity Sections 3 4 5 and 6 were meshed on both
the channel and the plenum With the entire target wall plane meshed these surface
meshes are coopered upwards to connect to the opposite wall The vertical spacing has
55
also been set up differently between the channel and the plenum The holes and the
plenum were also coopered The finished mesh was then exported as a msh file
Boundary conditions were set in GAMBIT once the mesh was imported into
Fluent values were set to every face depending on their location and purpose Figure 40
shows the four different boundary conditions Face 1 (blue) was set to be a mass flow
inlet The flow rate is half of the total flow rate at a given jet Reynolds number due to it
being only half of the entire domain Face 2 (yellow) is a symmetry plane face 3 (red) is
a pressure outlet at zero gauge pressure The rest of the faces in the channel denoted by
the number 4 (white) are set to walls The target side and front end wall had a heat flux
applied to them equal to 10000Wm2
Figure 40 Finished Mesh with Boundary Conditions
The model was imported into Fluent It was scaled down by a factor of 1000 due to it
being made in GAMBIT in millimeters The energy model was turned on The Realizable
k-ε model was used with enhanced wall functions on both the pressure and thermal
gradients The boundary conditions were set as discussed previously the mass flow inlet
was set to the specific flow rate normal to the surface the heat fluxes were set on the
56
heated walls the outflow gauge pressure was set to zero Two important reference values
characteristic length and reference temperature were set to be the diameter of the jet
(0075m) and 300K respectively The spatial discretization parameters were set to second
order upwind for momentum turbulent kinetic energy turbulent dissipation rate and
energy The under-relaxation factors were set to default Four monitors were created to
aid in the determination of convergence two of them read Nusselt numbers at the
stagnation region of the first and last jet the remaining two read the exit velocity at the
first and last jet The continuity x y and x velocities and energy equations residuals
were set to be 1E-6 while k and ε residuals were set to 1E-4 The solution was initialized
on the all zones at 1ms in the positive x direction The solution was set to autosave every
100 iterations while keeping only the two newest dat files The calculation was then run
for a maximum of 7000 iterations
A grid independence study was done on the domain to find the optimal size of
mesh that provides the correct solution while minimizing the compute time Two
monitors were set to check for grid independence both of them were vertex maximum
One of them read the Nusselt number at the impingement location of the first center jet
while the second one measures the velocity at the exit of the last jet Four different mesh
sizes were run to the convergence criterion explained before their sizes were 900000
15 million 28 million and 43 million cells
57
Figure 41 Grid Independence Study
It can be seen in Figure 41 that the difference between the 28 and 43 million cell
meshes are very small a difference of under 006 for velocity and 7 for Nusselt
number It can be safe to assume that the 28 million cell mesh is large enough to provide
a mesh independent solution The GAMBIT journal file used to create this mesh is
attached to the appendix The results shown hereafter are the ones obtained by the 28
million cell mesh
Figure 42 Residual Plots for the 26M Cell Run
67
69
71
73
75
77
79
81
83
85
485
4855
486
4865
487
4875
488
4885
489
0 1 2 3 4 5
Nu
sse
lt N
um
be
r
Cell Ammount (Millions)
Grid Independence Study
Velocity
Nusselt Number
58
For future reference Figure 42 shows the residuals of the 26M cell calculation
Up until around 4400 iterations the residuals were increasing shortly thereafter the
residuals started decreasing until it converged just after 5500 iterations All runs for the
differently sized meshes had the same residual patters with the peak of residuals and
point of convergence happening at different iterations
52 CFD Results
As describe previously all the results shown here are for the mesh containing 28 million
elements Figure 43 shows the total pressure contours It can be seen that the plenum
portion is at a constant total pressure Once the jets form since there are very small losses
in the jets due to the wall friction the total pressure still remains constant Only when the
jets enter the channel and start mixing with the cross flow is that they start losing the total
pressure head It is important to notice how the first two jets have the total pressure close
to the plenum arriving at the target wall This implies a successful impingement of the
undisturbed potential core As we move downstream the total pressure is lost quite
rapidly as the jets interact with the cross flow
Figure 43 Total Pressure Contours
59
Similar details can be drawn out from Figure 44 it can be seen that the first three
jets successfully impinge on the target wall while the rest of the downstream ones are
deflected by the cross flow As mentioned by Ricklick the velocity magnitude of the last
jet is larger than that of the first jet due to there being a lower static pressure at the end of
the channel providing it with a steeper pressure gradient hence higher velocity
Figure 44 Velocity Magnitude Contours
Turbulent kinetic energy was plotted in Figure 45 it is expected to have the
highest turbulent kinetic energy near the exit of the holes where the stagnant air is in
contact with the fast moving jet The mixing between the two regimes causes very
energetic eddies to form potentially enhancing the target and side wall heat transfer
coefficient As cross flow builds up towards the end of the channel the turbulent kinetic
energy increases due to larger overall velocities and fluctuations between the cross flow
and jets
60
Figure 45 Turbulent Kinetic Energy Contours
As Ricklick showed in his work the static temperature rise is quite small for such a small
channel It can be seen in Figure 46 that the driving temperature for heat transfer is that of
the plenum It is important to notice that a wall heat flux of 10000 Wm2 was used as the
boundary condition Not even in the most powerful tests would we ever use heat fluxes
that high they normally range between 2500 to a maximum of 7000 Wm2 A heat flux of
10000 Wm2 will increase the temperature at a faster rate than what it is normally used in
experimental testing
Figure 46 Static Temperature Contours
61
Figure 47 Target and Side Wall Heat Transfer Coefficient Contours
Figure 47 shows the target and sidewall heat transfer profiles Peaks can be seen at the
first three locations similar to that seen in Figure 22 The trend decreases rapidly to
eventually become a slowly increasing heat transfer profile due to the increase of mass
flow through the channel The sidewall provides the same results clear peaks in heat
transfer where the wall jets impinge on the sidewall seen in Figure 48 in more detail The
sidewall also shows a recirculation zone in between the first row of jets and the end wall
This is caused by the wall jet from the first row hitting the back wall moving upwards in
a circular pattern and coming back down when it encounters the first impingement row
Figure 48 Closer View of First few Rows of Impingement HTC Contours
62
Figure 49 Pathlines Generating from the First Row of Jets
Figure 49 helps explain the low heat transfer region between the first row of jets and
the end wall Pathlines are generated at the exit of each hole in the first row As the
air impinges on the surface half of it moves downstream and the other half movers
upstream to this recirculation zone where it circulates for a period of time before
reuniting with the remainder of the flow to move downstream The wall jet that
moves towards the second row of jets encounters the wall jet created by the second
row of jets causing the pathlines to drastically move upwards On the side of the
channel the pathlines behave erratically with no clear pattern clearly signifying the
highly turbulent and chaotic flow structure of this impingement channel
63
CHAPTER SIX CONCLUSIONS
It has been seen from this analysis that the side walls provide significant heat
transfer in an impingement channel especially at the relatively smaller channel
height This is primarily the result of successful impact of the wall jet with the side
walls It was shown that the tallest channel (ZD=10) has the most uniform profile with
low heat transfer coefficients when compared to the other channels The peaks of the
ZD=6 and 8 channels have a very similar profile which may indicate the successful
impingement of the potential core of the jet on the target surface As XD increases the
peaks diminish and a positive slope profile is attained by the increase of cross flow
velocity as more and more jets are introduced Tall impingement channels provide the
user with a heat transfer profile that is more uniform than those provided with the use of a
smaller channel while still maintaining higher convective coefficients when compared to
a smooth flow scenario The downstream shift of the wall jets is found to be independent
of Reynolds number and heavily dependent on streamwise position It was also found that
at XD=15 the wall jets decay faster than their XD=5 counterparts From the 3D heat
transfer profiles it was seen that the cross flow generated by multiple upstream jets is
deflected downward decreasing its effective flow area increasing its velocity hence
providing higher convective coefficients at the side wall at high xD and low zD
64
APPENDICES
Appendix A
Lateral Conduction Consideration
Thickness of foil heater Heat flux
Sample volume width
Volumetric heat generation
Volume of sample volume
Temperature profile from the first row of impingement ONLY valid for 02ltxlt045
t 50m k 20W
m K qflux 6000
W
m2
1mm
V 2
t qvol
qflux
t
T x( ) 298Kqflux
470630 x2
31244x 14842 W
m2K
N 15
x 02045 02
N 102 047
002 003 004 005314
315
316
317
318
319
320
T x( )
x
A t
qnet x( ) A kxT x
m
d
d xT x( )
d
d
1
m
002 003 004 0050
5 105
1 104
15 104
2 104
qnet x( )
x
65
Now comparing the net heat gained by lateral conduction to heat generated and convected out
It can be seen that the lateral conduction into the sample volume is two orders of magnitude smaller than the heat removed by convection
qgen qvol V 6 103
W
qconv x( ) 2
qflux qnet x( )
002 003 004 0051 10
5
1 104
1 103
001
qconv x( )
qnet x( )
x x
66
Appendix B
This is the journal file run on gambit to generate the geometry faces links
boundary layer face and volume meshes as well as the boundary conditions
set diameter
$d=75
$zc=6($d)
$xc=80($d)
$yc=4($d)
$y=2($d)
$x=5($d)
$zp=5($d)
$ztot=($zc)+($d)+($zp)
$jcf=(13)
$ocf=2
Boundary layer constants
$first=01
$growth=12
$rows=4
Meshing constants
$NumbNodes=5
$Numbtelnodes=6
$PLobnodes=5
$Chobnodes=5
$Plbenodes=($NumbNodes(4)+$rows)
$plsqnodes=($NumbNodes(3))
$Pllsnodes=($NumbNodes+$rows)
$Nojetcells=10
$Chzdnodes=($zc$Nojetcells)($d)
$Plzdnodes=($zp$Nojetcells)($d)
Boundary layer constants for channel
$firstch=001
$growthch=12
$rowsch=8
$CHbenodes=($NumbNodes(4)+$rowsch)
$CHlsnodes=($NumbNodes+$rowsch)
volume create body width ($xc) depth ($yc) height ($ztot) offset ($xc2) ($yc2) ($ztot2) brick
volume create cylinder height ($ztot) radius1 ($d2) radius3 ($d2) offset ($x) 0 ($ztot2) zaxis frustum
volume cmove cylinder multiple 1 offset 0 ($y) 0
volume cmove cylinder volume3 multiple 14 offset ($x) 0 0
volume create jetplate width ($xc) depth ($yc) height ($d)offset ($xc2) ($yc2) ($d2+$zc) brick
volume split body volumes jetplate connected
volume split jetplate volumes cylinder volume3 volume4 volume5
volume6 volume7 volume8 volume9 volume10 volume11
volume12 volume13 volume14 volume15 volume16 volume17
67
volume18 volume19 volume20 volume21 volume22 volume23
volume24 volume25 volume26 volume27 volume28 volume29
volume30 volume31 connected
face create jetcenter width ($jcf$d) height ($jcf$d) offset ($x) 0 0 xyplane rectangle
face create jetcircle radius ($d2) xyplane circle
face move jetcircle offset ($x) 0 0
face create outbox width ($ocf$d) height ($ocf$d) offset ($x) 0 0 xyplane rectangle
face split outbox connected faces jetcircle jetcenter
face split jetcircle connected faces face1
face split outbox connected faces face1
face cmove jetcenter outbox jetcircle face222 face223 multiple 1 offset 0 ($y) 0
face cmove jetcenter outbox jetcircle face222 face223 face224 face225 face226
face227 face228 multiple 14 offset ($x) 0 0
volume delete jetplate lowertopology
face split face1 connected keeptool faces jetcircle jetcenter outbox
face222 face223 face224 face225 face226 face227
face228 face229 face230 face231 face232 face233
face234 face235 face236 face237 face238 face239
face240 face241 face242 face243 face244 face245
face246 face247 face248 face249 face250 face251
face252 face253 face254 face255 face256 face257
face258 face259 face260 face261 face262 face263
face264 face265 face266 face267 face268 face269
face270 face271 face272 face273 face274 face275
face276 face277 face278 face279 face280 face281
face282 face283 face284 face285 face286 face287
face288 face289 face290 face291 face292 face293
face294 face295 face296 face297 face298 face299
face300 face301 face302 face303 face304 face305
face306 face307 face308 face309 face310 face311
face312 face313 face314 face315 face316 face317
face318 face319 face320 face321 face322 face323
face324 face325 face326 face327 face328 face329
face330 face331 face332 face333 face334 face335
face336 face337 face338 face339 face340 face341
face342 face343 face344 face345 face346 face347
face348 face349 face350 face351 face352 face353
face354 face355 face356 face357 face358 face359
face360 face361 face362 face363 face364 face365
face366 face367 face368
face move jetcircle jetcenter outbox face222 face223 face224
face225 face226 face227 face228 face229 face230
face231 face232 face233 face234 face235 face236
face237 face238 face239 face240 face241 face242
face243 face244 face245 face246 face247 face248
face249 face250 face251 face252 face253 face254
face255 face256 face257 face258 face259 face260
face261 face262 face263 face264 face265 face266
face267 face268 face269 face270 face271 face272
face273 face274 face275 face276 face277 face278
face279 face280 face281 face282 face283 face284
face285 face286 face287 face288 face289 face290
face291 face292 face293 face294 face295 face296
face297 face298 face299 face300 face301 face302
face303 face304 face305 face306 face307 face308
face309 face310 face311 face312 face313 face314
68
face315 face316 face317 face318 face319 face320
face321 face322 face323 face324 face325 face326
face327 face328 face329 face330 face331 face332
face333 face334 face335 face336 face337 face338
face339 face340 face341 face342 face343 face344
face345 face346 face347 face348 face349 face350
face351 face352 face353 face354 face355 face356
face357 face358 face359 face360 face361 face362
face363 face364 face365 face366 face367 face368 offset 0
0 $ztot
THIS SPLITS THE TOP PLENUM FACE WITH THE FACES CREATED IN THE BOTTOM
face split face6 connected keeptool faces jetcircle jetcenter outbox
face222 face223 face224 face225 face226 face227
face228 face229 face230 face231 face232 face233
face234 face235 face236 face237 face238 face239
face240 face241 face242 face243 face244 face245
face246 face247 face248 face249 face250 face251
face252 face253 face254 face255 face256 face257
face258 face259 face260 face261 face262 face263
face264 face265 face266 face267 face268 face269
face270 face271 face272 face273 face274 face275
face276 face277 face278 face279 face280 face281
face282 face283 face284 face285 face286 face287
face288 face289 face290 face291 face292 face293
face294 face295 face296 face297 face298 face299
face300 face301 face302 face303 face304 face305
face306 face307 face308 face309 face310 face311
face312 face313 face314 face315 face316 face317
face318 face319 face320 face321 face322 face323
face324 face325 face326 face327 face328 face329
face330 face331 face332 face333 face334 face335
face336 face337 face338 face339 face340 face341
face342 face343 face344 face345 face346 face347
face348 face349 face350 face351 face352 face353
face354 face355 face356 face357 face358 face359
face360 face361 face362 face363 face364 face365
face366 face367 face368
THIS MOVES THE FACES THAT WE ARE USING TO PLIT THE BOTTOM PLENUM SURFACE
face move jetcircle jetcenter outbox face222 face223 face224
face225 face226 face227 face228 face229 face230
face231 face232 face233 face234 face235 face236
face237 face238 face239 face240 face241 face242
face243 face244 face245 face246 face247 face248
face249 face250 face251 face252 face253 face254
face255 face256 face257 face258 face259 face260
face261 face262 face263 face264 face265 face266
face267 face268 face269 face270 face271 face272
face273 face274 face275 face276 face277 face278
face279 face280 face281 face282 face283 face284
face285 face286 face287 face288 face289 face290
face291 face292 face293 face294 face295 face296
face297 face298 face299 face300 face301 face302
69
face303 face304 face305 face306 face307 face308
face309 face310 face311 face312 face313 face314
face315 face316 face317 face318 face319 face320
face321 face322 face323 face324 face325 face326
face327 face328 face329 face330 face331 face332
face333 face334 face335 face336 face337 face338
face339 face340 face341 face342 face343 face344
face345 face346 face347 face348 face349 face350
face351 face352 face353 face354 face355 face356
face357 face358 face359 face360 face361 face362
face363 face364 face365 face366 face367 face368 offset 0
0 -$zp
SPLITS THE BOTTOM FACE OF THE PLENUM WITH THE FACES THAT ARE USED TO SPLIT
face split face114 connected keeptool faces jetcircle jetcenter
outbox face222 face223 face224 face225 face226 face227
face228 face229 face230 face231 face232 face233
face234 face235 face236 face237 face238 face239
face240 face241 face242 face243 face244 face245
face246 face247 face248 face249 face250 face251
face252 face253 face254 face255 face256 face257
face258 face259 face260 face261 face262 face263
face264 face265 face266 face267 face268 face269
face270 face271 face272 face273 face274 face275
face276 face277 face278 face279 face280 face281
face282 face283 face284 face285 face286 face287
face288 face289 face290 face291 face292 face293
face294 face295 face296 face297 face298 face299
face300 face301 face302 face303 face304 face305
face306 face307 face308 face309 face310 face311
face312 face313 face314 face315 face316 face317
face318 face319 face320 face321 face322 face323
face324 face325 face326 face327 face328 face329
face330 face331 face332 face333 face334 face335
face336 face337 face338 face339 face340 face341
face342 face343 face344 face345 face346 face347
face348 face349 face350 face351 face352 face353
face354 face355 face356 face357 face358 face359
face360 face361 face362 face363 face364 face365
face366 face367 face368
COPIES THE FACES THAT WE USED TO SPLIT TO BOTTOM OF THE PLENUM TO THE TOP OF
THE CHANNEL
face cmove jetcircle jetcenter outbox face222 face223 face224
face225 face226 face227 face228 face229 face230
face231 face232 face233 face234 face235 face236
face237 face238 face239 face240 face241 face242
face243 face244 face245 face246 face247 face248
face249 face250 face251 face252 face253 face254
face255 face256 face257 face258 face259 face260
face261 face262 face263 face264 face265 face266
face267 face268 face269 face270 face271 face272
face273 face274 face275 face276 face277 face278
face279 face280 face281 face282 face283 face284
70
face285 face286 face287 face288 face289 face290
face291 face292 face293 face294 face295 face296
face297 face298 face299 face300 face301 face302
face303 face304 face305 face306 face307 face308
face309 face310 face311 face312 face313 face314
face315 face316 face317 face318 face319 face320
face321 face322 face323 face324 face325 face326
face327 face328 face329 face330 face331 face332
face333 face334 face335 face336 face337 face338
face339 face340 face341 face342 face343 face344
face345 face346 face347 face348 face349 face350
face351 face352 face353 face354 face355 face356
face357 face358 face359 face360 face361 face362
face363 face364 face365 face366 face367 face368 multiple 1 offset 0
0 -$d
NAME OF COPIED NEW FACES
face1104 face1105 face1106 face1107 face1108 face1109 face1110 face1111
face1112 face1113 face1114 face1115 face1116 face1117 face1118 face1119
face1120 face1121 face1122 face1123 face1124 face1125 face1126 face1127
face1128 face1129 face1130 face1131 face1132 face1133 face1134 face1135
face1136 face1137 face1138 face1139 face1140 face1141 face1142 face1143
face1144 face1145 face1146 face1147 face1148 face1149 face1150 face1151
face1152 face1153 face1154 face1155 face1156 face1157 face1158 face1159
face1160 face1161 face1162 face1163 face1164 face1165 face1166 face1167
face1168 face1169 face1170 face1171 face1172 face1173 face1174 face1175
face1176 face1177 face1178 face1179 face1180 face1181 face1182 face1183
face1184 face1185 face1186 face1187 face1188 face1189 face1190 face1191
face1192 face1193 face1194 face1195 face1196 face1197 face1198 face1199
face1200 face1201 face1202 face1203 face1204 face1205 face1206 face1207
face1208 face1209 face1210 face1211 face1212 face1213 face1214 face1215
face1216 face1217 face1218 face1219 face1220 face1221 face1222 face1223
face1224 face1225 face1226 face1227 face1228 face1229 face1230 face1231
face1232 face1233 face1234 face1235 face1236 face1237 face1238 face1239
face1240 face1241 face1242 face1243 face1244 face1245 face1246 face1247
face1248 face1249 face1250 face1251 face1252 face1253
THIS SPLITS THE TOP OF THE CHANNEL WITH THE NEW COPIED FACES
face split face209 connected keeptool faces face1104 face1105 face1106 face1107
face1108 face1109 face1110 face1111 face1112 face1113 face1114 face1115
face1116 face1117 face1118 face1119 face1120 face1121 face1122 face1123
face1124 face1125 face1126 face1127 face1128 face1129 face1130 face1131
face1132 face1133 face1134 face1135 face1136 face1137 face1138 face1139
face1140 face1141 face1142 face1143 face1144 face1145 face1146 face1147
face1148 face1149 face1150 face1151 face1152 face1153 face1154 face1155
face1156 face1157 face1158 face1159 face1160 face1161 face1162 face1163
face1164 face1165 face1166 face1167 face1168 face1169 face1170 face1171
face1172 face1173 face1174 face1175 face1176 face1177 face1178 face1179
face1180 face1181 face1182 face1183 face1184 face1185 face1186 face1187
face1188 face1189 face1190 face1191 face1192 face1193 face1194 face1195
face1196 face1197 face1198 face1199 face1200 face1201 face1202 face1203
face1204 face1205 face1206 face1207 face1208 face1209 face1210 face1211
face1212 face1213 face1214 face1215 face1216 face1217 face1218 face1219
face1220 face1221 face1222 face1223 face1224 face1225 face1226 face1227
71
face1228 face1229 face1230 face1231 face1232 face1233 face1234 face1235
face1236 face1237 face1238 face1239 face1240 face1241 face1242 face1243
face1244 face1245 face1246 face1247 face1248 face1249 face1250 face1251
face1252 face1253
THIS UNITES THE RECTANGLE OUTSIDE FACES AND THE SEMICIRCLE SO THAT IT MAKES
A RECTANGLE WIHOUT THE CENTERJET
face unite faces jetcircle face223 real
face unite faces face222 outbox real
face unite faces face228 face226 real
face unite faces face225 face227 real
face unite faces face231 face233 real
face unite faces face232 face230 real
face unite faces face236 face238 real
face unite faces face237 face235 real
face unite faces face241 face243 real
face unite faces face242 face240 real
face unite faces face248 face246 real
face unite faces face245 face247 real
face unite faces face253 face251 real
face unite faces face252 face250 real
face unite faces face256 face258 real
face unite faces face257 face255 real
face unite faces face263 face261 real
face unite faces face260 face262 real
face unite faces face268 face266 real
face unite faces face265 face264 real
face unite faces face265 face267 real
face unite faces face273 face271 real
face unite faces face272 face270 real
face unite faces face276 face278 real
face unite faces face277 face275 real
face unite faces face281 face283 real
face unite faces face282 face280 real
face unite faces face286 face288 real
face unite faces face287 face285 real
face unite faces face291 face293 real
face unite faces face292 face290 real
face unite faces face296 face298 real
face unite faces face297 face295 real
face unite faces face301 face303 real
face unite faces face302 face300 real
face unite faces face306 face308 real
face unite faces face307 face305 real
face unite faces face316 face318 real
face unite faces face312 face310 real
face unite faces face311 face313 real
face unite faces face315 face317 real
face unite faces face321 face323 real
face unite faces face322 face320 real
face unite faces face326 face328 real
face unite faces face327 face325 real
face unite faces face331 face333 real
face unite faces face332 face330 real
face unite faces face336 face338 real
72
face unite faces face337 face335 real
face unite faces face347 face345 real
face unite faces face346 face348 real
face unite faces face342 face340 real
face unite faces face341 face343 real
face unite faces face356 face358 real
face unite faces face357 face355 real
face unite faces face352 face350 real
face unite faces face351 face353 real
face unite faces face361 face363 real
face unite faces face366 face368 real
face unite faces face360 face362 real
face unite faces face365 face367 real
SPLITTING ALL THE FACES OF THE CIRCLES IN THE BOTTOM OF THE PLENUM
face split face912 connected keeptool faces face222
face split face117 connected keeptool faces face228
face split face117 connected keeptool faces face225
face split face922 connected keeptool faces face232
face split face124 connected keeptool faces face236
face split face124 connected keeptool faces face237
face split face932 connected keeptool faces face242
face split face131 connected keeptool faces face248
face split face131 connected keeptool faces face245
face split face942 connected keeptool faces face252
face split face138 connected keeptool faces face256
face split face138 connected keeptool faces face257
face split face952 connected keeptool faces face260
face split face145 connected keeptool faces face268
face split face145 connected keeptool faces face265
face split face962 connected keeptool faces face272
face split face152 connected keeptool faces face276
face split face152 connected keeptool faces face277
face split face972 connected keeptool faces face282
face split face159 connected keeptool faces face286
face split face159 connected keeptool faces face287
face split face982 connected keeptool faces face292
face split face166 connected keeptool faces face296
face split face166 connected keeptool faces face297
face split face992 connected keeptool faces face302
face split face173 connected keeptool faces face306
face split face173 connected keeptool faces face307
face split face1002 connected keeptool faces face312
face split face180 connected keeptool faces face316
face split face180 connected keeptool faces face315
73
face split face1012 connected keeptool faces face322
face split face187 connected keeptool faces face326
face split face187 connected keeptool faces face327
face split face1022 connected keeptool faces face332
face split face194 connected keeptool faces face336
face split face194 connected keeptool faces face337
face split face1032 connected keeptool faces face342
face split face201 connected keeptool faces face346
face split face201 connected keeptool faces face347
face split face1042 connected keeptool faces face352
face split face208 connected keeptool faces face356
face split face208 connected keeptool faces face357
face split face1052 connected keeptool faces face360
face split face215 connected keeptool faces face366
face split face215 connected keeptool faces face365
THIS UNITES THE RECTANGLE OUTSIDE FACES AND THE SEMICIRCLE SO THAT IT MAKES
A RECTANGLE WIHOUT THE CENTERJET
face unite faces face1104 face1108 real
face unite faces face1107 face1106 real
face unite faces face1113 face1111 real
face unite faces face1112 face1110 real
face unite faces face1118 face1116 real
face unite faces face1117 face1115 real
face unite faces face1123 face1121 real
face unite faces face1122 face1120 real
face unite faces face1128 face1126 real
face unite faces face1127 face1125 real
face unite faces face1133 face1131 real
face unite faces face1132 face1130 real
face unite faces face1138 face1136 real
face unite faces face1137 face1135 real
face unite faces face1143 face1141 real
face unite faces face1142 face1140 real
face unite faces face1148 face1146 real
face unite faces face1147 face1145 real
face unite faces face1153 face1151 real
face unite faces face1152 face1150 real
face unite faces face1158 face1156 real
face unite faces face1157 face1155 real
face unite faces face1163 face1161 real
face unite faces face1162 face1160 real
face unite faces face1168 face1166 real
face unite faces face1167 face1165 real
face unite faces face1173 face1171 real
face unite faces face1172 face1170 real
face unite faces face1178 face1176 real
face unite faces face1177 face1175 real
face unite faces face1183 face1181 real
74
face unite faces face1182 face1180 real
face unite faces face1186 face1188 real
face unite faces face1187 face1185 real
face unite faces face1193 face1191 real
face unite faces face1192 face1190 real
face unite faces face1198 face1196 real
face unite faces face1197 face1195 real
face unite faces face1203 face1201 real
face unite faces face1202 face1200 real
face unite faces face1206 face1208 real
face unite faces face1207 face1205 real
face unite faces face1213 face1211 real
face unite faces face1212 face1210 real
face unite faces face1216 face1218 real
face unite faces face1217 face1215 real
face unite faces face1221 face1223 real
face unite faces face1222 face1220 real
face unite faces face1228 face1226 real
face unite faces face1227 face1225 real
face unite faces face1233 face1231 real
face unite faces face1232 face1230 real
face unite faces face1238 face1236 real
face unite faces face1237 face1235 real
face unite faces face1243 face1241 real
face unite faces face1242 face1240 real
face unite faces face1248 face1246 real
face unite faces face1247 face1245 real
face unite faces face1253 face1251 real
face unite faces face1252 face1250 real
SPLITTING ALL THE FACES OF THE CIRCLES IN THE TOP OF THE CHANNEL
face split face1257 connected keeptool faces face1107
face split face115 connected keeptool faces face1113
face split face115 connected keeptool faces face1112
face split face1267 connected keeptool faces face1117
face split face122 connected keeptool faces face1123
face split face122 connected keeptool faces face1122
face split face1277 connected keeptool faces face1127
face split face129 connected keeptool faces face1133
face split face129 connected keeptool faces face1132
face split face1287 connected keeptool faces face1137
face split face136 connected keeptool faces face1143
face split face136 connected keeptool faces face1142
face split face1297 connected keeptool faces face1147
face split face143 connected keeptool faces face1153
face split face143 connected keeptool faces face1152
face split face1307 connected keeptool faces face1157
face split face150 connected keeptool faces face1163
face split face150 connected keeptool faces face1162
75
face split face1317 connected keeptool faces face1167
face split face157 connected keeptool faces face1173
face split face157 connected keeptool faces face1172
face split face1327 connected keeptool faces face1177
face split face164 connected keeptool faces face1183
face split face164 connected keeptool faces face1182
face split face1337 connected keeptool faces face1187
face split face171 connected keeptool faces face1193
face split face171 connected keeptool faces face1192
face split face1347 connected keeptool faces face1197
face split face178 connected keeptool faces face1203
face split face178 connected keeptool faces face1202
face split face1357 connected keeptool faces face1207
face split face185 connected keeptool faces face1213
face split face185 connected keeptool faces face1212
face split face1367 connected keeptool faces face1217
face split face192 connected keeptool faces face1221
face split face192 connected keeptool faces face1222
face split face1377 connected keeptool faces face1227
face split face199 connected keeptool faces face1233
face split face199 connected keeptool faces face1232
face split face1387 connected keeptool faces face1237
face split face206 connected keeptool faces face1243
face split face206 connected keeptool faces face1242
face split face1397 connected keeptool faces face1247
face split face213 connected keeptool faces face1253
face split face213 connected keeptool faces face1252
face split face1452 connected keeptool faces face224
face split face1456 connected keeptool faces face234
face split face1460 connected keeptool faces face244
face split face1464 connected keeptool faces face254
face split face1468 connected keeptool faces face264
face split face1472 connected keeptool faces face274
face split face1476 connected keeptool faces face284
face split face1480 connected keeptool faces face294
face split face1484 connected keeptool faces face304
face split face1488 connected keeptool faces face314
face split face1492 connected keeptool faces face324
face split face1496 connected keeptool faces face334
face split face1500 connected keeptool faces face344
face split face1504 connected keeptool faces face354
face split face1508 connected keeptool faces face364
DELETING ALL THE FACES USED TO MAKE THE CUTS
face delete jetcircle face222 face228 face225 jetcenter
76
face224 face231 face232 face236 face237 face229
face1456 face241 face242 face239 face248 face244
face245 face253 face249 face252 face254 face256
face257 face263 face259 face260 face268 face264
face265 face273 face272 face269 face276 face277
face274 face281 face282 face286 face279 face287
face284 face291 face292 face296 face297 face289
face294 face301 face299 face302 face306 face307
face304 face311 face312 face316 face315 face309
face314 face321 face322 face326 face327 face319
face324 face331 face332 face329 face336 face334
face337 face341 face342 face339 face346 face344
face347 face351 face352 face349 face356 face354
face357 face361 face359 face360 face366 face364
face365 lowertopology
face delete face1104 face1105 face1107 face1113 face1112
face115 face234 face1118 face1114 face1117 face1123
face1122 face122 face1138 face1128 face1127 face1124
face1133 face1132 face129 face1134 face1137 face1143
face136 face1142 face1148 face1144 face1147 face1153
face143 face1152 face1158 face1154 face1157 face1163
face150 face1162 face1168 face1164 face1167 face1173
face157 face1172 face1178 face1174 face1177 face1183
face164 face1182 face1186 face1184 face1187 face1193
face171 face1192 face1198 face1194 face1197 face1203
face178 face1202 face1206 face1204 face1207 face1213
face185 face1212 face1216 face1214 face1217 face1221
face192 face1222 face1228 face1224 face1227 face1233
face199 face1232 face1238 face1234 face1237 face1243
face206 face1242 face1248 face1244 face1247 face1253
face213 face1252 lowertopology
face delete face1109 face1119 face1129 face1139 face1149 face1159
face1169 face1179 face1189 face1199 face1209 face1219
face1229 face1239 face1249 lowertopology
face create CP1 width 600 height 75 offset 300 (225+($d)2) 0 xyplane rectangle
face create CP2 width 600 height 75 offset 300 (225+($d)2) ($zc) xyplane rectangle
face create CP3 width 600 height 75 offset 300 (225+($d)2) ($zc+$d) xyplane rectangle
face create CP4 width 600 height 75 offset 300 (225+($d)2) ($zc+$d+$zp) xyplane rectangle
face split face6 connected faces CP4
face split face114 connected faces CP3
face split face209 connected faces CP2
face split face1 connected faces CP1
GEOMETRY IS FINISHED
face modify face912 side vertex6437 vertex6436
77
face modify face1600 side vertex7302 vertex7303
face modify face117 side vertex6446 vertex6447
face modify face646 side vertex3312
face modify face646 side vertex3313
face modify face647 side vertex3432 vertex3433
face modify face372 side vertex2040 vertex2041
face modify face376 side vertex2100 vertex2101
face modify face377 side vertex2221 vertex2220
LINKING ALL THE JET CENTERS
face link face1450 face640 edges edge6949 edge3518 vertices
vertex6437 vertex3253 reverse
face link face1450 face1257 edges edge6949 edge7340 vertices
vertex6437 vertex6797 reverse
face link face1257 face370 edges edge7340 edge2139 vertices
vertex6797 vertex2041 reverse
face link face1257 face1454 edges edge7340 edge6975 vertices
vertex6797 vertex6461 reverse
face link face1454 face649 edges edge6975 edge3519 vertices
vertex6461 vertex3255 reverse
face link face1454 face1267 edges edge6975 edge7377 vertices
vertex6461 vertex6831 reverse
face link face1267 face379 edges edge7377 edge2141 vertices
vertex6831 vertex2043 reverse
face link face1267 face1458 edges edge7377 edge7001 vertices
vertex6831 vertex6485 reverse
face link face1458 face659 edges edge7001 edge3520 vertices
vertex6485 vertex3257 reverse
face link face1458 face1277 edges edge7001 edge7414 vertices
vertex6485 vertex6865 reverse
face link face1277 face389 edges edge7414 edge2143 vertices
vertex6865 vertex2045 reverse
face link face1277 face1462 edges edge7414 edge7027 vertices
vertex6865 vertex6509 reverse
face link face1462 face669 edges edge7027 edge3521 vertices
vertex6509 vertex3259 reverse
face link face1462 face1287 edges edge7027 edge7451 vertices
vertex6509 vertex6899 reverse
face link face1287 face399 edges edge7451 edge2145 vertices
vertex6899 vertex2047 reverse
face link face1287 face1466 edges edge7451 edge7053 vertices
vertex6899 vertex6533 reverse
face link face1466 face679 edges edge7053 edge3522 vertices
vertex6533 vertex3261 reverse
face link face1466 face1297 edges edge7053 edge7488 vertices
vertex6533 vertex6933 reverse
face link face1297 face409 edges edge7488 edge2147 vertices
vertex6933 vertex2049 reverse
face link face1297 face1470 edges edge7488 edge7079 vertices
vertex6933 vertex6557 reverse
face link face1470 face689 edges edge7079 edge3523 vertices
vertex6557 vertex3263 reverse
face link face1470 face1307 edges edge7079 edge7525 vertices
vertex6557 vertex6967 reverse
face link face1307 face419 edges edge7525 edge2149 vertices
78
vertex6967 vertex2051 reverse
face link face1307 face1474 edges edge7525 edge7105 vertices
vertex6967 vertex6581 reverse
face link face1474 face1317 edges edge7105 edge7562 vertices
vertex6581 vertex7001 reverse
face link face1474 face699 edges edge7105 edge3524 vertices
vertex6581 vertex3265 reverse
face link face1317 face429 edges edge7562 edge2151 vertices
vertex7001 vertex2053 reverse
face link face1317 face1478 edges edge7562 edge7131 vertices
vertex7001 vertex6605 reverse
face link face1478 face1327 edges edge7131 edge7599 vertices
vertex6605 vertex7035 reverse
face link face1478 face709 edges edge7131 edge3525 vertices
vertex6605 vertex3267 reverse
face link face1327 face439 edges edge7599 edge2153 vertices
vertex7035 vertex2055 reverse
face link face1327 face1482 edges edge7599 edge7157 vertices
vertex7035 vertex6629 reverse
face link face1482 face719 edges edge7157 edge3526 vertices
vertex6629 vertex3269 reverse
face link face1482 face1337 edges edge7157 edge7636 vertices
vertex6629 vertex7069 reverse
face link face1337 face449 edges edge7636 edge2155 vertices
vertex7069 vertex2057 reverse
face link face1337 face1486 edges edge7636 edge7183 vertices
vertex7069 vertex6653 reverse
face link face1486 face1347 edges edge7183 edge7673 vertices
vertex6653 vertex7103 reverse
face link face1347 face459 edges edge7673 edge2157 vertices
vertex7103 vertex2059 reverse
face link face1486 face729 edges edge7183 edge3527 vertices
vertex6653 vertex3271 reverse
face link face1347 face1490 edges edge7673 edge7209 vertices
vertex7103 vertex6677 reverse
face link face1490 face1357 edges edge7209 edge7710 vertices
vertex6677 vertex7137 reverse
face link face1490 face739 edges edge7209 edge3528 vertices
vertex6677 vertex3273 reverse
face link face1357 face469 edges edge7710 edge2159 vertices
vertex7137 vertex2061 reverse
face link face1357 face1494 edges edge7710 edge7235 vertices
vertex7137 vertex6701 reverse
face link face1494 face1367 edges edge7235 edge7747 vertices
vertex6701 vertex7171 reverse
face link face1494 face749 edges edge7235 edge3529 vertices
vertex6701 vertex3275 reverse
face link face1367 face479 edges edge7747 edge2161 vertices
vertex7171 vertex2063 reverse
face link face1367 face1498 edges edge7747 edge7261 vertices
vertex7171 vertex6725 reverse
face link face1498 face1377 edges edge7261 edge7784 vertices
vertex6725 vertex7205 reverse
face link face1377 face489 edges edge7784 edge2163 vertices
vertex7205 vertex2065 reverse
face link face1498 face759 edges edge7261 edge3530 vertices
79
vertex6725 vertex3277 reverse
face link face1377 face1502 edges edge7784 edge7287 vertices
vertex7205 vertex6749 reverse
face link face1502 face1387 edges edge7287 edge7821 vertices
vertex6749 vertex7239 reverse
face link face1387 face499 edges edge7821 edge2165 vertices
vertex7239 vertex2067 reverse
face link face1387 face1506 edges edge7821 edge7313 vertices
vertex7239 vertex6773 reverse
face link face1502 face769 edges edge7287 edge3531 vertices
vertex6749 vertex3279 reverse
face link face1506 face1397 edges edge7313 edge7858 vertices
vertex6773 vertex7273 reverse
face link face1506 face779 edges edge7313 edge3532 vertices
vertex6773 vertex3281 reverse
face link face1397 face509 edges edge7858 edge2167 vertices
vertex7273 vertex2069 reverse
LINKING ALL THE COMPLETE JETCENTERS
face link face1452 face644 edges edge7891 edge3773 vertices
vertex7303 vertex3433
face link face1452 face115 edges edge7891 edge7364 vertices
vertex7303 vertex6819
face link face1452 face1456 edges edge7891 edge7900 vertices
vertex7303 vertex7311
face link face1456 face654 edges edge7900 edge3774 vertices
vertex7311 vertex3435
face link face1456 face122 edges edge7900 edge7401 vertices
vertex7311 vertex6853
face link face1456 face1460 edges edge7900 edge7909 vertices
vertex7311 vertex7319
face link face1460 face1464 edges edge7909 edge7918 vertices
vertex7319 vertex7327
face link face1460 face129 edges edge7909 edge7438 vertices
vertex7319 vertex6887
face link face1460 face664 edges edge7909 edge3775 vertices
vertex7319 vertex3437
face link face1464 face674 edges edge7918 edge3776 vertices
vertex7327 vertex3439
face link face1464 face136 edges edge7918 edge7475 vertices
vertex7327 vertex6921
face link face1464 face1468 edges edge7918 edge7927 vertices
vertex7327 vertex7335
face link face1472 face1468 edges edge7936 edge7927 vertices
vertex7343 vertex7335
face link face1468 face143 edges edge7927 edge7512 vertices
vertex7335 vertex6955
face link face1468 face684 edges edge7927 edge3777 vertices
vertex7335 vertex3441
face link face1472 face694 edges edge7936 edge3778 vertices
vertex7343 vertex3443
face link face1472 face150 edges edge7936 edge7549 vertices
vertex7343 vertex6989
face link face1472 face1476 edges edge7936 edge7945 vertices
80
vertex7343 vertex7351
face link face1476 face1480 edges edge7945 edge7954 vertices
vertex7351 vertex7359
face link face1476 face157 edges edge7945 edge7586 vertices
vertex7351 vertex7023
face link face1476 face704 edges edge7945 edge3779 vertices
vertex7351 vertex3445
face link face1480 face714 edges edge7954 edge3780 vertices
vertex7359 vertex3447
face link face1480 face164 edges edge7954 edge7623 vertices
vertex7359 vertex7057
face link face1480 face1484 edges edge7954 edge7963 vertices
vertex7359 vertex7367
face link face1484 face171 edges edge7963 edge7660 vertices
vertex7367 vertex7091
face link face1484 face724 edges edge7963 edge3781 vertices
vertex7367 vertex3449
face link face1480 face1488 edges edge7954 edge7972 vertices
vertex7359 vertex7375
face link face1488 face178 edges edge7972 edge7697 vertices
vertex7375 vertex7125
face link face1488 face734 edges edge7972 edge3782 vertices
vertex7375 vertex3451
face link face1488 face1492 edges edge7972 edge7981 vertices
vertex7375 vertex7383
face link face1492 face744 edges edge7981 edge3783 vertices
vertex7383 vertex3453
face link face1492 face185 edges edge7981 edge7734 vertices
vertex7383 vertex7159
face link face1492 face1496 edges edge7981 edge7990 vertices
vertex7383 vertex7391
face link face1496 face754 edges edge7990 edge3784 vertices
vertex7391 vertex3455
face link face1496 face192 edges edge7990 edge7771 vertices
vertex7391 vertex7193
face link face1496 face1500 edges edge7990 edge7999 vertices
vertex7391 vertex7399
face link face1500 face1504 edges edge7999 edge8008 vertices
vertex7399 vertex7407
face link face1504 face1508 edges edge8008 edge8017 vertices
vertex7407 vertex7415
face link face1500 face199 edges edge7999 edge7808 vertices
vertex7399 vertex7227
face link face1500 face764 edges edge7999 edge3785 vertices
vertex7399 vertex3457
face link face1504 face774 edges edge8008 edge3786 vertices
vertex7407 vertex3459
face link face1508 face784 edges edge8017 edge3787 vertices
vertex7415 vertex3461
face link face1504 face206 edges edge8008 edge7845 vertices
vertex7407 vertex7261
face link face1508 face213 edges edge8017 edge7882 vertices
vertex7415 vertex7295
linking the jetcenters of the bottom of the channel one of them has to be reversed but the otherones are not
81
face link face115 face374 edges edge7364 edge2394 vertices
vertex6819 vertex2221 reverse
face link face374 face384 edges edge2394 edge2396 vertices
vertex2221 vertex2223
face link face384 face394 edges edge2396 edge2398 vertices
vertex2223 vertex2225
face link face394 face404 edges edge2398 edge2400 vertices
vertex2225 vertex2227
face link face404 face414 edges edge2400 edge2402 vertices
vertex2227 vertex2229
face link face414 face424 edges edge2402 edge2404 vertices
vertex2229 vertex2231
face link face424 face434 edges edge2404 edge2406 vertices
vertex2231 vertex2233
face link face434 face444 edges edge2406 edge2408 vertices
vertex2233 vertex2235
face link face444 face454 edges edge2408 edge2410 vertices
vertex2235 vertex2237
face link face454 face464 edges edge2410 edge2412 vertices
vertex2237 vertex2239
face link face464 face474 edges edge2412 edge2414 vertices
vertex2239 vertex2241
face link face474 face484 edges edge2414 edge2416 vertices
vertex2241 vertex2243
face link face484 face494 edges edge2416 edge2418 vertices
vertex2243 vertex2245
face link face494 face504 edges edge2418 edge2420 vertices
vertex2245 vertex2247
face link face504 face514 edges edge2420 edge2422 vertices
vertex2247 vertex2249
UP TO THIS POINT ALL THE FACES ARE CONNCTED SUCCESSFULLY
LINKING THE FIRST THREE JET TELEPHONES
face link face912 face117 edges edge6950 edge6960 vertices
vertex6437 vertex6446 reverse
face link face912 face1600 edges edge6950 edge7890 vertices
vertex6437 vertex7303 reverse
face link face912 face372 edges edge6950 edge2168 vertices
vertex6437 vertex2041
face link face117 face376 edges edge6959 edge2304 vertices
vertex6447 vertex2101 reverse
face link face1600 face377 edges edge7890 edge2423 vertices
vertex7303 vertex2221 reverse
face link face372 face382 edges edge2168 edge2169 vertices
vertex2041 vertex2043
face link face377 face387 edges edge2423 edge2424 vertices
vertex2221 vertex2223
face link face376 face386 edges edge2304 edge2306 vertices
vertex2101 vertex2103
face link face387 face397 edges edge2424 edge2425 vertices
vertex2223 vertex2225
face link face386 face396 edges edge2306 edge2308 vertices
82
vertex2103 vertex2105
face link face382 face392 edges edge2169 edge2170 vertices
vertex2043 vertex2045
face link face382 face392 edges edge2169 edge2170 vertices
vertex2043 vertex2045
face link face382 face392 edges edge2169 edge2170 vertices
vertex2043 vertex2045
face link face382 face392 edges edge2169 edge2170 vertices
vertex2043 vertex2045
face link face397 face407 edges edge2425 edge2426 vertices
vertex2225 vertex2227
face link face392 face402 edges edge2170 edge2171 vertices
vertex2045 vertex2047
face link face396 face406 edges edge2290 edge2291 vertices
vertex2104 vertex2106
face link face407 face417 edges edge2426 edge2427 vertices
vertex2227 vertex2229
face link face417 face427 edges edge2427 edge2428 vertices
vertex2229 vertex2231
face link face427 face437 edges edge2428 edge2429 vertices
vertex2231 vertex2233
face link face437 face447 edges edge2429 edge2430 vertices
vertex2233 vertex2235
face link face447 face457 edges edge2430 edge2431 vertices
vertex2235 vertex2237
face link face457 face467 edges edge2431 edge2432 vertices
vertex2237 vertex2239
face link face467 face477 edges edge2432 edge2433 vertices
vertex2239 vertex2241
face link face477 face487 edges edge2433 edge2434 vertices
vertex2241 vertex2243
face link face487 face487 edges edge2434 edge2434 vertices
vertex2243 vertex2243
face link face487 face487 edges edge2434 edge2434 vertices
vertex2243 vertex2243
face link face487 face487 edges edge2434 edge2434 vertices
vertex2243 vertex2243
face link face487 face497 edges edge2434 edge2435 vertices
vertex2243 vertex2245
face link face497 face507 edges edge2435 edge2436 vertices
vertex2245 vertex2247
face link face507 face517 edges edge2436 edge2437 vertices
vertex2247 vertex2249
face link face406 face416 edges edge2291 edge2292 vertices
vertex2106 vertex2108
face link face416 face426 edges edge2292 edge2293 vertices
vertex2108 vertex2110
face link face426 face436 edges edge2293 edge2294 vertices
vertex2110 vertex2112
face link face436 face446 edges edge2294 edge2295 vertices
vertex2112 vertex2114
face link face446 face456 edges edge2295 edge2296 vertices
vertex2114 vertex2116
face link face456 face466 edges edge2296 edge2297 vertices
vertex2116 vertex2118
face link face466 face476 edges edge2297 edge2298 vertices
83
vertex2118 vertex2120
face link face486 face496 edges edge2299 edge2300 vertices
vertex2122 vertex2124
face link face476 face486 edges edge2298 edge2299 vertices
vertex2120 vertex2122
face link face496 face506 edges edge2300 edge2301 vertices
vertex2124 vertex2126
face link face506 face516 edges edge2301 edge2302 vertices
vertex2126 vertex2128
face link face392 face402 edges edge2142 edge2144 vertices
vertex2044 vertex2046
face link face402 face412 edges edge2171 edge2172 vertices
vertex2047 vertex2049
face link face412 face422 edges edge2172 edge2173 vertices
vertex2049 vertex2051
face link face422 face432 edges edge2173 edge2174 vertices
vertex2051 vertex2053
face link face432 face442 edges edge2174 edge2175 vertices
vertex2053 vertex2055
face link face442 face452 edges edge2175 edge2176 vertices
vertex2055 vertex2057
face link face452 face462 edges edge2176 edge2177 vertices
vertex2057 vertex2059
face link face462 face472 edges edge2177 edge2178 vertices
vertex2059 vertex2061
face link face472 face482 edges edge2178 edge2179 vertices
vertex2061 vertex2063
face link face482 face492 edges edge2179 edge2180 vertices
vertex2063 vertex2065
face link face492 face502 edges edge2180 edge2181 vertices
vertex2065 vertex2067
face link face502 face512 edges edge2181 edge2182 vertices
vertex2067 vertex2069
LINKING THE TELEPHONES OF THE BOTTOM OF THE PLENUM
face link face912 face922 edges edge6950 edge6976 vertices
vertex6437 vertex6461
face link face922 face932 edges edge6976 edge7002 vertices
vertex6461 vertex6485
face link face932 face942 edges edge7002 edge7028 vertices
vertex6485 vertex6509
face link face942 face952 edges edge7028 edge7054 vertices
vertex6509 vertex6533
face link face952 face962 edges edge7054 edge7080 vertices
vertex6533 vertex6557
face link face962 face972 edges edge7080 edge7106 vertices
vertex6557 vertex6581
face link face972 face982 edges edge7106 edge7132 vertices
vertex6581 vertex6605
face link face982 face992 edges edge7132 edge7158 vertices
vertex6605 vertex6629
face link face992 face1002 edges edge7158 edge7184 vertices
vertex6629 vertex6653
face link face1002 face1012 edges edge7184 edge7210 vertices
vertex6653 vertex6677
84
face link face1012 face1022 edges edge7210 edge7236 vertices
vertex6677 vertex6701
face link face1032 face1042 edges edge7262 edge7288 vertices
vertex6725 vertex6749
face link face1042 face1052 edges edge7288 edge7314 vertices
vertex6749 vertex6773
face link face117 face124 edges edge6960 edge6986 vertices
vertex6446 vertex6470
face link face124 face131 edges edge6986 edge7012 vertices
vertex6470 vertex6494
face link face131 face138 edges edge7012 edge7038 vertices
vertex6494 vertex6518
face link face138 face145 edges edge7038 edge7064 vertices
vertex6518 vertex6542
face link face145 face152 edges edge7064 edge7090 vertices
vertex6542 vertex6566
face link face152 face159 edges edge7090 edge7116 vertices
vertex6566 vertex6590
face link face159 face166 edges edge7116 edge7142 vertices
vertex6590 vertex6614
face link face166 face173 edges edge7142 edge7168 vertices
vertex6614 vertex6638
face link face173 face180 edges edge7168 edge7194 vertices
vertex6638 vertex6662
face link face180 face187 edges edge7194 edge7220 vertices
vertex6662 vertex6686
face link face187 face194 edges edge7220 edge7246 vertices
vertex6686 vertex6710
face link face194 face201 edges edge7246 edge7272 vertices
vertex6710 vertex6734
face link face1022 face1032 edges edge7236 edge7262 vertices
vertex6701 vertex6725
face link face1032 face1042 edges edge7262 edge7288 vertices
vertex6725 vertex6749
face link face201 face208 edges edge7271 edge7297 vertices
vertex6735 vertex6759
face link face208 face215 edges edge7297 edge7323 vertices
vertex6759 vertex6783
face link face1600 face1602 edges edge7890 edge7899 vertices
vertex7303 vertex7311
face link face1602 face1604 edges edge7899 edge7908 vertices
vertex7311 vertex7319
face link face1604 face1606 edges edge7908 edge7917 vertices
vertex7319 vertex7327
face link face1606 face1608 edges edge7917 edge7926 vertices
vertex7327 vertex7335
face link face1608 face1610 edges edge7926 edge7935 vertices
vertex7335 vertex7343
face link face1610 face1612 edges edge7935 edge7944 vertices
vertex7343 vertex7351
face link face1612 face1614 edges edge7944 edge7953 vertices
vertex7351 vertex7359
face link face1614 face1616 edges edge7953 edge7962 vertices
vertex7359 vertex7367
face link face1616 face1618 edges edge7962 edge7971 vertices
vertex7367 vertex7375
85
face link face1618 face1620 edges edge7971 edge7980 vertices
vertex7375 vertex7383
face link face1620 face1622 edges edge7980 edge7989 vertices
vertex7383 vertex7391
face link face1622 face1624 edges edge7989 edge7998 vertices
vertex7391 vertex7399
face link face1624 face1626 edges edge7998 edge8007 vertices
vertex7399 vertex7407
face link face1626 face1628 edges edge8007 edge8016 vertices
vertex7407 vertex7415
LINKING ALL THE TELEPHONES OF THE TOP OF THE CHANNEL
face link face912 face1510 edges edge6950 edge7339 vertices
vertex6437 vertex6797 reverse
face link face117 face1512 edges edge6959 edge7349 vertices
vertex6447 vertex6807
face link face1600 face1514 edges edge7890 edge7363 vertices
vertex7303 vertex6819
face link face1510 face1516 edges edge7339 edge7376 vertices
vertex6797 vertex6831
face link face1516 face1522 edges edge7376 edge7413 vertices
vertex6831 vertex6865
face link face1522 face1528 edges edge7413 edge7450 vertices
vertex6865 vertex6899
face link face1528 face1534 edges edge7450 edge7487 vertices
vertex6899 vertex6933
face link face1534 face1540 edges edge7487 edge7524 vertices
vertex6933 vertex6967
face link face1540 face1546 edges edge7524 edge7561 vertices
vertex6967 vertex7001
face link face1546 face1552 edges edge7561 edge7598 vertices
vertex7001 vertex7035
face link face1552 face1558 edges edge7598 edge7635 vertices
vertex7035 vertex7069
face link face1558 face1564 edges edge7635 edge7672 vertices
vertex7069 vertex7103
face link face1564 face1570 edges edge7672 edge7709 vertices
vertex7103 vertex7137
face link face1570 face1576 edges edge7709 edge7746 vertices
vertex7137 vertex7171
face link face1576 face1582 edges edge7746 edge7783 vertices
vertex7171 vertex7205
face link face1582 face1588 edges edge7783 edge7820 vertices
vertex7205 vertex7239
face link face1588 face1594 edges edge7820 edge7857 vertices
vertex7239 vertex7273
face link face1512 face1518 edges edge7350 edge7387 vertices
vertex6806 vertex6840
face link face1518 face1524 edges edge7387 edge7424 vertices
vertex6840 vertex6874
face link face1524 face1530 edges edge7424 edge7461 vertices
vertex6874 vertex6908
face link face1530 face1536 edges edge7461 edge7498 vertices
vertex6908 vertex6942
face link face1536 face1542 edges edge7498 edge7535 vertices
86
vertex6942 vertex6976
face link face1542 face1548 edges edge7535 edge7572 vertices
vertex6976 vertex7010
face link face1548 face1554 edges edge7572 edge7609 vertices
vertex7010 vertex7044
face link face1554 face1560 edges edge7609 edge7646 vertices
vertex7044 vertex7078
face link face1560 face1566 edges edge7646 edge7683 vertices
vertex7078 vertex7112
face link face1566 face1572 edges edge7683 edge7720 vertices
vertex7112 vertex7146
face link face1572 face1578 edges edge7720 edge7757 vertices
vertex7146 vertex7180
face link face1578 face1584 edges edge7757 edge7794 vertices
vertex7180 vertex7214
face link face1584 face1590 edges edge7794 edge7831 vertices
vertex7214 vertex7248
face link face1590 face1596 edges edge7831 edge7868 vertices
vertex7248 vertex7282
face link face1514 face1520 edges edge7363 edge7400 vertices
vertex6819 vertex6853
face link face1520 face1526 edges edge7400 edge7437 vertices
vertex6853 vertex6887
face link face1526 face1532 edges edge7437 edge7474 vertices
vertex6887 vertex6921
face link face1532 face1538 edges edge7474 edge7511 vertices
vertex6921 vertex6955
face link face1538 face1544 edges edge7511 edge7548 vertices
vertex6955 vertex6989
face link face1544 face1550 edges edge7548 edge7585 vertices
vertex6989 vertex7023
face link face1550 face1556 edges edge7585 edge7622 vertices
vertex7023 vertex7057
face link face1556 face1562 edges edge7622 edge7659 vertices
vertex7057 vertex7091
face link face1562 face1568 edges edge7659 edge7696 vertices
vertex7091 vertex7125
face link face1568 face1574 edges edge7696 edge7733 vertices
vertex7125 vertex7159
face link face1574 face1580 edges edge7733 edge7770 vertices
vertex7159 vertex7193
face link face1580 face1586 edges edge7770 edge7807 vertices
vertex7193 vertex7227
face link face1586 face1592 edges edge7807 edge7844 vertices
vertex7227 vertex7261
face link face1592 face1598 edges edge7844 edge7881 vertices
vertex7261 vertex7295
LINKING ALL THE TELEPHONES OF THE TOP OF THE PLENUM
face link face912 face642 edges edge6950 edge3489 vertices
vertex6437 vertex3253 reverse
face link face642 face647 edges edge3489 edge3744 vertices
vertex3253 vertex3433
face link face117 face646 edges edge6959 edge3638 vertices
vertex6447 vertex3313
87
face link face642 face652 edges edge3489 edge3491 vertices
vertex3253 vertex3255
face link face652 face662 edges edge3491 edge3493 vertices
vertex3255 vertex3257
face link face662 face672 edges edge3493 edge3495 vertices
vertex3257 vertex3259
face link face672 face682 edges edge3495 edge3497 vertices
vertex3259 vertex3261
face link face682 face692 edges edge3497 edge3499 vertices
vertex3261 vertex3263
face link face692 face702 edges edge3499 edge3501 vertices
vertex3263 vertex3265
face link face702 face712 edges edge3501 edge3503 vertices
vertex3265 vertex3267
face link face712 face722 edges edge3503 edge3505 vertices
vertex3267 vertex3269
face link face722 face732 edges edge3505 edge3507 vertices
vertex3269 vertex3271
face link face732 face742 edges edge3507 edge3509 vertices
vertex3271 vertex3273
face link face742 face752 edges edge3509 edge3511 vertices
vertex3273 vertex3275
face link face752 face762 edges edge3511 edge3513 vertices
vertex3275 vertex3277
face link face762 face772 edges edge3513 edge3515 vertices
vertex3277 vertex3279
face link face772 face782 edges edge3515 edge3517 vertices
vertex3279 vertex3281
face link face646 face656 edges edge3653 edge3655 vertices
vertex3312 vertex3314
face link face656 face666 edges edge3655 edge3657 vertices
vertex3314 vertex3316
face link face666 face676 edges edge3657 edge3659 vertices
vertex3316 vertex3318
face link face676 face686 edges edge3659 edge3661 vertices
vertex3318 vertex3320
face link face686 face696 edges edge3661 edge3663 vertices
vertex3320 vertex3322
face link face696 face706 edges edge3663 edge3665 vertices
vertex3322 vertex3324
face link face706 face716 edges edge3665 edge3667 vertices
vertex3324 vertex3326
face link face716 face726 edges edge3667 edge3669 vertices
vertex3326 vertex3328
face link face726 face736 edges edge3669 edge3671 vertices
vertex3328 vertex3330
face link face736 face746 edges edge3671 edge3673 vertices
vertex3330 vertex3332
face link face746 face756 edges edge3673 edge3675 vertices
vertex3332 vertex3334
face link face756 face766 edges edge3675 edge3677 vertices
vertex3334 vertex3336
face link face766 face776 edges edge3677 edge3679 vertices
vertex3336 vertex3338
face link face776 face786 edges edge3679 edge3681 vertices
88
vertex3338 vertex3340
face link face647 face657 edges edge3744 edge3746 vertices
vertex3433 vertex3435
face link face657 face667 edges edge3746 edge3748 vertices
vertex3435 vertex3437
face link face667 face677 edges edge3748 edge3750 vertices
vertex3437 vertex3439
face link face677 face687 edges edge3750 edge3752 vertices
vertex3439 vertex3441
face link face687 face697 edges edge3752 edge3754 vertices
vertex3441 vertex3443
face link face697 face707 edges edge3754 edge3756 vertices
vertex3443 vertex3445
face link face707 face717 edges edge3756 edge3758 vertices
vertex3445 vertex3447
face link face717 face727 edges edge3758 edge3760 vertices
vertex3447 vertex3449
face link face727 face737 edges edge3760 edge3762 vertices
vertex3449 vertex3451
face link face737 face747 edges edge3762 edge3764 vertices
vertex3451 vertex3453
face link face747 face757 edges edge3764 edge3766 vertices
vertex3453 vertex3455
face link face757 face767 edges edge3766 edge3768 vertices
vertex3455 vertex3457
face link face767 face777 edges edge3768 edge3770 vertices
vertex3457 vertex3459
face link face777 face787 edges edge3770 edge3772 vertices
vertex3459 vertex3461
face link face647 face1600 edges edge3685 edge6963 vertices
vertex3345 vertex6449
LINKING OUTBOXES ON THE PLENUM
face modify face911 side vertex4404 vertex4405
face modify face918 side vertex4405 vertex4404
face link face911 face915 edges edge4778 edge4898 vertices
vertex4374 vertex4434
face link face915 face645 edges edge4899 edge3833 vertices
vertex4480 vertex3463 reverse
face link face911 face641 edges edge4779 edge3578 vertices
vertex4405 vertex3283 reverse
face link face918 face648 edges edge4825 edge3686 vertices
vertex4436 vertex3347 reverse
face link face645 face655 edges edge3833 edge3834 vertices
vertex3463 vertex3465
face link face655 face665 edges edge3834 edge3835 vertices
vertex3465 vertex3467
face link face665 face675 edges edge3835 edge3836 vertices
vertex3467 vertex3469
face link face675 face685 edges edge3836 edge3837 vertices
vertex3469 vertex3471
face link face685 face695 edges edge3837 edge3838 vertices
89
vertex3471 vertex3473
face link face695 face705 edges edge3838 edge3839 vertices
vertex3473 vertex3475
face link face705 face715 edges edge3839 edge3840 vertices
vertex3475 vertex3477
face link face715 face725 edges edge3840 edge3841 vertices
vertex3477 vertex3479
face link face725 face735 edges edge3841 edge3842 vertices
vertex3479 vertex3481
face link face735 face745 edges edge3842 edge3843 vertices
vertex3481 vertex3483
face link face745 face755 edges edge3843 edge3844 vertices
vertex3483 vertex3485
face link face755 face765 edges edge3844 edge3845 vertices
vertex3485 vertex3487
face link face765 face775 edges edge3845 edge3846 vertices
vertex3487 vertex3489
face link face775 face785 edges edge3846 edge3847 vertices
vertex3489 vertex3491
face link face648 face658 edges edge3686 edge3690 vertices
vertex3347 vertex3353
face link face658 face668 edges edge3690 edge3694 vertices
vertex3353 vertex3359
face link face668 face678 edges edge3694 edge3698 vertices
vertex3359 vertex3365
face link face678 face688 edges edge3698 edge3702 vertices
vertex3365 vertex3371
face link face688 face698 edges edge3702 edge3706 vertices
vertex3371 vertex3377
face link face698 face708 edges edge3706 edge3710 vertices
vertex3377 vertex3383
face link face708 face718 edges edge3710 edge3714 vertices
vertex3383 vertex3389
face link face718 face728 edges edge3714 edge3718 vertices
vertex3389 vertex3395
face link face728 face738 edges edge3718 edge3722 vertices
vertex3395 vertex3401
face link face738 face748 edges edge3722 edge3726 vertices
vertex3401 vertex3407
face link face748 face758 edges edge3726 edge3730 vertices
vertex3407 vertex3413
face link face758 face768 edges edge3730 edge3734 vertices
vertex3413 vertex3419
face link face768 face778 edges edge3734 edge3738 vertices
vertex3419 vertex3425
face link face778 face788 edges edge3738 edge3742 vertices
vertex3425 vertex3431
face link face641 face650 edges edge3578 edge3579 vertices
vertex3283 vertex3285
face link face650 face660 edges edge3579 edge3580 vertices
vertex3285 vertex3287
face link face660 face670 edges edge3580 edge3581 vertices
vertex3287 vertex3289
face link face670 face680 edges edge3581 edge3582 vertices
vertex3289 vertex3291
face link face680 face690 edges edge3582 edge3583 vertices
90
vertex3291 vertex3293
face link face690 face700 edges edge3583 edge3584 vertices
vertex3293 vertex3295
face link face700 face710 edges edge3584 edge3585 vertices
vertex3295 vertex3297
face link face710 face720 edges edge3585 edge3586 vertices
vertex3297 vertex3299
face link face720 face730 edges edge3586 edge3587 vertices
vertex3299 vertex3301
face link face730 face740 edges edge3587 edge3588 vertices
vertex3301 vertex3303
face link face740 face750 edges edge3588 edge3589 vertices
vertex3303 vertex3305
face link face750 face760 edges edge3589 edge3590 vertices
vertex3305 vertex3307
face link face760 face770 edges edge3590 edge3591 vertices
vertex3307 vertex3309
face link face770 face780 edges edge3591 edge3592 vertices
vertex3309 vertex3311
face link face915 face925 edges edge4899 edge4901 vertices
vertex4480 vertex4482
face link face925 face935 edges edge4901 edge4903 vertices
vertex4482 vertex4484
face link face935 face945 edges edge4903 edge4905 vertices
vertex4484 vertex4486
face link face945 face955 edges edge4905 edge4907 vertices
vertex4486 vertex4488
face link face955 face965 edges edge4907 edge4909 vertices
vertex4488 vertex4490
face link face965 face975 edges edge4909 edge4911 vertices
vertex4490 vertex4492
face link face975 face985 edges edge4911 edge4913 vertices
vertex4492 vertex4494
face link face985 face995 edges edge4913 edge4915 vertices
vertex4494 vertex4496
face link face995 face1005 edges edge4915 edge4917 vertices
vertex4496 vertex4498
face link face1005 face1015 edges edge4917 edge4919 vertices
vertex4498 vertex4500
face link face1015 face1025 edges edge4919 edge4921 vertices
vertex4500 vertex4502
face link face1025 face1035 edges edge4921 edge4923 vertices
vertex4502 vertex4504
face link face1035 face1045 edges edge4923 edge4925 vertices
vertex4504 vertex4506
face link face1045 face1055 edges edge4925 edge4927 vertices
vertex4506 vertex4508
face link face918 face928 edges edge4825 edge4828 vertices
vertex4436 vertex4439
face link face928 face938 edges edge4828 edge4831 vertices
vertex4439 vertex4442
face link face938 face948 edges edge4831 edge4834 vertices
vertex4442 vertex4445
face link face948 face958 edges edge4834 edge4837 vertices
vertex4445 vertex4448
face link face958 face968 edges edge4837 edge4840 vertices
91
vertex4448 vertex4451
face link face968 face978 edges edge4840 edge4843 vertices
vertex4451 vertex4454
face link face978 face988 edges edge4843 edge4846 vertices
vertex4454 vertex4457
face link face988 face998 edges edge4846 edge4849 vertices
vertex4457 vertex4460
face link face998 face1008 edges edge4849 edge4852 vertices
vertex4460 vertex4463
face link face1008 face1018 edges edge4852 edge4855 vertices
vertex4463 vertex4466
face link face1018 face1028 edges edge4855 edge4858 vertices
vertex4466 vertex4469
face link face1028 face1038 edges edge4858 edge4861 vertices
vertex4469 vertex4472
face link face1038 face1048 edges edge4861 edge4864 vertices
vertex4472 vertex4475
face link face1048 face1058 edges edge4864 edge4867 vertices
vertex4475 vertex4478
face link face911 face920 edges edge108 edge118 vertices
vertex88 vertex94
face link face920 face930 edges edge118 edge128 vertices
vertex94 vertex100
face link face930 face940 edges edge4783 edge4785 vertices
vertex4409 vertex4411
face link face940 face950 edges edge4785 edge4787 vertices
vertex4411 vertex4413
face link face950 face960 edges edge4787 edge4789 vertices
vertex4413 vertex4415
face link face960 face970 edges edge4789 edge4791 vertices
vertex4415 vertex4417
face link face970 face980 edges edge4791 edge4793 vertices
vertex4417 vertex4419
face link face980 face990 edges edge4793 edge4795 vertices
vertex4419 vertex4421
face link face990 face1000 edges edge4795 edge4797 vertices
vertex4421 vertex4423
face link face1000 face1010 edges edge4797 edge4799 vertices
vertex4423 vertex4425
face link face1010 face1020 edges edge4799 edge4801 vertices
vertex4425 vertex4427
face link face1020 face1030 edges edge4801 edge4803 vertices
vertex4427 vertex4429
face link face1030 face1040 edges edge4803 edge4805 vertices
vertex4429 vertex4431
face link face1040 face1050 edges edge4805 edge4807 vertices
vertex4431 vertex4433
LINKING THE TOP OF THE CHANEL OUTBOXES
face modify face1256 side vertex6322 vertex6321
face modify face1263 side vertex6322 vertex6321
face modify face1260 side vertex6397 vertex6396
92
face link face1256 face1260 edges edge6803 edge6923 vertices
vertex6322 vertex6397
face link face1256 face371 edges edge6774 edge2053 vertices
vertex6292 vertex1955 reverse
face link face371 face375 edges edge2053 edge2336 vertices
vertex1955 vertex2135
face link face1263 face378 edges edge6820 edge2228 vertices
vertex6322 vertex2071 reverse
face link face1263 face1273 edges edge6820 edge6823 vertices
vertex6322 vertex6324
face link face1273 face1283 edges edge6823 edge6826 vertices
vertex6324 vertex6326
face link face1283 face1293 edges edge6826 edge6829 vertices
vertex6326 vertex6328
face link face1293 face1303 edges edge6829 edge6832 vertices
vertex6328 vertex6330
face link face1303 face1313 edges edge6832 edge6835 vertices
vertex6330 vertex6332
face link face1313 face1323 edges edge6835 edge6838 vertices
vertex6332 vertex6334
face link face1323 face1333 edges edge6838 edge6841 vertices
vertex6334 vertex6336
face link face1333 face1343 edges edge6841 edge6844 vertices
vertex6336 vertex6338
face link face1343 face1353 edges edge6844 edge6847 vertices
vertex6338 vertex6340
face link face1353 face1363 edges edge6847 edge6850 vertices
vertex6340 vertex6342
face link face1363 face1373 edges edge6850 edge6853 vertices
vertex6342 vertex6344
face link face1373 face1383 edges edge6853 edge6856 vertices
vertex6344 vertex6346
face link face1383 face1393 edges edge6856 edge6859 vertices
vertex6346 vertex6348
face link face1393 face1403 edges edge6859 edge6862 vertices
vertex6348 vertex6350
face link face1256 face1265 edges edge6774 edge6776 vertices
vertex6292 vertex6294
face link face1265 face1275 edges edge6776 edge6778 vertices
vertex6294 vertex6296
face link face1275 face1285 edges edge6778 edge6780 vertices
vertex6296 vertex6298
face link face1285 face1295 edges edge6780 edge6782 vertices
vertex6298 vertex6300
face link face1295 face1305 edges edge6782 edge6784 vertices
vertex6300 vertex6302
face link face1305 face1315 edges edge6784 edge6786 vertices
vertex6302 vertex6304
face link face1315 face1325 edges edge6786 edge6788 vertices
vertex6304 vertex6306
face link face1325 face1335 edges edge6788 edge6790 vertices
vertex6306 vertex6308
face link face1335 face1345 edges edge6790 edge6792 vertices
vertex6308 vertex6310
face link face1345 face1355 edges edge6792 edge6794 vertices
vertex6310 vertex6312
93
face link face1355 face1365 edges edge6794 edge6796 vertices
vertex6312 vertex6314
face link face1365 face1375 edges edge6796 edge6798 vertices
vertex6314 vertex6316
face link face1375 face1385 edges edge6798 edge6800 vertices
vertex6316 vertex6318
face link face1385 face1395 edges edge6800 edge6802 vertices
vertex6318 vertex6320
face link face1260 face1270 edges edge6894 edge6896 vertices
vertex6353 vertex6356
face link face1270 face1280 edges edge6896 edge6898 vertices
vertex6356 vertex6359
face link face1280 face1290 edges edge6898 edge6900 vertices
vertex6359 vertex6362
face link face1290 face1300 edges edge6900 edge6902 vertices
vertex6362 vertex6365
face link face1300 face1310 edges edge6902 edge6904 vertices
vertex6365 vertex6368
face link face1310 face1320 edges edge6904 edge6906 vertices
vertex6368 vertex6371
face link face1320 face1330 edges edge6906 edge6908 vertices
vertex6371 vertex6374
face link face1330 face1340 edges edge6908 edge6910 vertices
vertex6374 vertex6377
face link face1340 face1350 edges edge6910 edge6912 vertices
vertex6377 vertex6380
face link face1350 face1360 edges edge6912 edge6914 vertices
vertex6380 vertex6383
face link face1360 face1370 edges edge6914 edge6916 vertices
vertex6383 vertex6386
face link face1370 face1380 edges edge6916 edge6918 vertices
vertex6386 vertex6389
face link face1380 face1390 edges edge6918 edge6920 vertices
vertex6389 vertex6392
face link face1390 face1400 edges edge6920 edge6922 vertices
vertex6392 vertex6395
LINKING THE BOTTOM OF THE CHANEL OUTBOXES
face link face375 face385 edges edge2440 edge2443 vertices
vertex2251 vertex2253
face link face385 face395 edges edge2443 edge2446 vertices
vertex2253 vertex2255
face link face395 face405 edges edge2446 edge2449 vertices
vertex2255 vertex2257
face link face405 face415 edges edge2449 edge2452 vertices
vertex2257 vertex2259
face link face415 face425 edges edge2452 edge2455 vertices
vertex2259 vertex2261
face link face425 face435 edges edge2455 edge2458 vertices
vertex2261 vertex2263
face link face435 face445 edges edge2458 edge2461 vertices
vertex2263 vertex2265
face link face445 face455 edges edge2461 edge2464 vertices
vertex2265 vertex2267
face link face455 face465 edges edge2464 edge2467 vertices
94
vertex2267 vertex2269
face link face465 face475 edges edge2467 edge2470 vertices
vertex2269 vertex2271
face link face475 face485 edges edge2470 edge2473 vertices
vertex2271 vertex2273
face link face485 face495 edges edge2473 edge2476 vertices
vertex2273 vertex2275
face link face495 face505 edges edge2476 edge2479 vertices
vertex2275 vertex2277
face link face505 face515 edges edge2479 edge2482 vertices
vertex2277 vertex2279
face link face378 face388 edges edge2245 edge2248 vertices
vertex2135 vertex2141
face link face388 face398 edges edge2248 edge2251 vertices
vertex2141 vertex2147
face link face398 face408 edges edge2251 edge2254 vertices
vertex2147 vertex2153
face link face408 face418 edges edge2254 edge2257 vertices
vertex2153 vertex2159
face link face418 face428 edges edge2257 edge2260 vertices
vertex2159 vertex2165
face link face428 face438 edges edge2260 edge2263 vertices
vertex2165 vertex2171
face link face438 face448 edges edge2263 edge2266 vertices
vertex2171 vertex2177
face link face448 face458 edges edge2266 edge2269 vertices
vertex2177 vertex2183
face link face458 face468 edges edge2269 edge2272 vertices
vertex2183 vertex2189
face link face468 face478 edges edge2272 edge2275 vertices
vertex2189 vertex2195
face link face478 face488 edges edge2275 edge2278 vertices
vertex2195 vertex2201
face link face488 face498 edges edge2278 edge2281 vertices
vertex2201 vertex2207
face link face498 face508 edges edge2281 edge2284 vertices
vertex2207 vertex2213
face link face508 face518 edges edge2284 edge2287 vertices
vertex2213 vertex2219
face link face371 face380 edges edge2185 edge2188 vertices
vertex2071 vertex2073
face link face380 face390 edges edge2188 edge2191 vertices
vertex2073 vertex2075
face link face390 face400 edges edge2191 edge2194 vertices
vertex2075 vertex2077
face link face400 face410 edges edge2194 edge2197 vertices
vertex2077 vertex2079
face link face410 face420 edges edge2197 edge2200 vertices
vertex2079 vertex2081
face link face420 face430 edges edge2200 edge2203 vertices
vertex2081 vertex2083
face link face430 face440 edges edge2203 edge2206 vertices
vertex2083 vertex2085
face link face440 face450 edges edge2206 edge2209 vertices
vertex2085 vertex2087
face link face450 face460 edges edge2209 edge2212 vertices
95
vertex2087 vertex2089
face link face460 face470 edges edge2212 edge2215 vertices
vertex2089 vertex2091
face link face470 face480 edges edge2215 edge2218 vertices
vertex2091 vertex2093
face link face480 face490 edges edge2218 edge2221 vertices
vertex2093 vertex2095
face link face490 face500 edges edge2221 edge2224 vertices
vertex2095 vertex2097
face link face500 face510 edges edge2224 edge2227 vertices
vertex2097 vertex2099
TOP SIDE BOX beginning of channel
face link face1649 face1633 edges edge97 edge3533 vertices
vertex4374 vertex3162 reverse
TOP SIDE BOXES
face link face1650 face1651 edges edge4749 edge4751 vertices
vertex4376 vertex4378
face link face1652 face1653 edges edge4753 edge4755 vertices
vertex4380 vertex4382
face link face1653 face1654 edges edge4755 edge4757 vertices
vertex4382 vertex4384
face link face1654 face1655 edges edge4757 edge4759 vertices
vertex4384 vertex4386
face link face1655 face1656 edges edge4759 edge4761 vertices
vertex4386 vertex4388
face link face1656 face114 edges edge4761 edge4763 vertices
vertex4388 vertex4390
face link face114 face1657 edges edge4763 edge4765 vertices
vertex4390 vertex4392
face link face1657 face1658 edges edge4765 edge4767 vertices
vertex4392 vertex4394
face link face1658 face1659 edges edge4767 edge4769 vertices
vertex4394 vertex4396
face link face1659 face1660 edges edge4769 edge4771 vertices
vertex4396 vertex4398
face link face1660 face1661 edges edge4771 edge4773 vertices
vertex4398 vertex4400
face link face1661 face1662 edges edge4773 edge4775 vertices
vertex4400 vertex4402
face link face1650 face1634 edges edge4900 edge8036 vertices
vertex4481 vertex3464 reverse
face link face1634 face1635 edges edge8036 edge8037 vertices
vertex3464 vertex3466
face link face1635 face1636 edges edge8037 edge8038 vertices
vertex3466 vertex3468
face link face1636 face1637 edges edge8038 edge8039 vertices
vertex3468 vertex3470
face link face1637 face1638 edges edge8039 edge8040 vertices
vertex3470 vertex3472
face link face1638 face1639 edges edge8040 edge8041 vertices
vertex3472 vertex3474
face link face1639 face6 edges edge8041 edge8042 vertices
96
vertex3474 vertex3476
face link face6 face1640 edges edge8042 edge8043 vertices
vertex3476 vertex3478
face link face1640 face1641 edges edge8043 edge8044 vertices
vertex3478 vertex3480
face link face1641 face1642 edges edge8044 edge8045 vertices
vertex3480 vertex3482
face link face1642 face1643 edges edge8045 edge8046 vertices
vertex3482 vertex3484
face link face1643 face1644 edges edge8046 edge8047 vertices
vertex3484 vertex3486
face link face1644 face1645 edges edge8047 edge8048 vertices
vertex3486 vertex3488
face link face1645 face1646 edges edge8048 edge8049 vertices
vertex3488 vertex3490
face link face1651 face1652 edges edge4751 edge4753 vertices
vertex4378 vertex4380
TOP SIDE BOX END OF CHANNEL
face link face1647 face1663 edges edge8050 edge99 vertices
vertex7433 vertex7435 reverse
TOP SIDE BOX BACK OF CHANNEL
face link face1648 face1664 edges edge12 edge8069 vertices
vertex8 vertex84 reverse
BOTTOM SIDE BOX
face link face1665 face1681 edges edge6773 edge2048 vertices
vertex6291 vertex1950 reverse
face link face1680 face1696 edges edge8071 edge8105 vertices
vertex7436 vertex7438 reverse
face link face1666 face1667 edges edge6894 edge6896 vertices
vertex6397 vertex6399
face link face1667 face1668 edges edge6896 edge6898 vertices
vertex6399 vertex6401
face link face1668 face1669 edges edge6898 edge6900 vertices
vertex6401 vertex6403
face link face1669 face1670 edges edge6900 edge6902 vertices
vertex6403 vertex6405
face link face1670 face1671 edges edge6902 edge6904 vertices
vertex6405 vertex6407
face link face1671 face209 edges edge6904 edge6906 vertices
vertex6407 vertex6409
face link face209 face1672 edges edge6906 edge6908 vertices
vertex6409 vertex6411
face link face1672 face1673 edges edge6908 edge6910 vertices
vertex6411 vertex6413
face link face1673 face1674 edges edge6910 edge6912 vertices
vertex6413 vertex6415
face link face1674 face1675 edges edge6912 edge6914 vertices
vertex6415 vertex6417
face link face1675 face1676 edges edge6914 edge6916 vertices
vertex6417 vertex6419
97
face link face1676 face1677 edges edge6916 edge6918 vertices
vertex6419 vertex6421
face link face1677 face1678 edges edge6918 edge6920 vertices
vertex6421 vertex6423
face link face1666 face1682 edges edge6894 edge8090 vertices
vertex6397 vertex2251 reverse
face link face1682 face1683 edges edge8090 edge8091 vertices
vertex2251 vertex2253
face link face1683 face1684 edges edge8091 edge8092 vertices
vertex2253 vertex2255
face link face1684 face1685 edges edge8092 edge8093 vertices
vertex2255 vertex2257
face link face1685 face1686 edges edge8093 edge8094 vertices
vertex2257 vertex2259
face link face1686 face1687 edges edge8094 edge8095 vertices
vertex2259 vertex2261
face link face1687 face1688 edges edge8095 edge8096 vertices
vertex2261 vertex2263
face link face1688 face1 edges edge8096 edge8097 vertices
vertex2263 vertex2265
face link face1 face1689 edges edge8097 edge8098 vertices
vertex2265 vertex2267
face link face1689 face1690 edges edge8098 edge8099 vertices
vertex2267 vertex2269
face link face1690 face1691 edges edge8099 edge8100 vertices
vertex2269 vertex2271
face link face1691 face1692 edges edge8100 edge8101 vertices
vertex2271 vertex2273
face link face1692 face1693 edges edge8101 edge8102 vertices
vertex2273 vertex2275
face link face1693 face1694 edges edge8102 edge8103 vertices
vertex2275 vertex2277
face link face1679 face1695 edges edge89 edge2227 vertices
vertex6320 vertex2039 reverse
MESHING BEGINS HERE
BOUNDARY LAYERS BEGINS HERE
BOUNDARY LAYER FOR THE bottom of plenum
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer1 face face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
98
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 edge edge97
edge4748 edge106 edge6946 edge6947 edge107 edge4749
edge4750 edge116 edge6972 edge6973 edge117 edge4751
edge4752 edge126 edge6998 edge6999 edge127 edge4753
edge4754 edge136 edge7024 edge7025 edge137 edge4755
edge4756 edge146 edge7050 edge7051 edge147 edge4757
edge4758 edge156 edge7076 edge7077 edge157 edge4759
edge4760 edge166 edge7102 edge7103 edge167 edge4761
edge4762 edge176 edge7128 edge7129 edge177 edge4763
edge4764 edge186 edge7154 edge7155 edge187 edge4765
edge4766 edge196 edge7180 edge7181 edge197 edge4767
edge4768 edge206 edge7206 edge7207 edge207 edge4769
edge4770 edge216 edge7232 edge7233 edge217 edge4771
edge4772 edge226 edge7258 edge7259 edge227 edge4773
edge4774 edge236 edge7284 edge7285 edge237 edge4775
edge4776 edge246 edge7310 edge7311 edge247 edge4777 add
MESHING THE PLENUM
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer2 face face4 face4 face5 face110
face110 edge edge99 edge8069 edge100 edge8052 edge98 add
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer4 face face1649 face1664 face1664
face1664 face1663 edge edge8052 edge98 edge100 edge8069
edge99 add
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer4 face face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face4 face2 face2 face2 face2 face2 face4
face5 face110 face110 edge edge9 edge3398 edge3399
edge3400 edge3401 edge3402 edge3403 edge3404 edge3406
edge3405 edge3407 edge3408 edge3409 edge3415 edge3410
edge3411 edge3412 edge3413 edge3414 edge3416 edge3417
edge3418 edge3419 edge3420 edge3421 edge3422 edge3423
edge3424 edge3425 edge3426 edge3427 edge3428 edge3429
edge3430 edge3431 edge3432 edge3433 edge3434 edge3435
edge3436 edge3437 edge3438 edge3439 edge3440 edge3441
edge3442 edge3443 edge3444 edge3445 edge3446 edge3447
99
edge3448 edge3449 edge3450 edge3451 edge3457 edge3452
edge3453 edge3454 edge3455 edge3456 edge3458 edge3459
edge3460 edge3461 edge3462 edge3463 edge3464 edge3465
edge3466 edge3467 edge3468 edge3469 edge3475 edge3481
edge3470 edge3471 edge3472 edge3473 edge3474 edge3476
edge3477 edge3478 edge3479 edge3480 edge3487 edge11
edge3482 edge3483 edge3484 edge3485 edge3486 edge8051
edge12 edge10 edge8034 add
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer5 face face1663 face1664 face1664
face1664 face1649 edge edge99 edge8069 edge100 edge98
edge8052 add
BOUNDARY LAYER OF THE HOLES
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer1 face face642 edge edge3534 add
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer7 face face117 face1600 edge edge4824
edge110 add
BONDARY LAYER OF THE CHANNEL
TARGET WALL BOUNDARY LAYER
BBBL
BBL
BBL
BBBL
BBL
BBL
BBBLLLLL
blayer create first $firstch growth $growthch rows $rowsch transition 1 trows 0
uniform
blayer attach b_layer8 face face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
100
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face105 face105 face106
face104 face104 edge edge2048 edge2049 edge2050 edge2051
edge2052 edge2053 edge2054 edge2055 edge2056 edge2057
edge2058 edge2059 edge2060 edge2061 edge2062 edge2063
edge2064 edge2065 edge2066 edge2072 edge2067 edge2068
edge2069 edge2070 edge2071 edge2084 edge2078 edge2073
edge2074 edge2075 edge2076 edge2077 edge2079 edge2080
edge2081 edge2082 edge2083 edge2090 edge2096 edge2085
edge2086 edge2087 edge2088 edge2089 edge2091 edge2092
edge2093 edge2094 edge2095 edge2102 edge2108 edge2097
edge2098 edge2099 edge2100 edge2101 edge2103 edge2104
edge2105 edge2106 edge2107 edge2114 edge2120 edge2109
edge2110 edge2111 edge2112 edge2113 edge2115 edge2116
edge2117 edge2118 edge2119 edge2126 edge2132 edge2121
edge2122 edge2123 edge2124 edge2125 edge2127 edge2128
edge2129 edge2130 edge2131 edge2133 edge2134 edge2136
edge2137 edge1 edge2135 edge8088 edge3 edge4 edge8105
edge2 add
blayer create first $firstch growth $growthch rows $rowsch transition 1 trows 0
uniform
blayer attach b_layer9 face face1681 face1696 face1696
face1696 face1695 edge edge2 edge8105 edge4 edge3
edge8088 add
blayer create first $firstch growth $growthch rows $rowsch transition 1 trows 0
uniform
blayer attach b_layer10 face face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face105 face105
face106 face104 face104 edge edge6743 edge101
edge7336 edge7337 edge102 edge6744 edge6745 edge111
edge7373 edge7374 edge112 edge6746 edge6747 edge121
edge7410 edge7411 edge122 edge6748 edge6749 edge131
edge7447 edge7448 edge132 edge6750 edge6751 edge141
edge7484 edge7485 edge142 edge6752 edge6755 edge6753
edge151 edge6754 edge7521 edge7522 edge152 edge161
101
edge6756 edge6757 edge7558 edge7559 edge162 edge171
edge7595 edge7596 edge172 edge6758 edge6759 edge181
edge7632 edge7633 edge182 edge6760 edge6761 edge191
edge7669 edge7670 edge192 edge6762 edge6763 edge6767
edge6765 edge201 edge7706 edge7707 edge202 edge6764
edge211 edge6766 edge7743 edge7744 edge212 edge6769
edge221 edge6768 edge7780 edge7781 edge222 edge6771
edge231 edge6770 edge7817 edge7818 edge232 edge241
edge7854 edge7855 edge242 edge6772 edge89 edge8070
edge91 edge92 edge8087 edge90 add
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer11 face face4 face5 face2 face5
face110 face2 edge edge8 edge8 edge6 edge7 edge7
edge5 add
blayer create first $firstch growth $growthch rows $rowsch transition 1 trows 0
uniform
blayer attach b_layer12 face face106 face104 face103 face105
edge edge87 edge87 edge85 edge88 add
BOUNDARY LAYERS ENDS HERE
edge picklink edge6948 edge6949
edge mesh edge6949 edge6948 successive ratio1 1 intervals $NumbNodes
edge picklink edge6950
edge mesh edge6950 successive ratio1 1 intervals ($NumbNodes2)
face mesh face1450 map
edge picklink edge6963 edge6947
edge mesh edge6947 edge6963 successive ratio1 1 intervals ($Numbtelnodes+$rows)
face mesh face912 map
edge picklink edge6961 edge6960 edge7889 edge7890
edge mesh edge7890 edge7889 edge6960 edge6961 successive ratio1 1
intervals ($NumbNodes)
edge picklink edge6959 edge7891
edge mesh edge7891 edge6959 successive ratio1 1 intervals ($NumbNodes2)
face mesh face1452 map
face mesh face1600 face117 map
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer12 face face2 face110 face5 face110
face2 face4 face5 face4 edge edge5 edge5 edge7
edge7 edge6 edge6 edge8 edge8 add
Meshing constants
$NumbNodes=5
$Numbtelnodes=6
$PLobnodes=5
$Chobnodes=5
$Plbenodes=($NumbNodes(4)+$rows)
$plsqnodes=($NumbNodes(3))
102
$Pllsnodes=($NumbNodes+$rows)
$Nojetcells=10
edge picklink edge3686 edge3402
edge mesh edge3686 edge3402 successive ratio1 1 intervals ($PLobnodes)
edge picklink edge6744 edge6864
edge mesh edge6864 edge6744 successive ratio1 1 intervals 5
face link face1260 face375 edges edge6923 edge2440 vertices
vertex6397 vertex2251 reverse
face modify face915 side vertex4479 vertex4480
face mesh face915 face918 face911 map size 1
face mesh face1260 face1263 face1256 map size 1
edge picklink edge8068 edge8053
edge mesh edge8068 edge8053 successive ratio1 1 intervals ($Plbenodes)
edge picklink edge8086 edge8071
edge mesh edge8071 edge8086 successive ratio1 1 intervals ($CHbenodes)
edge delete edge8053 edge8068 keepsettings onlymesh
edge mesh edge8053 edge8068 successive ratio1 1 intervals ($Plbenodes)
edge delete edge8090 keepsettings onlymesh
edge picklink edge8090
edge mesh edge8090 successive ratio1 1 intervals ($plsqnodes)
edge delete edge8054 keepsettings onlymesh
edge picklink edge8054
edge mesh edge8054 successive ratio1 1 intervals ($plsqnodes)
face mesh face1647 face1679 face1678 face1646 face1633
face1665 map
edge delete edge98 edge8087 keepsettings onlymesh
edge picklink edge8087 edge98
edge mesh edge98 successive ratio1 1 intervals ($Pllsnodes)
edge mesh edge8087 successive ratio1 1 intervals ($CHlsnodes)
face mesh face1648 face1680 map
COOPERING ALL THE JETS
volume mesh volume3 cooper source face1600 face1452 face117
face1514 face1512 face115 intervals ($Nojetcells)
volume mesh volume5 cooper source face1456 face1602 face124
face1518 face1520 face122 intervals ($Nojetcells)
volume mesh volume7 cooper source face1460 face1604 face131
face1526 face1524 face129 intervals ($Nojetcells)
volume mesh volume9 cooper source face1464 face1606 face138
face1532 face1530 face136 intervals ($Nojetcells)
volume mesh volume11 cooper source face1468 face1608 face145
face1538 face143 face1536 intervals ($Nojetcells)
volume mesh volume13 cooper source face1472 face1610 face152
face1544 face1542 face150 intervals ($Nojetcells)
volume mesh volume15 cooper source face1476 face1612 face159
face1550 face1548 face157 intervals ($Nojetcells)
volume mesh volume17 cooper source face1480 face1614 face166
face1556 face1554 face164 intervals ($Nojetcells)
volume mesh volume19 cooper source face1484 face1616 face173
face1562 face171 face1560 intervals ($Nojetcells)
volume mesh volume21 cooper source face1488 face1618 face180
face1568 face1566 face178 intervals ($Nojetcells)
103
volume mesh volume23 cooper source face1492 face1620 face187
face1574 face1572 face185 intervals ($Nojetcells)
volume mesh volume25 cooper source face1496 face1622 face194
face1578 face1580 face192 intervals ($Nojetcells)
volume mesh volume27 cooper source face1624 face1500 face201
face1586 face1584 face199 intervals ($Nojetcells)
volume mesh volume29 cooper source face1504 face1626 face208
face1592 face1590 face206 intervals ($Nojetcells)
volume mesh volume31 cooper source face1628 face1508 face215
face1596 face1598 face213 intervals ($Nojetcells)
volume mesh volume30 cooper source face1506 face1052 face1594
face1397 intervals ($Nojetcells)
volume mesh volume28 cooper source face1502 face1042 face1588
face1387 intervals ($Nojetcells)
volume mesh volume26 cooper source face1498 face1032 face1582
face1377 intervals ($Nojetcells)
volume mesh volume24 cooper source face1494 face1022 face1576
face1367 intervals ($Nojetcells)
volume mesh volume22 cooper source face1490 face1012 face1570
face1357 intervals ($Nojetcells)
volume mesh volume20 cooper source face1486 face1002 face1564
face1347 intervals ($Nojetcells)
volume mesh volume18 cooper source face1482 face992 face1558
face1337 intervals ($Nojetcells)
volume mesh volume16 cooper source face1478 face982 face1552
face1327 intervals ($Nojetcells)
volume mesh volume14 cooper source face1474 face972 face1546
face1317 intervals ($Nojetcells)
volume mesh volume12 cooper source face1470 face962 face1540
face1307 intervals ($Nojetcells)
volume mesh volume10 cooper source face1466 face952 face1534
face1297 intervals ($Nojetcells)
volume mesh volume8 cooper source face1462 face942 face1528
face1287 intervals ($Nojetcells)
volume mesh volume6 cooper source face1458 face932 face1522
face1277 intervals ($Nojetcells)
volume mesh volume4 cooper source face1454 face922 face1516
face1267 intervals ($Nojetcells)
volume mesh cylinder cooper source face1450 face912 face1510
face1257 intervals ($Nojetcells)
window modify invisible mesh
volume mesh volume34 cooper source face1649 face1650 face1651
face1652 face1653 face1654 face1655 face1664 face1639
face1638 face1637 face1636 face1635 face1634 face1633
face1648 face1610 face1608 face1606 face1604 face1602
face1600 face1472 face962 face1468 face952 face1464
face942 face1460 face932 face1456 face922 face1452
face912 face915 face918 face911 face925 face928
face920 face935 face938 face930 face945 face948
face940 face955 face958 face950 face965 face968
face960 face694 face689 face684 face679 face674
face669 face664 face659 face654 face649 face644
face640 face697 face696 face692 face687 face686
face682 face677 face676 face672 face667 face666
104
face662 face657 face656 face652 face647 face646
face642 face695 face698 face690 face685 face688
face680 face675 face678 face670 face665 face668
face660 face655 face658 face650 face645 face648
face641 face152 face1470 face145 face1466 face138
face1462 face131 face1458 face124 face1454 face117
face1450 face1657 face1658 face1659 face1660 face1661
face1662 face1663 face788 face1656 face1474 face159
face1647 face1646 face1645 face1644 face1643 face1642
face1641 face1640 face1478 face1628 face1626 face1624
face1622 face1620 face1618 face1616 face1614 face1612
face1508 face1052 face1504 face1042 face1500 face1032
face1496 face1022 face1492 face1012 face1488 face1002
face1484 face992 face1480 face982 face1476 face972
face975 face978 face970 face985 face988 face980
face995 face998 face990 face1005 face1008 face1000
face1015 face1018 face1010 face1025 face1028 face1020
face1035 face1038 face1030 face1045 face1048 face1040
face1050 face114 face1058 face774 face769 face764
face759 face754 face749 face744 face739 face734
face729 face724 face719 face714 face709 face704
face699 face777 face776 face772 face767 face766
face762 face757 face756 face752 face747 face746
face742 face737 face736 face732 face727 face726
face722 face717 face716 face712 face707 face706
face702 face779 face784 face787 face775 face778
face770 face765 face768 face760 face755 face758
face750 face745 face748 face740 face735 face738
face730 face725 face728 face720 face715 face718
face710 face705 face708 face700 face782 face786
face785 face6 face780 face1055 face215 face1506
face208 face1502 face201 face1498 face194 face1494
face187 face1490 face180 face1486 face173 face1482
face166 intervals ($Plzdnodes)
volume delete body onlymesh
volume mesh body cooper source face1689 face1690 face1691
face1692 face1693 face1681 face1682 face1683 face1684
face1685 face1686 face1687 face1688 face1696 face1671
face1670 face1669 face1668 face1667 face1666 face1665
face1677 face1676 face1675 face1674 face1673 face1672
face1680 face199 face1584 face1377 face192 face1578
face1367 face185 face1572 face1357 face178 face1566
face1347 face171 face1560 face1337 face164 face1554
face1327 face157 face1548 face1317 face150 face1542
face1307 face143 face1536 face1297 face136 face1530
face1287 face129 face1524 face1277 face122 face1518
face1267 face115 face1512 face1257 face1380 face1383
face1375 face1370 face1373 face1365 face1360 face1363
face1355 face1350 face1353 face1345 face1340 face1343
face1335 face1330 face1333 face1325 face1320 face1323
face1315 face1310 face1313 face1305 face1300 face1303
face1295 face1290 face1293 face1285 face1280 face1283
face1275 face1270 face1273 face1265 face1260 face1263
face1256 face209 face374 face370 face384 face379
face394 face389 face404 face399 face414 face409
105
face424 face419 face434 face429 face444 face439
face454 face449 face464 face459 face474 face469
face484 face479 face494 face489 face377 face376
face372 face387 face386 face382 face397 face396
face392 face407 face406 face402 face417 face416
face412 face427 face426 face422 face437 face436
face432 face447 face446 face442 face457 face456
face452 face467 face466 face462 face477 face476
face472 face487 face486 face482 face497 face496
face492 face375 face378 face371 face385 face388
face380 face395 face398 face390 face405 face408
face400 face415 face418 face410 face425 face428
face420 face435 face438 face430 face445 face448
face440 face455 face458 face450 face465 face468
face460 face475 face478 face470 face485 face488
face480 face495 face498 face490 face1 face1586
face1582 face1580 face1576 face1574 face1570 face1568
face1564 face1562 face1558 face1556 face1552 face1550
face1546 face1544 face1540 face1538 face1534 face1532
face1528 face1526 face1522 face1520 face1516 face1514
face1510 face1403 face518 face1588 face1592 face1594
face1694 face1695 face1598 face1679 face1678 face515
face516 face510 face500 face508 face505 face213
face1596 face1397 face206 face1590 face1387 face517
face514 face512 face502 face506 face507 face509
face499 face504 face1400 face1395 face1385 face1390
face1393 intervals ($Chzdnodes)
BOUNDARY CONDITIONS
physics create Symmetry btype SYMMETRY face face2 face103
face211 face204 face197 face190 face183 face176
face169 face162 face155 face148 face141 face134
face127 face120 face112
physics create Wall btype SYMMETRY face face110 face5 face1649
face1664 face918 face915 face911 face925 face1650
face928 face920 face935 face938 face930 face1652
face1651 face948 face945 face940 face1653 face1654
face958 face955 face950 face1655 face965 face968
face960 face978 face975 face970 face1656 face114
face985 face988 face980 face995 face998 face990
face1657 face1005 face1008 face1000 face1658 face1015
face1018 face1010 face1659 face1028 face1025 face1020
face1035 face1660 face1038 face1030 face1045 face1661
face1048 face1040 face1055 face1662 face1058 face1050
face1663 face4 face1395 face1679 face1403 face1400
face1680 face1385 face1678 face1393 face1390 face1375
face1677 face1383 face1380 face1676 face1365 face1373
face1370 face1675 face1355 face1363 face1360 face1674
face1345 face1353 face1350 face1673 face1335 face1343
face1340 face1672 face1325 face1333 face1330 face209
face1315 face1323 face1320 face1671 face1305 face1313
face1310 face1670 face1295 face1303 face1300 face1669
106
face1285 face1293 face1290 face1668 face1275 face1283
face1280 face1667 face1265 face1273 face1270 face1666
face1256 face1263 face1260 face1665 face214 face91
face207 face85 face200 face79 face193 face73 face186
face67 face179 face61 face172 face55 face165 face49
face158 face43 face151 face37 face144 face31 face137
face25 face130 face19 face123 face13 face116 face8
physics modify Wall btype WALL face face110 face5 face1649
face1664 face918 face915 face911 face925 face1650
face928 face920 face935 face938 face930 face1652
face1651 face948 face945 face940 face1653 face1654
face958 face955 face950 face1655 face965 face968
face960 face978 face975 face970 face1656 face114
face985 face988 face980 face995 face998 face990
face1657 face1005 face1008 face1000 face1658 face1015
face1018 face1010 face1659 face1028 face1025 face1020
face1035 face1660 face1038 face1030 face1045 face1661
face1048 face1040 face1055 face1662 face1058 face1050
face1663 face4 face1395 face1679 face1403 face1400
face1680 face1385 face1678 face1393 face1390 face1375
face1677 face1383 face1380 face1676 face1365 face1373
face1370 face1675 face1355 face1363 face1360 face1674
face1345 face1353 face1350 face1673 face1335 face1343
face1340 face1672 face1325 face1333 face1330 face209
face1315 face1323 face1320 face1671 face1305 face1313
face1310 face1670 face1295 face1303 face1300 face1669
face1285 face1293 face1290 face1668 face1275 face1283
face1280 face1667 face1265 face1273 face1270 face1666
face1256 face1263 face1260 face1665 face214 face91
face207 face85 face200 face79 face193 face73 face186
face67 face179 face61 face172 face55 face165 face49
face158 face43 face151 face37 face144 face31 face137
face25 face130 face19 face123 face13 face116 face8
physics create Heat Fluxes btype WALL face face104 face106
face370 face379 face389 face372 face382 face392
face371 face380 face390 face378 face388 face398
face376 face386 face396 face374 face384 face394
face377 face387 face397 face375 face385 face395
face1681 face1682 face1683 face1684 face1696 face402
face412 face422 face432 face442 face400 face410
face420 face430 face440 face408 face418 face428
face438 face448 face406 face416 face426 face436
face446 face404 face414 face424 face434 face444
face407 face417 face427 face437 face447 face405
face415 face425 face435 face445 face1688 face1685
face1686 face1687 face452 face462 face472 face482
face492 face1693 face450 face460 face470 face480
face490 face1692 face458 face468 face478 face488
face498 face1 face456 face466 face476 face486 face496
face454 face464 face474 face484 face494 face457
face467 face477 face487 face497 face1691 face455
face465 face475 face485 face495 face1689 face1690
face518 face502 face512 face1695 face500 face510
face1694 face508 face506 face516 face504 face514
face507 face517 face515 face505
physics create Mass flow inlet btype SYMMETRY face face640 face649
107
face659 face642 face652 face662 face672 face641
face650 face660 face670 face648 face658 face668
face678 face646 face656 face666 face676 face644
face654 face664 face674 face647 face657 face667
face677 face645 face655 face665 face675 face1633
face1634 face1635 face1636 face1637 face1648 face679
face689 face699 face682 face692 face702 face712
face680 face690 face700 face710 face688 face698
face708 face718 face6 face686 face696 face706 face716
face684 face694 face704 face714 face687 face697
face707 face717 face685 face695 face705 face715
face1640 face1638 face1639 face719 face729 face739
face749 face722 face732 face742 face752 face762
face720 face730 face740 face750 face760 face728
face738 face748 face758 face768 face726 face736
face746 face756 face766 face724 face734 face744
face754 face764 face727 face737 face747 face757
face767 face725 face735 face745 face755 face765
face1645 face1641 face1642 face1643 face1644 face788
face769 face779 face772 face782 face770 face780
face778 face776 face786 face774 face784 face777
face787 face775 face785 face1647 face1646
physics create Outflow btype OUTFLOW face face105
108
REFERENCES
Al-Aqal O M A 2003 ldquoHeat transfer distributions on the walls of a narrow channel
with jet impingement and cross flowrdquo PhD Thesis University of Pittsburgh
Bunker Ronald S 2007 Gas Turbine Heat Transfer Ten Remaining Hot Gas Path
Challengesrdquo Journal of Turbomachinery April Vol 129 pp 193-201
Downs James P Landis Kenneth K 2009 ldquoTurbine Cooling Systems Design- Past
Present and Futurerdquo Proceedings of ASME Turbo Expo 2009 June 8-12 2009
GT2009-59991
Florschuetz LW Berry R A Metzger D E 1980 ldquoPeriodic streamswise variations of
heat transfer coefficients for inline and staggered arrays of circular jets with cross
flow of spent airrdquo ASME J of Heat Transfer 102 p 132-137
Florschuetz L W Truman C R Metzger D E 1981 ldquoStreamwise Flow and Heat
Transfer Distributions for Jet Array Impingement with Cross flowrdquo Journal of
Heat Transfer Vol 103 pp 337
Florschuetz L W Isoda Y 1983 ldquoFlow Distributions and Discharge Coefficient for
Jet Array Impingement With Initial Cross flowrdquo Journal of Engineering for
Power Vol 105 pp 296
Incropera Frank P DeWitt D P 2002 Fundamentals of Heat and Mass Transfer John
Wiley amp Sons Inc New Jersey pp 491-493
Liu Quan Kapat J May 2006 ldquoStudy of Heat Transfer Characteristics of Impinging
Air Jet Using Pressure and Temperature Sensitive Luminescent Paintrdquo UCF
Dissertation
109
Martin H 1977 ldquoImpinging jet flow heat and mass transferrdquo Advances in heat transfer
Vol 13
Ricklick Mark Kapat J December 2009 ldquoCharacterization of an Inline Row
Impingement Channel for Turbine Blade Cooling Applicationsrdquo UCF
Dissertation
Zuckerman N Lior N 2005 ldquoImpingement Heat transfer Correlations and Numerical
Modelingrdquo Journal of Heat Transfer Vol 127 pp 544
ix
Figure 40 Finished Mesh with Boundary Conditions 55
Figure 41 Grid Independence Study 57
Figure 42 Residual Plots for the 26M Cell Run 57
Figure 43 Total Pressure Contours 58
Figure 44 Velocity Magnitude Contours 59
Figure 45 Turbulent Kinetic Energy Contours 60
Figure 46 Static Temperature Contours 60
Figure 47 Target and Side Wall Heat Transfer Coefficient Contours 61
Figure 48 Closer View of First few Rows of Impingement HTC Contours 61
Figure 49 Pathlines Generating from the First Row of Jets 62
NOMENCLATURE
Cross Sectional Area
Heater Surface Area (m2)
Specific Heat at Constant Pressure (kJkgK)
D Jet Diameter (m)
Channel Hydraulic Diameter (m)
Friction Factor
Heat Transfer Coefficient (HTC) (Wm2K)
Average Heat Transfer Coefficient (Wm2K)
Channel Length (m)
Mass Flow Rate (kgs)
Static Pressure (kPa)
x
Total Pressure (kPa)
Pr Prandtl Number
Heat Flux (Wm2)
Total Heat Input (W)
Heater Resistance (ohm)
Re Reynolds Number
SW Side Wall
Temperature (K)
TW Target Wall
Voltage Potential
Streamwise Location
y Spanwise Location
z Height from Target Wall
X Streamwise Distance (m)
Y Spanwise Distance (m)
Z Impingement Height (m)
Thermal Performance Parameter
Ratio of Specific Heats
Air Density (kgm3)
Subscripts
C Cold
H Hot
xi
Carnot Describing a Carnot cycle
Exit
Effective
Quantity Lost to the Environment
Reference Value
Wall Value
Base Line Value
1
CHAPTER ONE INTRODUCTION
11 Gas Turbine as a Heat Engine
Gas turbine is a form of heat engine where the hot reservoir is created by the
combustion of fuel and the cold reservoir is the open atmosphere It is well known that
the maximum efficiency of any heat engine is denoted as the Carnot efficiency
A more accurate cycle is used to describe the processes inside a gas turbine ndash the
Brayton Cycle The Brayton cycle as seen in Figure 1 is composed of four processes In
a gas turbine air is drawn in at state 1 it is compressed until it reaches state 2 The
compressed air is mixed with fuel and ignited as it passes through the combustor The hot
air then passes through the turbines where work is extracted The process from state 4 to
state 1 happens throughout the atmosphere therefore the Brayton cycle is an open loop
cycle as the same air is not continuously being fed through the motor
Figure 1 Brayton Cycle Flow Path and T-s Diagram (Adapted from UPTB Website)
The Brayton cycle has an isentropic efficiency similar to the carnot the Brayton
cycle efficiency is defined as
2
It can be seen that increasing the temperature at which air enters the first turbine
stage T3 increases the overall efficiency of the turbine Moreover increasing the
pressure ratio Pr also aids in the increase of the efficiency One of the hurdles of
increasing T3 is the fact that the post combustion gas is a few hundred degrees Celsius
above the melting point of the super alloys used to make the turbine stator vanes and
rotor blades For this reason it is important to cool the hot components of the gas turbine
in order to assure a reasonable life for the machine
12 Cooling of Hot Components
The transition duct that connects the combustor to the first stage turbine as well
as the first stage of the turbine are the parts that are subject to the harshest thermal
loadings and must therefore be cooled aggressively to maintain them in working
conditions for a long period of time Since the first stage guide vanes and rotor extrude
into the flow they are subject to the highest convection coefficients These heat transfer
coefficients can reach up to 4000 Wm2K (Downs 2009) Figure 2 shows the different
magnitudes of convection coefficient around the blade High heat transfer coefficients
occur where the air stagnates into the leading edge of the airfoil This high heat transfer
region is not only caused by the lack of a thermal boundary layer to protect the airfoil but
also because the effective heat transfer driving temperature is the recovery temperature
At the high Mach numbers that occur in turbines the ratio of total to static temperatures
is significant causing the leading edge to have the highest effective heat load Another
3
peak occurs on the suction side of the blade as the boundary layer created by the airfoil
switches from being a laminar boundary layer into a turbulent one Due to the nozzling
effect of the turbine rotor and stators the flow gathers speed toward the trailing edge of
the airfoil leading to higher convection coefficients on the pressure side of the airfoil
Figure 2 Thermal Loading Throughout a Turbine Blade (Daniels 1982)
Simple convection channels were implemented in the early nineteen sixties as
years passed the cooling techniques became more and more sophisticated allowing the
free stream temperature to increase to previously impossible levels Currently the use of
film cooling coupled with backside impingement leads the turbine cooling technology
The trend of allowable turbine inlet temperature is shown in Figure 3 from this figure it
can be seen that the allowable free stream temperature has increased around 600 degrees
in the past 50 years The addition of thermal barrier coatings also helps in the increase in
allowable combustion temperatures by creating an extra resistance that the heat needs to
move through as it moves from the combustion gasses into the coolant air It is impotatnt
to notice that as seen in Figure 4 the increase in turbine inlet temperatures is done with
the combined benefits of new alloys TBC and cooling technologies
4
Figure 3 Allowable Turbine Inlet Temperature vs Cooling Techniques over the Years (Clifford 1985)
Figure 4 Turbine Inlet Temperature Increase with the help of TBC New Super Alloys and Cooling
Technologies (Kapat and Kiesow Lectures 2010)
The cooling of inlet guide vanes can be done with the use of impingement inserts
inside the airfoils As air passes through the miniscule holes in the inserts a jet is formed
which then impinges on the wall of the airfoil producing one of the largest single phase
heat transfer coefficients This already impinged coolant air is then bled out as film
5
cooling as well as bled out through the trailing edge Figure 5 shows a stator vane with
the impingement insert in black the film cooling extraction as well as the trailing edge
bleed
Figure 5 Turbine Stator Cooled with Impingement Coupled with Film Cooling (Florschuetz 1980)
The cooling of turbine airfoils with the use of an impingement insert is only
possible in stationary components as the rotating ones are subject to centrifugal loadings
making it unfeasible to cool them with this setup Rotor blades are typically cooled with
serpentine passages that have heat transfer enhancing features such as ribs dimples and
other turbulators these serpentine passages are located in the mid chord of the blade On
the trailing edge a bank of pins are used to obtain high convective coefficients in the thin
region the coolant is the bled out to compensate for the boundary layer created around
the airfoil Rows of impingement holes cool the leading edge The spent air is then bled
out through showerhead cooling Figure 6 and Figure 7 show in detail the cooling
channels around two similar airfoils airfoils
6
Figure 6 Rotor Blade Cooling Configuration (Gladden 1988)
Figure 7 Cross-section of Turbine Airfoil with Cooling Channels (Han et al 1984)
7
The coolant air is bled out from the later stages of the compressor This air is
expensive as it has been compressed and not under gown the heat addition by
combustion It is imperative that the minimum amount of coolant is used in these cooling
configurations The cooling must also be as uniform as possible to reduce thermal
stresses within the blades leading to a higher component life Figure 8 shows freestream
metal and coolant temperatures of the flow blade and coolant air It can be seen that a
decrease of 25degrees in the surface temperature of the blade can provide an airfoil with
twice the working life Impingement cooling has great potential to provide high heat
transfer coefficients at a small flow rate Impingement of a jet onto a surface provides
high heat transfer coefficients due to a starting boundary layer as well as its high
turbulence When the jet is located around 3 diameters from the target surface the heat
transfer profile has two peaks one located at the stagnation region and the other located
between one and 3 diameters from the stagnation region As the jet is moved away from
the target wall the secondary peak diminishes leaving a profile with a maximum at the
stagnation region decreasing radialy
Figure 8 Relative Temperatures for Hot Gas Metal Temperature and Coolant Temperature (Cardwell 2005)
Cardwell N D 2005
8
Figure 9 shows a diagram of a jet impinging on a target surface The potential
core is the part of the jet that has not been affected by the surrounding stagnant fluid As
the jet moves towards the target wall its momentum diffuses into the surrounding fluid
decreasing the velocity at which it reaches the target wall and potentially decreasing the
corresponding heat transfer coefficient Studies have shown (Martin 1973 for example)
that the potential core may last anywhere between 7 to 10 diameters The successful
impingement of the potential core yields significantly higher heat transfer coefficients
than a fully diffused jet this comes however at a cost of higher pressure drop across the
jet plate as well as a highly non uniform heat transfer profile
Figure 9 (a) The Development of the Wall Jet (b) Jet Diffusion to Surroundings (Liu 2006)
9
CHAPTER TWO LITERATURE REVIEW
21 Impingement Literature Cornerstone
From the early days of simple convective cooling channels in turbine airfoils
studies have been done on modes of enhancing heat transfer coefficients while
maintaining a low pressure drop and minimum mass flow rate Heat transfer
characteristics of single round nozzle impingement were studied in the late 1960rsquos and
early 1970rsquos The collected works of many authors is combined into ldquoHeat and Mass
Transfer between Impinging Gas Jets and Solid Surfacesrdquo by Holger Martin 1977 The
paper collects works from multiple authors who studied single round nozzle impingement
effects on heat and mass transfer coefficients In this compilation non dimensional jet to
target spacing was studied they ranged from ZD=12-10 providing plots of Sherwood
number as a function of radius for four different jet to target spacings The local
Sherwood number was also given for a slot jet for HS ranging from 5 to 20 Studies on
impingement jet arrays were also gathered alongside an array of slot jets Correlations
were given for multiple setups present in the paper Circular jet arrays and slot arrays are
studied in detail with both analytical and experimental approaches The paper also
combines studies done on swirling jets turbulence enhancers on the target surface
impingement on concave surfaces and angle of attack variations Optimization studies
were also done to find the optimal spacing for round and slot jet arrays
Florschuetz studied the heat transfer characteristics of an array of jets impinging
on a flat surface This study was guided towards finding an optimal spacing for an array
for jets used to cool the midchord of turbine airfoils similar to that found in Figure 5 His
main contributions include a Nusselt number correlation as a function of jet to target
10
spacing jet Reynolds number and other flow and geometric parameters He found that an
increase in hole spacing and channel height resulted in a decrease of heat transfer He
also provided a one dimensional jet mass flux and channel mass flux correlations
His Nusselt number correlation takes the form of
Where A B and n are dependent by the two different types of arrays inline or staggered
Liu studied new techniques in temperature and pressure measurements of a single
slot jet with the use of temperature sensitive paint or TSP and pressure sensitive paint or
PSP In his work both measurement techniques are explained in detail Since TSP is the
only tool from that study currently used in this work it will be explained further in the
experimental setup section
11
22 Relevant Impingement Channel Studies
Al-Aqal 2003 studied three different types of impingement channels The use of
TLC was implemented in this work to obtain heat transfer distributions for the target
wall The three different configurations varied the number of holes in the streamwise and
spanwise directions The first channel had a single row of 6 streamwise jets the second
consisted of 2 rows of 12 streamwise holes summing up to a total of 24 holes The last
channel is a triple spanwise row with 18 streamwise jets This last geometry is the most
similar to the one present in the current study The third geometry will be used to
compare results There are differences however the total width of the channel is of 16
diameters as opposed to 8 in this study The streamwise jet spacing is also different Al-
Aqal used an XD of 65 compared to XD = 5 in this study The jet to target plate
spacings are similar on two occasions as he studied a ZD=4 6 and 8 while this work
uses a ZD = 6 8 and 10 Average jet Reynolds numbers also fall within the range of this
study as they range between 5000 and 33000 The author provides span averaged plots
for all cases and Reynolds numbers convenient when comparing the results
Ricklick 2009 studied a channel similar to the one found in this study His
channel was composed of a single row of 15 jets with a YcD = 4 XD = 5 and 15 and
ZD = 1 3 and 5 Two channels were tested one was pressure fed while the other was fed
by suction TSP was used to gather temperature data of all four wetted surfaces on the
pressure channel and two surfaces on the suction channel Since the maximum jet Mach
number was less than 03 the flow was assumed to be incompressible leading to the
conclusion that both channels contain identical flow patterns Thin foil heaters were used
to create the required heat flux for the channel Besides channel geometry Reynolds
12
numbers and heater geometry Ricklicksrsquo experimental setup is identical to the one
presented in this work The author also provided an ample comparison of his results to
literature He provided thermal performances of the entire channel at different Reynolds
numbers and channel heights
A small CFD study was also done A paved mesh was created on the target wall
with finer mesh near the impingement locations The resulting y+ at the wall was higher
than one yielding potentially faulty heat transfer values however this is acceptable since
the CFD was used as a tool to better understand the flow physics and help understand the
experimental heat transfer profiles
23 Computational Studies on Impingement Channels
El-Gabry did a numerical study of jet impingement with cross flow Two different
turbulence models were compared in their ability to predict surface Nusselt number The
Yang-Shih and standard k-ε models were used to compute the flow generated by jets
angled at 30 60 and 90 degrees with cross flow The computational results were
compared to previous experimental work by El-Gabry Comparisons to experimental
results at ZD = 1 and 2 90deg injection angle between Yang-Shih and standard k-ε The
error in the average Nu from the experimental results and both turbulence models were
calculated It was found that the Yang-Shih model behaved well at low Reynolds
numbers with the average Nusselt number being 5 off from the experimental value
while the standard k-ε was off my 94 As jet Reynolds number was increased the error
of the standard k-ε model dropped to as low as 39 while the error from the Yang-shih
model increased to -76 The span average plots show the experimental data Nusselt
number alongside the span averages of the results acquired by the Yang-Shih and
13
standard k-ε models High Nusselt numbers occur at the impingement location decreasing
thereafter after another impingement location is found The frequencies of these
variations are all the same for the experimental and the two numerical solutions The
amplitude of fluctuations between the impingement locations and the areas in between
are much larger for both of the numerical results however the Yang-Shih model over
predicts at the high Reynolds number for the ZD=2 case Since the amplitude of
fluctuations is greater for the CFD solutions it is important to note that even though the
error in average Nusselt number is not great the actual differences in the profile are much
greater upwards of 20 difference of heat transfer coefficients between the experimental
and numerical heat transfer peaks Other variations were studied (Injection angles for
example) but will not be discussed as their importance to the current study is minimal
Zuckerman compared a much wider set of turbulence models in their ability to
successfully predict Nusselt numbers caused by jet impingement The models tested were
k ndash ε k-ω Reynolds Stress Model algebraic stress models shear stress transport and
lastly the υ2f turbulence model DNS runs are extremely time consuming to run
therefore LES was run on its behalf to provide results for the unsteady turbulence
models The paper summarizes all the different models used their computational cost
impingement heat transfer coefficient and their ability to predict the second peak in heat
transfer As expected DNSLES provide the best prediction of both stagnation and
secondary peak heat transfer coefficient however this comes at a large computational
cost The k ndash ε and k-ω provide poor heat transfer results for the stagnation region where
they can have 30 error from the correct value The Realizable k ndash ε model provides
14
better heat transfer results while still maintaining a low computational cost The highest
accuracy to cost ratio was achieved by the υ2f model where it predicts the heat transfer
coefficient for the surface with a minimum of 2 error while not being as expensive as
the other unsteady models such as DNS and LES Ideally the CFD portion of this work
would be run with the υ2f model however since the code used to run the simulation
FLUENT does not have the υ2f model a realizable k ndash ε model will be used with
enhanced wall functions for both thermal and velocity gradients
15
CHAPTER THREE EXPERIMENTAL SETUP AND TECHNIQUES
31 Temperature Measurements with TSP
Temperature sensitive paint or TSP provides the capability of measuring
temperatures over the painted area This measurement technique supersedes the
advantages of other temperature measurement devices such as thermocouples because it
provides the user with data over a large area rather than point temperatures given by
thermocouples
Uni-Coat TSP is purchased from ISSI It is very robust to different working
conditions Calibration done on one batch of paint can be used for multiple cans as the
product is highly consistent The paint is calibrated in a dark booth a painted coupon is
placed on the hot side of a thermoelectric heat pump working on the Peltier effect
thermal paste is used to minimize contact resistance between the hot side and the TSP
coupon Calibrated thermocouples are placed in between the TSP and the thermoelectric
heat pump A reference temperature and picture are taken and the calibration commences
At least 5 or 6 data points should be taken to form the calibration Intensity ratios are
taken between the hot and cold pictures They are then plotted versus their corresponding
temperature
The paint consists of fluorescent molecules suspended in a binder These
molecules with a certain wavelength of light will be exited to a higher energy level The
molecules then can dissipate some of the energy by transferring it vibrationally to its
neighboring binder particles and dissipate the remainder of the energy by radiating it as a
photon as the molecule comes down to its original ground state Since the amount of
16
energy that the particle can transmit to others through vibration is directly proportional on
temperature and the total initial energy is fixed by measuring the ratio of the intensity at
a known temperature (reference picture) and intensity of the unknown temperature
feeding it through the correlation the unknown temperature can be found to an
uncertainty of 1 K Figure 10 shows a simplified Jablonski diagram adapted from the
suppliers website The blue arrows signify the blue light used to excite the luminescent
molecule Tris(22rsquo-bipyridyl) Ruthenium(II) Chloride Hexahydrate with a shellac binder
in our case The shellac binder is impermeable to oxygen opposite of that found in PSP
due to PSP relying on the presence of oxygen for it to function Once the particle is
excited it can give off the energy in two different ways one is by emitting it back out as
another photon of the same energy and therefore wavelength The second mode of the
particle to lose its energy is through vibrational relaxation This second process is directly
dependent on the temperature ie the higher the temperature the higher the probability
for it to lose energy to its surroundings Once it loses some energy to the surrounding
particles it releases the remainder of the energy as a photon of less energy of that which
excited it originally hence why a long pass filter is installed in the CCD camera For a
more descriptive explanation of the way TSP works refer to Liu 2006
17
Figure 10 Simplified Jablonski Diagram (Adapted from ISSI Website)
Throughout the past two years there have been numerous projects at CATER that
have used TSP Painting surfaces with TSP should be done carefully by someone who
has experience with spray painting since every single can costs $500 A single can should
be able to paint an area the size of an acrylic plate that is 36rdquo wide and 24rdquotallThe
sidewalls and the target wall of the impingement channel were painted with the use of
less than one can Painting on different surfaces is difficult for example when painting
Rohacell the paint canister can be held very close to the surface while spraying due to
the surface being somewhat porous and rough however when painting straight onto
metal heater strips the can should be placed as far back as possible for the first run
Ideally for the first pass through only a slight mist should be applied If the can is being
held too close to the surface the paint will run Figure 11 shows a set of heater strips that
has been painted too closely leading the paint to drip down Ideally the paint would be
applied to the surface in as many coats as possible Of course this would be time
18
demanding and impractical therefore with the knowledge that I have gained through the
multiple TSP paintings on different surfaces I have compiled a list of TSP dos and
donrsquots
Dos
Clean the surface to be painted with acetone or break parts cleaner Break
parts cleaner is preferable over acetone as it does not leave an oily residual
after cleaning
Paint the first coat as thin as possible Most of the surface should not be
covered There should be an even mist of miniscule TSP circles This will
give the later coats something to attach to
When positioning the test section to paint make sure to wipe it one last
time as small dust particles may have attached to the surface
Stop if you see small bumps in the paint This is caused by dust particles
collecting all the paint around it while it is still wet due to surface tension
Clean the surface and repaint This should be noticeable in the first few
coats If you see this pattern happening do not continue thinking it will be
covered by future coats What will happen is the problem will get worse
and worse ultimately the surface will have to be cleaned again and
repainted
When painting test sections try to paint the smallest section as possible
This will not only save paint but will make it very simple for the post
processing code to crop out the unpainted areas
19
Let the finished painted surface to sit at least for 90 minutes after the last
coat before baking There have been problems when baking steel and
acrylic test sections with the paint cracking while baking right after the
last coat Normally the finished surface is left to dry overnight and baked
first thing in the morning
For test sections that are too large to be baked in the oven the heat gun
may be used Carefully place a thermocouple in a central location with
blue painters tape The heating should be uniform and should not take
more than 20 minutes of continuous blowing When the thermocouple
reaches 80-90 C the plate can be assumed to be baked To introduce a
factor of safety in the baking it does not hurt to bake it longer than it
normally takes
Once the test section is mounted and ready to run cover it with cloth that
does not let any light through This will protect the paint for further uses
This is especially important on test sections that can be used multiple
times like the ones found in this study
When the test is running turn off the LED lights This light is the most
damaging to the TSP as it degrades the quality of the fluorescent
molecules
If there is a particular head of the TSP can that you prefer over others you
can remove it once the can is empty It is difficult to get used to a single
kind of nozzle being able to transfer it from can to can is a must if
painting consistency is to be kept
20
Donrsquots
Do not clean a test section that has already been used with too much
acetone The acetone is volatile evaporating quickly cooling the test
section rapidly If this test section has had heaters attached to it and run
previously the acrylic will crack due to uneven stresses inside of it
If paint is dripping stop painting immediately Clean the surface and start
over Hold the can far from the surface in order for it not to drip
Do not use TSP to teach new apprentices undergrads or graduate students
how to paint Regular spray paint is two orders of magnitude lower in cost
while the painting process is exactly the same
Do not paint with the doors closed The paint contains carcinogens that
can harm the lungs Always use a respirator and keep the room well
ventilated In-situ painting and baking has not been tried however it may
be a real option if the test section is difficult to disassemble and easily
accessible to painting and baking
If there is a can of paint that contains too little paint for the test section
that needs to be painted try to find a new can The mixing of two different
cans of TSP can be dangerous at times however it has been noticed over
the years that ISSI provides a very robust and dependable product that
does not vary significantly from batch to batch
21
Figure 11 Heater Strips Painted with TSP Too Closely
32 Experimental Setup of Suction Channel
The impingement channel is fed under suction As seen in Figure 12 air enters
through the plenum it crosses the jet plate as it gains speed to form the jets
which then impinge on the target wall The flow then passes through a venturi
flow meter and finally through the blower into the atmosphere A bypass valve is
used to control the flow rate of the impingement channel
22
Figure 12 Flow Loop of Impingement Channel
The impingement channel consists of 15 streamwise rows of 3 spanwise jets each The
total width of the channel YcD is of 8 diameters while the streamwise spacing between
the rows is XD=5 the spanwise distance between the holes is of YD=2 Figure 13shows
the top view of the jet plate The plate is counter bored to ensure that a nearly flat
velocity profile of the jet is achieved Figure 14 shows the front view of the channel Z is
denoted as the distance between the jet and target plates Side walls are interchangeable
to change the height of the channel to 6 8 and 10 diameters Two thirds of the
streamwise rows can be covered to change the XD from 5 to 15
Figure 13 Top View of Jet Plate
23
Figure 14 Front View of Impingement Channel
The target and sidewalls had heaters made specifically for them in a serpentine
style This was necessary to increase the resistance as the VARIACs used to power them
only had a maximum current output of 20 amps The heater strips are two diameters
wide at each end copper tape with conductive adhesive was used to connect the leads to
the power supply The heater consists of 50 micron thick steel sheet sandwiched between
two pieces of Kapton tape The heater is attached to the painted surface with the use of
double sided Kapton tape The target test section can be seen in Figure 15 also seen in
this figure are the two Teflon gaskets lined on the sides of the target plate With the target
wall bolted onto the sidewall the gasket is compressed generating a strong seal
Figure 15 Target Wall Test Section with Heater Leads
24
For this study the test matrix shown in Table 1 will be run Target and side wall
data will be taken at three different impingement heights at two different Reynolds
numbers of 7500 and 15000 denoted by A and B respectively A streamwise jet spacing
study is also done by testing the target and side wall heat transfer at an XD=15 for the
low impingement height channel
Table 1 Test Matrix
XD ZD Wall Re
5
10 TW
7500
15000
SW 7500
15000
8 TW
7500
15000
SW 7500
15000
6 TW
7500
15000
SW 7500
15000
15 6 TW
7500
15000
SW 7500
15000
33 Data Processing and Reduction
As described previously when taking temperature measurements with the use of TSP
reference temperatures are noted and a reference picture is taken The experiment is the
run once the experiment reaches steady state a new set of 4 pictures is taken Given the
calibration curve temperatures are backed out
25
Given the amount of heat generated inside the heater
Dividing by the heated area to get heat flux
Heat loss tests were run to consider how much of the heat flux generated by the heaters
goes through the backside instead of into the flow It was found that 25 of the heat flux
leaks out to the atmosphere through the acrylic In order to account for this heat leakage
it must be subtracted from the calculated value to become
Where Ah is the effective heated area given by
Where Aunheated is an estimate of how much unheated area is between the heater strips (~
3 of the total area)
To obtain heat transfer coefficient
Where Tref is the reference temperature Typically set in literature to be the jet
temperature
To obtain the average Reynolds number for the jets the total mass flow rate is used
Where Dj is the jet diameter and μ is dynamic viscosity (1983kgm s at 300K)
26
Pressure measurements were taken at the sidewall after the last jet entered the channel
These pressure measurements were used to determine the thermal performance of the
tallest two channels (ZD = 8 and 10)
The thermal performance at constant pumping power is found by using the equation
Where h is the average heat transfer coefficient for the target wall of them impingement
channel and ho is the heat transfer coefficient obtained by passing the same amount of
flow through a smooth duct ie the Dittus-Boelter correlation The friction factor f is
found with the use of
Where Ppl is the plenum static pressure assumed to be atmospheric and Plast jet is
the pressure read after the last jet V is the volumetric flow rate divided by the cross-
sectional area of the duct after the last impingement row The hydraulic diameter of the
channel is set to be
The baseline friction factor was calculated with the use of the Moody chart the hydraulic
diameter and the total mass flow rate though the channel Thermal performance at
constant pressure drop was also calculated with
27
34 Uncertainty Analysis
A simple uncertainty analysis was done to estimate the error in calculation of the
heat transfer coefficient from the given outputs of the test data From the bare basic
measurements for voltage area current temperature of thermocouples and temperature
profiles of paint a simple uncertainty analysis can be done to estimate the error for the
calculated heat transfer coefficient Figure 16 shows the different sources of error in the
calculation of heat transfer coefficient The effective uncertainty was calculated by taking
the root of the sum of the squares of all the individual percentage errors The
experimental uncertainty for heat transfer coefficient was of 703 This error may be
reduced by acquiring higher temperatures of the TSP reading current with a more
accurate ammeter or reading reference temperatures with the use of a thermopile instead
of a single thermocouple
Figure 16 Heat Transfer Coefficient Uncertainty Tree
28
35 Lateral Conduction Analysis
To take into account the lateral conduction occurring inside the heater foil while
the test is running two simple 1D conduction and convection equations were used to
quantify the amount of heat moving through the heater laterally and the amount of heat
convecting into the air The lateral conduction is expected to be at a maximum at the
places where there are large spatial variations of surface temperature which is why the
ZD = 6 XD = 5 case at high Re is chosen to be studied Figure 17 shows the
temperature distribution of the aforementioned case Four cold spots can be seen by their
distinct blue and yellow color located at the stagnation regions The maximum
temperature gradient occurs between the third jet impingement and the middle region
between jets The temperature difference was seen to be of 13degC The distance in between
these two temperatures is of 25D=01875m The corresponding heat flux between these
two points was calculated to be 13000Wm2 with ksteel~20Wm K A region of 1cm by
1cm was then created and the amount of heat calculated through conduction and
convection were compared To acquire the amount of heat removed through conduction
a heat flux of 13000Wm2 was imposed through an area of 01m by 00005m this
equaled to 00277 W The amount of heat moved through convection was calculated by
multiplying the heat flux used during the test by the area of the square 0001m2 the
resulting heat moving through the heater onto the air is 6 W Since the heat moving
through to the air is two orders of magnitudes larger than the heat moving laterally the
effective lateral conduction can be neglected
29
Figure 17 Temperature Profile of First Five Impingement Rows
A second order approach was also taken to quantify the amount of lateral
conduction in the heater The temperature gradient was taken from high peaks in heat
transfer caused by the second row of impingement of the same ZD=6 XD=5 channel at
high Re Figure 18 shows the high heat transfer coefficients created by the second row of
jets A quadratic curve fit was obtained by for this small region so that a continuous
equation of heat transfer coefficients as a function of streamwise distance was quantified
30
Figure 18 Detailed View of First Heat Transfer Peak with a Polynomial Curve Fit
The net heat gained by a differential volume from lateral conduction is the
difference in the temperature gradient at the entrance and the exit multiplied by the
thermal conductivity and cross sectional area Using this method shown in Figure 19 the
net change in convective heat transfer due to lateral conduction can be studied
Figure 19 Control Volume Heat Transfer Analysis
By taking the difference between the out flowing heat trough the right side and
the inflowing heat from the left side a net gain or loss can be found Figure 20 shows the
y = -470630x2 + 31244x - 14842Rsup2 = 09934
300
310
320
330
340
350
360
370
380
0 001 002 003 004 005
HTC
(W
m2K
)
x (m)
Heat Transfer Peak
Poly (Heat Transfer Peak)
31
difference in magnitude between the out flowing heat through convection seen in red and
the net inflow of heat from lateral conduction in blue From these calculations it was also
found that the amount of heat moving through lateral conduction is tow orders of
magnitude smaller than the amount of heat moving out through convection leading to the
belief that even at high temperature gradients lateral conduction does not play an
important role in the ongoing heat transfer processes in the impingement channel A more
detailed calculation of this work can be seen in appendix A
Figure 20 Heat Loss through Convection and Lateral Conduction
002 003 004 0051 10
5
1 104
1 103
001
qconv x( )
qnet x( )
x x
32
CHAPTER FOUR HEAT TRANSFER RESULTS
41 Heat Transfer Validation
In order to obtain confidence in our experimental setup an experiment was made
to test something that has already been published in literature A smooth channel was the
obvious choice as it was easy to setup by taking off the end cap and blocking all the holes
with smooth blue painters tape on the flow side and metal tape on the plenum side to
ensure no leaks into the channel from the jet plate The smooth channel has been studied
widely and multiple correlations exist one of these equations is the Dittus-Boelter
correlation (Incropera 2007) The test was run using the ZD=6 side wall so that the
hydraulic diameter was a minimum Figure 21 shows the span averaged results versus
non dimensional distance into the channel
Figure 21 Validation Spanwise Averaged Results
0
10
20
30
40
50
60
0 1 2 3 4 5 6 7 8 9
HTC
(W
m2K
)
XDc
Span Avg
Dittus Boelter
33
The plot shows decreasing heat transfer coefficient with increasing XDc due to
the developing thermal boundary layer The span average does not reach the Dittus-
Boelter due to it not being fully developed in the limited space it is given Typical flows
can take up to 60 diameters to achieve a fully developed profile with the current setup
the maximum length of the channel was of 9 diameters The profile however seems to
have an asymptote at the Dittus-Boelter correlation value leading to the belief that if the
channel was longer that value given by the correlation would be reached One important
factor to take into account in determining whether the experimental setup is validated is
the fact that the Dittus-Boelter correlation has an uncertainty near 30 Since the span
average at high XDc is well within 30 from the calculated value it is safe to assume
that the current experimental setup is validated
42 Heat Transfer Results
Heat transfer results are compared based on variations in channel height and
average jet Reynolds number As discussed earlier there are numerous other parameters
also affecting the heat transfer in these channels As these parameters are changed flow
structures within the channel are expected to be altered as well as discussed in the
literature Two of the major contributors to heat transfer in these channels are the
successful jet impingement and the resulting cross flow The same domain is captured in
both the local and averaged results
Figure 22 through Figure 25 highlights the heat transfer distribution for the cases
with a jet to jet spacing of 5 diameters in the streamwise direction and of 2 in the
spanwise direction It is evident that the smallest channel height (ZD=6) performs the
best at all Reynolds numbers on all surfaces It is also interesting to note the similarity
34
in the target wall profiles between case 528A and B where the curves are very similar
other than the obvious offset due to the change of the Reynolds number At this large
spacing we also see the degradation of the jets a few diameters downstream of each
impingement location The downstream shifts of the peaks are evident after the second
and third row of jets Also evident in these plots is the deflection of the impinging jet and
the wall jets from the cross flow The cross flow is forced to flow around the jet
deflecting the spread of the wall jet in the downstream direction Impingement locations
are also very evident at low XD however as XD and therefore the cross flow increase
the magnitude of the peaks start decreasing and eventually level out to pure internal flow
Figure 22 Target Wall Heat Transfer Coefficient Distributions
35
Figure 23 Span-averaged Target Wall Heat Transfer Distribution
36
Figure 24 Side Wall Heat Transfer Coefficient Distributions
37
Figure 25 Span-averaged Side wall Heat Transfer Distribution
Figure 23 and Figure 25 show similar details with impingement peaks clearly
diminishing and shifting in the downstream direction The cross flow clearly has some
negative influence on these geometries when compared to the more traditional
impingement highest on the order of 1 to 5 jet diameters The heat transfer profiles of the
target wall for all heights seen in Figure 22 and Figure 24 show the rapid decay in heat
transfer after the third jet This can be explained by understanding that the first jet does
not have any cross flow to deflect it the second jet only has the first jet worth of
momentum deflecting it downstream however since the channel is so tall the
momentum of the cross flow after the first and second jet are not enough to greatly
disturb the incoming jets After the third jet however the cross flow builds up enough
momentum to greatly affect the integrity of the jets downstream causing the span-
0
20
40
60
80
100
120
140
160
2 12 22 32 42 52 62 72
HTC
(W
m2K
)
XD
5210B_SW 528A_SW Jet Location
526A_TW 526B_TW
38
averaged heat transfer to rapidly drop The point at which the crossflow starts taking a
considerable effect occurs around XD =35 The target wall profile of the ZD=10
channel shows the outside jets on the second row of jet deflecting downstream It can be
conjectured that the bending of the outside jets downstream is caused by the wall jet
created by the first row of jets separating from the side wall and deflecting the outside
jets of the following rows of jets The heat transfer profile for the ZD case excludes the
first jet due to shadows being present when the data was taken
Also evident from this spanwise averaged data is the increase in heat transfer
with increases in Reynolds numbers and decreases in impingement height Results tend
to be the closest from case to case at the first impingement jet This is a reasonable
result as the effects of cross flow have little to no effect at the first few impingement
locations The impact of the jet would then be the driving force at these locations and
would be similar between cases except if the potential core is not reaching the target
surface The potential core of a jet tends to last between 6 and 10 diameters from its
origin It can be seen that the difference in heat transfer coefficient in the first two jets for
the ZD=8 and ZD=10 channel is much different than the corresponding difference
between the ZD=6 and ZD=8 heights This decreased difference between the heights of
the peaks may be attributed to the potential core reaching the target wall at the heights of
6 and 8 diameters leading to similar profiles and may not be reaching the surface at the
height of 10 diameters The heat transfer values of the peaks diminish in the downstream
direction The range of fluctuation also drops that is the profile becomes more uniform
at large XD This drop in fluctuation is more visible at the tallest channel height
(ZD=10) and less pronounced at the smallest channel This is due to the jet in the small
39
channel having to travel a shorter distance to impinge on the target plate leaving the
crossflow less time for it to deflect the jet as opposed to the tall channel where the jet has
to travel almost twice the distance as the ZD=6 channel for it to impinge on the target
wall This effect cannot be solely explained by the built up cross flow in the channel
Mixing loses also take part in the degradation of the stagnation size of the downstream
jets The mixing losses have much greater effect on the taller channels due to the same
reason that the cross flow has a higher impact on them too the jets have to travel a large
distance before hitting the target plate leading the stagnant or moving surrounding air to
be a sink of its downward momentum for a longer time and distance than the respective
smaller channels The heat transfer coefficient of the side wall was also analyzed
Similar effects are expected on the side wall due to the expected impact of the wall jet
As expected the strength of the cross flow is not enough to prevent wall jets from
successfully impacting the side wall at small XD jet locations however the crossflow
takes dominance at around XD=25 Also evident in these plots is the concentration of the
wall jet impact to the bottom of the channel on the order of 1-2 diameters in height It is
interesting to note that for the 5210B case in Figure 24 as the first jet diffuses outward
it impacts the sidewall at a height of ZD=6 The height at which the diffused jet affects
the sidewall heat transfer coefficient decreases as the crossflow increases The stagnation
regions are also deflected in the downstream direction similar to the target surface
results These effects are most evident in the 5210B Similar characteristics can be
explained from the spanwise-averaged plots shown in Figure 25 These results again
clearly show the effects of increasing the impingement height and increases in Reynolds
number As the height is increased the effect of the wall jet is significantly reduced
40
partially due to the increased surface area much of which is not affected by the wall jet
The diminishing effect of the cross flow accumulation is also evident in these plots as the
heat transfer peaks decrease in the downstream direction
43 XD Comparisons
The streamwise jet spacing was changed from XD=5 to 15 by covering two out
of three rows of jets This was done by covering the impingement holes inside the
channel with smooth blue painters tape and sealing the plenum side of the jet plate with
metal tape to ensure no leakage The profile is expected to be less uniform than the case
where XD=5 due to the large spreading of the high heat transfer peaks Due to the large
separation between the rows of jets there is a lower amount of downward momentum
than the equivalent XD=5 geometry for this reason it is expected to see a lower heat
transfer peak due to the jets momentum diffusing out faster to the stagnant air decreasing
the effective impingement velocity Figure 26 shows the target wall heat transfer
distribution Similar to the XD=5 profile it can be seen that the heat transfer due to the
jet impingement drastically reduces after the third jet This phenomenon leads us to
believe that at both Reynolds numbers the cross flow generated by the first three jets is
powerful enough to effectively deflect the fourth jet downstream diminishing its heat
transfer performance The similarity seen in Figure 26 between high and low Reynolds
number implies that the downstream deflection of the jets is not dependent on the jet
Reynolds numbers
41
Figure 26 XD=15 Target Wall Heat Transfer Profile
42
Figure 27 XD=15 Span-averaged Target Wall Heat Transfer Distribution
On the span averaged plots seen in Figure 27 the downstream deflection of the
jets is evident however as described previously the shifts in the peaks of heat transfer
occur at the same xD for both Reynolds numbers The amplitude of fluctuation of heat
transfer coefficients for the high Reynolds number case is larger than that of the low
Reynolds number Both profiles seem to start to level off at the end of the impingement
channel with the lowest span average being located just before the fourth jet at both
Reynolds numbers
A comparison of target wall heat transfer coefficients between XD =15 and 5 is
shown in Figure 28 At first glance it is clearly visible that the XD=15 average heat
transfer coefficient is smaller than its XD=5 counterpart This is also noticed by Ricklick
where he showed average HTC profiles for larger XD to be smaller than those at lower
XD (Ricklick 2009) This may occur due to there not being as high downward
0
50
100
150
200
250
300
350
0 20 40 60 80
HTC
(W
m2
K)
XD
Low Re
High Re
Impingement Location
43
momentum for the XD=15 case as compared to the XD=5 due to the lack of close jets
The stagnant air around the spaced out jets is taking away more of its momentum
decreasing the effective impingement Reynolds number Also important to notice is the
fact that since the XD=5 case has three times the flow impinged into it the cross flow
velocity and therefore Reynolds number will be three times as large increasing the heat
transfer coefficient
Figure 28 Target Wall Span-average Comparison of XD=5 and 15 at High Re
The side walls also show similar patterns to their XD=15 counterparts Strong
wall jet impingement can be seen on the side wall at low xD and zD Figure 29 shows
areas where the wall jet generated by the target wall impinges on the sidewall Similar to
the profile seen in Figure 24 the high heat transfer region reaches upward in the z
direction up to a height of 4-5 diameters for the first jet This high heat transfer stagnation
region decreases as xD increases to the point where the wall jet created by the last jet is
negligible when coupled with pure channel flow
0
50
100
150
200
250
300
350
400
0 10 20 30 40 50 60 70 80
HTC
(W
m2K
)
XD
XD = 5 XD = 15 Jet Location
- Blocked for XD =15
44
Figure 29 Side Wall Heat transfer Coefficient Profile
The span averaged plot seen in Figure 30 shows a nearly flat profile with peaks
located at the stagnation regions of the wall jets Thw downstream deflection for the
XD=15 case is much more pronounced than the one for the XD=5 case This is due to
the jet not being constrained by the wall jets generated by the previous and latter
impingement locations In the XD=15 case the wall jet is free to move downstream
more so than the XD=5 due to it not being disturbed by anything other than the cross
flow
45
Figure 30 XD=15 Side Wall Span-averaged Heat Transfer Coefficients
44 3D Comparison of the Heat Transfer Profiles
In order to further understand the targetsidewall interactions both heat transfer profiles
were positioned in an isometric view representative of the channel One important thing
to note is that both target and side wall profiles are not on the same scale This form of
data display is only qualitative way to describe the heat transfer profiles Figure 31 shows
the 3D profile of the XD=5 ZD=6 case The both stagnation regions of the jet onto the
target wall and the wall jet into the sidewall can be seen to occur at the same location for
the first three streamwise rows After the fourth and fifth row the wall jet diminishes in
magnitude Also visible in this view is the increasing heat transfer at low zD towards the
end of the channel of the side wall The constant input of mass and downward momentum
into the channel causes the cross flow generated by the previous jets to be squeezed into
the lower third of the channel increasing the velocity and the heat transfer of the target
wall
0
20
40
60
80
100
120
0 20 40 60 80
HTC
(W
m2K
)
XD
Low Re High Re Jet Locations
46
Figure 31 3D Heat Transfer Profile for ZD=6 XD=5
Similar patterns are seen in the taller ZD=8 channel seen in Figure 32 The wall jet
generate by the third streamwise row of jets is been deflected downward more than its
ZD=6 counterpart This can be attributed to the fact that the jet located at the ZD=8
channel has lost much of its momentum and is more easily bent downstream by the cross
flow generated by the first two jets The ZD=8 sidewall shows similar increasing heat
transfer at high xD however the increase is not as drastic as the one found in the ZD=6
channel This is caused due to the extra two diameters the jets have to cover to impinge
on the surface since the ZD=8 channel is one third larger than the ZD=6 one the flow
has to have more area to flow through The last few jets only deflect the cross flow
downward about 4 diameters this leaves two diameters for the flow to pass through on
the ZD=6 channel causing the velocity to increase rapidly and therefore increasing the
heat transfer coefficient at the low zD Since the ZD=8 channel has four remaining
47
diameters for the flow to move through it does not deflect it as much as the ZD=6
channel does only increasing the cross flow velocity and resulting heat transfer
coefficient slightly over the area at low zD and high xD
Figure 32 3D Heat Transfer Profile for ZD=8 XD=5
The 3D heat transfer profile for ZD=6 and xD=15 channel seen in Figure 33 shows
similar details to those seen in the XD=5 channels The stagnation regions of the jet and
wall jet occur at the same x location for the first three rows of jets the wall jet generated
by the fourth row of jets is deflected downstream only generating as small region of high
convective coefficients at the side wall The region located at the top right corner of the
side wall is colored red signifying high heat transfer however this area is generated by
the heaters providing non uniform heat flux at this location This region of high heat
transfer coefficients also occur at xD=0-4 of the target wall where the heater coil bends
48
Figure 33 3D Heat Transfer Profile for ZD=6 XD=15
45 Thermal Performance Calculations
Thermal performance calculations were done on the two tallest channels (ZD=8 and 10)
The pumping power was calculated for both channels at two Reynolds numbers Figure
34 shows the ratio of pressures required to pull the same amount of flow through as
smooth duct as opposed to through the jet plate The ZD=10 channel at high Reynolds
number requires the largest pressure as seen in the Figure however in order to pull the
same amount of flow rate through it requires a smaller pressure difference due to the
large cross section
49
Figure 34 Pressure Drop Ratio with Respect to Smooth Channel
Next the heat transfer enhancement was calculated A total area averaged heat
transfer coefficient was taken for the target wall and compared to the smooth channel
Dittus-Boelter value while using the same total mass flow rate Figure 35 shows an
average heat transfer enhancement of four times that of a smooth channel Similar trends
were noticed in the literature (Ricklick 2009) of decreasing heat transfer enhancement
with an increase of jet Reynolds number Ricklick also showed an increase in heat
transfer enhancement with an increase of jet to target spacing similar to the one seen in
Figure 35
0
10
20
30
40
50
60
528A_TW 528B_TW 5210A_TW 5210B_TW
PP
o
50
Figure 35 Heat Transfer Enhancement
Thermal performances at constant pressure drop were then calculated by dividing
the heat transfer enhancement by the pressure increase As seen in Figure 36 all the
values fall well below 1 making the impingement channel an unfeasible mode of heat
transfer enhancement when a constant pressure is supplied
Figure 36 Thermal Performance at Constant Pressure Drop
0
05
1
15
2
25
3
35
4
45
528A_TW 528B_TW 5210A_TW 5210B_TW
hh
o
0
002
004
006
008
01
012
014
528A_TW 528B_TW 5210A_TW 5210B_TW
(hh
o)
(PP
o)
51
The thermal performance at constant pumping drop was calculated in the same
way that the constant pressure drop was calculated the only difference being the pressure
ratio term was raised to the one third power As seen in Figure 37 the thermal
performances at constant pumping power are all higher than unity this signifies that if a
surface needs to be cooled with the supply of a constant pumping power the
impingement channel is a feasible option Similar to the figure literature (Ricklick 2009)
showed a decrease of thermal performance with an increase of channel height and
Reynolds number
Figure 37 Thermal Performance at Constant Pumping Power
0
02
04
06
08
1
12
14
528A_TW 528B_TW 5210A_TW 5210B_TW
(hh
o)
(PP
o)1
3
52
CHAPTER FIVE COMPUTATIONAL FLUID DYNAMICS
51 Problem Setup
In order to further enhance the understanding of the heat transfer profiles showed
previously a computational study was performed Even though CFD does not yield
accurate quantitative results it produces good qualitative data that can be used to explain
the flow physics in the channel and therefore increase the understanding of the patterns
seen previously The channel was meshed with the use of GAMBIT Due to the
symmetry the channel was split in half in the streamwise direction All horizontal
surfaces (parallel to the target wall) were divided into 6 different regions that are later on
going to be meshed individually The six regions are seen in Figure 38 section 1 is
located at the center of every jet also referred to as ldquojet centerrdquo This region was created
to reduce the squewness of the elements near the center of the jet by allowing the mesh to
be completely linear with a squewness of zero Section two complements section 1 to
complete the impingement hole The half impingement hole located at the symmetry wall
contains the same exact region 2 however it only has one half of the jet center Section 3
was made in order to bring the polar geometry of the holes to match the cartesian aspect
of the remainder of the channel With the addition of section 3 to the channel the only
remaining sections are square or rectangular regions Region 4 lies in between
streamwise rows of jets Section 5 is located at the entrance and the exit of the channel
These sections are not square in contrast with section 4 The last remaining section is
located near the side wall of the channel extending from the beginning to the exit of the
channel
53
Figure 38 Horizontal Plane of Impingement Channel Geometry
All the faces of sections 1 and 2 are linked throughout the channel and the
plenum however in order to have greater control of the mesh in the plenum and the
channel the remaining sections 3 4 5 and 6 are not linked to every single similar face
instead they are only linked to similar faces in either the plenum or the channel
Boundary layer spacing number of rows and growth factor are placed around the
channel In order to maintain a y+ of less than unity the first cell spacing of the boundary
layer inside the channel was set to be 000001 m (01mm) This first cell spacing yielded
y+
values varying between zero and 9 at the target side and front end wall Figure 39
shows a contour of y+ values on the heated walls The maximum values occur near the
impingement locations as expected due to large shear caused by the steep velocity
gradient normal to the wall On the downstream direction the y+ also increases due to the
increase of flow rate and therefore the increased skin friction on the wall At the
impingement location of the first jet the y+ is close to zero due to the velocity having its
direction mostly normal to the surface yielding no shear
54
Figure 39 Target Side and Front End Wall y+ Values
Once the faces were linked edge meshes were created on the sides of the jet center
Section 2rsquos inner edge was also meshed using a different parameter than the one used for
the jet center in order to allow for more freedom when trying to refine the mesh These
two edge meshes is followed by meshing all of section 2 faces alongside all the jet
centers Once these were complete section 3rsquos inner edge was meshed with different
parameters for the channel and plenum Sections 4 and 5 sides that connected with the
face made by section 6 were meshed so that their spacing was similar again the plenum
and channel were meshed separately for increased control of mesh density in both of
these areas The upstream-most edge of section 6 was meshed so that the spacing is
similar to the edge mesh in sections 4 and 5 this was done in order to have aspect ratios
of the wall be as close as possible to unity Sections 3 4 5 and 6 were meshed on both
the channel and the plenum With the entire target wall plane meshed these surface
meshes are coopered upwards to connect to the opposite wall The vertical spacing has
55
also been set up differently between the channel and the plenum The holes and the
plenum were also coopered The finished mesh was then exported as a msh file
Boundary conditions were set in GAMBIT once the mesh was imported into
Fluent values were set to every face depending on their location and purpose Figure 40
shows the four different boundary conditions Face 1 (blue) was set to be a mass flow
inlet The flow rate is half of the total flow rate at a given jet Reynolds number due to it
being only half of the entire domain Face 2 (yellow) is a symmetry plane face 3 (red) is
a pressure outlet at zero gauge pressure The rest of the faces in the channel denoted by
the number 4 (white) are set to walls The target side and front end wall had a heat flux
applied to them equal to 10000Wm2
Figure 40 Finished Mesh with Boundary Conditions
The model was imported into Fluent It was scaled down by a factor of 1000 due to it
being made in GAMBIT in millimeters The energy model was turned on The Realizable
k-ε model was used with enhanced wall functions on both the pressure and thermal
gradients The boundary conditions were set as discussed previously the mass flow inlet
was set to the specific flow rate normal to the surface the heat fluxes were set on the
56
heated walls the outflow gauge pressure was set to zero Two important reference values
characteristic length and reference temperature were set to be the diameter of the jet
(0075m) and 300K respectively The spatial discretization parameters were set to second
order upwind for momentum turbulent kinetic energy turbulent dissipation rate and
energy The under-relaxation factors were set to default Four monitors were created to
aid in the determination of convergence two of them read Nusselt numbers at the
stagnation region of the first and last jet the remaining two read the exit velocity at the
first and last jet The continuity x y and x velocities and energy equations residuals
were set to be 1E-6 while k and ε residuals were set to 1E-4 The solution was initialized
on the all zones at 1ms in the positive x direction The solution was set to autosave every
100 iterations while keeping only the two newest dat files The calculation was then run
for a maximum of 7000 iterations
A grid independence study was done on the domain to find the optimal size of
mesh that provides the correct solution while minimizing the compute time Two
monitors were set to check for grid independence both of them were vertex maximum
One of them read the Nusselt number at the impingement location of the first center jet
while the second one measures the velocity at the exit of the last jet Four different mesh
sizes were run to the convergence criterion explained before their sizes were 900000
15 million 28 million and 43 million cells
57
Figure 41 Grid Independence Study
It can be seen in Figure 41 that the difference between the 28 and 43 million cell
meshes are very small a difference of under 006 for velocity and 7 for Nusselt
number It can be safe to assume that the 28 million cell mesh is large enough to provide
a mesh independent solution The GAMBIT journal file used to create this mesh is
attached to the appendix The results shown hereafter are the ones obtained by the 28
million cell mesh
Figure 42 Residual Plots for the 26M Cell Run
67
69
71
73
75
77
79
81
83
85
485
4855
486
4865
487
4875
488
4885
489
0 1 2 3 4 5
Nu
sse
lt N
um
be
r
Cell Ammount (Millions)
Grid Independence Study
Velocity
Nusselt Number
58
For future reference Figure 42 shows the residuals of the 26M cell calculation
Up until around 4400 iterations the residuals were increasing shortly thereafter the
residuals started decreasing until it converged just after 5500 iterations All runs for the
differently sized meshes had the same residual patters with the peak of residuals and
point of convergence happening at different iterations
52 CFD Results
As describe previously all the results shown here are for the mesh containing 28 million
elements Figure 43 shows the total pressure contours It can be seen that the plenum
portion is at a constant total pressure Once the jets form since there are very small losses
in the jets due to the wall friction the total pressure still remains constant Only when the
jets enter the channel and start mixing with the cross flow is that they start losing the total
pressure head It is important to notice how the first two jets have the total pressure close
to the plenum arriving at the target wall This implies a successful impingement of the
undisturbed potential core As we move downstream the total pressure is lost quite
rapidly as the jets interact with the cross flow
Figure 43 Total Pressure Contours
59
Similar details can be drawn out from Figure 44 it can be seen that the first three
jets successfully impinge on the target wall while the rest of the downstream ones are
deflected by the cross flow As mentioned by Ricklick the velocity magnitude of the last
jet is larger than that of the first jet due to there being a lower static pressure at the end of
the channel providing it with a steeper pressure gradient hence higher velocity
Figure 44 Velocity Magnitude Contours
Turbulent kinetic energy was plotted in Figure 45 it is expected to have the
highest turbulent kinetic energy near the exit of the holes where the stagnant air is in
contact with the fast moving jet The mixing between the two regimes causes very
energetic eddies to form potentially enhancing the target and side wall heat transfer
coefficient As cross flow builds up towards the end of the channel the turbulent kinetic
energy increases due to larger overall velocities and fluctuations between the cross flow
and jets
60
Figure 45 Turbulent Kinetic Energy Contours
As Ricklick showed in his work the static temperature rise is quite small for such a small
channel It can be seen in Figure 46 that the driving temperature for heat transfer is that of
the plenum It is important to notice that a wall heat flux of 10000 Wm2 was used as the
boundary condition Not even in the most powerful tests would we ever use heat fluxes
that high they normally range between 2500 to a maximum of 7000 Wm2 A heat flux of
10000 Wm2 will increase the temperature at a faster rate than what it is normally used in
experimental testing
Figure 46 Static Temperature Contours
61
Figure 47 Target and Side Wall Heat Transfer Coefficient Contours
Figure 47 shows the target and sidewall heat transfer profiles Peaks can be seen at the
first three locations similar to that seen in Figure 22 The trend decreases rapidly to
eventually become a slowly increasing heat transfer profile due to the increase of mass
flow through the channel The sidewall provides the same results clear peaks in heat
transfer where the wall jets impinge on the sidewall seen in Figure 48 in more detail The
sidewall also shows a recirculation zone in between the first row of jets and the end wall
This is caused by the wall jet from the first row hitting the back wall moving upwards in
a circular pattern and coming back down when it encounters the first impingement row
Figure 48 Closer View of First few Rows of Impingement HTC Contours
62
Figure 49 Pathlines Generating from the First Row of Jets
Figure 49 helps explain the low heat transfer region between the first row of jets and
the end wall Pathlines are generated at the exit of each hole in the first row As the
air impinges on the surface half of it moves downstream and the other half movers
upstream to this recirculation zone where it circulates for a period of time before
reuniting with the remainder of the flow to move downstream The wall jet that
moves towards the second row of jets encounters the wall jet created by the second
row of jets causing the pathlines to drastically move upwards On the side of the
channel the pathlines behave erratically with no clear pattern clearly signifying the
highly turbulent and chaotic flow structure of this impingement channel
63
CHAPTER SIX CONCLUSIONS
It has been seen from this analysis that the side walls provide significant heat
transfer in an impingement channel especially at the relatively smaller channel
height This is primarily the result of successful impact of the wall jet with the side
walls It was shown that the tallest channel (ZD=10) has the most uniform profile with
low heat transfer coefficients when compared to the other channels The peaks of the
ZD=6 and 8 channels have a very similar profile which may indicate the successful
impingement of the potential core of the jet on the target surface As XD increases the
peaks diminish and a positive slope profile is attained by the increase of cross flow
velocity as more and more jets are introduced Tall impingement channels provide the
user with a heat transfer profile that is more uniform than those provided with the use of a
smaller channel while still maintaining higher convective coefficients when compared to
a smooth flow scenario The downstream shift of the wall jets is found to be independent
of Reynolds number and heavily dependent on streamwise position It was also found that
at XD=15 the wall jets decay faster than their XD=5 counterparts From the 3D heat
transfer profiles it was seen that the cross flow generated by multiple upstream jets is
deflected downward decreasing its effective flow area increasing its velocity hence
providing higher convective coefficients at the side wall at high xD and low zD
64
APPENDICES
Appendix A
Lateral Conduction Consideration
Thickness of foil heater Heat flux
Sample volume width
Volumetric heat generation
Volume of sample volume
Temperature profile from the first row of impingement ONLY valid for 02ltxlt045
t 50m k 20W
m K qflux 6000
W
m2
1mm
V 2
t qvol
qflux
t
T x( ) 298Kqflux
470630 x2
31244x 14842 W
m2K
N 15
x 02045 02
N 102 047
002 003 004 005314
315
316
317
318
319
320
T x( )
x
A t
qnet x( ) A kxT x
m
d
d xT x( )
d
d
1
m
002 003 004 0050
5 105
1 104
15 104
2 104
qnet x( )
x
65
Now comparing the net heat gained by lateral conduction to heat generated and convected out
It can be seen that the lateral conduction into the sample volume is two orders of magnitude smaller than the heat removed by convection
qgen qvol V 6 103
W
qconv x( ) 2
qflux qnet x( )
002 003 004 0051 10
5
1 104
1 103
001
qconv x( )
qnet x( )
x x
66
Appendix B
This is the journal file run on gambit to generate the geometry faces links
boundary layer face and volume meshes as well as the boundary conditions
set diameter
$d=75
$zc=6($d)
$xc=80($d)
$yc=4($d)
$y=2($d)
$x=5($d)
$zp=5($d)
$ztot=($zc)+($d)+($zp)
$jcf=(13)
$ocf=2
Boundary layer constants
$first=01
$growth=12
$rows=4
Meshing constants
$NumbNodes=5
$Numbtelnodes=6
$PLobnodes=5
$Chobnodes=5
$Plbenodes=($NumbNodes(4)+$rows)
$plsqnodes=($NumbNodes(3))
$Pllsnodes=($NumbNodes+$rows)
$Nojetcells=10
$Chzdnodes=($zc$Nojetcells)($d)
$Plzdnodes=($zp$Nojetcells)($d)
Boundary layer constants for channel
$firstch=001
$growthch=12
$rowsch=8
$CHbenodes=($NumbNodes(4)+$rowsch)
$CHlsnodes=($NumbNodes+$rowsch)
volume create body width ($xc) depth ($yc) height ($ztot) offset ($xc2) ($yc2) ($ztot2) brick
volume create cylinder height ($ztot) radius1 ($d2) radius3 ($d2) offset ($x) 0 ($ztot2) zaxis frustum
volume cmove cylinder multiple 1 offset 0 ($y) 0
volume cmove cylinder volume3 multiple 14 offset ($x) 0 0
volume create jetplate width ($xc) depth ($yc) height ($d)offset ($xc2) ($yc2) ($d2+$zc) brick
volume split body volumes jetplate connected
volume split jetplate volumes cylinder volume3 volume4 volume5
volume6 volume7 volume8 volume9 volume10 volume11
volume12 volume13 volume14 volume15 volume16 volume17
67
volume18 volume19 volume20 volume21 volume22 volume23
volume24 volume25 volume26 volume27 volume28 volume29
volume30 volume31 connected
face create jetcenter width ($jcf$d) height ($jcf$d) offset ($x) 0 0 xyplane rectangle
face create jetcircle radius ($d2) xyplane circle
face move jetcircle offset ($x) 0 0
face create outbox width ($ocf$d) height ($ocf$d) offset ($x) 0 0 xyplane rectangle
face split outbox connected faces jetcircle jetcenter
face split jetcircle connected faces face1
face split outbox connected faces face1
face cmove jetcenter outbox jetcircle face222 face223 multiple 1 offset 0 ($y) 0
face cmove jetcenter outbox jetcircle face222 face223 face224 face225 face226
face227 face228 multiple 14 offset ($x) 0 0
volume delete jetplate lowertopology
face split face1 connected keeptool faces jetcircle jetcenter outbox
face222 face223 face224 face225 face226 face227
face228 face229 face230 face231 face232 face233
face234 face235 face236 face237 face238 face239
face240 face241 face242 face243 face244 face245
face246 face247 face248 face249 face250 face251
face252 face253 face254 face255 face256 face257
face258 face259 face260 face261 face262 face263
face264 face265 face266 face267 face268 face269
face270 face271 face272 face273 face274 face275
face276 face277 face278 face279 face280 face281
face282 face283 face284 face285 face286 face287
face288 face289 face290 face291 face292 face293
face294 face295 face296 face297 face298 face299
face300 face301 face302 face303 face304 face305
face306 face307 face308 face309 face310 face311
face312 face313 face314 face315 face316 face317
face318 face319 face320 face321 face322 face323
face324 face325 face326 face327 face328 face329
face330 face331 face332 face333 face334 face335
face336 face337 face338 face339 face340 face341
face342 face343 face344 face345 face346 face347
face348 face349 face350 face351 face352 face353
face354 face355 face356 face357 face358 face359
face360 face361 face362 face363 face364 face365
face366 face367 face368
face move jetcircle jetcenter outbox face222 face223 face224
face225 face226 face227 face228 face229 face230
face231 face232 face233 face234 face235 face236
face237 face238 face239 face240 face241 face242
face243 face244 face245 face246 face247 face248
face249 face250 face251 face252 face253 face254
face255 face256 face257 face258 face259 face260
face261 face262 face263 face264 face265 face266
face267 face268 face269 face270 face271 face272
face273 face274 face275 face276 face277 face278
face279 face280 face281 face282 face283 face284
face285 face286 face287 face288 face289 face290
face291 face292 face293 face294 face295 face296
face297 face298 face299 face300 face301 face302
face303 face304 face305 face306 face307 face308
face309 face310 face311 face312 face313 face314
68
face315 face316 face317 face318 face319 face320
face321 face322 face323 face324 face325 face326
face327 face328 face329 face330 face331 face332
face333 face334 face335 face336 face337 face338
face339 face340 face341 face342 face343 face344
face345 face346 face347 face348 face349 face350
face351 face352 face353 face354 face355 face356
face357 face358 face359 face360 face361 face362
face363 face364 face365 face366 face367 face368 offset 0
0 $ztot
THIS SPLITS THE TOP PLENUM FACE WITH THE FACES CREATED IN THE BOTTOM
face split face6 connected keeptool faces jetcircle jetcenter outbox
face222 face223 face224 face225 face226 face227
face228 face229 face230 face231 face232 face233
face234 face235 face236 face237 face238 face239
face240 face241 face242 face243 face244 face245
face246 face247 face248 face249 face250 face251
face252 face253 face254 face255 face256 face257
face258 face259 face260 face261 face262 face263
face264 face265 face266 face267 face268 face269
face270 face271 face272 face273 face274 face275
face276 face277 face278 face279 face280 face281
face282 face283 face284 face285 face286 face287
face288 face289 face290 face291 face292 face293
face294 face295 face296 face297 face298 face299
face300 face301 face302 face303 face304 face305
face306 face307 face308 face309 face310 face311
face312 face313 face314 face315 face316 face317
face318 face319 face320 face321 face322 face323
face324 face325 face326 face327 face328 face329
face330 face331 face332 face333 face334 face335
face336 face337 face338 face339 face340 face341
face342 face343 face344 face345 face346 face347
face348 face349 face350 face351 face352 face353
face354 face355 face356 face357 face358 face359
face360 face361 face362 face363 face364 face365
face366 face367 face368
THIS MOVES THE FACES THAT WE ARE USING TO PLIT THE BOTTOM PLENUM SURFACE
face move jetcircle jetcenter outbox face222 face223 face224
face225 face226 face227 face228 face229 face230
face231 face232 face233 face234 face235 face236
face237 face238 face239 face240 face241 face242
face243 face244 face245 face246 face247 face248
face249 face250 face251 face252 face253 face254
face255 face256 face257 face258 face259 face260
face261 face262 face263 face264 face265 face266
face267 face268 face269 face270 face271 face272
face273 face274 face275 face276 face277 face278
face279 face280 face281 face282 face283 face284
face285 face286 face287 face288 face289 face290
face291 face292 face293 face294 face295 face296
face297 face298 face299 face300 face301 face302
69
face303 face304 face305 face306 face307 face308
face309 face310 face311 face312 face313 face314
face315 face316 face317 face318 face319 face320
face321 face322 face323 face324 face325 face326
face327 face328 face329 face330 face331 face332
face333 face334 face335 face336 face337 face338
face339 face340 face341 face342 face343 face344
face345 face346 face347 face348 face349 face350
face351 face352 face353 face354 face355 face356
face357 face358 face359 face360 face361 face362
face363 face364 face365 face366 face367 face368 offset 0
0 -$zp
SPLITS THE BOTTOM FACE OF THE PLENUM WITH THE FACES THAT ARE USED TO SPLIT
face split face114 connected keeptool faces jetcircle jetcenter
outbox face222 face223 face224 face225 face226 face227
face228 face229 face230 face231 face232 face233
face234 face235 face236 face237 face238 face239
face240 face241 face242 face243 face244 face245
face246 face247 face248 face249 face250 face251
face252 face253 face254 face255 face256 face257
face258 face259 face260 face261 face262 face263
face264 face265 face266 face267 face268 face269
face270 face271 face272 face273 face274 face275
face276 face277 face278 face279 face280 face281
face282 face283 face284 face285 face286 face287
face288 face289 face290 face291 face292 face293
face294 face295 face296 face297 face298 face299
face300 face301 face302 face303 face304 face305
face306 face307 face308 face309 face310 face311
face312 face313 face314 face315 face316 face317
face318 face319 face320 face321 face322 face323
face324 face325 face326 face327 face328 face329
face330 face331 face332 face333 face334 face335
face336 face337 face338 face339 face340 face341
face342 face343 face344 face345 face346 face347
face348 face349 face350 face351 face352 face353
face354 face355 face356 face357 face358 face359
face360 face361 face362 face363 face364 face365
face366 face367 face368
COPIES THE FACES THAT WE USED TO SPLIT TO BOTTOM OF THE PLENUM TO THE TOP OF
THE CHANNEL
face cmove jetcircle jetcenter outbox face222 face223 face224
face225 face226 face227 face228 face229 face230
face231 face232 face233 face234 face235 face236
face237 face238 face239 face240 face241 face242
face243 face244 face245 face246 face247 face248
face249 face250 face251 face252 face253 face254
face255 face256 face257 face258 face259 face260
face261 face262 face263 face264 face265 face266
face267 face268 face269 face270 face271 face272
face273 face274 face275 face276 face277 face278
face279 face280 face281 face282 face283 face284
70
face285 face286 face287 face288 face289 face290
face291 face292 face293 face294 face295 face296
face297 face298 face299 face300 face301 face302
face303 face304 face305 face306 face307 face308
face309 face310 face311 face312 face313 face314
face315 face316 face317 face318 face319 face320
face321 face322 face323 face324 face325 face326
face327 face328 face329 face330 face331 face332
face333 face334 face335 face336 face337 face338
face339 face340 face341 face342 face343 face344
face345 face346 face347 face348 face349 face350
face351 face352 face353 face354 face355 face356
face357 face358 face359 face360 face361 face362
face363 face364 face365 face366 face367 face368 multiple 1 offset 0
0 -$d
NAME OF COPIED NEW FACES
face1104 face1105 face1106 face1107 face1108 face1109 face1110 face1111
face1112 face1113 face1114 face1115 face1116 face1117 face1118 face1119
face1120 face1121 face1122 face1123 face1124 face1125 face1126 face1127
face1128 face1129 face1130 face1131 face1132 face1133 face1134 face1135
face1136 face1137 face1138 face1139 face1140 face1141 face1142 face1143
face1144 face1145 face1146 face1147 face1148 face1149 face1150 face1151
face1152 face1153 face1154 face1155 face1156 face1157 face1158 face1159
face1160 face1161 face1162 face1163 face1164 face1165 face1166 face1167
face1168 face1169 face1170 face1171 face1172 face1173 face1174 face1175
face1176 face1177 face1178 face1179 face1180 face1181 face1182 face1183
face1184 face1185 face1186 face1187 face1188 face1189 face1190 face1191
face1192 face1193 face1194 face1195 face1196 face1197 face1198 face1199
face1200 face1201 face1202 face1203 face1204 face1205 face1206 face1207
face1208 face1209 face1210 face1211 face1212 face1213 face1214 face1215
face1216 face1217 face1218 face1219 face1220 face1221 face1222 face1223
face1224 face1225 face1226 face1227 face1228 face1229 face1230 face1231
face1232 face1233 face1234 face1235 face1236 face1237 face1238 face1239
face1240 face1241 face1242 face1243 face1244 face1245 face1246 face1247
face1248 face1249 face1250 face1251 face1252 face1253
THIS SPLITS THE TOP OF THE CHANNEL WITH THE NEW COPIED FACES
face split face209 connected keeptool faces face1104 face1105 face1106 face1107
face1108 face1109 face1110 face1111 face1112 face1113 face1114 face1115
face1116 face1117 face1118 face1119 face1120 face1121 face1122 face1123
face1124 face1125 face1126 face1127 face1128 face1129 face1130 face1131
face1132 face1133 face1134 face1135 face1136 face1137 face1138 face1139
face1140 face1141 face1142 face1143 face1144 face1145 face1146 face1147
face1148 face1149 face1150 face1151 face1152 face1153 face1154 face1155
face1156 face1157 face1158 face1159 face1160 face1161 face1162 face1163
face1164 face1165 face1166 face1167 face1168 face1169 face1170 face1171
face1172 face1173 face1174 face1175 face1176 face1177 face1178 face1179
face1180 face1181 face1182 face1183 face1184 face1185 face1186 face1187
face1188 face1189 face1190 face1191 face1192 face1193 face1194 face1195
face1196 face1197 face1198 face1199 face1200 face1201 face1202 face1203
face1204 face1205 face1206 face1207 face1208 face1209 face1210 face1211
face1212 face1213 face1214 face1215 face1216 face1217 face1218 face1219
face1220 face1221 face1222 face1223 face1224 face1225 face1226 face1227
71
face1228 face1229 face1230 face1231 face1232 face1233 face1234 face1235
face1236 face1237 face1238 face1239 face1240 face1241 face1242 face1243
face1244 face1245 face1246 face1247 face1248 face1249 face1250 face1251
face1252 face1253
THIS UNITES THE RECTANGLE OUTSIDE FACES AND THE SEMICIRCLE SO THAT IT MAKES
A RECTANGLE WIHOUT THE CENTERJET
face unite faces jetcircle face223 real
face unite faces face222 outbox real
face unite faces face228 face226 real
face unite faces face225 face227 real
face unite faces face231 face233 real
face unite faces face232 face230 real
face unite faces face236 face238 real
face unite faces face237 face235 real
face unite faces face241 face243 real
face unite faces face242 face240 real
face unite faces face248 face246 real
face unite faces face245 face247 real
face unite faces face253 face251 real
face unite faces face252 face250 real
face unite faces face256 face258 real
face unite faces face257 face255 real
face unite faces face263 face261 real
face unite faces face260 face262 real
face unite faces face268 face266 real
face unite faces face265 face264 real
face unite faces face265 face267 real
face unite faces face273 face271 real
face unite faces face272 face270 real
face unite faces face276 face278 real
face unite faces face277 face275 real
face unite faces face281 face283 real
face unite faces face282 face280 real
face unite faces face286 face288 real
face unite faces face287 face285 real
face unite faces face291 face293 real
face unite faces face292 face290 real
face unite faces face296 face298 real
face unite faces face297 face295 real
face unite faces face301 face303 real
face unite faces face302 face300 real
face unite faces face306 face308 real
face unite faces face307 face305 real
face unite faces face316 face318 real
face unite faces face312 face310 real
face unite faces face311 face313 real
face unite faces face315 face317 real
face unite faces face321 face323 real
face unite faces face322 face320 real
face unite faces face326 face328 real
face unite faces face327 face325 real
face unite faces face331 face333 real
face unite faces face332 face330 real
face unite faces face336 face338 real
72
face unite faces face337 face335 real
face unite faces face347 face345 real
face unite faces face346 face348 real
face unite faces face342 face340 real
face unite faces face341 face343 real
face unite faces face356 face358 real
face unite faces face357 face355 real
face unite faces face352 face350 real
face unite faces face351 face353 real
face unite faces face361 face363 real
face unite faces face366 face368 real
face unite faces face360 face362 real
face unite faces face365 face367 real
SPLITTING ALL THE FACES OF THE CIRCLES IN THE BOTTOM OF THE PLENUM
face split face912 connected keeptool faces face222
face split face117 connected keeptool faces face228
face split face117 connected keeptool faces face225
face split face922 connected keeptool faces face232
face split face124 connected keeptool faces face236
face split face124 connected keeptool faces face237
face split face932 connected keeptool faces face242
face split face131 connected keeptool faces face248
face split face131 connected keeptool faces face245
face split face942 connected keeptool faces face252
face split face138 connected keeptool faces face256
face split face138 connected keeptool faces face257
face split face952 connected keeptool faces face260
face split face145 connected keeptool faces face268
face split face145 connected keeptool faces face265
face split face962 connected keeptool faces face272
face split face152 connected keeptool faces face276
face split face152 connected keeptool faces face277
face split face972 connected keeptool faces face282
face split face159 connected keeptool faces face286
face split face159 connected keeptool faces face287
face split face982 connected keeptool faces face292
face split face166 connected keeptool faces face296
face split face166 connected keeptool faces face297
face split face992 connected keeptool faces face302
face split face173 connected keeptool faces face306
face split face173 connected keeptool faces face307
face split face1002 connected keeptool faces face312
face split face180 connected keeptool faces face316
face split face180 connected keeptool faces face315
73
face split face1012 connected keeptool faces face322
face split face187 connected keeptool faces face326
face split face187 connected keeptool faces face327
face split face1022 connected keeptool faces face332
face split face194 connected keeptool faces face336
face split face194 connected keeptool faces face337
face split face1032 connected keeptool faces face342
face split face201 connected keeptool faces face346
face split face201 connected keeptool faces face347
face split face1042 connected keeptool faces face352
face split face208 connected keeptool faces face356
face split face208 connected keeptool faces face357
face split face1052 connected keeptool faces face360
face split face215 connected keeptool faces face366
face split face215 connected keeptool faces face365
THIS UNITES THE RECTANGLE OUTSIDE FACES AND THE SEMICIRCLE SO THAT IT MAKES
A RECTANGLE WIHOUT THE CENTERJET
face unite faces face1104 face1108 real
face unite faces face1107 face1106 real
face unite faces face1113 face1111 real
face unite faces face1112 face1110 real
face unite faces face1118 face1116 real
face unite faces face1117 face1115 real
face unite faces face1123 face1121 real
face unite faces face1122 face1120 real
face unite faces face1128 face1126 real
face unite faces face1127 face1125 real
face unite faces face1133 face1131 real
face unite faces face1132 face1130 real
face unite faces face1138 face1136 real
face unite faces face1137 face1135 real
face unite faces face1143 face1141 real
face unite faces face1142 face1140 real
face unite faces face1148 face1146 real
face unite faces face1147 face1145 real
face unite faces face1153 face1151 real
face unite faces face1152 face1150 real
face unite faces face1158 face1156 real
face unite faces face1157 face1155 real
face unite faces face1163 face1161 real
face unite faces face1162 face1160 real
face unite faces face1168 face1166 real
face unite faces face1167 face1165 real
face unite faces face1173 face1171 real
face unite faces face1172 face1170 real
face unite faces face1178 face1176 real
face unite faces face1177 face1175 real
face unite faces face1183 face1181 real
74
face unite faces face1182 face1180 real
face unite faces face1186 face1188 real
face unite faces face1187 face1185 real
face unite faces face1193 face1191 real
face unite faces face1192 face1190 real
face unite faces face1198 face1196 real
face unite faces face1197 face1195 real
face unite faces face1203 face1201 real
face unite faces face1202 face1200 real
face unite faces face1206 face1208 real
face unite faces face1207 face1205 real
face unite faces face1213 face1211 real
face unite faces face1212 face1210 real
face unite faces face1216 face1218 real
face unite faces face1217 face1215 real
face unite faces face1221 face1223 real
face unite faces face1222 face1220 real
face unite faces face1228 face1226 real
face unite faces face1227 face1225 real
face unite faces face1233 face1231 real
face unite faces face1232 face1230 real
face unite faces face1238 face1236 real
face unite faces face1237 face1235 real
face unite faces face1243 face1241 real
face unite faces face1242 face1240 real
face unite faces face1248 face1246 real
face unite faces face1247 face1245 real
face unite faces face1253 face1251 real
face unite faces face1252 face1250 real
SPLITTING ALL THE FACES OF THE CIRCLES IN THE TOP OF THE CHANNEL
face split face1257 connected keeptool faces face1107
face split face115 connected keeptool faces face1113
face split face115 connected keeptool faces face1112
face split face1267 connected keeptool faces face1117
face split face122 connected keeptool faces face1123
face split face122 connected keeptool faces face1122
face split face1277 connected keeptool faces face1127
face split face129 connected keeptool faces face1133
face split face129 connected keeptool faces face1132
face split face1287 connected keeptool faces face1137
face split face136 connected keeptool faces face1143
face split face136 connected keeptool faces face1142
face split face1297 connected keeptool faces face1147
face split face143 connected keeptool faces face1153
face split face143 connected keeptool faces face1152
face split face1307 connected keeptool faces face1157
face split face150 connected keeptool faces face1163
face split face150 connected keeptool faces face1162
75
face split face1317 connected keeptool faces face1167
face split face157 connected keeptool faces face1173
face split face157 connected keeptool faces face1172
face split face1327 connected keeptool faces face1177
face split face164 connected keeptool faces face1183
face split face164 connected keeptool faces face1182
face split face1337 connected keeptool faces face1187
face split face171 connected keeptool faces face1193
face split face171 connected keeptool faces face1192
face split face1347 connected keeptool faces face1197
face split face178 connected keeptool faces face1203
face split face178 connected keeptool faces face1202
face split face1357 connected keeptool faces face1207
face split face185 connected keeptool faces face1213
face split face185 connected keeptool faces face1212
face split face1367 connected keeptool faces face1217
face split face192 connected keeptool faces face1221
face split face192 connected keeptool faces face1222
face split face1377 connected keeptool faces face1227
face split face199 connected keeptool faces face1233
face split face199 connected keeptool faces face1232
face split face1387 connected keeptool faces face1237
face split face206 connected keeptool faces face1243
face split face206 connected keeptool faces face1242
face split face1397 connected keeptool faces face1247
face split face213 connected keeptool faces face1253
face split face213 connected keeptool faces face1252
face split face1452 connected keeptool faces face224
face split face1456 connected keeptool faces face234
face split face1460 connected keeptool faces face244
face split face1464 connected keeptool faces face254
face split face1468 connected keeptool faces face264
face split face1472 connected keeptool faces face274
face split face1476 connected keeptool faces face284
face split face1480 connected keeptool faces face294
face split face1484 connected keeptool faces face304
face split face1488 connected keeptool faces face314
face split face1492 connected keeptool faces face324
face split face1496 connected keeptool faces face334
face split face1500 connected keeptool faces face344
face split face1504 connected keeptool faces face354
face split face1508 connected keeptool faces face364
DELETING ALL THE FACES USED TO MAKE THE CUTS
face delete jetcircle face222 face228 face225 jetcenter
76
face224 face231 face232 face236 face237 face229
face1456 face241 face242 face239 face248 face244
face245 face253 face249 face252 face254 face256
face257 face263 face259 face260 face268 face264
face265 face273 face272 face269 face276 face277
face274 face281 face282 face286 face279 face287
face284 face291 face292 face296 face297 face289
face294 face301 face299 face302 face306 face307
face304 face311 face312 face316 face315 face309
face314 face321 face322 face326 face327 face319
face324 face331 face332 face329 face336 face334
face337 face341 face342 face339 face346 face344
face347 face351 face352 face349 face356 face354
face357 face361 face359 face360 face366 face364
face365 lowertopology
face delete face1104 face1105 face1107 face1113 face1112
face115 face234 face1118 face1114 face1117 face1123
face1122 face122 face1138 face1128 face1127 face1124
face1133 face1132 face129 face1134 face1137 face1143
face136 face1142 face1148 face1144 face1147 face1153
face143 face1152 face1158 face1154 face1157 face1163
face150 face1162 face1168 face1164 face1167 face1173
face157 face1172 face1178 face1174 face1177 face1183
face164 face1182 face1186 face1184 face1187 face1193
face171 face1192 face1198 face1194 face1197 face1203
face178 face1202 face1206 face1204 face1207 face1213
face185 face1212 face1216 face1214 face1217 face1221
face192 face1222 face1228 face1224 face1227 face1233
face199 face1232 face1238 face1234 face1237 face1243
face206 face1242 face1248 face1244 face1247 face1253
face213 face1252 lowertopology
face delete face1109 face1119 face1129 face1139 face1149 face1159
face1169 face1179 face1189 face1199 face1209 face1219
face1229 face1239 face1249 lowertopology
face create CP1 width 600 height 75 offset 300 (225+($d)2) 0 xyplane rectangle
face create CP2 width 600 height 75 offset 300 (225+($d)2) ($zc) xyplane rectangle
face create CP3 width 600 height 75 offset 300 (225+($d)2) ($zc+$d) xyplane rectangle
face create CP4 width 600 height 75 offset 300 (225+($d)2) ($zc+$d+$zp) xyplane rectangle
face split face6 connected faces CP4
face split face114 connected faces CP3
face split face209 connected faces CP2
face split face1 connected faces CP1
GEOMETRY IS FINISHED
face modify face912 side vertex6437 vertex6436
77
face modify face1600 side vertex7302 vertex7303
face modify face117 side vertex6446 vertex6447
face modify face646 side vertex3312
face modify face646 side vertex3313
face modify face647 side vertex3432 vertex3433
face modify face372 side vertex2040 vertex2041
face modify face376 side vertex2100 vertex2101
face modify face377 side vertex2221 vertex2220
LINKING ALL THE JET CENTERS
face link face1450 face640 edges edge6949 edge3518 vertices
vertex6437 vertex3253 reverse
face link face1450 face1257 edges edge6949 edge7340 vertices
vertex6437 vertex6797 reverse
face link face1257 face370 edges edge7340 edge2139 vertices
vertex6797 vertex2041 reverse
face link face1257 face1454 edges edge7340 edge6975 vertices
vertex6797 vertex6461 reverse
face link face1454 face649 edges edge6975 edge3519 vertices
vertex6461 vertex3255 reverse
face link face1454 face1267 edges edge6975 edge7377 vertices
vertex6461 vertex6831 reverse
face link face1267 face379 edges edge7377 edge2141 vertices
vertex6831 vertex2043 reverse
face link face1267 face1458 edges edge7377 edge7001 vertices
vertex6831 vertex6485 reverse
face link face1458 face659 edges edge7001 edge3520 vertices
vertex6485 vertex3257 reverse
face link face1458 face1277 edges edge7001 edge7414 vertices
vertex6485 vertex6865 reverse
face link face1277 face389 edges edge7414 edge2143 vertices
vertex6865 vertex2045 reverse
face link face1277 face1462 edges edge7414 edge7027 vertices
vertex6865 vertex6509 reverse
face link face1462 face669 edges edge7027 edge3521 vertices
vertex6509 vertex3259 reverse
face link face1462 face1287 edges edge7027 edge7451 vertices
vertex6509 vertex6899 reverse
face link face1287 face399 edges edge7451 edge2145 vertices
vertex6899 vertex2047 reverse
face link face1287 face1466 edges edge7451 edge7053 vertices
vertex6899 vertex6533 reverse
face link face1466 face679 edges edge7053 edge3522 vertices
vertex6533 vertex3261 reverse
face link face1466 face1297 edges edge7053 edge7488 vertices
vertex6533 vertex6933 reverse
face link face1297 face409 edges edge7488 edge2147 vertices
vertex6933 vertex2049 reverse
face link face1297 face1470 edges edge7488 edge7079 vertices
vertex6933 vertex6557 reverse
face link face1470 face689 edges edge7079 edge3523 vertices
vertex6557 vertex3263 reverse
face link face1470 face1307 edges edge7079 edge7525 vertices
vertex6557 vertex6967 reverse
face link face1307 face419 edges edge7525 edge2149 vertices
78
vertex6967 vertex2051 reverse
face link face1307 face1474 edges edge7525 edge7105 vertices
vertex6967 vertex6581 reverse
face link face1474 face1317 edges edge7105 edge7562 vertices
vertex6581 vertex7001 reverse
face link face1474 face699 edges edge7105 edge3524 vertices
vertex6581 vertex3265 reverse
face link face1317 face429 edges edge7562 edge2151 vertices
vertex7001 vertex2053 reverse
face link face1317 face1478 edges edge7562 edge7131 vertices
vertex7001 vertex6605 reverse
face link face1478 face1327 edges edge7131 edge7599 vertices
vertex6605 vertex7035 reverse
face link face1478 face709 edges edge7131 edge3525 vertices
vertex6605 vertex3267 reverse
face link face1327 face439 edges edge7599 edge2153 vertices
vertex7035 vertex2055 reverse
face link face1327 face1482 edges edge7599 edge7157 vertices
vertex7035 vertex6629 reverse
face link face1482 face719 edges edge7157 edge3526 vertices
vertex6629 vertex3269 reverse
face link face1482 face1337 edges edge7157 edge7636 vertices
vertex6629 vertex7069 reverse
face link face1337 face449 edges edge7636 edge2155 vertices
vertex7069 vertex2057 reverse
face link face1337 face1486 edges edge7636 edge7183 vertices
vertex7069 vertex6653 reverse
face link face1486 face1347 edges edge7183 edge7673 vertices
vertex6653 vertex7103 reverse
face link face1347 face459 edges edge7673 edge2157 vertices
vertex7103 vertex2059 reverse
face link face1486 face729 edges edge7183 edge3527 vertices
vertex6653 vertex3271 reverse
face link face1347 face1490 edges edge7673 edge7209 vertices
vertex7103 vertex6677 reverse
face link face1490 face1357 edges edge7209 edge7710 vertices
vertex6677 vertex7137 reverse
face link face1490 face739 edges edge7209 edge3528 vertices
vertex6677 vertex3273 reverse
face link face1357 face469 edges edge7710 edge2159 vertices
vertex7137 vertex2061 reverse
face link face1357 face1494 edges edge7710 edge7235 vertices
vertex7137 vertex6701 reverse
face link face1494 face1367 edges edge7235 edge7747 vertices
vertex6701 vertex7171 reverse
face link face1494 face749 edges edge7235 edge3529 vertices
vertex6701 vertex3275 reverse
face link face1367 face479 edges edge7747 edge2161 vertices
vertex7171 vertex2063 reverse
face link face1367 face1498 edges edge7747 edge7261 vertices
vertex7171 vertex6725 reverse
face link face1498 face1377 edges edge7261 edge7784 vertices
vertex6725 vertex7205 reverse
face link face1377 face489 edges edge7784 edge2163 vertices
vertex7205 vertex2065 reverse
face link face1498 face759 edges edge7261 edge3530 vertices
79
vertex6725 vertex3277 reverse
face link face1377 face1502 edges edge7784 edge7287 vertices
vertex7205 vertex6749 reverse
face link face1502 face1387 edges edge7287 edge7821 vertices
vertex6749 vertex7239 reverse
face link face1387 face499 edges edge7821 edge2165 vertices
vertex7239 vertex2067 reverse
face link face1387 face1506 edges edge7821 edge7313 vertices
vertex7239 vertex6773 reverse
face link face1502 face769 edges edge7287 edge3531 vertices
vertex6749 vertex3279 reverse
face link face1506 face1397 edges edge7313 edge7858 vertices
vertex6773 vertex7273 reverse
face link face1506 face779 edges edge7313 edge3532 vertices
vertex6773 vertex3281 reverse
face link face1397 face509 edges edge7858 edge2167 vertices
vertex7273 vertex2069 reverse
LINKING ALL THE COMPLETE JETCENTERS
face link face1452 face644 edges edge7891 edge3773 vertices
vertex7303 vertex3433
face link face1452 face115 edges edge7891 edge7364 vertices
vertex7303 vertex6819
face link face1452 face1456 edges edge7891 edge7900 vertices
vertex7303 vertex7311
face link face1456 face654 edges edge7900 edge3774 vertices
vertex7311 vertex3435
face link face1456 face122 edges edge7900 edge7401 vertices
vertex7311 vertex6853
face link face1456 face1460 edges edge7900 edge7909 vertices
vertex7311 vertex7319
face link face1460 face1464 edges edge7909 edge7918 vertices
vertex7319 vertex7327
face link face1460 face129 edges edge7909 edge7438 vertices
vertex7319 vertex6887
face link face1460 face664 edges edge7909 edge3775 vertices
vertex7319 vertex3437
face link face1464 face674 edges edge7918 edge3776 vertices
vertex7327 vertex3439
face link face1464 face136 edges edge7918 edge7475 vertices
vertex7327 vertex6921
face link face1464 face1468 edges edge7918 edge7927 vertices
vertex7327 vertex7335
face link face1472 face1468 edges edge7936 edge7927 vertices
vertex7343 vertex7335
face link face1468 face143 edges edge7927 edge7512 vertices
vertex7335 vertex6955
face link face1468 face684 edges edge7927 edge3777 vertices
vertex7335 vertex3441
face link face1472 face694 edges edge7936 edge3778 vertices
vertex7343 vertex3443
face link face1472 face150 edges edge7936 edge7549 vertices
vertex7343 vertex6989
face link face1472 face1476 edges edge7936 edge7945 vertices
80
vertex7343 vertex7351
face link face1476 face1480 edges edge7945 edge7954 vertices
vertex7351 vertex7359
face link face1476 face157 edges edge7945 edge7586 vertices
vertex7351 vertex7023
face link face1476 face704 edges edge7945 edge3779 vertices
vertex7351 vertex3445
face link face1480 face714 edges edge7954 edge3780 vertices
vertex7359 vertex3447
face link face1480 face164 edges edge7954 edge7623 vertices
vertex7359 vertex7057
face link face1480 face1484 edges edge7954 edge7963 vertices
vertex7359 vertex7367
face link face1484 face171 edges edge7963 edge7660 vertices
vertex7367 vertex7091
face link face1484 face724 edges edge7963 edge3781 vertices
vertex7367 vertex3449
face link face1480 face1488 edges edge7954 edge7972 vertices
vertex7359 vertex7375
face link face1488 face178 edges edge7972 edge7697 vertices
vertex7375 vertex7125
face link face1488 face734 edges edge7972 edge3782 vertices
vertex7375 vertex3451
face link face1488 face1492 edges edge7972 edge7981 vertices
vertex7375 vertex7383
face link face1492 face744 edges edge7981 edge3783 vertices
vertex7383 vertex3453
face link face1492 face185 edges edge7981 edge7734 vertices
vertex7383 vertex7159
face link face1492 face1496 edges edge7981 edge7990 vertices
vertex7383 vertex7391
face link face1496 face754 edges edge7990 edge3784 vertices
vertex7391 vertex3455
face link face1496 face192 edges edge7990 edge7771 vertices
vertex7391 vertex7193
face link face1496 face1500 edges edge7990 edge7999 vertices
vertex7391 vertex7399
face link face1500 face1504 edges edge7999 edge8008 vertices
vertex7399 vertex7407
face link face1504 face1508 edges edge8008 edge8017 vertices
vertex7407 vertex7415
face link face1500 face199 edges edge7999 edge7808 vertices
vertex7399 vertex7227
face link face1500 face764 edges edge7999 edge3785 vertices
vertex7399 vertex3457
face link face1504 face774 edges edge8008 edge3786 vertices
vertex7407 vertex3459
face link face1508 face784 edges edge8017 edge3787 vertices
vertex7415 vertex3461
face link face1504 face206 edges edge8008 edge7845 vertices
vertex7407 vertex7261
face link face1508 face213 edges edge8017 edge7882 vertices
vertex7415 vertex7295
linking the jetcenters of the bottom of the channel one of them has to be reversed but the otherones are not
81
face link face115 face374 edges edge7364 edge2394 vertices
vertex6819 vertex2221 reverse
face link face374 face384 edges edge2394 edge2396 vertices
vertex2221 vertex2223
face link face384 face394 edges edge2396 edge2398 vertices
vertex2223 vertex2225
face link face394 face404 edges edge2398 edge2400 vertices
vertex2225 vertex2227
face link face404 face414 edges edge2400 edge2402 vertices
vertex2227 vertex2229
face link face414 face424 edges edge2402 edge2404 vertices
vertex2229 vertex2231
face link face424 face434 edges edge2404 edge2406 vertices
vertex2231 vertex2233
face link face434 face444 edges edge2406 edge2408 vertices
vertex2233 vertex2235
face link face444 face454 edges edge2408 edge2410 vertices
vertex2235 vertex2237
face link face454 face464 edges edge2410 edge2412 vertices
vertex2237 vertex2239
face link face464 face474 edges edge2412 edge2414 vertices
vertex2239 vertex2241
face link face474 face484 edges edge2414 edge2416 vertices
vertex2241 vertex2243
face link face484 face494 edges edge2416 edge2418 vertices
vertex2243 vertex2245
face link face494 face504 edges edge2418 edge2420 vertices
vertex2245 vertex2247
face link face504 face514 edges edge2420 edge2422 vertices
vertex2247 vertex2249
UP TO THIS POINT ALL THE FACES ARE CONNCTED SUCCESSFULLY
LINKING THE FIRST THREE JET TELEPHONES
face link face912 face117 edges edge6950 edge6960 vertices
vertex6437 vertex6446 reverse
face link face912 face1600 edges edge6950 edge7890 vertices
vertex6437 vertex7303 reverse
face link face912 face372 edges edge6950 edge2168 vertices
vertex6437 vertex2041
face link face117 face376 edges edge6959 edge2304 vertices
vertex6447 vertex2101 reverse
face link face1600 face377 edges edge7890 edge2423 vertices
vertex7303 vertex2221 reverse
face link face372 face382 edges edge2168 edge2169 vertices
vertex2041 vertex2043
face link face377 face387 edges edge2423 edge2424 vertices
vertex2221 vertex2223
face link face376 face386 edges edge2304 edge2306 vertices
vertex2101 vertex2103
face link face387 face397 edges edge2424 edge2425 vertices
vertex2223 vertex2225
face link face386 face396 edges edge2306 edge2308 vertices
82
vertex2103 vertex2105
face link face382 face392 edges edge2169 edge2170 vertices
vertex2043 vertex2045
face link face382 face392 edges edge2169 edge2170 vertices
vertex2043 vertex2045
face link face382 face392 edges edge2169 edge2170 vertices
vertex2043 vertex2045
face link face382 face392 edges edge2169 edge2170 vertices
vertex2043 vertex2045
face link face397 face407 edges edge2425 edge2426 vertices
vertex2225 vertex2227
face link face392 face402 edges edge2170 edge2171 vertices
vertex2045 vertex2047
face link face396 face406 edges edge2290 edge2291 vertices
vertex2104 vertex2106
face link face407 face417 edges edge2426 edge2427 vertices
vertex2227 vertex2229
face link face417 face427 edges edge2427 edge2428 vertices
vertex2229 vertex2231
face link face427 face437 edges edge2428 edge2429 vertices
vertex2231 vertex2233
face link face437 face447 edges edge2429 edge2430 vertices
vertex2233 vertex2235
face link face447 face457 edges edge2430 edge2431 vertices
vertex2235 vertex2237
face link face457 face467 edges edge2431 edge2432 vertices
vertex2237 vertex2239
face link face467 face477 edges edge2432 edge2433 vertices
vertex2239 vertex2241
face link face477 face487 edges edge2433 edge2434 vertices
vertex2241 vertex2243
face link face487 face487 edges edge2434 edge2434 vertices
vertex2243 vertex2243
face link face487 face487 edges edge2434 edge2434 vertices
vertex2243 vertex2243
face link face487 face487 edges edge2434 edge2434 vertices
vertex2243 vertex2243
face link face487 face497 edges edge2434 edge2435 vertices
vertex2243 vertex2245
face link face497 face507 edges edge2435 edge2436 vertices
vertex2245 vertex2247
face link face507 face517 edges edge2436 edge2437 vertices
vertex2247 vertex2249
face link face406 face416 edges edge2291 edge2292 vertices
vertex2106 vertex2108
face link face416 face426 edges edge2292 edge2293 vertices
vertex2108 vertex2110
face link face426 face436 edges edge2293 edge2294 vertices
vertex2110 vertex2112
face link face436 face446 edges edge2294 edge2295 vertices
vertex2112 vertex2114
face link face446 face456 edges edge2295 edge2296 vertices
vertex2114 vertex2116
face link face456 face466 edges edge2296 edge2297 vertices
vertex2116 vertex2118
face link face466 face476 edges edge2297 edge2298 vertices
83
vertex2118 vertex2120
face link face486 face496 edges edge2299 edge2300 vertices
vertex2122 vertex2124
face link face476 face486 edges edge2298 edge2299 vertices
vertex2120 vertex2122
face link face496 face506 edges edge2300 edge2301 vertices
vertex2124 vertex2126
face link face506 face516 edges edge2301 edge2302 vertices
vertex2126 vertex2128
face link face392 face402 edges edge2142 edge2144 vertices
vertex2044 vertex2046
face link face402 face412 edges edge2171 edge2172 vertices
vertex2047 vertex2049
face link face412 face422 edges edge2172 edge2173 vertices
vertex2049 vertex2051
face link face422 face432 edges edge2173 edge2174 vertices
vertex2051 vertex2053
face link face432 face442 edges edge2174 edge2175 vertices
vertex2053 vertex2055
face link face442 face452 edges edge2175 edge2176 vertices
vertex2055 vertex2057
face link face452 face462 edges edge2176 edge2177 vertices
vertex2057 vertex2059
face link face462 face472 edges edge2177 edge2178 vertices
vertex2059 vertex2061
face link face472 face482 edges edge2178 edge2179 vertices
vertex2061 vertex2063
face link face482 face492 edges edge2179 edge2180 vertices
vertex2063 vertex2065
face link face492 face502 edges edge2180 edge2181 vertices
vertex2065 vertex2067
face link face502 face512 edges edge2181 edge2182 vertices
vertex2067 vertex2069
LINKING THE TELEPHONES OF THE BOTTOM OF THE PLENUM
face link face912 face922 edges edge6950 edge6976 vertices
vertex6437 vertex6461
face link face922 face932 edges edge6976 edge7002 vertices
vertex6461 vertex6485
face link face932 face942 edges edge7002 edge7028 vertices
vertex6485 vertex6509
face link face942 face952 edges edge7028 edge7054 vertices
vertex6509 vertex6533
face link face952 face962 edges edge7054 edge7080 vertices
vertex6533 vertex6557
face link face962 face972 edges edge7080 edge7106 vertices
vertex6557 vertex6581
face link face972 face982 edges edge7106 edge7132 vertices
vertex6581 vertex6605
face link face982 face992 edges edge7132 edge7158 vertices
vertex6605 vertex6629
face link face992 face1002 edges edge7158 edge7184 vertices
vertex6629 vertex6653
face link face1002 face1012 edges edge7184 edge7210 vertices
vertex6653 vertex6677
84
face link face1012 face1022 edges edge7210 edge7236 vertices
vertex6677 vertex6701
face link face1032 face1042 edges edge7262 edge7288 vertices
vertex6725 vertex6749
face link face1042 face1052 edges edge7288 edge7314 vertices
vertex6749 vertex6773
face link face117 face124 edges edge6960 edge6986 vertices
vertex6446 vertex6470
face link face124 face131 edges edge6986 edge7012 vertices
vertex6470 vertex6494
face link face131 face138 edges edge7012 edge7038 vertices
vertex6494 vertex6518
face link face138 face145 edges edge7038 edge7064 vertices
vertex6518 vertex6542
face link face145 face152 edges edge7064 edge7090 vertices
vertex6542 vertex6566
face link face152 face159 edges edge7090 edge7116 vertices
vertex6566 vertex6590
face link face159 face166 edges edge7116 edge7142 vertices
vertex6590 vertex6614
face link face166 face173 edges edge7142 edge7168 vertices
vertex6614 vertex6638
face link face173 face180 edges edge7168 edge7194 vertices
vertex6638 vertex6662
face link face180 face187 edges edge7194 edge7220 vertices
vertex6662 vertex6686
face link face187 face194 edges edge7220 edge7246 vertices
vertex6686 vertex6710
face link face194 face201 edges edge7246 edge7272 vertices
vertex6710 vertex6734
face link face1022 face1032 edges edge7236 edge7262 vertices
vertex6701 vertex6725
face link face1032 face1042 edges edge7262 edge7288 vertices
vertex6725 vertex6749
face link face201 face208 edges edge7271 edge7297 vertices
vertex6735 vertex6759
face link face208 face215 edges edge7297 edge7323 vertices
vertex6759 vertex6783
face link face1600 face1602 edges edge7890 edge7899 vertices
vertex7303 vertex7311
face link face1602 face1604 edges edge7899 edge7908 vertices
vertex7311 vertex7319
face link face1604 face1606 edges edge7908 edge7917 vertices
vertex7319 vertex7327
face link face1606 face1608 edges edge7917 edge7926 vertices
vertex7327 vertex7335
face link face1608 face1610 edges edge7926 edge7935 vertices
vertex7335 vertex7343
face link face1610 face1612 edges edge7935 edge7944 vertices
vertex7343 vertex7351
face link face1612 face1614 edges edge7944 edge7953 vertices
vertex7351 vertex7359
face link face1614 face1616 edges edge7953 edge7962 vertices
vertex7359 vertex7367
face link face1616 face1618 edges edge7962 edge7971 vertices
vertex7367 vertex7375
85
face link face1618 face1620 edges edge7971 edge7980 vertices
vertex7375 vertex7383
face link face1620 face1622 edges edge7980 edge7989 vertices
vertex7383 vertex7391
face link face1622 face1624 edges edge7989 edge7998 vertices
vertex7391 vertex7399
face link face1624 face1626 edges edge7998 edge8007 vertices
vertex7399 vertex7407
face link face1626 face1628 edges edge8007 edge8016 vertices
vertex7407 vertex7415
LINKING ALL THE TELEPHONES OF THE TOP OF THE CHANNEL
face link face912 face1510 edges edge6950 edge7339 vertices
vertex6437 vertex6797 reverse
face link face117 face1512 edges edge6959 edge7349 vertices
vertex6447 vertex6807
face link face1600 face1514 edges edge7890 edge7363 vertices
vertex7303 vertex6819
face link face1510 face1516 edges edge7339 edge7376 vertices
vertex6797 vertex6831
face link face1516 face1522 edges edge7376 edge7413 vertices
vertex6831 vertex6865
face link face1522 face1528 edges edge7413 edge7450 vertices
vertex6865 vertex6899
face link face1528 face1534 edges edge7450 edge7487 vertices
vertex6899 vertex6933
face link face1534 face1540 edges edge7487 edge7524 vertices
vertex6933 vertex6967
face link face1540 face1546 edges edge7524 edge7561 vertices
vertex6967 vertex7001
face link face1546 face1552 edges edge7561 edge7598 vertices
vertex7001 vertex7035
face link face1552 face1558 edges edge7598 edge7635 vertices
vertex7035 vertex7069
face link face1558 face1564 edges edge7635 edge7672 vertices
vertex7069 vertex7103
face link face1564 face1570 edges edge7672 edge7709 vertices
vertex7103 vertex7137
face link face1570 face1576 edges edge7709 edge7746 vertices
vertex7137 vertex7171
face link face1576 face1582 edges edge7746 edge7783 vertices
vertex7171 vertex7205
face link face1582 face1588 edges edge7783 edge7820 vertices
vertex7205 vertex7239
face link face1588 face1594 edges edge7820 edge7857 vertices
vertex7239 vertex7273
face link face1512 face1518 edges edge7350 edge7387 vertices
vertex6806 vertex6840
face link face1518 face1524 edges edge7387 edge7424 vertices
vertex6840 vertex6874
face link face1524 face1530 edges edge7424 edge7461 vertices
vertex6874 vertex6908
face link face1530 face1536 edges edge7461 edge7498 vertices
vertex6908 vertex6942
face link face1536 face1542 edges edge7498 edge7535 vertices
86
vertex6942 vertex6976
face link face1542 face1548 edges edge7535 edge7572 vertices
vertex6976 vertex7010
face link face1548 face1554 edges edge7572 edge7609 vertices
vertex7010 vertex7044
face link face1554 face1560 edges edge7609 edge7646 vertices
vertex7044 vertex7078
face link face1560 face1566 edges edge7646 edge7683 vertices
vertex7078 vertex7112
face link face1566 face1572 edges edge7683 edge7720 vertices
vertex7112 vertex7146
face link face1572 face1578 edges edge7720 edge7757 vertices
vertex7146 vertex7180
face link face1578 face1584 edges edge7757 edge7794 vertices
vertex7180 vertex7214
face link face1584 face1590 edges edge7794 edge7831 vertices
vertex7214 vertex7248
face link face1590 face1596 edges edge7831 edge7868 vertices
vertex7248 vertex7282
face link face1514 face1520 edges edge7363 edge7400 vertices
vertex6819 vertex6853
face link face1520 face1526 edges edge7400 edge7437 vertices
vertex6853 vertex6887
face link face1526 face1532 edges edge7437 edge7474 vertices
vertex6887 vertex6921
face link face1532 face1538 edges edge7474 edge7511 vertices
vertex6921 vertex6955
face link face1538 face1544 edges edge7511 edge7548 vertices
vertex6955 vertex6989
face link face1544 face1550 edges edge7548 edge7585 vertices
vertex6989 vertex7023
face link face1550 face1556 edges edge7585 edge7622 vertices
vertex7023 vertex7057
face link face1556 face1562 edges edge7622 edge7659 vertices
vertex7057 vertex7091
face link face1562 face1568 edges edge7659 edge7696 vertices
vertex7091 vertex7125
face link face1568 face1574 edges edge7696 edge7733 vertices
vertex7125 vertex7159
face link face1574 face1580 edges edge7733 edge7770 vertices
vertex7159 vertex7193
face link face1580 face1586 edges edge7770 edge7807 vertices
vertex7193 vertex7227
face link face1586 face1592 edges edge7807 edge7844 vertices
vertex7227 vertex7261
face link face1592 face1598 edges edge7844 edge7881 vertices
vertex7261 vertex7295
LINKING ALL THE TELEPHONES OF THE TOP OF THE PLENUM
face link face912 face642 edges edge6950 edge3489 vertices
vertex6437 vertex3253 reverse
face link face642 face647 edges edge3489 edge3744 vertices
vertex3253 vertex3433
face link face117 face646 edges edge6959 edge3638 vertices
vertex6447 vertex3313
87
face link face642 face652 edges edge3489 edge3491 vertices
vertex3253 vertex3255
face link face652 face662 edges edge3491 edge3493 vertices
vertex3255 vertex3257
face link face662 face672 edges edge3493 edge3495 vertices
vertex3257 vertex3259
face link face672 face682 edges edge3495 edge3497 vertices
vertex3259 vertex3261
face link face682 face692 edges edge3497 edge3499 vertices
vertex3261 vertex3263
face link face692 face702 edges edge3499 edge3501 vertices
vertex3263 vertex3265
face link face702 face712 edges edge3501 edge3503 vertices
vertex3265 vertex3267
face link face712 face722 edges edge3503 edge3505 vertices
vertex3267 vertex3269
face link face722 face732 edges edge3505 edge3507 vertices
vertex3269 vertex3271
face link face732 face742 edges edge3507 edge3509 vertices
vertex3271 vertex3273
face link face742 face752 edges edge3509 edge3511 vertices
vertex3273 vertex3275
face link face752 face762 edges edge3511 edge3513 vertices
vertex3275 vertex3277
face link face762 face772 edges edge3513 edge3515 vertices
vertex3277 vertex3279
face link face772 face782 edges edge3515 edge3517 vertices
vertex3279 vertex3281
face link face646 face656 edges edge3653 edge3655 vertices
vertex3312 vertex3314
face link face656 face666 edges edge3655 edge3657 vertices
vertex3314 vertex3316
face link face666 face676 edges edge3657 edge3659 vertices
vertex3316 vertex3318
face link face676 face686 edges edge3659 edge3661 vertices
vertex3318 vertex3320
face link face686 face696 edges edge3661 edge3663 vertices
vertex3320 vertex3322
face link face696 face706 edges edge3663 edge3665 vertices
vertex3322 vertex3324
face link face706 face716 edges edge3665 edge3667 vertices
vertex3324 vertex3326
face link face716 face726 edges edge3667 edge3669 vertices
vertex3326 vertex3328
face link face726 face736 edges edge3669 edge3671 vertices
vertex3328 vertex3330
face link face736 face746 edges edge3671 edge3673 vertices
vertex3330 vertex3332
face link face746 face756 edges edge3673 edge3675 vertices
vertex3332 vertex3334
face link face756 face766 edges edge3675 edge3677 vertices
vertex3334 vertex3336
face link face766 face776 edges edge3677 edge3679 vertices
vertex3336 vertex3338
face link face776 face786 edges edge3679 edge3681 vertices
88
vertex3338 vertex3340
face link face647 face657 edges edge3744 edge3746 vertices
vertex3433 vertex3435
face link face657 face667 edges edge3746 edge3748 vertices
vertex3435 vertex3437
face link face667 face677 edges edge3748 edge3750 vertices
vertex3437 vertex3439
face link face677 face687 edges edge3750 edge3752 vertices
vertex3439 vertex3441
face link face687 face697 edges edge3752 edge3754 vertices
vertex3441 vertex3443
face link face697 face707 edges edge3754 edge3756 vertices
vertex3443 vertex3445
face link face707 face717 edges edge3756 edge3758 vertices
vertex3445 vertex3447
face link face717 face727 edges edge3758 edge3760 vertices
vertex3447 vertex3449
face link face727 face737 edges edge3760 edge3762 vertices
vertex3449 vertex3451
face link face737 face747 edges edge3762 edge3764 vertices
vertex3451 vertex3453
face link face747 face757 edges edge3764 edge3766 vertices
vertex3453 vertex3455
face link face757 face767 edges edge3766 edge3768 vertices
vertex3455 vertex3457
face link face767 face777 edges edge3768 edge3770 vertices
vertex3457 vertex3459
face link face777 face787 edges edge3770 edge3772 vertices
vertex3459 vertex3461
face link face647 face1600 edges edge3685 edge6963 vertices
vertex3345 vertex6449
LINKING OUTBOXES ON THE PLENUM
face modify face911 side vertex4404 vertex4405
face modify face918 side vertex4405 vertex4404
face link face911 face915 edges edge4778 edge4898 vertices
vertex4374 vertex4434
face link face915 face645 edges edge4899 edge3833 vertices
vertex4480 vertex3463 reverse
face link face911 face641 edges edge4779 edge3578 vertices
vertex4405 vertex3283 reverse
face link face918 face648 edges edge4825 edge3686 vertices
vertex4436 vertex3347 reverse
face link face645 face655 edges edge3833 edge3834 vertices
vertex3463 vertex3465
face link face655 face665 edges edge3834 edge3835 vertices
vertex3465 vertex3467
face link face665 face675 edges edge3835 edge3836 vertices
vertex3467 vertex3469
face link face675 face685 edges edge3836 edge3837 vertices
vertex3469 vertex3471
face link face685 face695 edges edge3837 edge3838 vertices
89
vertex3471 vertex3473
face link face695 face705 edges edge3838 edge3839 vertices
vertex3473 vertex3475
face link face705 face715 edges edge3839 edge3840 vertices
vertex3475 vertex3477
face link face715 face725 edges edge3840 edge3841 vertices
vertex3477 vertex3479
face link face725 face735 edges edge3841 edge3842 vertices
vertex3479 vertex3481
face link face735 face745 edges edge3842 edge3843 vertices
vertex3481 vertex3483
face link face745 face755 edges edge3843 edge3844 vertices
vertex3483 vertex3485
face link face755 face765 edges edge3844 edge3845 vertices
vertex3485 vertex3487
face link face765 face775 edges edge3845 edge3846 vertices
vertex3487 vertex3489
face link face775 face785 edges edge3846 edge3847 vertices
vertex3489 vertex3491
face link face648 face658 edges edge3686 edge3690 vertices
vertex3347 vertex3353
face link face658 face668 edges edge3690 edge3694 vertices
vertex3353 vertex3359
face link face668 face678 edges edge3694 edge3698 vertices
vertex3359 vertex3365
face link face678 face688 edges edge3698 edge3702 vertices
vertex3365 vertex3371
face link face688 face698 edges edge3702 edge3706 vertices
vertex3371 vertex3377
face link face698 face708 edges edge3706 edge3710 vertices
vertex3377 vertex3383
face link face708 face718 edges edge3710 edge3714 vertices
vertex3383 vertex3389
face link face718 face728 edges edge3714 edge3718 vertices
vertex3389 vertex3395
face link face728 face738 edges edge3718 edge3722 vertices
vertex3395 vertex3401
face link face738 face748 edges edge3722 edge3726 vertices
vertex3401 vertex3407
face link face748 face758 edges edge3726 edge3730 vertices
vertex3407 vertex3413
face link face758 face768 edges edge3730 edge3734 vertices
vertex3413 vertex3419
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LINKING THE TOP OF THE CHANEL OUTBOXES
face modify face1256 side vertex6322 vertex6321
face modify face1263 side vertex6322 vertex6321
face modify face1260 side vertex6397 vertex6396
92
face link face1256 face1260 edges edge6803 edge6923 vertices
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93
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LINKING THE BOTTOM OF THE CHANEL OUTBOXES
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94
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95
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TOP SIDE BOX beginning of channel
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TOP SIDE BOXES
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96
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TOP SIDE BOX END OF CHANNEL
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TOP SIDE BOX BACK OF CHANNEL
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vertex8 vertex84 reverse
BOTTOM SIDE BOX
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97
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MESHING BEGINS HERE
BOUNDARY LAYERS BEGINS HERE
BOUNDARY LAYER FOR THE bottom of plenum
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer1 face face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
98
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 edge edge97
edge4748 edge106 edge6946 edge6947 edge107 edge4749
edge4750 edge116 edge6972 edge6973 edge117 edge4751
edge4752 edge126 edge6998 edge6999 edge127 edge4753
edge4754 edge136 edge7024 edge7025 edge137 edge4755
edge4756 edge146 edge7050 edge7051 edge147 edge4757
edge4758 edge156 edge7076 edge7077 edge157 edge4759
edge4760 edge166 edge7102 edge7103 edge167 edge4761
edge4762 edge176 edge7128 edge7129 edge177 edge4763
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edge4768 edge206 edge7206 edge7207 edge207 edge4769
edge4770 edge216 edge7232 edge7233 edge217 edge4771
edge4772 edge226 edge7258 edge7259 edge227 edge4773
edge4774 edge236 edge7284 edge7285 edge237 edge4775
edge4776 edge246 edge7310 edge7311 edge247 edge4777 add
MESHING THE PLENUM
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer2 face face4 face4 face5 face110
face110 edge edge99 edge8069 edge100 edge8052 edge98 add
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer4 face face1649 face1664 face1664
face1664 face1663 edge edge8052 edge98 edge100 edge8069
edge99 add
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer4 face face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face4 face2 face2 face2 face2 face2 face4
face5 face110 face110 edge edge9 edge3398 edge3399
edge3400 edge3401 edge3402 edge3403 edge3404 edge3406
edge3405 edge3407 edge3408 edge3409 edge3415 edge3410
edge3411 edge3412 edge3413 edge3414 edge3416 edge3417
edge3418 edge3419 edge3420 edge3421 edge3422 edge3423
edge3424 edge3425 edge3426 edge3427 edge3428 edge3429
edge3430 edge3431 edge3432 edge3433 edge3434 edge3435
edge3436 edge3437 edge3438 edge3439 edge3440 edge3441
edge3442 edge3443 edge3444 edge3445 edge3446 edge3447
99
edge3448 edge3449 edge3450 edge3451 edge3457 edge3452
edge3453 edge3454 edge3455 edge3456 edge3458 edge3459
edge3460 edge3461 edge3462 edge3463 edge3464 edge3465
edge3466 edge3467 edge3468 edge3469 edge3475 edge3481
edge3470 edge3471 edge3472 edge3473 edge3474 edge3476
edge3477 edge3478 edge3479 edge3480 edge3487 edge11
edge3482 edge3483 edge3484 edge3485 edge3486 edge8051
edge12 edge10 edge8034 add
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer5 face face1663 face1664 face1664
face1664 face1649 edge edge99 edge8069 edge100 edge98
edge8052 add
BOUNDARY LAYER OF THE HOLES
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer1 face face642 edge edge3534 add
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer7 face face117 face1600 edge edge4824
edge110 add
BONDARY LAYER OF THE CHANNEL
TARGET WALL BOUNDARY LAYER
BBBL
BBL
BBL
BBBL
BBL
BBL
BBBLLLLL
blayer create first $firstch growth $growthch rows $rowsch transition 1 trows 0
uniform
blayer attach b_layer8 face face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
100
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face105 face105 face106
face104 face104 edge edge2048 edge2049 edge2050 edge2051
edge2052 edge2053 edge2054 edge2055 edge2056 edge2057
edge2058 edge2059 edge2060 edge2061 edge2062 edge2063
edge2064 edge2065 edge2066 edge2072 edge2067 edge2068
edge2069 edge2070 edge2071 edge2084 edge2078 edge2073
edge2074 edge2075 edge2076 edge2077 edge2079 edge2080
edge2081 edge2082 edge2083 edge2090 edge2096 edge2085
edge2086 edge2087 edge2088 edge2089 edge2091 edge2092
edge2093 edge2094 edge2095 edge2102 edge2108 edge2097
edge2098 edge2099 edge2100 edge2101 edge2103 edge2104
edge2105 edge2106 edge2107 edge2114 edge2120 edge2109
edge2110 edge2111 edge2112 edge2113 edge2115 edge2116
edge2117 edge2118 edge2119 edge2126 edge2132 edge2121
edge2122 edge2123 edge2124 edge2125 edge2127 edge2128
edge2129 edge2130 edge2131 edge2133 edge2134 edge2136
edge2137 edge1 edge2135 edge8088 edge3 edge4 edge8105
edge2 add
blayer create first $firstch growth $growthch rows $rowsch transition 1 trows 0
uniform
blayer attach b_layer9 face face1681 face1696 face1696
face1696 face1695 edge edge2 edge8105 edge4 edge3
edge8088 add
blayer create first $firstch growth $growthch rows $rowsch transition 1 trows 0
uniform
blayer attach b_layer10 face face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face105 face105
face106 face104 face104 edge edge6743 edge101
edge7336 edge7337 edge102 edge6744 edge6745 edge111
edge7373 edge7374 edge112 edge6746 edge6747 edge121
edge7410 edge7411 edge122 edge6748 edge6749 edge131
edge7447 edge7448 edge132 edge6750 edge6751 edge141
edge7484 edge7485 edge142 edge6752 edge6755 edge6753
edge151 edge6754 edge7521 edge7522 edge152 edge161
101
edge6756 edge6757 edge7558 edge7559 edge162 edge171
edge7595 edge7596 edge172 edge6758 edge6759 edge181
edge7632 edge7633 edge182 edge6760 edge6761 edge191
edge7669 edge7670 edge192 edge6762 edge6763 edge6767
edge6765 edge201 edge7706 edge7707 edge202 edge6764
edge211 edge6766 edge7743 edge7744 edge212 edge6769
edge221 edge6768 edge7780 edge7781 edge222 edge6771
edge231 edge6770 edge7817 edge7818 edge232 edge241
edge7854 edge7855 edge242 edge6772 edge89 edge8070
edge91 edge92 edge8087 edge90 add
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer11 face face4 face5 face2 face5
face110 face2 edge edge8 edge8 edge6 edge7 edge7
edge5 add
blayer create first $firstch growth $growthch rows $rowsch transition 1 trows 0
uniform
blayer attach b_layer12 face face106 face104 face103 face105
edge edge87 edge87 edge85 edge88 add
BOUNDARY LAYERS ENDS HERE
edge picklink edge6948 edge6949
edge mesh edge6949 edge6948 successive ratio1 1 intervals $NumbNodes
edge picklink edge6950
edge mesh edge6950 successive ratio1 1 intervals ($NumbNodes2)
face mesh face1450 map
edge picklink edge6963 edge6947
edge mesh edge6947 edge6963 successive ratio1 1 intervals ($Numbtelnodes+$rows)
face mesh face912 map
edge picklink edge6961 edge6960 edge7889 edge7890
edge mesh edge7890 edge7889 edge6960 edge6961 successive ratio1 1
intervals ($NumbNodes)
edge picklink edge6959 edge7891
edge mesh edge7891 edge6959 successive ratio1 1 intervals ($NumbNodes2)
face mesh face1452 map
face mesh face1600 face117 map
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer12 face face2 face110 face5 face110
face2 face4 face5 face4 edge edge5 edge5 edge7
edge7 edge6 edge6 edge8 edge8 add
Meshing constants
$NumbNodes=5
$Numbtelnodes=6
$PLobnodes=5
$Chobnodes=5
$Plbenodes=($NumbNodes(4)+$rows)
$plsqnodes=($NumbNodes(3))
102
$Pllsnodes=($NumbNodes+$rows)
$Nojetcells=10
edge picklink edge3686 edge3402
edge mesh edge3686 edge3402 successive ratio1 1 intervals ($PLobnodes)
edge picklink edge6744 edge6864
edge mesh edge6864 edge6744 successive ratio1 1 intervals 5
face link face1260 face375 edges edge6923 edge2440 vertices
vertex6397 vertex2251 reverse
face modify face915 side vertex4479 vertex4480
face mesh face915 face918 face911 map size 1
face mesh face1260 face1263 face1256 map size 1
edge picklink edge8068 edge8053
edge mesh edge8068 edge8053 successive ratio1 1 intervals ($Plbenodes)
edge picklink edge8086 edge8071
edge mesh edge8071 edge8086 successive ratio1 1 intervals ($CHbenodes)
edge delete edge8053 edge8068 keepsettings onlymesh
edge mesh edge8053 edge8068 successive ratio1 1 intervals ($Plbenodes)
edge delete edge8090 keepsettings onlymesh
edge picklink edge8090
edge mesh edge8090 successive ratio1 1 intervals ($plsqnodes)
edge delete edge8054 keepsettings onlymesh
edge picklink edge8054
edge mesh edge8054 successive ratio1 1 intervals ($plsqnodes)
face mesh face1647 face1679 face1678 face1646 face1633
face1665 map
edge delete edge98 edge8087 keepsettings onlymesh
edge picklink edge8087 edge98
edge mesh edge98 successive ratio1 1 intervals ($Pllsnodes)
edge mesh edge8087 successive ratio1 1 intervals ($CHlsnodes)
face mesh face1648 face1680 map
COOPERING ALL THE JETS
volume mesh volume3 cooper source face1600 face1452 face117
face1514 face1512 face115 intervals ($Nojetcells)
volume mesh volume5 cooper source face1456 face1602 face124
face1518 face1520 face122 intervals ($Nojetcells)
volume mesh volume7 cooper source face1460 face1604 face131
face1526 face1524 face129 intervals ($Nojetcells)
volume mesh volume9 cooper source face1464 face1606 face138
face1532 face1530 face136 intervals ($Nojetcells)
volume mesh volume11 cooper source face1468 face1608 face145
face1538 face143 face1536 intervals ($Nojetcells)
volume mesh volume13 cooper source face1472 face1610 face152
face1544 face1542 face150 intervals ($Nojetcells)
volume mesh volume15 cooper source face1476 face1612 face159
face1550 face1548 face157 intervals ($Nojetcells)
volume mesh volume17 cooper source face1480 face1614 face166
face1556 face1554 face164 intervals ($Nojetcells)
volume mesh volume19 cooper source face1484 face1616 face173
face1562 face171 face1560 intervals ($Nojetcells)
volume mesh volume21 cooper source face1488 face1618 face180
face1568 face1566 face178 intervals ($Nojetcells)
103
volume mesh volume23 cooper source face1492 face1620 face187
face1574 face1572 face185 intervals ($Nojetcells)
volume mesh volume25 cooper source face1496 face1622 face194
face1578 face1580 face192 intervals ($Nojetcells)
volume mesh volume27 cooper source face1624 face1500 face201
face1586 face1584 face199 intervals ($Nojetcells)
volume mesh volume29 cooper source face1504 face1626 face208
face1592 face1590 face206 intervals ($Nojetcells)
volume mesh volume31 cooper source face1628 face1508 face215
face1596 face1598 face213 intervals ($Nojetcells)
volume mesh volume30 cooper source face1506 face1052 face1594
face1397 intervals ($Nojetcells)
volume mesh volume28 cooper source face1502 face1042 face1588
face1387 intervals ($Nojetcells)
volume mesh volume26 cooper source face1498 face1032 face1582
face1377 intervals ($Nojetcells)
volume mesh volume24 cooper source face1494 face1022 face1576
face1367 intervals ($Nojetcells)
volume mesh volume22 cooper source face1490 face1012 face1570
face1357 intervals ($Nojetcells)
volume mesh volume20 cooper source face1486 face1002 face1564
face1347 intervals ($Nojetcells)
volume mesh volume18 cooper source face1482 face992 face1558
face1337 intervals ($Nojetcells)
volume mesh volume16 cooper source face1478 face982 face1552
face1327 intervals ($Nojetcells)
volume mesh volume14 cooper source face1474 face972 face1546
face1317 intervals ($Nojetcells)
volume mesh volume12 cooper source face1470 face962 face1540
face1307 intervals ($Nojetcells)
volume mesh volume10 cooper source face1466 face952 face1534
face1297 intervals ($Nojetcells)
volume mesh volume8 cooper source face1462 face942 face1528
face1287 intervals ($Nojetcells)
volume mesh volume6 cooper source face1458 face932 face1522
face1277 intervals ($Nojetcells)
volume mesh volume4 cooper source face1454 face922 face1516
face1267 intervals ($Nojetcells)
volume mesh cylinder cooper source face1450 face912 face1510
face1257 intervals ($Nojetcells)
window modify invisible mesh
volume mesh volume34 cooper source face1649 face1650 face1651
face1652 face1653 face1654 face1655 face1664 face1639
face1638 face1637 face1636 face1635 face1634 face1633
face1648 face1610 face1608 face1606 face1604 face1602
face1600 face1472 face962 face1468 face952 face1464
face942 face1460 face932 face1456 face922 face1452
face912 face915 face918 face911 face925 face928
face920 face935 face938 face930 face945 face948
face940 face955 face958 face950 face965 face968
face960 face694 face689 face684 face679 face674
face669 face664 face659 face654 face649 face644
face640 face697 face696 face692 face687 face686
face682 face677 face676 face672 face667 face666
104
face662 face657 face656 face652 face647 face646
face642 face695 face698 face690 face685 face688
face680 face675 face678 face670 face665 face668
face660 face655 face658 face650 face645 face648
face641 face152 face1470 face145 face1466 face138
face1462 face131 face1458 face124 face1454 face117
face1450 face1657 face1658 face1659 face1660 face1661
face1662 face1663 face788 face1656 face1474 face159
face1647 face1646 face1645 face1644 face1643 face1642
face1641 face1640 face1478 face1628 face1626 face1624
face1622 face1620 face1618 face1616 face1614 face1612
face1508 face1052 face1504 face1042 face1500 face1032
face1496 face1022 face1492 face1012 face1488 face1002
face1484 face992 face1480 face982 face1476 face972
face975 face978 face970 face985 face988 face980
face995 face998 face990 face1005 face1008 face1000
face1015 face1018 face1010 face1025 face1028 face1020
face1035 face1038 face1030 face1045 face1048 face1040
face1050 face114 face1058 face774 face769 face764
face759 face754 face749 face744 face739 face734
face729 face724 face719 face714 face709 face704
face699 face777 face776 face772 face767 face766
face762 face757 face756 face752 face747 face746
face742 face737 face736 face732 face727 face726
face722 face717 face716 face712 face707 face706
face702 face779 face784 face787 face775 face778
face770 face765 face768 face760 face755 face758
face750 face745 face748 face740 face735 face738
face730 face725 face728 face720 face715 face718
face710 face705 face708 face700 face782 face786
face785 face6 face780 face1055 face215 face1506
face208 face1502 face201 face1498 face194 face1494
face187 face1490 face180 face1486 face173 face1482
face166 intervals ($Plzdnodes)
volume delete body onlymesh
volume mesh body cooper source face1689 face1690 face1691
face1692 face1693 face1681 face1682 face1683 face1684
face1685 face1686 face1687 face1688 face1696 face1671
face1670 face1669 face1668 face1667 face1666 face1665
face1677 face1676 face1675 face1674 face1673 face1672
face1680 face199 face1584 face1377 face192 face1578
face1367 face185 face1572 face1357 face178 face1566
face1347 face171 face1560 face1337 face164 face1554
face1327 face157 face1548 face1317 face150 face1542
face1307 face143 face1536 face1297 face136 face1530
face1287 face129 face1524 face1277 face122 face1518
face1267 face115 face1512 face1257 face1380 face1383
face1375 face1370 face1373 face1365 face1360 face1363
face1355 face1350 face1353 face1345 face1340 face1343
face1335 face1330 face1333 face1325 face1320 face1323
face1315 face1310 face1313 face1305 face1300 face1303
face1295 face1290 face1293 face1285 face1280 face1283
face1275 face1270 face1273 face1265 face1260 face1263
face1256 face209 face374 face370 face384 face379
face394 face389 face404 face399 face414 face409
105
face424 face419 face434 face429 face444 face439
face454 face449 face464 face459 face474 face469
face484 face479 face494 face489 face377 face376
face372 face387 face386 face382 face397 face396
face392 face407 face406 face402 face417 face416
face412 face427 face426 face422 face437 face436
face432 face447 face446 face442 face457 face456
face452 face467 face466 face462 face477 face476
face472 face487 face486 face482 face497 face496
face492 face375 face378 face371 face385 face388
face380 face395 face398 face390 face405 face408
face400 face415 face418 face410 face425 face428
face420 face435 face438 face430 face445 face448
face440 face455 face458 face450 face465 face468
face460 face475 face478 face470 face485 face488
face480 face495 face498 face490 face1 face1586
face1582 face1580 face1576 face1574 face1570 face1568
face1564 face1562 face1558 face1556 face1552 face1550
face1546 face1544 face1540 face1538 face1534 face1532
face1528 face1526 face1522 face1520 face1516 face1514
face1510 face1403 face518 face1588 face1592 face1594
face1694 face1695 face1598 face1679 face1678 face515
face516 face510 face500 face508 face505 face213
face1596 face1397 face206 face1590 face1387 face517
face514 face512 face502 face506 face507 face509
face499 face504 face1400 face1395 face1385 face1390
face1393 intervals ($Chzdnodes)
BOUNDARY CONDITIONS
physics create Symmetry btype SYMMETRY face face2 face103
face211 face204 face197 face190 face183 face176
face169 face162 face155 face148 face141 face134
face127 face120 face112
physics create Wall btype SYMMETRY face face110 face5 face1649
face1664 face918 face915 face911 face925 face1650
face928 face920 face935 face938 face930 face1652
face1651 face948 face945 face940 face1653 face1654
face958 face955 face950 face1655 face965 face968
face960 face978 face975 face970 face1656 face114
face985 face988 face980 face995 face998 face990
face1657 face1005 face1008 face1000 face1658 face1015
face1018 face1010 face1659 face1028 face1025 face1020
face1035 face1660 face1038 face1030 face1045 face1661
face1048 face1040 face1055 face1662 face1058 face1050
face1663 face4 face1395 face1679 face1403 face1400
face1680 face1385 face1678 face1393 face1390 face1375
face1677 face1383 face1380 face1676 face1365 face1373
face1370 face1675 face1355 face1363 face1360 face1674
face1345 face1353 face1350 face1673 face1335 face1343
face1340 face1672 face1325 face1333 face1330 face209
face1315 face1323 face1320 face1671 face1305 face1313
face1310 face1670 face1295 face1303 face1300 face1669
106
face1285 face1293 face1290 face1668 face1275 face1283
face1280 face1667 face1265 face1273 face1270 face1666
face1256 face1263 face1260 face1665 face214 face91
face207 face85 face200 face79 face193 face73 face186
face67 face179 face61 face172 face55 face165 face49
face158 face43 face151 face37 face144 face31 face137
face25 face130 face19 face123 face13 face116 face8
physics modify Wall btype WALL face face110 face5 face1649
face1664 face918 face915 face911 face925 face1650
face928 face920 face935 face938 face930 face1652
face1651 face948 face945 face940 face1653 face1654
face958 face955 face950 face1655 face965 face968
face960 face978 face975 face970 face1656 face114
face985 face988 face980 face995 face998 face990
face1657 face1005 face1008 face1000 face1658 face1015
face1018 face1010 face1659 face1028 face1025 face1020
face1035 face1660 face1038 face1030 face1045 face1661
face1048 face1040 face1055 face1662 face1058 face1050
face1663 face4 face1395 face1679 face1403 face1400
face1680 face1385 face1678 face1393 face1390 face1375
face1677 face1383 face1380 face1676 face1365 face1373
face1370 face1675 face1355 face1363 face1360 face1674
face1345 face1353 face1350 face1673 face1335 face1343
face1340 face1672 face1325 face1333 face1330 face209
face1315 face1323 face1320 face1671 face1305 face1313
face1310 face1670 face1295 face1303 face1300 face1669
face1285 face1293 face1290 face1668 face1275 face1283
face1280 face1667 face1265 face1273 face1270 face1666
face1256 face1263 face1260 face1665 face214 face91
face207 face85 face200 face79 face193 face73 face186
face67 face179 face61 face172 face55 face165 face49
face158 face43 face151 face37 face144 face31 face137
face25 face130 face19 face123 face13 face116 face8
physics create Heat Fluxes btype WALL face face104 face106
face370 face379 face389 face372 face382 face392
face371 face380 face390 face378 face388 face398
face376 face386 face396 face374 face384 face394
face377 face387 face397 face375 face385 face395
face1681 face1682 face1683 face1684 face1696 face402
face412 face422 face432 face442 face400 face410
face420 face430 face440 face408 face418 face428
face438 face448 face406 face416 face426 face436
face446 face404 face414 face424 face434 face444
face407 face417 face427 face437 face447 face405
face415 face425 face435 face445 face1688 face1685
face1686 face1687 face452 face462 face472 face482
face492 face1693 face450 face460 face470 face480
face490 face1692 face458 face468 face478 face488
face498 face1 face456 face466 face476 face486 face496
face454 face464 face474 face484 face494 face457
face467 face477 face487 face497 face1691 face455
face465 face475 face485 face495 face1689 face1690
face518 face502 face512 face1695 face500 face510
face1694 face508 face506 face516 face504 face514
face507 face517 face515 face505
physics create Mass flow inlet btype SYMMETRY face face640 face649
107
face659 face642 face652 face662 face672 face641
face650 face660 face670 face648 face658 face668
face678 face646 face656 face666 face676 face644
face654 face664 face674 face647 face657 face667
face677 face645 face655 face665 face675 face1633
face1634 face1635 face1636 face1637 face1648 face679
face689 face699 face682 face692 face702 face712
face680 face690 face700 face710 face688 face698
face708 face718 face6 face686 face696 face706 face716
face684 face694 face704 face714 face687 face697
face707 face717 face685 face695 face705 face715
face1640 face1638 face1639 face719 face729 face739
face749 face722 face732 face742 face752 face762
face720 face730 face740 face750 face760 face728
face738 face748 face758 face768 face726 face736
face746 face756 face766 face724 face734 face744
face754 face764 face727 face737 face747 face757
face767 face725 face735 face745 face755 face765
face1645 face1641 face1642 face1643 face1644 face788
face769 face779 face772 face782 face770 face780
face778 face776 face786 face774 face784 face777
face787 face775 face785 face1647 face1646
physics create Outflow btype OUTFLOW face face105
108
REFERENCES
Al-Aqal O M A 2003 ldquoHeat transfer distributions on the walls of a narrow channel
with jet impingement and cross flowrdquo PhD Thesis University of Pittsburgh
Bunker Ronald S 2007 Gas Turbine Heat Transfer Ten Remaining Hot Gas Path
Challengesrdquo Journal of Turbomachinery April Vol 129 pp 193-201
Downs James P Landis Kenneth K 2009 ldquoTurbine Cooling Systems Design- Past
Present and Futurerdquo Proceedings of ASME Turbo Expo 2009 June 8-12 2009
GT2009-59991
Florschuetz LW Berry R A Metzger D E 1980 ldquoPeriodic streamswise variations of
heat transfer coefficients for inline and staggered arrays of circular jets with cross
flow of spent airrdquo ASME J of Heat Transfer 102 p 132-137
Florschuetz L W Truman C R Metzger D E 1981 ldquoStreamwise Flow and Heat
Transfer Distributions for Jet Array Impingement with Cross flowrdquo Journal of
Heat Transfer Vol 103 pp 337
Florschuetz L W Isoda Y 1983 ldquoFlow Distributions and Discharge Coefficient for
Jet Array Impingement With Initial Cross flowrdquo Journal of Engineering for
Power Vol 105 pp 296
Incropera Frank P DeWitt D P 2002 Fundamentals of Heat and Mass Transfer John
Wiley amp Sons Inc New Jersey pp 491-493
Liu Quan Kapat J May 2006 ldquoStudy of Heat Transfer Characteristics of Impinging
Air Jet Using Pressure and Temperature Sensitive Luminescent Paintrdquo UCF
Dissertation
109
Martin H 1977 ldquoImpinging jet flow heat and mass transferrdquo Advances in heat transfer
Vol 13
Ricklick Mark Kapat J December 2009 ldquoCharacterization of an Inline Row
Impingement Channel for Turbine Blade Cooling Applicationsrdquo UCF
Dissertation
Zuckerman N Lior N 2005 ldquoImpingement Heat transfer Correlations and Numerical
Modelingrdquo Journal of Heat Transfer Vol 127 pp 544
x
Total Pressure (kPa)
Pr Prandtl Number
Heat Flux (Wm2)
Total Heat Input (W)
Heater Resistance (ohm)
Re Reynolds Number
SW Side Wall
Temperature (K)
TW Target Wall
Voltage Potential
Streamwise Location
y Spanwise Location
z Height from Target Wall
X Streamwise Distance (m)
Y Spanwise Distance (m)
Z Impingement Height (m)
Thermal Performance Parameter
Ratio of Specific Heats
Air Density (kgm3)
Subscripts
C Cold
H Hot
xi
Carnot Describing a Carnot cycle
Exit
Effective
Quantity Lost to the Environment
Reference Value
Wall Value
Base Line Value
1
CHAPTER ONE INTRODUCTION
11 Gas Turbine as a Heat Engine
Gas turbine is a form of heat engine where the hot reservoir is created by the
combustion of fuel and the cold reservoir is the open atmosphere It is well known that
the maximum efficiency of any heat engine is denoted as the Carnot efficiency
A more accurate cycle is used to describe the processes inside a gas turbine ndash the
Brayton Cycle The Brayton cycle as seen in Figure 1 is composed of four processes In
a gas turbine air is drawn in at state 1 it is compressed until it reaches state 2 The
compressed air is mixed with fuel and ignited as it passes through the combustor The hot
air then passes through the turbines where work is extracted The process from state 4 to
state 1 happens throughout the atmosphere therefore the Brayton cycle is an open loop
cycle as the same air is not continuously being fed through the motor
Figure 1 Brayton Cycle Flow Path and T-s Diagram (Adapted from UPTB Website)
The Brayton cycle has an isentropic efficiency similar to the carnot the Brayton
cycle efficiency is defined as
2
It can be seen that increasing the temperature at which air enters the first turbine
stage T3 increases the overall efficiency of the turbine Moreover increasing the
pressure ratio Pr also aids in the increase of the efficiency One of the hurdles of
increasing T3 is the fact that the post combustion gas is a few hundred degrees Celsius
above the melting point of the super alloys used to make the turbine stator vanes and
rotor blades For this reason it is important to cool the hot components of the gas turbine
in order to assure a reasonable life for the machine
12 Cooling of Hot Components
The transition duct that connects the combustor to the first stage turbine as well
as the first stage of the turbine are the parts that are subject to the harshest thermal
loadings and must therefore be cooled aggressively to maintain them in working
conditions for a long period of time Since the first stage guide vanes and rotor extrude
into the flow they are subject to the highest convection coefficients These heat transfer
coefficients can reach up to 4000 Wm2K (Downs 2009) Figure 2 shows the different
magnitudes of convection coefficient around the blade High heat transfer coefficients
occur where the air stagnates into the leading edge of the airfoil This high heat transfer
region is not only caused by the lack of a thermal boundary layer to protect the airfoil but
also because the effective heat transfer driving temperature is the recovery temperature
At the high Mach numbers that occur in turbines the ratio of total to static temperatures
is significant causing the leading edge to have the highest effective heat load Another
3
peak occurs on the suction side of the blade as the boundary layer created by the airfoil
switches from being a laminar boundary layer into a turbulent one Due to the nozzling
effect of the turbine rotor and stators the flow gathers speed toward the trailing edge of
the airfoil leading to higher convection coefficients on the pressure side of the airfoil
Figure 2 Thermal Loading Throughout a Turbine Blade (Daniels 1982)
Simple convection channels were implemented in the early nineteen sixties as
years passed the cooling techniques became more and more sophisticated allowing the
free stream temperature to increase to previously impossible levels Currently the use of
film cooling coupled with backside impingement leads the turbine cooling technology
The trend of allowable turbine inlet temperature is shown in Figure 3 from this figure it
can be seen that the allowable free stream temperature has increased around 600 degrees
in the past 50 years The addition of thermal barrier coatings also helps in the increase in
allowable combustion temperatures by creating an extra resistance that the heat needs to
move through as it moves from the combustion gasses into the coolant air It is impotatnt
to notice that as seen in Figure 4 the increase in turbine inlet temperatures is done with
the combined benefits of new alloys TBC and cooling technologies
4
Figure 3 Allowable Turbine Inlet Temperature vs Cooling Techniques over the Years (Clifford 1985)
Figure 4 Turbine Inlet Temperature Increase with the help of TBC New Super Alloys and Cooling
Technologies (Kapat and Kiesow Lectures 2010)
The cooling of inlet guide vanes can be done with the use of impingement inserts
inside the airfoils As air passes through the miniscule holes in the inserts a jet is formed
which then impinges on the wall of the airfoil producing one of the largest single phase
heat transfer coefficients This already impinged coolant air is then bled out as film
5
cooling as well as bled out through the trailing edge Figure 5 shows a stator vane with
the impingement insert in black the film cooling extraction as well as the trailing edge
bleed
Figure 5 Turbine Stator Cooled with Impingement Coupled with Film Cooling (Florschuetz 1980)
The cooling of turbine airfoils with the use of an impingement insert is only
possible in stationary components as the rotating ones are subject to centrifugal loadings
making it unfeasible to cool them with this setup Rotor blades are typically cooled with
serpentine passages that have heat transfer enhancing features such as ribs dimples and
other turbulators these serpentine passages are located in the mid chord of the blade On
the trailing edge a bank of pins are used to obtain high convective coefficients in the thin
region the coolant is the bled out to compensate for the boundary layer created around
the airfoil Rows of impingement holes cool the leading edge The spent air is then bled
out through showerhead cooling Figure 6 and Figure 7 show in detail the cooling
channels around two similar airfoils airfoils
6
Figure 6 Rotor Blade Cooling Configuration (Gladden 1988)
Figure 7 Cross-section of Turbine Airfoil with Cooling Channels (Han et al 1984)
7
The coolant air is bled out from the later stages of the compressor This air is
expensive as it has been compressed and not under gown the heat addition by
combustion It is imperative that the minimum amount of coolant is used in these cooling
configurations The cooling must also be as uniform as possible to reduce thermal
stresses within the blades leading to a higher component life Figure 8 shows freestream
metal and coolant temperatures of the flow blade and coolant air It can be seen that a
decrease of 25degrees in the surface temperature of the blade can provide an airfoil with
twice the working life Impingement cooling has great potential to provide high heat
transfer coefficients at a small flow rate Impingement of a jet onto a surface provides
high heat transfer coefficients due to a starting boundary layer as well as its high
turbulence When the jet is located around 3 diameters from the target surface the heat
transfer profile has two peaks one located at the stagnation region and the other located
between one and 3 diameters from the stagnation region As the jet is moved away from
the target wall the secondary peak diminishes leaving a profile with a maximum at the
stagnation region decreasing radialy
Figure 8 Relative Temperatures for Hot Gas Metal Temperature and Coolant Temperature (Cardwell 2005)
Cardwell N D 2005
8
Figure 9 shows a diagram of a jet impinging on a target surface The potential
core is the part of the jet that has not been affected by the surrounding stagnant fluid As
the jet moves towards the target wall its momentum diffuses into the surrounding fluid
decreasing the velocity at which it reaches the target wall and potentially decreasing the
corresponding heat transfer coefficient Studies have shown (Martin 1973 for example)
that the potential core may last anywhere between 7 to 10 diameters The successful
impingement of the potential core yields significantly higher heat transfer coefficients
than a fully diffused jet this comes however at a cost of higher pressure drop across the
jet plate as well as a highly non uniform heat transfer profile
Figure 9 (a) The Development of the Wall Jet (b) Jet Diffusion to Surroundings (Liu 2006)
9
CHAPTER TWO LITERATURE REVIEW
21 Impingement Literature Cornerstone
From the early days of simple convective cooling channels in turbine airfoils
studies have been done on modes of enhancing heat transfer coefficients while
maintaining a low pressure drop and minimum mass flow rate Heat transfer
characteristics of single round nozzle impingement were studied in the late 1960rsquos and
early 1970rsquos The collected works of many authors is combined into ldquoHeat and Mass
Transfer between Impinging Gas Jets and Solid Surfacesrdquo by Holger Martin 1977 The
paper collects works from multiple authors who studied single round nozzle impingement
effects on heat and mass transfer coefficients In this compilation non dimensional jet to
target spacing was studied they ranged from ZD=12-10 providing plots of Sherwood
number as a function of radius for four different jet to target spacings The local
Sherwood number was also given for a slot jet for HS ranging from 5 to 20 Studies on
impingement jet arrays were also gathered alongside an array of slot jets Correlations
were given for multiple setups present in the paper Circular jet arrays and slot arrays are
studied in detail with both analytical and experimental approaches The paper also
combines studies done on swirling jets turbulence enhancers on the target surface
impingement on concave surfaces and angle of attack variations Optimization studies
were also done to find the optimal spacing for round and slot jet arrays
Florschuetz studied the heat transfer characteristics of an array of jets impinging
on a flat surface This study was guided towards finding an optimal spacing for an array
for jets used to cool the midchord of turbine airfoils similar to that found in Figure 5 His
main contributions include a Nusselt number correlation as a function of jet to target
10
spacing jet Reynolds number and other flow and geometric parameters He found that an
increase in hole spacing and channel height resulted in a decrease of heat transfer He
also provided a one dimensional jet mass flux and channel mass flux correlations
His Nusselt number correlation takes the form of
Where A B and n are dependent by the two different types of arrays inline or staggered
Liu studied new techniques in temperature and pressure measurements of a single
slot jet with the use of temperature sensitive paint or TSP and pressure sensitive paint or
PSP In his work both measurement techniques are explained in detail Since TSP is the
only tool from that study currently used in this work it will be explained further in the
experimental setup section
11
22 Relevant Impingement Channel Studies
Al-Aqal 2003 studied three different types of impingement channels The use of
TLC was implemented in this work to obtain heat transfer distributions for the target
wall The three different configurations varied the number of holes in the streamwise and
spanwise directions The first channel had a single row of 6 streamwise jets the second
consisted of 2 rows of 12 streamwise holes summing up to a total of 24 holes The last
channel is a triple spanwise row with 18 streamwise jets This last geometry is the most
similar to the one present in the current study The third geometry will be used to
compare results There are differences however the total width of the channel is of 16
diameters as opposed to 8 in this study The streamwise jet spacing is also different Al-
Aqal used an XD of 65 compared to XD = 5 in this study The jet to target plate
spacings are similar on two occasions as he studied a ZD=4 6 and 8 while this work
uses a ZD = 6 8 and 10 Average jet Reynolds numbers also fall within the range of this
study as they range between 5000 and 33000 The author provides span averaged plots
for all cases and Reynolds numbers convenient when comparing the results
Ricklick 2009 studied a channel similar to the one found in this study His
channel was composed of a single row of 15 jets with a YcD = 4 XD = 5 and 15 and
ZD = 1 3 and 5 Two channels were tested one was pressure fed while the other was fed
by suction TSP was used to gather temperature data of all four wetted surfaces on the
pressure channel and two surfaces on the suction channel Since the maximum jet Mach
number was less than 03 the flow was assumed to be incompressible leading to the
conclusion that both channels contain identical flow patterns Thin foil heaters were used
to create the required heat flux for the channel Besides channel geometry Reynolds
12
numbers and heater geometry Ricklicksrsquo experimental setup is identical to the one
presented in this work The author also provided an ample comparison of his results to
literature He provided thermal performances of the entire channel at different Reynolds
numbers and channel heights
A small CFD study was also done A paved mesh was created on the target wall
with finer mesh near the impingement locations The resulting y+ at the wall was higher
than one yielding potentially faulty heat transfer values however this is acceptable since
the CFD was used as a tool to better understand the flow physics and help understand the
experimental heat transfer profiles
23 Computational Studies on Impingement Channels
El-Gabry did a numerical study of jet impingement with cross flow Two different
turbulence models were compared in their ability to predict surface Nusselt number The
Yang-Shih and standard k-ε models were used to compute the flow generated by jets
angled at 30 60 and 90 degrees with cross flow The computational results were
compared to previous experimental work by El-Gabry Comparisons to experimental
results at ZD = 1 and 2 90deg injection angle between Yang-Shih and standard k-ε The
error in the average Nu from the experimental results and both turbulence models were
calculated It was found that the Yang-Shih model behaved well at low Reynolds
numbers with the average Nusselt number being 5 off from the experimental value
while the standard k-ε was off my 94 As jet Reynolds number was increased the error
of the standard k-ε model dropped to as low as 39 while the error from the Yang-shih
model increased to -76 The span average plots show the experimental data Nusselt
number alongside the span averages of the results acquired by the Yang-Shih and
13
standard k-ε models High Nusselt numbers occur at the impingement location decreasing
thereafter after another impingement location is found The frequencies of these
variations are all the same for the experimental and the two numerical solutions The
amplitude of fluctuations between the impingement locations and the areas in between
are much larger for both of the numerical results however the Yang-Shih model over
predicts at the high Reynolds number for the ZD=2 case Since the amplitude of
fluctuations is greater for the CFD solutions it is important to note that even though the
error in average Nusselt number is not great the actual differences in the profile are much
greater upwards of 20 difference of heat transfer coefficients between the experimental
and numerical heat transfer peaks Other variations were studied (Injection angles for
example) but will not be discussed as their importance to the current study is minimal
Zuckerman compared a much wider set of turbulence models in their ability to
successfully predict Nusselt numbers caused by jet impingement The models tested were
k ndash ε k-ω Reynolds Stress Model algebraic stress models shear stress transport and
lastly the υ2f turbulence model DNS runs are extremely time consuming to run
therefore LES was run on its behalf to provide results for the unsteady turbulence
models The paper summarizes all the different models used their computational cost
impingement heat transfer coefficient and their ability to predict the second peak in heat
transfer As expected DNSLES provide the best prediction of both stagnation and
secondary peak heat transfer coefficient however this comes at a large computational
cost The k ndash ε and k-ω provide poor heat transfer results for the stagnation region where
they can have 30 error from the correct value The Realizable k ndash ε model provides
14
better heat transfer results while still maintaining a low computational cost The highest
accuracy to cost ratio was achieved by the υ2f model where it predicts the heat transfer
coefficient for the surface with a minimum of 2 error while not being as expensive as
the other unsteady models such as DNS and LES Ideally the CFD portion of this work
would be run with the υ2f model however since the code used to run the simulation
FLUENT does not have the υ2f model a realizable k ndash ε model will be used with
enhanced wall functions for both thermal and velocity gradients
15
CHAPTER THREE EXPERIMENTAL SETUP AND TECHNIQUES
31 Temperature Measurements with TSP
Temperature sensitive paint or TSP provides the capability of measuring
temperatures over the painted area This measurement technique supersedes the
advantages of other temperature measurement devices such as thermocouples because it
provides the user with data over a large area rather than point temperatures given by
thermocouples
Uni-Coat TSP is purchased from ISSI It is very robust to different working
conditions Calibration done on one batch of paint can be used for multiple cans as the
product is highly consistent The paint is calibrated in a dark booth a painted coupon is
placed on the hot side of a thermoelectric heat pump working on the Peltier effect
thermal paste is used to minimize contact resistance between the hot side and the TSP
coupon Calibrated thermocouples are placed in between the TSP and the thermoelectric
heat pump A reference temperature and picture are taken and the calibration commences
At least 5 or 6 data points should be taken to form the calibration Intensity ratios are
taken between the hot and cold pictures They are then plotted versus their corresponding
temperature
The paint consists of fluorescent molecules suspended in a binder These
molecules with a certain wavelength of light will be exited to a higher energy level The
molecules then can dissipate some of the energy by transferring it vibrationally to its
neighboring binder particles and dissipate the remainder of the energy by radiating it as a
photon as the molecule comes down to its original ground state Since the amount of
16
energy that the particle can transmit to others through vibration is directly proportional on
temperature and the total initial energy is fixed by measuring the ratio of the intensity at
a known temperature (reference picture) and intensity of the unknown temperature
feeding it through the correlation the unknown temperature can be found to an
uncertainty of 1 K Figure 10 shows a simplified Jablonski diagram adapted from the
suppliers website The blue arrows signify the blue light used to excite the luminescent
molecule Tris(22rsquo-bipyridyl) Ruthenium(II) Chloride Hexahydrate with a shellac binder
in our case The shellac binder is impermeable to oxygen opposite of that found in PSP
due to PSP relying on the presence of oxygen for it to function Once the particle is
excited it can give off the energy in two different ways one is by emitting it back out as
another photon of the same energy and therefore wavelength The second mode of the
particle to lose its energy is through vibrational relaxation This second process is directly
dependent on the temperature ie the higher the temperature the higher the probability
for it to lose energy to its surroundings Once it loses some energy to the surrounding
particles it releases the remainder of the energy as a photon of less energy of that which
excited it originally hence why a long pass filter is installed in the CCD camera For a
more descriptive explanation of the way TSP works refer to Liu 2006
17
Figure 10 Simplified Jablonski Diagram (Adapted from ISSI Website)
Throughout the past two years there have been numerous projects at CATER that
have used TSP Painting surfaces with TSP should be done carefully by someone who
has experience with spray painting since every single can costs $500 A single can should
be able to paint an area the size of an acrylic plate that is 36rdquo wide and 24rdquotallThe
sidewalls and the target wall of the impingement channel were painted with the use of
less than one can Painting on different surfaces is difficult for example when painting
Rohacell the paint canister can be held very close to the surface while spraying due to
the surface being somewhat porous and rough however when painting straight onto
metal heater strips the can should be placed as far back as possible for the first run
Ideally for the first pass through only a slight mist should be applied If the can is being
held too close to the surface the paint will run Figure 11 shows a set of heater strips that
has been painted too closely leading the paint to drip down Ideally the paint would be
applied to the surface in as many coats as possible Of course this would be time
18
demanding and impractical therefore with the knowledge that I have gained through the
multiple TSP paintings on different surfaces I have compiled a list of TSP dos and
donrsquots
Dos
Clean the surface to be painted with acetone or break parts cleaner Break
parts cleaner is preferable over acetone as it does not leave an oily residual
after cleaning
Paint the first coat as thin as possible Most of the surface should not be
covered There should be an even mist of miniscule TSP circles This will
give the later coats something to attach to
When positioning the test section to paint make sure to wipe it one last
time as small dust particles may have attached to the surface
Stop if you see small bumps in the paint This is caused by dust particles
collecting all the paint around it while it is still wet due to surface tension
Clean the surface and repaint This should be noticeable in the first few
coats If you see this pattern happening do not continue thinking it will be
covered by future coats What will happen is the problem will get worse
and worse ultimately the surface will have to be cleaned again and
repainted
When painting test sections try to paint the smallest section as possible
This will not only save paint but will make it very simple for the post
processing code to crop out the unpainted areas
19
Let the finished painted surface to sit at least for 90 minutes after the last
coat before baking There have been problems when baking steel and
acrylic test sections with the paint cracking while baking right after the
last coat Normally the finished surface is left to dry overnight and baked
first thing in the morning
For test sections that are too large to be baked in the oven the heat gun
may be used Carefully place a thermocouple in a central location with
blue painters tape The heating should be uniform and should not take
more than 20 minutes of continuous blowing When the thermocouple
reaches 80-90 C the plate can be assumed to be baked To introduce a
factor of safety in the baking it does not hurt to bake it longer than it
normally takes
Once the test section is mounted and ready to run cover it with cloth that
does not let any light through This will protect the paint for further uses
This is especially important on test sections that can be used multiple
times like the ones found in this study
When the test is running turn off the LED lights This light is the most
damaging to the TSP as it degrades the quality of the fluorescent
molecules
If there is a particular head of the TSP can that you prefer over others you
can remove it once the can is empty It is difficult to get used to a single
kind of nozzle being able to transfer it from can to can is a must if
painting consistency is to be kept
20
Donrsquots
Do not clean a test section that has already been used with too much
acetone The acetone is volatile evaporating quickly cooling the test
section rapidly If this test section has had heaters attached to it and run
previously the acrylic will crack due to uneven stresses inside of it
If paint is dripping stop painting immediately Clean the surface and start
over Hold the can far from the surface in order for it not to drip
Do not use TSP to teach new apprentices undergrads or graduate students
how to paint Regular spray paint is two orders of magnitude lower in cost
while the painting process is exactly the same
Do not paint with the doors closed The paint contains carcinogens that
can harm the lungs Always use a respirator and keep the room well
ventilated In-situ painting and baking has not been tried however it may
be a real option if the test section is difficult to disassemble and easily
accessible to painting and baking
If there is a can of paint that contains too little paint for the test section
that needs to be painted try to find a new can The mixing of two different
cans of TSP can be dangerous at times however it has been noticed over
the years that ISSI provides a very robust and dependable product that
does not vary significantly from batch to batch
21
Figure 11 Heater Strips Painted with TSP Too Closely
32 Experimental Setup of Suction Channel
The impingement channel is fed under suction As seen in Figure 12 air enters
through the plenum it crosses the jet plate as it gains speed to form the jets
which then impinge on the target wall The flow then passes through a venturi
flow meter and finally through the blower into the atmosphere A bypass valve is
used to control the flow rate of the impingement channel
22
Figure 12 Flow Loop of Impingement Channel
The impingement channel consists of 15 streamwise rows of 3 spanwise jets each The
total width of the channel YcD is of 8 diameters while the streamwise spacing between
the rows is XD=5 the spanwise distance between the holes is of YD=2 Figure 13shows
the top view of the jet plate The plate is counter bored to ensure that a nearly flat
velocity profile of the jet is achieved Figure 14 shows the front view of the channel Z is
denoted as the distance between the jet and target plates Side walls are interchangeable
to change the height of the channel to 6 8 and 10 diameters Two thirds of the
streamwise rows can be covered to change the XD from 5 to 15
Figure 13 Top View of Jet Plate
23
Figure 14 Front View of Impingement Channel
The target and sidewalls had heaters made specifically for them in a serpentine
style This was necessary to increase the resistance as the VARIACs used to power them
only had a maximum current output of 20 amps The heater strips are two diameters
wide at each end copper tape with conductive adhesive was used to connect the leads to
the power supply The heater consists of 50 micron thick steel sheet sandwiched between
two pieces of Kapton tape The heater is attached to the painted surface with the use of
double sided Kapton tape The target test section can be seen in Figure 15 also seen in
this figure are the two Teflon gaskets lined on the sides of the target plate With the target
wall bolted onto the sidewall the gasket is compressed generating a strong seal
Figure 15 Target Wall Test Section with Heater Leads
24
For this study the test matrix shown in Table 1 will be run Target and side wall
data will be taken at three different impingement heights at two different Reynolds
numbers of 7500 and 15000 denoted by A and B respectively A streamwise jet spacing
study is also done by testing the target and side wall heat transfer at an XD=15 for the
low impingement height channel
Table 1 Test Matrix
XD ZD Wall Re
5
10 TW
7500
15000
SW 7500
15000
8 TW
7500
15000
SW 7500
15000
6 TW
7500
15000
SW 7500
15000
15 6 TW
7500
15000
SW 7500
15000
33 Data Processing and Reduction
As described previously when taking temperature measurements with the use of TSP
reference temperatures are noted and a reference picture is taken The experiment is the
run once the experiment reaches steady state a new set of 4 pictures is taken Given the
calibration curve temperatures are backed out
25
Given the amount of heat generated inside the heater
Dividing by the heated area to get heat flux
Heat loss tests were run to consider how much of the heat flux generated by the heaters
goes through the backside instead of into the flow It was found that 25 of the heat flux
leaks out to the atmosphere through the acrylic In order to account for this heat leakage
it must be subtracted from the calculated value to become
Where Ah is the effective heated area given by
Where Aunheated is an estimate of how much unheated area is between the heater strips (~
3 of the total area)
To obtain heat transfer coefficient
Where Tref is the reference temperature Typically set in literature to be the jet
temperature
To obtain the average Reynolds number for the jets the total mass flow rate is used
Where Dj is the jet diameter and μ is dynamic viscosity (1983kgm s at 300K)
26
Pressure measurements were taken at the sidewall after the last jet entered the channel
These pressure measurements were used to determine the thermal performance of the
tallest two channels (ZD = 8 and 10)
The thermal performance at constant pumping power is found by using the equation
Where h is the average heat transfer coefficient for the target wall of them impingement
channel and ho is the heat transfer coefficient obtained by passing the same amount of
flow through a smooth duct ie the Dittus-Boelter correlation The friction factor f is
found with the use of
Where Ppl is the plenum static pressure assumed to be atmospheric and Plast jet is
the pressure read after the last jet V is the volumetric flow rate divided by the cross-
sectional area of the duct after the last impingement row The hydraulic diameter of the
channel is set to be
The baseline friction factor was calculated with the use of the Moody chart the hydraulic
diameter and the total mass flow rate though the channel Thermal performance at
constant pressure drop was also calculated with
27
34 Uncertainty Analysis
A simple uncertainty analysis was done to estimate the error in calculation of the
heat transfer coefficient from the given outputs of the test data From the bare basic
measurements for voltage area current temperature of thermocouples and temperature
profiles of paint a simple uncertainty analysis can be done to estimate the error for the
calculated heat transfer coefficient Figure 16 shows the different sources of error in the
calculation of heat transfer coefficient The effective uncertainty was calculated by taking
the root of the sum of the squares of all the individual percentage errors The
experimental uncertainty for heat transfer coefficient was of 703 This error may be
reduced by acquiring higher temperatures of the TSP reading current with a more
accurate ammeter or reading reference temperatures with the use of a thermopile instead
of a single thermocouple
Figure 16 Heat Transfer Coefficient Uncertainty Tree
28
35 Lateral Conduction Analysis
To take into account the lateral conduction occurring inside the heater foil while
the test is running two simple 1D conduction and convection equations were used to
quantify the amount of heat moving through the heater laterally and the amount of heat
convecting into the air The lateral conduction is expected to be at a maximum at the
places where there are large spatial variations of surface temperature which is why the
ZD = 6 XD = 5 case at high Re is chosen to be studied Figure 17 shows the
temperature distribution of the aforementioned case Four cold spots can be seen by their
distinct blue and yellow color located at the stagnation regions The maximum
temperature gradient occurs between the third jet impingement and the middle region
between jets The temperature difference was seen to be of 13degC The distance in between
these two temperatures is of 25D=01875m The corresponding heat flux between these
two points was calculated to be 13000Wm2 with ksteel~20Wm K A region of 1cm by
1cm was then created and the amount of heat calculated through conduction and
convection were compared To acquire the amount of heat removed through conduction
a heat flux of 13000Wm2 was imposed through an area of 01m by 00005m this
equaled to 00277 W The amount of heat moved through convection was calculated by
multiplying the heat flux used during the test by the area of the square 0001m2 the
resulting heat moving through the heater onto the air is 6 W Since the heat moving
through to the air is two orders of magnitudes larger than the heat moving laterally the
effective lateral conduction can be neglected
29
Figure 17 Temperature Profile of First Five Impingement Rows
A second order approach was also taken to quantify the amount of lateral
conduction in the heater The temperature gradient was taken from high peaks in heat
transfer caused by the second row of impingement of the same ZD=6 XD=5 channel at
high Re Figure 18 shows the high heat transfer coefficients created by the second row of
jets A quadratic curve fit was obtained by for this small region so that a continuous
equation of heat transfer coefficients as a function of streamwise distance was quantified
30
Figure 18 Detailed View of First Heat Transfer Peak with a Polynomial Curve Fit
The net heat gained by a differential volume from lateral conduction is the
difference in the temperature gradient at the entrance and the exit multiplied by the
thermal conductivity and cross sectional area Using this method shown in Figure 19 the
net change in convective heat transfer due to lateral conduction can be studied
Figure 19 Control Volume Heat Transfer Analysis
By taking the difference between the out flowing heat trough the right side and
the inflowing heat from the left side a net gain or loss can be found Figure 20 shows the
y = -470630x2 + 31244x - 14842Rsup2 = 09934
300
310
320
330
340
350
360
370
380
0 001 002 003 004 005
HTC
(W
m2K
)
x (m)
Heat Transfer Peak
Poly (Heat Transfer Peak)
31
difference in magnitude between the out flowing heat through convection seen in red and
the net inflow of heat from lateral conduction in blue From these calculations it was also
found that the amount of heat moving through lateral conduction is tow orders of
magnitude smaller than the amount of heat moving out through convection leading to the
belief that even at high temperature gradients lateral conduction does not play an
important role in the ongoing heat transfer processes in the impingement channel A more
detailed calculation of this work can be seen in appendix A
Figure 20 Heat Loss through Convection and Lateral Conduction
002 003 004 0051 10
5
1 104
1 103
001
qconv x( )
qnet x( )
x x
32
CHAPTER FOUR HEAT TRANSFER RESULTS
41 Heat Transfer Validation
In order to obtain confidence in our experimental setup an experiment was made
to test something that has already been published in literature A smooth channel was the
obvious choice as it was easy to setup by taking off the end cap and blocking all the holes
with smooth blue painters tape on the flow side and metal tape on the plenum side to
ensure no leaks into the channel from the jet plate The smooth channel has been studied
widely and multiple correlations exist one of these equations is the Dittus-Boelter
correlation (Incropera 2007) The test was run using the ZD=6 side wall so that the
hydraulic diameter was a minimum Figure 21 shows the span averaged results versus
non dimensional distance into the channel
Figure 21 Validation Spanwise Averaged Results
0
10
20
30
40
50
60
0 1 2 3 4 5 6 7 8 9
HTC
(W
m2K
)
XDc
Span Avg
Dittus Boelter
33
The plot shows decreasing heat transfer coefficient with increasing XDc due to
the developing thermal boundary layer The span average does not reach the Dittus-
Boelter due to it not being fully developed in the limited space it is given Typical flows
can take up to 60 diameters to achieve a fully developed profile with the current setup
the maximum length of the channel was of 9 diameters The profile however seems to
have an asymptote at the Dittus-Boelter correlation value leading to the belief that if the
channel was longer that value given by the correlation would be reached One important
factor to take into account in determining whether the experimental setup is validated is
the fact that the Dittus-Boelter correlation has an uncertainty near 30 Since the span
average at high XDc is well within 30 from the calculated value it is safe to assume
that the current experimental setup is validated
42 Heat Transfer Results
Heat transfer results are compared based on variations in channel height and
average jet Reynolds number As discussed earlier there are numerous other parameters
also affecting the heat transfer in these channels As these parameters are changed flow
structures within the channel are expected to be altered as well as discussed in the
literature Two of the major contributors to heat transfer in these channels are the
successful jet impingement and the resulting cross flow The same domain is captured in
both the local and averaged results
Figure 22 through Figure 25 highlights the heat transfer distribution for the cases
with a jet to jet spacing of 5 diameters in the streamwise direction and of 2 in the
spanwise direction It is evident that the smallest channel height (ZD=6) performs the
best at all Reynolds numbers on all surfaces It is also interesting to note the similarity
34
in the target wall profiles between case 528A and B where the curves are very similar
other than the obvious offset due to the change of the Reynolds number At this large
spacing we also see the degradation of the jets a few diameters downstream of each
impingement location The downstream shifts of the peaks are evident after the second
and third row of jets Also evident in these plots is the deflection of the impinging jet and
the wall jets from the cross flow The cross flow is forced to flow around the jet
deflecting the spread of the wall jet in the downstream direction Impingement locations
are also very evident at low XD however as XD and therefore the cross flow increase
the magnitude of the peaks start decreasing and eventually level out to pure internal flow
Figure 22 Target Wall Heat Transfer Coefficient Distributions
35
Figure 23 Span-averaged Target Wall Heat Transfer Distribution
36
Figure 24 Side Wall Heat Transfer Coefficient Distributions
37
Figure 25 Span-averaged Side wall Heat Transfer Distribution
Figure 23 and Figure 25 show similar details with impingement peaks clearly
diminishing and shifting in the downstream direction The cross flow clearly has some
negative influence on these geometries when compared to the more traditional
impingement highest on the order of 1 to 5 jet diameters The heat transfer profiles of the
target wall for all heights seen in Figure 22 and Figure 24 show the rapid decay in heat
transfer after the third jet This can be explained by understanding that the first jet does
not have any cross flow to deflect it the second jet only has the first jet worth of
momentum deflecting it downstream however since the channel is so tall the
momentum of the cross flow after the first and second jet are not enough to greatly
disturb the incoming jets After the third jet however the cross flow builds up enough
momentum to greatly affect the integrity of the jets downstream causing the span-
0
20
40
60
80
100
120
140
160
2 12 22 32 42 52 62 72
HTC
(W
m2K
)
XD
5210B_SW 528A_SW Jet Location
526A_TW 526B_TW
38
averaged heat transfer to rapidly drop The point at which the crossflow starts taking a
considerable effect occurs around XD =35 The target wall profile of the ZD=10
channel shows the outside jets on the second row of jet deflecting downstream It can be
conjectured that the bending of the outside jets downstream is caused by the wall jet
created by the first row of jets separating from the side wall and deflecting the outside
jets of the following rows of jets The heat transfer profile for the ZD case excludes the
first jet due to shadows being present when the data was taken
Also evident from this spanwise averaged data is the increase in heat transfer
with increases in Reynolds numbers and decreases in impingement height Results tend
to be the closest from case to case at the first impingement jet This is a reasonable
result as the effects of cross flow have little to no effect at the first few impingement
locations The impact of the jet would then be the driving force at these locations and
would be similar between cases except if the potential core is not reaching the target
surface The potential core of a jet tends to last between 6 and 10 diameters from its
origin It can be seen that the difference in heat transfer coefficient in the first two jets for
the ZD=8 and ZD=10 channel is much different than the corresponding difference
between the ZD=6 and ZD=8 heights This decreased difference between the heights of
the peaks may be attributed to the potential core reaching the target wall at the heights of
6 and 8 diameters leading to similar profiles and may not be reaching the surface at the
height of 10 diameters The heat transfer values of the peaks diminish in the downstream
direction The range of fluctuation also drops that is the profile becomes more uniform
at large XD This drop in fluctuation is more visible at the tallest channel height
(ZD=10) and less pronounced at the smallest channel This is due to the jet in the small
39
channel having to travel a shorter distance to impinge on the target plate leaving the
crossflow less time for it to deflect the jet as opposed to the tall channel where the jet has
to travel almost twice the distance as the ZD=6 channel for it to impinge on the target
wall This effect cannot be solely explained by the built up cross flow in the channel
Mixing loses also take part in the degradation of the stagnation size of the downstream
jets The mixing losses have much greater effect on the taller channels due to the same
reason that the cross flow has a higher impact on them too the jets have to travel a large
distance before hitting the target plate leading the stagnant or moving surrounding air to
be a sink of its downward momentum for a longer time and distance than the respective
smaller channels The heat transfer coefficient of the side wall was also analyzed
Similar effects are expected on the side wall due to the expected impact of the wall jet
As expected the strength of the cross flow is not enough to prevent wall jets from
successfully impacting the side wall at small XD jet locations however the crossflow
takes dominance at around XD=25 Also evident in these plots is the concentration of the
wall jet impact to the bottom of the channel on the order of 1-2 diameters in height It is
interesting to note that for the 5210B case in Figure 24 as the first jet diffuses outward
it impacts the sidewall at a height of ZD=6 The height at which the diffused jet affects
the sidewall heat transfer coefficient decreases as the crossflow increases The stagnation
regions are also deflected in the downstream direction similar to the target surface
results These effects are most evident in the 5210B Similar characteristics can be
explained from the spanwise-averaged plots shown in Figure 25 These results again
clearly show the effects of increasing the impingement height and increases in Reynolds
number As the height is increased the effect of the wall jet is significantly reduced
40
partially due to the increased surface area much of which is not affected by the wall jet
The diminishing effect of the cross flow accumulation is also evident in these plots as the
heat transfer peaks decrease in the downstream direction
43 XD Comparisons
The streamwise jet spacing was changed from XD=5 to 15 by covering two out
of three rows of jets This was done by covering the impingement holes inside the
channel with smooth blue painters tape and sealing the plenum side of the jet plate with
metal tape to ensure no leakage The profile is expected to be less uniform than the case
where XD=5 due to the large spreading of the high heat transfer peaks Due to the large
separation between the rows of jets there is a lower amount of downward momentum
than the equivalent XD=5 geometry for this reason it is expected to see a lower heat
transfer peak due to the jets momentum diffusing out faster to the stagnant air decreasing
the effective impingement velocity Figure 26 shows the target wall heat transfer
distribution Similar to the XD=5 profile it can be seen that the heat transfer due to the
jet impingement drastically reduces after the third jet This phenomenon leads us to
believe that at both Reynolds numbers the cross flow generated by the first three jets is
powerful enough to effectively deflect the fourth jet downstream diminishing its heat
transfer performance The similarity seen in Figure 26 between high and low Reynolds
number implies that the downstream deflection of the jets is not dependent on the jet
Reynolds numbers
41
Figure 26 XD=15 Target Wall Heat Transfer Profile
42
Figure 27 XD=15 Span-averaged Target Wall Heat Transfer Distribution
On the span averaged plots seen in Figure 27 the downstream deflection of the
jets is evident however as described previously the shifts in the peaks of heat transfer
occur at the same xD for both Reynolds numbers The amplitude of fluctuation of heat
transfer coefficients for the high Reynolds number case is larger than that of the low
Reynolds number Both profiles seem to start to level off at the end of the impingement
channel with the lowest span average being located just before the fourth jet at both
Reynolds numbers
A comparison of target wall heat transfer coefficients between XD =15 and 5 is
shown in Figure 28 At first glance it is clearly visible that the XD=15 average heat
transfer coefficient is smaller than its XD=5 counterpart This is also noticed by Ricklick
where he showed average HTC profiles for larger XD to be smaller than those at lower
XD (Ricklick 2009) This may occur due to there not being as high downward
0
50
100
150
200
250
300
350
0 20 40 60 80
HTC
(W
m2
K)
XD
Low Re
High Re
Impingement Location
43
momentum for the XD=15 case as compared to the XD=5 due to the lack of close jets
The stagnant air around the spaced out jets is taking away more of its momentum
decreasing the effective impingement Reynolds number Also important to notice is the
fact that since the XD=5 case has three times the flow impinged into it the cross flow
velocity and therefore Reynolds number will be three times as large increasing the heat
transfer coefficient
Figure 28 Target Wall Span-average Comparison of XD=5 and 15 at High Re
The side walls also show similar patterns to their XD=15 counterparts Strong
wall jet impingement can be seen on the side wall at low xD and zD Figure 29 shows
areas where the wall jet generated by the target wall impinges on the sidewall Similar to
the profile seen in Figure 24 the high heat transfer region reaches upward in the z
direction up to a height of 4-5 diameters for the first jet This high heat transfer stagnation
region decreases as xD increases to the point where the wall jet created by the last jet is
negligible when coupled with pure channel flow
0
50
100
150
200
250
300
350
400
0 10 20 30 40 50 60 70 80
HTC
(W
m2K
)
XD
XD = 5 XD = 15 Jet Location
- Blocked for XD =15
44
Figure 29 Side Wall Heat transfer Coefficient Profile
The span averaged plot seen in Figure 30 shows a nearly flat profile with peaks
located at the stagnation regions of the wall jets Thw downstream deflection for the
XD=15 case is much more pronounced than the one for the XD=5 case This is due to
the jet not being constrained by the wall jets generated by the previous and latter
impingement locations In the XD=15 case the wall jet is free to move downstream
more so than the XD=5 due to it not being disturbed by anything other than the cross
flow
45
Figure 30 XD=15 Side Wall Span-averaged Heat Transfer Coefficients
44 3D Comparison of the Heat Transfer Profiles
In order to further understand the targetsidewall interactions both heat transfer profiles
were positioned in an isometric view representative of the channel One important thing
to note is that both target and side wall profiles are not on the same scale This form of
data display is only qualitative way to describe the heat transfer profiles Figure 31 shows
the 3D profile of the XD=5 ZD=6 case The both stagnation regions of the jet onto the
target wall and the wall jet into the sidewall can be seen to occur at the same location for
the first three streamwise rows After the fourth and fifth row the wall jet diminishes in
magnitude Also visible in this view is the increasing heat transfer at low zD towards the
end of the channel of the side wall The constant input of mass and downward momentum
into the channel causes the cross flow generated by the previous jets to be squeezed into
the lower third of the channel increasing the velocity and the heat transfer of the target
wall
0
20
40
60
80
100
120
0 20 40 60 80
HTC
(W
m2K
)
XD
Low Re High Re Jet Locations
46
Figure 31 3D Heat Transfer Profile for ZD=6 XD=5
Similar patterns are seen in the taller ZD=8 channel seen in Figure 32 The wall jet
generate by the third streamwise row of jets is been deflected downward more than its
ZD=6 counterpart This can be attributed to the fact that the jet located at the ZD=8
channel has lost much of its momentum and is more easily bent downstream by the cross
flow generated by the first two jets The ZD=8 sidewall shows similar increasing heat
transfer at high xD however the increase is not as drastic as the one found in the ZD=6
channel This is caused due to the extra two diameters the jets have to cover to impinge
on the surface since the ZD=8 channel is one third larger than the ZD=6 one the flow
has to have more area to flow through The last few jets only deflect the cross flow
downward about 4 diameters this leaves two diameters for the flow to pass through on
the ZD=6 channel causing the velocity to increase rapidly and therefore increasing the
heat transfer coefficient at the low zD Since the ZD=8 channel has four remaining
47
diameters for the flow to move through it does not deflect it as much as the ZD=6
channel does only increasing the cross flow velocity and resulting heat transfer
coefficient slightly over the area at low zD and high xD
Figure 32 3D Heat Transfer Profile for ZD=8 XD=5
The 3D heat transfer profile for ZD=6 and xD=15 channel seen in Figure 33 shows
similar details to those seen in the XD=5 channels The stagnation regions of the jet and
wall jet occur at the same x location for the first three rows of jets the wall jet generated
by the fourth row of jets is deflected downstream only generating as small region of high
convective coefficients at the side wall The region located at the top right corner of the
side wall is colored red signifying high heat transfer however this area is generated by
the heaters providing non uniform heat flux at this location This region of high heat
transfer coefficients also occur at xD=0-4 of the target wall where the heater coil bends
48
Figure 33 3D Heat Transfer Profile for ZD=6 XD=15
45 Thermal Performance Calculations
Thermal performance calculations were done on the two tallest channels (ZD=8 and 10)
The pumping power was calculated for both channels at two Reynolds numbers Figure
34 shows the ratio of pressures required to pull the same amount of flow through as
smooth duct as opposed to through the jet plate The ZD=10 channel at high Reynolds
number requires the largest pressure as seen in the Figure however in order to pull the
same amount of flow rate through it requires a smaller pressure difference due to the
large cross section
49
Figure 34 Pressure Drop Ratio with Respect to Smooth Channel
Next the heat transfer enhancement was calculated A total area averaged heat
transfer coefficient was taken for the target wall and compared to the smooth channel
Dittus-Boelter value while using the same total mass flow rate Figure 35 shows an
average heat transfer enhancement of four times that of a smooth channel Similar trends
were noticed in the literature (Ricklick 2009) of decreasing heat transfer enhancement
with an increase of jet Reynolds number Ricklick also showed an increase in heat
transfer enhancement with an increase of jet to target spacing similar to the one seen in
Figure 35
0
10
20
30
40
50
60
528A_TW 528B_TW 5210A_TW 5210B_TW
PP
o
50
Figure 35 Heat Transfer Enhancement
Thermal performances at constant pressure drop were then calculated by dividing
the heat transfer enhancement by the pressure increase As seen in Figure 36 all the
values fall well below 1 making the impingement channel an unfeasible mode of heat
transfer enhancement when a constant pressure is supplied
Figure 36 Thermal Performance at Constant Pressure Drop
0
05
1
15
2
25
3
35
4
45
528A_TW 528B_TW 5210A_TW 5210B_TW
hh
o
0
002
004
006
008
01
012
014
528A_TW 528B_TW 5210A_TW 5210B_TW
(hh
o)
(PP
o)
51
The thermal performance at constant pumping drop was calculated in the same
way that the constant pressure drop was calculated the only difference being the pressure
ratio term was raised to the one third power As seen in Figure 37 the thermal
performances at constant pumping power are all higher than unity this signifies that if a
surface needs to be cooled with the supply of a constant pumping power the
impingement channel is a feasible option Similar to the figure literature (Ricklick 2009)
showed a decrease of thermal performance with an increase of channel height and
Reynolds number
Figure 37 Thermal Performance at Constant Pumping Power
0
02
04
06
08
1
12
14
528A_TW 528B_TW 5210A_TW 5210B_TW
(hh
o)
(PP
o)1
3
52
CHAPTER FIVE COMPUTATIONAL FLUID DYNAMICS
51 Problem Setup
In order to further enhance the understanding of the heat transfer profiles showed
previously a computational study was performed Even though CFD does not yield
accurate quantitative results it produces good qualitative data that can be used to explain
the flow physics in the channel and therefore increase the understanding of the patterns
seen previously The channel was meshed with the use of GAMBIT Due to the
symmetry the channel was split in half in the streamwise direction All horizontal
surfaces (parallel to the target wall) were divided into 6 different regions that are later on
going to be meshed individually The six regions are seen in Figure 38 section 1 is
located at the center of every jet also referred to as ldquojet centerrdquo This region was created
to reduce the squewness of the elements near the center of the jet by allowing the mesh to
be completely linear with a squewness of zero Section two complements section 1 to
complete the impingement hole The half impingement hole located at the symmetry wall
contains the same exact region 2 however it only has one half of the jet center Section 3
was made in order to bring the polar geometry of the holes to match the cartesian aspect
of the remainder of the channel With the addition of section 3 to the channel the only
remaining sections are square or rectangular regions Region 4 lies in between
streamwise rows of jets Section 5 is located at the entrance and the exit of the channel
These sections are not square in contrast with section 4 The last remaining section is
located near the side wall of the channel extending from the beginning to the exit of the
channel
53
Figure 38 Horizontal Plane of Impingement Channel Geometry
All the faces of sections 1 and 2 are linked throughout the channel and the
plenum however in order to have greater control of the mesh in the plenum and the
channel the remaining sections 3 4 5 and 6 are not linked to every single similar face
instead they are only linked to similar faces in either the plenum or the channel
Boundary layer spacing number of rows and growth factor are placed around the
channel In order to maintain a y+ of less than unity the first cell spacing of the boundary
layer inside the channel was set to be 000001 m (01mm) This first cell spacing yielded
y+
values varying between zero and 9 at the target side and front end wall Figure 39
shows a contour of y+ values on the heated walls The maximum values occur near the
impingement locations as expected due to large shear caused by the steep velocity
gradient normal to the wall On the downstream direction the y+ also increases due to the
increase of flow rate and therefore the increased skin friction on the wall At the
impingement location of the first jet the y+ is close to zero due to the velocity having its
direction mostly normal to the surface yielding no shear
54
Figure 39 Target Side and Front End Wall y+ Values
Once the faces were linked edge meshes were created on the sides of the jet center
Section 2rsquos inner edge was also meshed using a different parameter than the one used for
the jet center in order to allow for more freedom when trying to refine the mesh These
two edge meshes is followed by meshing all of section 2 faces alongside all the jet
centers Once these were complete section 3rsquos inner edge was meshed with different
parameters for the channel and plenum Sections 4 and 5 sides that connected with the
face made by section 6 were meshed so that their spacing was similar again the plenum
and channel were meshed separately for increased control of mesh density in both of
these areas The upstream-most edge of section 6 was meshed so that the spacing is
similar to the edge mesh in sections 4 and 5 this was done in order to have aspect ratios
of the wall be as close as possible to unity Sections 3 4 5 and 6 were meshed on both
the channel and the plenum With the entire target wall plane meshed these surface
meshes are coopered upwards to connect to the opposite wall The vertical spacing has
55
also been set up differently between the channel and the plenum The holes and the
plenum were also coopered The finished mesh was then exported as a msh file
Boundary conditions were set in GAMBIT once the mesh was imported into
Fluent values were set to every face depending on their location and purpose Figure 40
shows the four different boundary conditions Face 1 (blue) was set to be a mass flow
inlet The flow rate is half of the total flow rate at a given jet Reynolds number due to it
being only half of the entire domain Face 2 (yellow) is a symmetry plane face 3 (red) is
a pressure outlet at zero gauge pressure The rest of the faces in the channel denoted by
the number 4 (white) are set to walls The target side and front end wall had a heat flux
applied to them equal to 10000Wm2
Figure 40 Finished Mesh with Boundary Conditions
The model was imported into Fluent It was scaled down by a factor of 1000 due to it
being made in GAMBIT in millimeters The energy model was turned on The Realizable
k-ε model was used with enhanced wall functions on both the pressure and thermal
gradients The boundary conditions were set as discussed previously the mass flow inlet
was set to the specific flow rate normal to the surface the heat fluxes were set on the
56
heated walls the outflow gauge pressure was set to zero Two important reference values
characteristic length and reference temperature were set to be the diameter of the jet
(0075m) and 300K respectively The spatial discretization parameters were set to second
order upwind for momentum turbulent kinetic energy turbulent dissipation rate and
energy The under-relaxation factors were set to default Four monitors were created to
aid in the determination of convergence two of them read Nusselt numbers at the
stagnation region of the first and last jet the remaining two read the exit velocity at the
first and last jet The continuity x y and x velocities and energy equations residuals
were set to be 1E-6 while k and ε residuals were set to 1E-4 The solution was initialized
on the all zones at 1ms in the positive x direction The solution was set to autosave every
100 iterations while keeping only the two newest dat files The calculation was then run
for a maximum of 7000 iterations
A grid independence study was done on the domain to find the optimal size of
mesh that provides the correct solution while minimizing the compute time Two
monitors were set to check for grid independence both of them were vertex maximum
One of them read the Nusselt number at the impingement location of the first center jet
while the second one measures the velocity at the exit of the last jet Four different mesh
sizes were run to the convergence criterion explained before their sizes were 900000
15 million 28 million and 43 million cells
57
Figure 41 Grid Independence Study
It can be seen in Figure 41 that the difference between the 28 and 43 million cell
meshes are very small a difference of under 006 for velocity and 7 for Nusselt
number It can be safe to assume that the 28 million cell mesh is large enough to provide
a mesh independent solution The GAMBIT journal file used to create this mesh is
attached to the appendix The results shown hereafter are the ones obtained by the 28
million cell mesh
Figure 42 Residual Plots for the 26M Cell Run
67
69
71
73
75
77
79
81
83
85
485
4855
486
4865
487
4875
488
4885
489
0 1 2 3 4 5
Nu
sse
lt N
um
be
r
Cell Ammount (Millions)
Grid Independence Study
Velocity
Nusselt Number
58
For future reference Figure 42 shows the residuals of the 26M cell calculation
Up until around 4400 iterations the residuals were increasing shortly thereafter the
residuals started decreasing until it converged just after 5500 iterations All runs for the
differently sized meshes had the same residual patters with the peak of residuals and
point of convergence happening at different iterations
52 CFD Results
As describe previously all the results shown here are for the mesh containing 28 million
elements Figure 43 shows the total pressure contours It can be seen that the plenum
portion is at a constant total pressure Once the jets form since there are very small losses
in the jets due to the wall friction the total pressure still remains constant Only when the
jets enter the channel and start mixing with the cross flow is that they start losing the total
pressure head It is important to notice how the first two jets have the total pressure close
to the plenum arriving at the target wall This implies a successful impingement of the
undisturbed potential core As we move downstream the total pressure is lost quite
rapidly as the jets interact with the cross flow
Figure 43 Total Pressure Contours
59
Similar details can be drawn out from Figure 44 it can be seen that the first three
jets successfully impinge on the target wall while the rest of the downstream ones are
deflected by the cross flow As mentioned by Ricklick the velocity magnitude of the last
jet is larger than that of the first jet due to there being a lower static pressure at the end of
the channel providing it with a steeper pressure gradient hence higher velocity
Figure 44 Velocity Magnitude Contours
Turbulent kinetic energy was plotted in Figure 45 it is expected to have the
highest turbulent kinetic energy near the exit of the holes where the stagnant air is in
contact with the fast moving jet The mixing between the two regimes causes very
energetic eddies to form potentially enhancing the target and side wall heat transfer
coefficient As cross flow builds up towards the end of the channel the turbulent kinetic
energy increases due to larger overall velocities and fluctuations between the cross flow
and jets
60
Figure 45 Turbulent Kinetic Energy Contours
As Ricklick showed in his work the static temperature rise is quite small for such a small
channel It can be seen in Figure 46 that the driving temperature for heat transfer is that of
the plenum It is important to notice that a wall heat flux of 10000 Wm2 was used as the
boundary condition Not even in the most powerful tests would we ever use heat fluxes
that high they normally range between 2500 to a maximum of 7000 Wm2 A heat flux of
10000 Wm2 will increase the temperature at a faster rate than what it is normally used in
experimental testing
Figure 46 Static Temperature Contours
61
Figure 47 Target and Side Wall Heat Transfer Coefficient Contours
Figure 47 shows the target and sidewall heat transfer profiles Peaks can be seen at the
first three locations similar to that seen in Figure 22 The trend decreases rapidly to
eventually become a slowly increasing heat transfer profile due to the increase of mass
flow through the channel The sidewall provides the same results clear peaks in heat
transfer where the wall jets impinge on the sidewall seen in Figure 48 in more detail The
sidewall also shows a recirculation zone in between the first row of jets and the end wall
This is caused by the wall jet from the first row hitting the back wall moving upwards in
a circular pattern and coming back down when it encounters the first impingement row
Figure 48 Closer View of First few Rows of Impingement HTC Contours
62
Figure 49 Pathlines Generating from the First Row of Jets
Figure 49 helps explain the low heat transfer region between the first row of jets and
the end wall Pathlines are generated at the exit of each hole in the first row As the
air impinges on the surface half of it moves downstream and the other half movers
upstream to this recirculation zone where it circulates for a period of time before
reuniting with the remainder of the flow to move downstream The wall jet that
moves towards the second row of jets encounters the wall jet created by the second
row of jets causing the pathlines to drastically move upwards On the side of the
channel the pathlines behave erratically with no clear pattern clearly signifying the
highly turbulent and chaotic flow structure of this impingement channel
63
CHAPTER SIX CONCLUSIONS
It has been seen from this analysis that the side walls provide significant heat
transfer in an impingement channel especially at the relatively smaller channel
height This is primarily the result of successful impact of the wall jet with the side
walls It was shown that the tallest channel (ZD=10) has the most uniform profile with
low heat transfer coefficients when compared to the other channels The peaks of the
ZD=6 and 8 channels have a very similar profile which may indicate the successful
impingement of the potential core of the jet on the target surface As XD increases the
peaks diminish and a positive slope profile is attained by the increase of cross flow
velocity as more and more jets are introduced Tall impingement channels provide the
user with a heat transfer profile that is more uniform than those provided with the use of a
smaller channel while still maintaining higher convective coefficients when compared to
a smooth flow scenario The downstream shift of the wall jets is found to be independent
of Reynolds number and heavily dependent on streamwise position It was also found that
at XD=15 the wall jets decay faster than their XD=5 counterparts From the 3D heat
transfer profiles it was seen that the cross flow generated by multiple upstream jets is
deflected downward decreasing its effective flow area increasing its velocity hence
providing higher convective coefficients at the side wall at high xD and low zD
64
APPENDICES
Appendix A
Lateral Conduction Consideration
Thickness of foil heater Heat flux
Sample volume width
Volumetric heat generation
Volume of sample volume
Temperature profile from the first row of impingement ONLY valid for 02ltxlt045
t 50m k 20W
m K qflux 6000
W
m2
1mm
V 2
t qvol
qflux
t
T x( ) 298Kqflux
470630 x2
31244x 14842 W
m2K
N 15
x 02045 02
N 102 047
002 003 004 005314
315
316
317
318
319
320
T x( )
x
A t
qnet x( ) A kxT x
m
d
d xT x( )
d
d
1
m
002 003 004 0050
5 105
1 104
15 104
2 104
qnet x( )
x
65
Now comparing the net heat gained by lateral conduction to heat generated and convected out
It can be seen that the lateral conduction into the sample volume is two orders of magnitude smaller than the heat removed by convection
qgen qvol V 6 103
W
qconv x( ) 2
qflux qnet x( )
002 003 004 0051 10
5
1 104
1 103
001
qconv x( )
qnet x( )
x x
66
Appendix B
This is the journal file run on gambit to generate the geometry faces links
boundary layer face and volume meshes as well as the boundary conditions
set diameter
$d=75
$zc=6($d)
$xc=80($d)
$yc=4($d)
$y=2($d)
$x=5($d)
$zp=5($d)
$ztot=($zc)+($d)+($zp)
$jcf=(13)
$ocf=2
Boundary layer constants
$first=01
$growth=12
$rows=4
Meshing constants
$NumbNodes=5
$Numbtelnodes=6
$PLobnodes=5
$Chobnodes=5
$Plbenodes=($NumbNodes(4)+$rows)
$plsqnodes=($NumbNodes(3))
$Pllsnodes=($NumbNodes+$rows)
$Nojetcells=10
$Chzdnodes=($zc$Nojetcells)($d)
$Plzdnodes=($zp$Nojetcells)($d)
Boundary layer constants for channel
$firstch=001
$growthch=12
$rowsch=8
$CHbenodes=($NumbNodes(4)+$rowsch)
$CHlsnodes=($NumbNodes+$rowsch)
volume create body width ($xc) depth ($yc) height ($ztot) offset ($xc2) ($yc2) ($ztot2) brick
volume create cylinder height ($ztot) radius1 ($d2) radius3 ($d2) offset ($x) 0 ($ztot2) zaxis frustum
volume cmove cylinder multiple 1 offset 0 ($y) 0
volume cmove cylinder volume3 multiple 14 offset ($x) 0 0
volume create jetplate width ($xc) depth ($yc) height ($d)offset ($xc2) ($yc2) ($d2+$zc) brick
volume split body volumes jetplate connected
volume split jetplate volumes cylinder volume3 volume4 volume5
volume6 volume7 volume8 volume9 volume10 volume11
volume12 volume13 volume14 volume15 volume16 volume17
67
volume18 volume19 volume20 volume21 volume22 volume23
volume24 volume25 volume26 volume27 volume28 volume29
volume30 volume31 connected
face create jetcenter width ($jcf$d) height ($jcf$d) offset ($x) 0 0 xyplane rectangle
face create jetcircle radius ($d2) xyplane circle
face move jetcircle offset ($x) 0 0
face create outbox width ($ocf$d) height ($ocf$d) offset ($x) 0 0 xyplane rectangle
face split outbox connected faces jetcircle jetcenter
face split jetcircle connected faces face1
face split outbox connected faces face1
face cmove jetcenter outbox jetcircle face222 face223 multiple 1 offset 0 ($y) 0
face cmove jetcenter outbox jetcircle face222 face223 face224 face225 face226
face227 face228 multiple 14 offset ($x) 0 0
volume delete jetplate lowertopology
face split face1 connected keeptool faces jetcircle jetcenter outbox
face222 face223 face224 face225 face226 face227
face228 face229 face230 face231 face232 face233
face234 face235 face236 face237 face238 face239
face240 face241 face242 face243 face244 face245
face246 face247 face248 face249 face250 face251
face252 face253 face254 face255 face256 face257
face258 face259 face260 face261 face262 face263
face264 face265 face266 face267 face268 face269
face270 face271 face272 face273 face274 face275
face276 face277 face278 face279 face280 face281
face282 face283 face284 face285 face286 face287
face288 face289 face290 face291 face292 face293
face294 face295 face296 face297 face298 face299
face300 face301 face302 face303 face304 face305
face306 face307 face308 face309 face310 face311
face312 face313 face314 face315 face316 face317
face318 face319 face320 face321 face322 face323
face324 face325 face326 face327 face328 face329
face330 face331 face332 face333 face334 face335
face336 face337 face338 face339 face340 face341
face342 face343 face344 face345 face346 face347
face348 face349 face350 face351 face352 face353
face354 face355 face356 face357 face358 face359
face360 face361 face362 face363 face364 face365
face366 face367 face368
face move jetcircle jetcenter outbox face222 face223 face224
face225 face226 face227 face228 face229 face230
face231 face232 face233 face234 face235 face236
face237 face238 face239 face240 face241 face242
face243 face244 face245 face246 face247 face248
face249 face250 face251 face252 face253 face254
face255 face256 face257 face258 face259 face260
face261 face262 face263 face264 face265 face266
face267 face268 face269 face270 face271 face272
face273 face274 face275 face276 face277 face278
face279 face280 face281 face282 face283 face284
face285 face286 face287 face288 face289 face290
face291 face292 face293 face294 face295 face296
face297 face298 face299 face300 face301 face302
face303 face304 face305 face306 face307 face308
face309 face310 face311 face312 face313 face314
68
face315 face316 face317 face318 face319 face320
face321 face322 face323 face324 face325 face326
face327 face328 face329 face330 face331 face332
face333 face334 face335 face336 face337 face338
face339 face340 face341 face342 face343 face344
face345 face346 face347 face348 face349 face350
face351 face352 face353 face354 face355 face356
face357 face358 face359 face360 face361 face362
face363 face364 face365 face366 face367 face368 offset 0
0 $ztot
THIS SPLITS THE TOP PLENUM FACE WITH THE FACES CREATED IN THE BOTTOM
face split face6 connected keeptool faces jetcircle jetcenter outbox
face222 face223 face224 face225 face226 face227
face228 face229 face230 face231 face232 face233
face234 face235 face236 face237 face238 face239
face240 face241 face242 face243 face244 face245
face246 face247 face248 face249 face250 face251
face252 face253 face254 face255 face256 face257
face258 face259 face260 face261 face262 face263
face264 face265 face266 face267 face268 face269
face270 face271 face272 face273 face274 face275
face276 face277 face278 face279 face280 face281
face282 face283 face284 face285 face286 face287
face288 face289 face290 face291 face292 face293
face294 face295 face296 face297 face298 face299
face300 face301 face302 face303 face304 face305
face306 face307 face308 face309 face310 face311
face312 face313 face314 face315 face316 face317
face318 face319 face320 face321 face322 face323
face324 face325 face326 face327 face328 face329
face330 face331 face332 face333 face334 face335
face336 face337 face338 face339 face340 face341
face342 face343 face344 face345 face346 face347
face348 face349 face350 face351 face352 face353
face354 face355 face356 face357 face358 face359
face360 face361 face362 face363 face364 face365
face366 face367 face368
THIS MOVES THE FACES THAT WE ARE USING TO PLIT THE BOTTOM PLENUM SURFACE
face move jetcircle jetcenter outbox face222 face223 face224
face225 face226 face227 face228 face229 face230
face231 face232 face233 face234 face235 face236
face237 face238 face239 face240 face241 face242
face243 face244 face245 face246 face247 face248
face249 face250 face251 face252 face253 face254
face255 face256 face257 face258 face259 face260
face261 face262 face263 face264 face265 face266
face267 face268 face269 face270 face271 face272
face273 face274 face275 face276 face277 face278
face279 face280 face281 face282 face283 face284
face285 face286 face287 face288 face289 face290
face291 face292 face293 face294 face295 face296
face297 face298 face299 face300 face301 face302
69
face303 face304 face305 face306 face307 face308
face309 face310 face311 face312 face313 face314
face315 face316 face317 face318 face319 face320
face321 face322 face323 face324 face325 face326
face327 face328 face329 face330 face331 face332
face333 face334 face335 face336 face337 face338
face339 face340 face341 face342 face343 face344
face345 face346 face347 face348 face349 face350
face351 face352 face353 face354 face355 face356
face357 face358 face359 face360 face361 face362
face363 face364 face365 face366 face367 face368 offset 0
0 -$zp
SPLITS THE BOTTOM FACE OF THE PLENUM WITH THE FACES THAT ARE USED TO SPLIT
face split face114 connected keeptool faces jetcircle jetcenter
outbox face222 face223 face224 face225 face226 face227
face228 face229 face230 face231 face232 face233
face234 face235 face236 face237 face238 face239
face240 face241 face242 face243 face244 face245
face246 face247 face248 face249 face250 face251
face252 face253 face254 face255 face256 face257
face258 face259 face260 face261 face262 face263
face264 face265 face266 face267 face268 face269
face270 face271 face272 face273 face274 face275
face276 face277 face278 face279 face280 face281
face282 face283 face284 face285 face286 face287
face288 face289 face290 face291 face292 face293
face294 face295 face296 face297 face298 face299
face300 face301 face302 face303 face304 face305
face306 face307 face308 face309 face310 face311
face312 face313 face314 face315 face316 face317
face318 face319 face320 face321 face322 face323
face324 face325 face326 face327 face328 face329
face330 face331 face332 face333 face334 face335
face336 face337 face338 face339 face340 face341
face342 face343 face344 face345 face346 face347
face348 face349 face350 face351 face352 face353
face354 face355 face356 face357 face358 face359
face360 face361 face362 face363 face364 face365
face366 face367 face368
COPIES THE FACES THAT WE USED TO SPLIT TO BOTTOM OF THE PLENUM TO THE TOP OF
THE CHANNEL
face cmove jetcircle jetcenter outbox face222 face223 face224
face225 face226 face227 face228 face229 face230
face231 face232 face233 face234 face235 face236
face237 face238 face239 face240 face241 face242
face243 face244 face245 face246 face247 face248
face249 face250 face251 face252 face253 face254
face255 face256 face257 face258 face259 face260
face261 face262 face263 face264 face265 face266
face267 face268 face269 face270 face271 face272
face273 face274 face275 face276 face277 face278
face279 face280 face281 face282 face283 face284
70
face285 face286 face287 face288 face289 face290
face291 face292 face293 face294 face295 face296
face297 face298 face299 face300 face301 face302
face303 face304 face305 face306 face307 face308
face309 face310 face311 face312 face313 face314
face315 face316 face317 face318 face319 face320
face321 face322 face323 face324 face325 face326
face327 face328 face329 face330 face331 face332
face333 face334 face335 face336 face337 face338
face339 face340 face341 face342 face343 face344
face345 face346 face347 face348 face349 face350
face351 face352 face353 face354 face355 face356
face357 face358 face359 face360 face361 face362
face363 face364 face365 face366 face367 face368 multiple 1 offset 0
0 -$d
NAME OF COPIED NEW FACES
face1104 face1105 face1106 face1107 face1108 face1109 face1110 face1111
face1112 face1113 face1114 face1115 face1116 face1117 face1118 face1119
face1120 face1121 face1122 face1123 face1124 face1125 face1126 face1127
face1128 face1129 face1130 face1131 face1132 face1133 face1134 face1135
face1136 face1137 face1138 face1139 face1140 face1141 face1142 face1143
face1144 face1145 face1146 face1147 face1148 face1149 face1150 face1151
face1152 face1153 face1154 face1155 face1156 face1157 face1158 face1159
face1160 face1161 face1162 face1163 face1164 face1165 face1166 face1167
face1168 face1169 face1170 face1171 face1172 face1173 face1174 face1175
face1176 face1177 face1178 face1179 face1180 face1181 face1182 face1183
face1184 face1185 face1186 face1187 face1188 face1189 face1190 face1191
face1192 face1193 face1194 face1195 face1196 face1197 face1198 face1199
face1200 face1201 face1202 face1203 face1204 face1205 face1206 face1207
face1208 face1209 face1210 face1211 face1212 face1213 face1214 face1215
face1216 face1217 face1218 face1219 face1220 face1221 face1222 face1223
face1224 face1225 face1226 face1227 face1228 face1229 face1230 face1231
face1232 face1233 face1234 face1235 face1236 face1237 face1238 face1239
face1240 face1241 face1242 face1243 face1244 face1245 face1246 face1247
face1248 face1249 face1250 face1251 face1252 face1253
THIS SPLITS THE TOP OF THE CHANNEL WITH THE NEW COPIED FACES
face split face209 connected keeptool faces face1104 face1105 face1106 face1107
face1108 face1109 face1110 face1111 face1112 face1113 face1114 face1115
face1116 face1117 face1118 face1119 face1120 face1121 face1122 face1123
face1124 face1125 face1126 face1127 face1128 face1129 face1130 face1131
face1132 face1133 face1134 face1135 face1136 face1137 face1138 face1139
face1140 face1141 face1142 face1143 face1144 face1145 face1146 face1147
face1148 face1149 face1150 face1151 face1152 face1153 face1154 face1155
face1156 face1157 face1158 face1159 face1160 face1161 face1162 face1163
face1164 face1165 face1166 face1167 face1168 face1169 face1170 face1171
face1172 face1173 face1174 face1175 face1176 face1177 face1178 face1179
face1180 face1181 face1182 face1183 face1184 face1185 face1186 face1187
face1188 face1189 face1190 face1191 face1192 face1193 face1194 face1195
face1196 face1197 face1198 face1199 face1200 face1201 face1202 face1203
face1204 face1205 face1206 face1207 face1208 face1209 face1210 face1211
face1212 face1213 face1214 face1215 face1216 face1217 face1218 face1219
face1220 face1221 face1222 face1223 face1224 face1225 face1226 face1227
71
face1228 face1229 face1230 face1231 face1232 face1233 face1234 face1235
face1236 face1237 face1238 face1239 face1240 face1241 face1242 face1243
face1244 face1245 face1246 face1247 face1248 face1249 face1250 face1251
face1252 face1253
THIS UNITES THE RECTANGLE OUTSIDE FACES AND THE SEMICIRCLE SO THAT IT MAKES
A RECTANGLE WIHOUT THE CENTERJET
face unite faces jetcircle face223 real
face unite faces face222 outbox real
face unite faces face228 face226 real
face unite faces face225 face227 real
face unite faces face231 face233 real
face unite faces face232 face230 real
face unite faces face236 face238 real
face unite faces face237 face235 real
face unite faces face241 face243 real
face unite faces face242 face240 real
face unite faces face248 face246 real
face unite faces face245 face247 real
face unite faces face253 face251 real
face unite faces face252 face250 real
face unite faces face256 face258 real
face unite faces face257 face255 real
face unite faces face263 face261 real
face unite faces face260 face262 real
face unite faces face268 face266 real
face unite faces face265 face264 real
face unite faces face265 face267 real
face unite faces face273 face271 real
face unite faces face272 face270 real
face unite faces face276 face278 real
face unite faces face277 face275 real
face unite faces face281 face283 real
face unite faces face282 face280 real
face unite faces face286 face288 real
face unite faces face287 face285 real
face unite faces face291 face293 real
face unite faces face292 face290 real
face unite faces face296 face298 real
face unite faces face297 face295 real
face unite faces face301 face303 real
face unite faces face302 face300 real
face unite faces face306 face308 real
face unite faces face307 face305 real
face unite faces face316 face318 real
face unite faces face312 face310 real
face unite faces face311 face313 real
face unite faces face315 face317 real
face unite faces face321 face323 real
face unite faces face322 face320 real
face unite faces face326 face328 real
face unite faces face327 face325 real
face unite faces face331 face333 real
face unite faces face332 face330 real
face unite faces face336 face338 real
72
face unite faces face337 face335 real
face unite faces face347 face345 real
face unite faces face346 face348 real
face unite faces face342 face340 real
face unite faces face341 face343 real
face unite faces face356 face358 real
face unite faces face357 face355 real
face unite faces face352 face350 real
face unite faces face351 face353 real
face unite faces face361 face363 real
face unite faces face366 face368 real
face unite faces face360 face362 real
face unite faces face365 face367 real
SPLITTING ALL THE FACES OF THE CIRCLES IN THE BOTTOM OF THE PLENUM
face split face912 connected keeptool faces face222
face split face117 connected keeptool faces face228
face split face117 connected keeptool faces face225
face split face922 connected keeptool faces face232
face split face124 connected keeptool faces face236
face split face124 connected keeptool faces face237
face split face932 connected keeptool faces face242
face split face131 connected keeptool faces face248
face split face131 connected keeptool faces face245
face split face942 connected keeptool faces face252
face split face138 connected keeptool faces face256
face split face138 connected keeptool faces face257
face split face952 connected keeptool faces face260
face split face145 connected keeptool faces face268
face split face145 connected keeptool faces face265
face split face962 connected keeptool faces face272
face split face152 connected keeptool faces face276
face split face152 connected keeptool faces face277
face split face972 connected keeptool faces face282
face split face159 connected keeptool faces face286
face split face159 connected keeptool faces face287
face split face982 connected keeptool faces face292
face split face166 connected keeptool faces face296
face split face166 connected keeptool faces face297
face split face992 connected keeptool faces face302
face split face173 connected keeptool faces face306
face split face173 connected keeptool faces face307
face split face1002 connected keeptool faces face312
face split face180 connected keeptool faces face316
face split face180 connected keeptool faces face315
73
face split face1012 connected keeptool faces face322
face split face187 connected keeptool faces face326
face split face187 connected keeptool faces face327
face split face1022 connected keeptool faces face332
face split face194 connected keeptool faces face336
face split face194 connected keeptool faces face337
face split face1032 connected keeptool faces face342
face split face201 connected keeptool faces face346
face split face201 connected keeptool faces face347
face split face1042 connected keeptool faces face352
face split face208 connected keeptool faces face356
face split face208 connected keeptool faces face357
face split face1052 connected keeptool faces face360
face split face215 connected keeptool faces face366
face split face215 connected keeptool faces face365
THIS UNITES THE RECTANGLE OUTSIDE FACES AND THE SEMICIRCLE SO THAT IT MAKES
A RECTANGLE WIHOUT THE CENTERJET
face unite faces face1104 face1108 real
face unite faces face1107 face1106 real
face unite faces face1113 face1111 real
face unite faces face1112 face1110 real
face unite faces face1118 face1116 real
face unite faces face1117 face1115 real
face unite faces face1123 face1121 real
face unite faces face1122 face1120 real
face unite faces face1128 face1126 real
face unite faces face1127 face1125 real
face unite faces face1133 face1131 real
face unite faces face1132 face1130 real
face unite faces face1138 face1136 real
face unite faces face1137 face1135 real
face unite faces face1143 face1141 real
face unite faces face1142 face1140 real
face unite faces face1148 face1146 real
face unite faces face1147 face1145 real
face unite faces face1153 face1151 real
face unite faces face1152 face1150 real
face unite faces face1158 face1156 real
face unite faces face1157 face1155 real
face unite faces face1163 face1161 real
face unite faces face1162 face1160 real
face unite faces face1168 face1166 real
face unite faces face1167 face1165 real
face unite faces face1173 face1171 real
face unite faces face1172 face1170 real
face unite faces face1178 face1176 real
face unite faces face1177 face1175 real
face unite faces face1183 face1181 real
74
face unite faces face1182 face1180 real
face unite faces face1186 face1188 real
face unite faces face1187 face1185 real
face unite faces face1193 face1191 real
face unite faces face1192 face1190 real
face unite faces face1198 face1196 real
face unite faces face1197 face1195 real
face unite faces face1203 face1201 real
face unite faces face1202 face1200 real
face unite faces face1206 face1208 real
face unite faces face1207 face1205 real
face unite faces face1213 face1211 real
face unite faces face1212 face1210 real
face unite faces face1216 face1218 real
face unite faces face1217 face1215 real
face unite faces face1221 face1223 real
face unite faces face1222 face1220 real
face unite faces face1228 face1226 real
face unite faces face1227 face1225 real
face unite faces face1233 face1231 real
face unite faces face1232 face1230 real
face unite faces face1238 face1236 real
face unite faces face1237 face1235 real
face unite faces face1243 face1241 real
face unite faces face1242 face1240 real
face unite faces face1248 face1246 real
face unite faces face1247 face1245 real
face unite faces face1253 face1251 real
face unite faces face1252 face1250 real
SPLITTING ALL THE FACES OF THE CIRCLES IN THE TOP OF THE CHANNEL
face split face1257 connected keeptool faces face1107
face split face115 connected keeptool faces face1113
face split face115 connected keeptool faces face1112
face split face1267 connected keeptool faces face1117
face split face122 connected keeptool faces face1123
face split face122 connected keeptool faces face1122
face split face1277 connected keeptool faces face1127
face split face129 connected keeptool faces face1133
face split face129 connected keeptool faces face1132
face split face1287 connected keeptool faces face1137
face split face136 connected keeptool faces face1143
face split face136 connected keeptool faces face1142
face split face1297 connected keeptool faces face1147
face split face143 connected keeptool faces face1153
face split face143 connected keeptool faces face1152
face split face1307 connected keeptool faces face1157
face split face150 connected keeptool faces face1163
face split face150 connected keeptool faces face1162
75
face split face1317 connected keeptool faces face1167
face split face157 connected keeptool faces face1173
face split face157 connected keeptool faces face1172
face split face1327 connected keeptool faces face1177
face split face164 connected keeptool faces face1183
face split face164 connected keeptool faces face1182
face split face1337 connected keeptool faces face1187
face split face171 connected keeptool faces face1193
face split face171 connected keeptool faces face1192
face split face1347 connected keeptool faces face1197
face split face178 connected keeptool faces face1203
face split face178 connected keeptool faces face1202
face split face1357 connected keeptool faces face1207
face split face185 connected keeptool faces face1213
face split face185 connected keeptool faces face1212
face split face1367 connected keeptool faces face1217
face split face192 connected keeptool faces face1221
face split face192 connected keeptool faces face1222
face split face1377 connected keeptool faces face1227
face split face199 connected keeptool faces face1233
face split face199 connected keeptool faces face1232
face split face1387 connected keeptool faces face1237
face split face206 connected keeptool faces face1243
face split face206 connected keeptool faces face1242
face split face1397 connected keeptool faces face1247
face split face213 connected keeptool faces face1253
face split face213 connected keeptool faces face1252
face split face1452 connected keeptool faces face224
face split face1456 connected keeptool faces face234
face split face1460 connected keeptool faces face244
face split face1464 connected keeptool faces face254
face split face1468 connected keeptool faces face264
face split face1472 connected keeptool faces face274
face split face1476 connected keeptool faces face284
face split face1480 connected keeptool faces face294
face split face1484 connected keeptool faces face304
face split face1488 connected keeptool faces face314
face split face1492 connected keeptool faces face324
face split face1496 connected keeptool faces face334
face split face1500 connected keeptool faces face344
face split face1504 connected keeptool faces face354
face split face1508 connected keeptool faces face364
DELETING ALL THE FACES USED TO MAKE THE CUTS
face delete jetcircle face222 face228 face225 jetcenter
76
face224 face231 face232 face236 face237 face229
face1456 face241 face242 face239 face248 face244
face245 face253 face249 face252 face254 face256
face257 face263 face259 face260 face268 face264
face265 face273 face272 face269 face276 face277
face274 face281 face282 face286 face279 face287
face284 face291 face292 face296 face297 face289
face294 face301 face299 face302 face306 face307
face304 face311 face312 face316 face315 face309
face314 face321 face322 face326 face327 face319
face324 face331 face332 face329 face336 face334
face337 face341 face342 face339 face346 face344
face347 face351 face352 face349 face356 face354
face357 face361 face359 face360 face366 face364
face365 lowertopology
face delete face1104 face1105 face1107 face1113 face1112
face115 face234 face1118 face1114 face1117 face1123
face1122 face122 face1138 face1128 face1127 face1124
face1133 face1132 face129 face1134 face1137 face1143
face136 face1142 face1148 face1144 face1147 face1153
face143 face1152 face1158 face1154 face1157 face1163
face150 face1162 face1168 face1164 face1167 face1173
face157 face1172 face1178 face1174 face1177 face1183
face164 face1182 face1186 face1184 face1187 face1193
face171 face1192 face1198 face1194 face1197 face1203
face178 face1202 face1206 face1204 face1207 face1213
face185 face1212 face1216 face1214 face1217 face1221
face192 face1222 face1228 face1224 face1227 face1233
face199 face1232 face1238 face1234 face1237 face1243
face206 face1242 face1248 face1244 face1247 face1253
face213 face1252 lowertopology
face delete face1109 face1119 face1129 face1139 face1149 face1159
face1169 face1179 face1189 face1199 face1209 face1219
face1229 face1239 face1249 lowertopology
face create CP1 width 600 height 75 offset 300 (225+($d)2) 0 xyplane rectangle
face create CP2 width 600 height 75 offset 300 (225+($d)2) ($zc) xyplane rectangle
face create CP3 width 600 height 75 offset 300 (225+($d)2) ($zc+$d) xyplane rectangle
face create CP4 width 600 height 75 offset 300 (225+($d)2) ($zc+$d+$zp) xyplane rectangle
face split face6 connected faces CP4
face split face114 connected faces CP3
face split face209 connected faces CP2
face split face1 connected faces CP1
GEOMETRY IS FINISHED
face modify face912 side vertex6437 vertex6436
77
face modify face1600 side vertex7302 vertex7303
face modify face117 side vertex6446 vertex6447
face modify face646 side vertex3312
face modify face646 side vertex3313
face modify face647 side vertex3432 vertex3433
face modify face372 side vertex2040 vertex2041
face modify face376 side vertex2100 vertex2101
face modify face377 side vertex2221 vertex2220
LINKING ALL THE JET CENTERS
face link face1450 face640 edges edge6949 edge3518 vertices
vertex6437 vertex3253 reverse
face link face1450 face1257 edges edge6949 edge7340 vertices
vertex6437 vertex6797 reverse
face link face1257 face370 edges edge7340 edge2139 vertices
vertex6797 vertex2041 reverse
face link face1257 face1454 edges edge7340 edge6975 vertices
vertex6797 vertex6461 reverse
face link face1454 face649 edges edge6975 edge3519 vertices
vertex6461 vertex3255 reverse
face link face1454 face1267 edges edge6975 edge7377 vertices
vertex6461 vertex6831 reverse
face link face1267 face379 edges edge7377 edge2141 vertices
vertex6831 vertex2043 reverse
face link face1267 face1458 edges edge7377 edge7001 vertices
vertex6831 vertex6485 reverse
face link face1458 face659 edges edge7001 edge3520 vertices
vertex6485 vertex3257 reverse
face link face1458 face1277 edges edge7001 edge7414 vertices
vertex6485 vertex6865 reverse
face link face1277 face389 edges edge7414 edge2143 vertices
vertex6865 vertex2045 reverse
face link face1277 face1462 edges edge7414 edge7027 vertices
vertex6865 vertex6509 reverse
face link face1462 face669 edges edge7027 edge3521 vertices
vertex6509 vertex3259 reverse
face link face1462 face1287 edges edge7027 edge7451 vertices
vertex6509 vertex6899 reverse
face link face1287 face399 edges edge7451 edge2145 vertices
vertex6899 vertex2047 reverse
face link face1287 face1466 edges edge7451 edge7053 vertices
vertex6899 vertex6533 reverse
face link face1466 face679 edges edge7053 edge3522 vertices
vertex6533 vertex3261 reverse
face link face1466 face1297 edges edge7053 edge7488 vertices
vertex6533 vertex6933 reverse
face link face1297 face409 edges edge7488 edge2147 vertices
vertex6933 vertex2049 reverse
face link face1297 face1470 edges edge7488 edge7079 vertices
vertex6933 vertex6557 reverse
face link face1470 face689 edges edge7079 edge3523 vertices
vertex6557 vertex3263 reverse
face link face1470 face1307 edges edge7079 edge7525 vertices
vertex6557 vertex6967 reverse
face link face1307 face419 edges edge7525 edge2149 vertices
78
vertex6967 vertex2051 reverse
face link face1307 face1474 edges edge7525 edge7105 vertices
vertex6967 vertex6581 reverse
face link face1474 face1317 edges edge7105 edge7562 vertices
vertex6581 vertex7001 reverse
face link face1474 face699 edges edge7105 edge3524 vertices
vertex6581 vertex3265 reverse
face link face1317 face429 edges edge7562 edge2151 vertices
vertex7001 vertex2053 reverse
face link face1317 face1478 edges edge7562 edge7131 vertices
vertex7001 vertex6605 reverse
face link face1478 face1327 edges edge7131 edge7599 vertices
vertex6605 vertex7035 reverse
face link face1478 face709 edges edge7131 edge3525 vertices
vertex6605 vertex3267 reverse
face link face1327 face439 edges edge7599 edge2153 vertices
vertex7035 vertex2055 reverse
face link face1327 face1482 edges edge7599 edge7157 vertices
vertex7035 vertex6629 reverse
face link face1482 face719 edges edge7157 edge3526 vertices
vertex6629 vertex3269 reverse
face link face1482 face1337 edges edge7157 edge7636 vertices
vertex6629 vertex7069 reverse
face link face1337 face449 edges edge7636 edge2155 vertices
vertex7069 vertex2057 reverse
face link face1337 face1486 edges edge7636 edge7183 vertices
vertex7069 vertex6653 reverse
face link face1486 face1347 edges edge7183 edge7673 vertices
vertex6653 vertex7103 reverse
face link face1347 face459 edges edge7673 edge2157 vertices
vertex7103 vertex2059 reverse
face link face1486 face729 edges edge7183 edge3527 vertices
vertex6653 vertex3271 reverse
face link face1347 face1490 edges edge7673 edge7209 vertices
vertex7103 vertex6677 reverse
face link face1490 face1357 edges edge7209 edge7710 vertices
vertex6677 vertex7137 reverse
face link face1490 face739 edges edge7209 edge3528 vertices
vertex6677 vertex3273 reverse
face link face1357 face469 edges edge7710 edge2159 vertices
vertex7137 vertex2061 reverse
face link face1357 face1494 edges edge7710 edge7235 vertices
vertex7137 vertex6701 reverse
face link face1494 face1367 edges edge7235 edge7747 vertices
vertex6701 vertex7171 reverse
face link face1494 face749 edges edge7235 edge3529 vertices
vertex6701 vertex3275 reverse
face link face1367 face479 edges edge7747 edge2161 vertices
vertex7171 vertex2063 reverse
face link face1367 face1498 edges edge7747 edge7261 vertices
vertex7171 vertex6725 reverse
face link face1498 face1377 edges edge7261 edge7784 vertices
vertex6725 vertex7205 reverse
face link face1377 face489 edges edge7784 edge2163 vertices
vertex7205 vertex2065 reverse
face link face1498 face759 edges edge7261 edge3530 vertices
79
vertex6725 vertex3277 reverse
face link face1377 face1502 edges edge7784 edge7287 vertices
vertex7205 vertex6749 reverse
face link face1502 face1387 edges edge7287 edge7821 vertices
vertex6749 vertex7239 reverse
face link face1387 face499 edges edge7821 edge2165 vertices
vertex7239 vertex2067 reverse
face link face1387 face1506 edges edge7821 edge7313 vertices
vertex7239 vertex6773 reverse
face link face1502 face769 edges edge7287 edge3531 vertices
vertex6749 vertex3279 reverse
face link face1506 face1397 edges edge7313 edge7858 vertices
vertex6773 vertex7273 reverse
face link face1506 face779 edges edge7313 edge3532 vertices
vertex6773 vertex3281 reverse
face link face1397 face509 edges edge7858 edge2167 vertices
vertex7273 vertex2069 reverse
LINKING ALL THE COMPLETE JETCENTERS
face link face1452 face644 edges edge7891 edge3773 vertices
vertex7303 vertex3433
face link face1452 face115 edges edge7891 edge7364 vertices
vertex7303 vertex6819
face link face1452 face1456 edges edge7891 edge7900 vertices
vertex7303 vertex7311
face link face1456 face654 edges edge7900 edge3774 vertices
vertex7311 vertex3435
face link face1456 face122 edges edge7900 edge7401 vertices
vertex7311 vertex6853
face link face1456 face1460 edges edge7900 edge7909 vertices
vertex7311 vertex7319
face link face1460 face1464 edges edge7909 edge7918 vertices
vertex7319 vertex7327
face link face1460 face129 edges edge7909 edge7438 vertices
vertex7319 vertex6887
face link face1460 face664 edges edge7909 edge3775 vertices
vertex7319 vertex3437
face link face1464 face674 edges edge7918 edge3776 vertices
vertex7327 vertex3439
face link face1464 face136 edges edge7918 edge7475 vertices
vertex7327 vertex6921
face link face1464 face1468 edges edge7918 edge7927 vertices
vertex7327 vertex7335
face link face1472 face1468 edges edge7936 edge7927 vertices
vertex7343 vertex7335
face link face1468 face143 edges edge7927 edge7512 vertices
vertex7335 vertex6955
face link face1468 face684 edges edge7927 edge3777 vertices
vertex7335 vertex3441
face link face1472 face694 edges edge7936 edge3778 vertices
vertex7343 vertex3443
face link face1472 face150 edges edge7936 edge7549 vertices
vertex7343 vertex6989
face link face1472 face1476 edges edge7936 edge7945 vertices
80
vertex7343 vertex7351
face link face1476 face1480 edges edge7945 edge7954 vertices
vertex7351 vertex7359
face link face1476 face157 edges edge7945 edge7586 vertices
vertex7351 vertex7023
face link face1476 face704 edges edge7945 edge3779 vertices
vertex7351 vertex3445
face link face1480 face714 edges edge7954 edge3780 vertices
vertex7359 vertex3447
face link face1480 face164 edges edge7954 edge7623 vertices
vertex7359 vertex7057
face link face1480 face1484 edges edge7954 edge7963 vertices
vertex7359 vertex7367
face link face1484 face171 edges edge7963 edge7660 vertices
vertex7367 vertex7091
face link face1484 face724 edges edge7963 edge3781 vertices
vertex7367 vertex3449
face link face1480 face1488 edges edge7954 edge7972 vertices
vertex7359 vertex7375
face link face1488 face178 edges edge7972 edge7697 vertices
vertex7375 vertex7125
face link face1488 face734 edges edge7972 edge3782 vertices
vertex7375 vertex3451
face link face1488 face1492 edges edge7972 edge7981 vertices
vertex7375 vertex7383
face link face1492 face744 edges edge7981 edge3783 vertices
vertex7383 vertex3453
face link face1492 face185 edges edge7981 edge7734 vertices
vertex7383 vertex7159
face link face1492 face1496 edges edge7981 edge7990 vertices
vertex7383 vertex7391
face link face1496 face754 edges edge7990 edge3784 vertices
vertex7391 vertex3455
face link face1496 face192 edges edge7990 edge7771 vertices
vertex7391 vertex7193
face link face1496 face1500 edges edge7990 edge7999 vertices
vertex7391 vertex7399
face link face1500 face1504 edges edge7999 edge8008 vertices
vertex7399 vertex7407
face link face1504 face1508 edges edge8008 edge8017 vertices
vertex7407 vertex7415
face link face1500 face199 edges edge7999 edge7808 vertices
vertex7399 vertex7227
face link face1500 face764 edges edge7999 edge3785 vertices
vertex7399 vertex3457
face link face1504 face774 edges edge8008 edge3786 vertices
vertex7407 vertex3459
face link face1508 face784 edges edge8017 edge3787 vertices
vertex7415 vertex3461
face link face1504 face206 edges edge8008 edge7845 vertices
vertex7407 vertex7261
face link face1508 face213 edges edge8017 edge7882 vertices
vertex7415 vertex7295
linking the jetcenters of the bottom of the channel one of them has to be reversed but the otherones are not
81
face link face115 face374 edges edge7364 edge2394 vertices
vertex6819 vertex2221 reverse
face link face374 face384 edges edge2394 edge2396 vertices
vertex2221 vertex2223
face link face384 face394 edges edge2396 edge2398 vertices
vertex2223 vertex2225
face link face394 face404 edges edge2398 edge2400 vertices
vertex2225 vertex2227
face link face404 face414 edges edge2400 edge2402 vertices
vertex2227 vertex2229
face link face414 face424 edges edge2402 edge2404 vertices
vertex2229 vertex2231
face link face424 face434 edges edge2404 edge2406 vertices
vertex2231 vertex2233
face link face434 face444 edges edge2406 edge2408 vertices
vertex2233 vertex2235
face link face444 face454 edges edge2408 edge2410 vertices
vertex2235 vertex2237
face link face454 face464 edges edge2410 edge2412 vertices
vertex2237 vertex2239
face link face464 face474 edges edge2412 edge2414 vertices
vertex2239 vertex2241
face link face474 face484 edges edge2414 edge2416 vertices
vertex2241 vertex2243
face link face484 face494 edges edge2416 edge2418 vertices
vertex2243 vertex2245
face link face494 face504 edges edge2418 edge2420 vertices
vertex2245 vertex2247
face link face504 face514 edges edge2420 edge2422 vertices
vertex2247 vertex2249
UP TO THIS POINT ALL THE FACES ARE CONNCTED SUCCESSFULLY
LINKING THE FIRST THREE JET TELEPHONES
face link face912 face117 edges edge6950 edge6960 vertices
vertex6437 vertex6446 reverse
face link face912 face1600 edges edge6950 edge7890 vertices
vertex6437 vertex7303 reverse
face link face912 face372 edges edge6950 edge2168 vertices
vertex6437 vertex2041
face link face117 face376 edges edge6959 edge2304 vertices
vertex6447 vertex2101 reverse
face link face1600 face377 edges edge7890 edge2423 vertices
vertex7303 vertex2221 reverse
face link face372 face382 edges edge2168 edge2169 vertices
vertex2041 vertex2043
face link face377 face387 edges edge2423 edge2424 vertices
vertex2221 vertex2223
face link face376 face386 edges edge2304 edge2306 vertices
vertex2101 vertex2103
face link face387 face397 edges edge2424 edge2425 vertices
vertex2223 vertex2225
face link face386 face396 edges edge2306 edge2308 vertices
82
vertex2103 vertex2105
face link face382 face392 edges edge2169 edge2170 vertices
vertex2043 vertex2045
face link face382 face392 edges edge2169 edge2170 vertices
vertex2043 vertex2045
face link face382 face392 edges edge2169 edge2170 vertices
vertex2043 vertex2045
face link face382 face392 edges edge2169 edge2170 vertices
vertex2043 vertex2045
face link face397 face407 edges edge2425 edge2426 vertices
vertex2225 vertex2227
face link face392 face402 edges edge2170 edge2171 vertices
vertex2045 vertex2047
face link face396 face406 edges edge2290 edge2291 vertices
vertex2104 vertex2106
face link face407 face417 edges edge2426 edge2427 vertices
vertex2227 vertex2229
face link face417 face427 edges edge2427 edge2428 vertices
vertex2229 vertex2231
face link face427 face437 edges edge2428 edge2429 vertices
vertex2231 vertex2233
face link face437 face447 edges edge2429 edge2430 vertices
vertex2233 vertex2235
face link face447 face457 edges edge2430 edge2431 vertices
vertex2235 vertex2237
face link face457 face467 edges edge2431 edge2432 vertices
vertex2237 vertex2239
face link face467 face477 edges edge2432 edge2433 vertices
vertex2239 vertex2241
face link face477 face487 edges edge2433 edge2434 vertices
vertex2241 vertex2243
face link face487 face487 edges edge2434 edge2434 vertices
vertex2243 vertex2243
face link face487 face487 edges edge2434 edge2434 vertices
vertex2243 vertex2243
face link face487 face487 edges edge2434 edge2434 vertices
vertex2243 vertex2243
face link face487 face497 edges edge2434 edge2435 vertices
vertex2243 vertex2245
face link face497 face507 edges edge2435 edge2436 vertices
vertex2245 vertex2247
face link face507 face517 edges edge2436 edge2437 vertices
vertex2247 vertex2249
face link face406 face416 edges edge2291 edge2292 vertices
vertex2106 vertex2108
face link face416 face426 edges edge2292 edge2293 vertices
vertex2108 vertex2110
face link face426 face436 edges edge2293 edge2294 vertices
vertex2110 vertex2112
face link face436 face446 edges edge2294 edge2295 vertices
vertex2112 vertex2114
face link face446 face456 edges edge2295 edge2296 vertices
vertex2114 vertex2116
face link face456 face466 edges edge2296 edge2297 vertices
vertex2116 vertex2118
face link face466 face476 edges edge2297 edge2298 vertices
83
vertex2118 vertex2120
face link face486 face496 edges edge2299 edge2300 vertices
vertex2122 vertex2124
face link face476 face486 edges edge2298 edge2299 vertices
vertex2120 vertex2122
face link face496 face506 edges edge2300 edge2301 vertices
vertex2124 vertex2126
face link face506 face516 edges edge2301 edge2302 vertices
vertex2126 vertex2128
face link face392 face402 edges edge2142 edge2144 vertices
vertex2044 vertex2046
face link face402 face412 edges edge2171 edge2172 vertices
vertex2047 vertex2049
face link face412 face422 edges edge2172 edge2173 vertices
vertex2049 vertex2051
face link face422 face432 edges edge2173 edge2174 vertices
vertex2051 vertex2053
face link face432 face442 edges edge2174 edge2175 vertices
vertex2053 vertex2055
face link face442 face452 edges edge2175 edge2176 vertices
vertex2055 vertex2057
face link face452 face462 edges edge2176 edge2177 vertices
vertex2057 vertex2059
face link face462 face472 edges edge2177 edge2178 vertices
vertex2059 vertex2061
face link face472 face482 edges edge2178 edge2179 vertices
vertex2061 vertex2063
face link face482 face492 edges edge2179 edge2180 vertices
vertex2063 vertex2065
face link face492 face502 edges edge2180 edge2181 vertices
vertex2065 vertex2067
face link face502 face512 edges edge2181 edge2182 vertices
vertex2067 vertex2069
LINKING THE TELEPHONES OF THE BOTTOM OF THE PLENUM
face link face912 face922 edges edge6950 edge6976 vertices
vertex6437 vertex6461
face link face922 face932 edges edge6976 edge7002 vertices
vertex6461 vertex6485
face link face932 face942 edges edge7002 edge7028 vertices
vertex6485 vertex6509
face link face942 face952 edges edge7028 edge7054 vertices
vertex6509 vertex6533
face link face952 face962 edges edge7054 edge7080 vertices
vertex6533 vertex6557
face link face962 face972 edges edge7080 edge7106 vertices
vertex6557 vertex6581
face link face972 face982 edges edge7106 edge7132 vertices
vertex6581 vertex6605
face link face982 face992 edges edge7132 edge7158 vertices
vertex6605 vertex6629
face link face992 face1002 edges edge7158 edge7184 vertices
vertex6629 vertex6653
face link face1002 face1012 edges edge7184 edge7210 vertices
vertex6653 vertex6677
84
face link face1012 face1022 edges edge7210 edge7236 vertices
vertex6677 vertex6701
face link face1032 face1042 edges edge7262 edge7288 vertices
vertex6725 vertex6749
face link face1042 face1052 edges edge7288 edge7314 vertices
vertex6749 vertex6773
face link face117 face124 edges edge6960 edge6986 vertices
vertex6446 vertex6470
face link face124 face131 edges edge6986 edge7012 vertices
vertex6470 vertex6494
face link face131 face138 edges edge7012 edge7038 vertices
vertex6494 vertex6518
face link face138 face145 edges edge7038 edge7064 vertices
vertex6518 vertex6542
face link face145 face152 edges edge7064 edge7090 vertices
vertex6542 vertex6566
face link face152 face159 edges edge7090 edge7116 vertices
vertex6566 vertex6590
face link face159 face166 edges edge7116 edge7142 vertices
vertex6590 vertex6614
face link face166 face173 edges edge7142 edge7168 vertices
vertex6614 vertex6638
face link face173 face180 edges edge7168 edge7194 vertices
vertex6638 vertex6662
face link face180 face187 edges edge7194 edge7220 vertices
vertex6662 vertex6686
face link face187 face194 edges edge7220 edge7246 vertices
vertex6686 vertex6710
face link face194 face201 edges edge7246 edge7272 vertices
vertex6710 vertex6734
face link face1022 face1032 edges edge7236 edge7262 vertices
vertex6701 vertex6725
face link face1032 face1042 edges edge7262 edge7288 vertices
vertex6725 vertex6749
face link face201 face208 edges edge7271 edge7297 vertices
vertex6735 vertex6759
face link face208 face215 edges edge7297 edge7323 vertices
vertex6759 vertex6783
face link face1600 face1602 edges edge7890 edge7899 vertices
vertex7303 vertex7311
face link face1602 face1604 edges edge7899 edge7908 vertices
vertex7311 vertex7319
face link face1604 face1606 edges edge7908 edge7917 vertices
vertex7319 vertex7327
face link face1606 face1608 edges edge7917 edge7926 vertices
vertex7327 vertex7335
face link face1608 face1610 edges edge7926 edge7935 vertices
vertex7335 vertex7343
face link face1610 face1612 edges edge7935 edge7944 vertices
vertex7343 vertex7351
face link face1612 face1614 edges edge7944 edge7953 vertices
vertex7351 vertex7359
face link face1614 face1616 edges edge7953 edge7962 vertices
vertex7359 vertex7367
face link face1616 face1618 edges edge7962 edge7971 vertices
vertex7367 vertex7375
85
face link face1618 face1620 edges edge7971 edge7980 vertices
vertex7375 vertex7383
face link face1620 face1622 edges edge7980 edge7989 vertices
vertex7383 vertex7391
face link face1622 face1624 edges edge7989 edge7998 vertices
vertex7391 vertex7399
face link face1624 face1626 edges edge7998 edge8007 vertices
vertex7399 vertex7407
face link face1626 face1628 edges edge8007 edge8016 vertices
vertex7407 vertex7415
LINKING ALL THE TELEPHONES OF THE TOP OF THE CHANNEL
face link face912 face1510 edges edge6950 edge7339 vertices
vertex6437 vertex6797 reverse
face link face117 face1512 edges edge6959 edge7349 vertices
vertex6447 vertex6807
face link face1600 face1514 edges edge7890 edge7363 vertices
vertex7303 vertex6819
face link face1510 face1516 edges edge7339 edge7376 vertices
vertex6797 vertex6831
face link face1516 face1522 edges edge7376 edge7413 vertices
vertex6831 vertex6865
face link face1522 face1528 edges edge7413 edge7450 vertices
vertex6865 vertex6899
face link face1528 face1534 edges edge7450 edge7487 vertices
vertex6899 vertex6933
face link face1534 face1540 edges edge7487 edge7524 vertices
vertex6933 vertex6967
face link face1540 face1546 edges edge7524 edge7561 vertices
vertex6967 vertex7001
face link face1546 face1552 edges edge7561 edge7598 vertices
vertex7001 vertex7035
face link face1552 face1558 edges edge7598 edge7635 vertices
vertex7035 vertex7069
face link face1558 face1564 edges edge7635 edge7672 vertices
vertex7069 vertex7103
face link face1564 face1570 edges edge7672 edge7709 vertices
vertex7103 vertex7137
face link face1570 face1576 edges edge7709 edge7746 vertices
vertex7137 vertex7171
face link face1576 face1582 edges edge7746 edge7783 vertices
vertex7171 vertex7205
face link face1582 face1588 edges edge7783 edge7820 vertices
vertex7205 vertex7239
face link face1588 face1594 edges edge7820 edge7857 vertices
vertex7239 vertex7273
face link face1512 face1518 edges edge7350 edge7387 vertices
vertex6806 vertex6840
face link face1518 face1524 edges edge7387 edge7424 vertices
vertex6840 vertex6874
face link face1524 face1530 edges edge7424 edge7461 vertices
vertex6874 vertex6908
face link face1530 face1536 edges edge7461 edge7498 vertices
vertex6908 vertex6942
face link face1536 face1542 edges edge7498 edge7535 vertices
86
vertex6942 vertex6976
face link face1542 face1548 edges edge7535 edge7572 vertices
vertex6976 vertex7010
face link face1548 face1554 edges edge7572 edge7609 vertices
vertex7010 vertex7044
face link face1554 face1560 edges edge7609 edge7646 vertices
vertex7044 vertex7078
face link face1560 face1566 edges edge7646 edge7683 vertices
vertex7078 vertex7112
face link face1566 face1572 edges edge7683 edge7720 vertices
vertex7112 vertex7146
face link face1572 face1578 edges edge7720 edge7757 vertices
vertex7146 vertex7180
face link face1578 face1584 edges edge7757 edge7794 vertices
vertex7180 vertex7214
face link face1584 face1590 edges edge7794 edge7831 vertices
vertex7214 vertex7248
face link face1590 face1596 edges edge7831 edge7868 vertices
vertex7248 vertex7282
face link face1514 face1520 edges edge7363 edge7400 vertices
vertex6819 vertex6853
face link face1520 face1526 edges edge7400 edge7437 vertices
vertex6853 vertex6887
face link face1526 face1532 edges edge7437 edge7474 vertices
vertex6887 vertex6921
face link face1532 face1538 edges edge7474 edge7511 vertices
vertex6921 vertex6955
face link face1538 face1544 edges edge7511 edge7548 vertices
vertex6955 vertex6989
face link face1544 face1550 edges edge7548 edge7585 vertices
vertex6989 vertex7023
face link face1550 face1556 edges edge7585 edge7622 vertices
vertex7023 vertex7057
face link face1556 face1562 edges edge7622 edge7659 vertices
vertex7057 vertex7091
face link face1562 face1568 edges edge7659 edge7696 vertices
vertex7091 vertex7125
face link face1568 face1574 edges edge7696 edge7733 vertices
vertex7125 vertex7159
face link face1574 face1580 edges edge7733 edge7770 vertices
vertex7159 vertex7193
face link face1580 face1586 edges edge7770 edge7807 vertices
vertex7193 vertex7227
face link face1586 face1592 edges edge7807 edge7844 vertices
vertex7227 vertex7261
face link face1592 face1598 edges edge7844 edge7881 vertices
vertex7261 vertex7295
LINKING ALL THE TELEPHONES OF THE TOP OF THE PLENUM
face link face912 face642 edges edge6950 edge3489 vertices
vertex6437 vertex3253 reverse
face link face642 face647 edges edge3489 edge3744 vertices
vertex3253 vertex3433
face link face117 face646 edges edge6959 edge3638 vertices
vertex6447 vertex3313
87
face link face642 face652 edges edge3489 edge3491 vertices
vertex3253 vertex3255
face link face652 face662 edges edge3491 edge3493 vertices
vertex3255 vertex3257
face link face662 face672 edges edge3493 edge3495 vertices
vertex3257 vertex3259
face link face672 face682 edges edge3495 edge3497 vertices
vertex3259 vertex3261
face link face682 face692 edges edge3497 edge3499 vertices
vertex3261 vertex3263
face link face692 face702 edges edge3499 edge3501 vertices
vertex3263 vertex3265
face link face702 face712 edges edge3501 edge3503 vertices
vertex3265 vertex3267
face link face712 face722 edges edge3503 edge3505 vertices
vertex3267 vertex3269
face link face722 face732 edges edge3505 edge3507 vertices
vertex3269 vertex3271
face link face732 face742 edges edge3507 edge3509 vertices
vertex3271 vertex3273
face link face742 face752 edges edge3509 edge3511 vertices
vertex3273 vertex3275
face link face752 face762 edges edge3511 edge3513 vertices
vertex3275 vertex3277
face link face762 face772 edges edge3513 edge3515 vertices
vertex3277 vertex3279
face link face772 face782 edges edge3515 edge3517 vertices
vertex3279 vertex3281
face link face646 face656 edges edge3653 edge3655 vertices
vertex3312 vertex3314
face link face656 face666 edges edge3655 edge3657 vertices
vertex3314 vertex3316
face link face666 face676 edges edge3657 edge3659 vertices
vertex3316 vertex3318
face link face676 face686 edges edge3659 edge3661 vertices
vertex3318 vertex3320
face link face686 face696 edges edge3661 edge3663 vertices
vertex3320 vertex3322
face link face696 face706 edges edge3663 edge3665 vertices
vertex3322 vertex3324
face link face706 face716 edges edge3665 edge3667 vertices
vertex3324 vertex3326
face link face716 face726 edges edge3667 edge3669 vertices
vertex3326 vertex3328
face link face726 face736 edges edge3669 edge3671 vertices
vertex3328 vertex3330
face link face736 face746 edges edge3671 edge3673 vertices
vertex3330 vertex3332
face link face746 face756 edges edge3673 edge3675 vertices
vertex3332 vertex3334
face link face756 face766 edges edge3675 edge3677 vertices
vertex3334 vertex3336
face link face766 face776 edges edge3677 edge3679 vertices
vertex3336 vertex3338
face link face776 face786 edges edge3679 edge3681 vertices
88
vertex3338 vertex3340
face link face647 face657 edges edge3744 edge3746 vertices
vertex3433 vertex3435
face link face657 face667 edges edge3746 edge3748 vertices
vertex3435 vertex3437
face link face667 face677 edges edge3748 edge3750 vertices
vertex3437 vertex3439
face link face677 face687 edges edge3750 edge3752 vertices
vertex3439 vertex3441
face link face687 face697 edges edge3752 edge3754 vertices
vertex3441 vertex3443
face link face697 face707 edges edge3754 edge3756 vertices
vertex3443 vertex3445
face link face707 face717 edges edge3756 edge3758 vertices
vertex3445 vertex3447
face link face717 face727 edges edge3758 edge3760 vertices
vertex3447 vertex3449
face link face727 face737 edges edge3760 edge3762 vertices
vertex3449 vertex3451
face link face737 face747 edges edge3762 edge3764 vertices
vertex3451 vertex3453
face link face747 face757 edges edge3764 edge3766 vertices
vertex3453 vertex3455
face link face757 face767 edges edge3766 edge3768 vertices
vertex3455 vertex3457
face link face767 face777 edges edge3768 edge3770 vertices
vertex3457 vertex3459
face link face777 face787 edges edge3770 edge3772 vertices
vertex3459 vertex3461
face link face647 face1600 edges edge3685 edge6963 vertices
vertex3345 vertex6449
LINKING OUTBOXES ON THE PLENUM
face modify face911 side vertex4404 vertex4405
face modify face918 side vertex4405 vertex4404
face link face911 face915 edges edge4778 edge4898 vertices
vertex4374 vertex4434
face link face915 face645 edges edge4899 edge3833 vertices
vertex4480 vertex3463 reverse
face link face911 face641 edges edge4779 edge3578 vertices
vertex4405 vertex3283 reverse
face link face918 face648 edges edge4825 edge3686 vertices
vertex4436 vertex3347 reverse
face link face645 face655 edges edge3833 edge3834 vertices
vertex3463 vertex3465
face link face655 face665 edges edge3834 edge3835 vertices
vertex3465 vertex3467
face link face665 face675 edges edge3835 edge3836 vertices
vertex3467 vertex3469
face link face675 face685 edges edge3836 edge3837 vertices
vertex3469 vertex3471
face link face685 face695 edges edge3837 edge3838 vertices
89
vertex3471 vertex3473
face link face695 face705 edges edge3838 edge3839 vertices
vertex3473 vertex3475
face link face705 face715 edges edge3839 edge3840 vertices
vertex3475 vertex3477
face link face715 face725 edges edge3840 edge3841 vertices
vertex3477 vertex3479
face link face725 face735 edges edge3841 edge3842 vertices
vertex3479 vertex3481
face link face735 face745 edges edge3842 edge3843 vertices
vertex3481 vertex3483
face link face745 face755 edges edge3843 edge3844 vertices
vertex3483 vertex3485
face link face755 face765 edges edge3844 edge3845 vertices
vertex3485 vertex3487
face link face765 face775 edges edge3845 edge3846 vertices
vertex3487 vertex3489
face link face775 face785 edges edge3846 edge3847 vertices
vertex3489 vertex3491
face link face648 face658 edges edge3686 edge3690 vertices
vertex3347 vertex3353
face link face658 face668 edges edge3690 edge3694 vertices
vertex3353 vertex3359
face link face668 face678 edges edge3694 edge3698 vertices
vertex3359 vertex3365
face link face678 face688 edges edge3698 edge3702 vertices
vertex3365 vertex3371
face link face688 face698 edges edge3702 edge3706 vertices
vertex3371 vertex3377
face link face698 face708 edges edge3706 edge3710 vertices
vertex3377 vertex3383
face link face708 face718 edges edge3710 edge3714 vertices
vertex3383 vertex3389
face link face718 face728 edges edge3714 edge3718 vertices
vertex3389 vertex3395
face link face728 face738 edges edge3718 edge3722 vertices
vertex3395 vertex3401
face link face738 face748 edges edge3722 edge3726 vertices
vertex3401 vertex3407
face link face748 face758 edges edge3726 edge3730 vertices
vertex3407 vertex3413
face link face758 face768 edges edge3730 edge3734 vertices
vertex3413 vertex3419
face link face768 face778 edges edge3734 edge3738 vertices
vertex3419 vertex3425
face link face778 face788 edges edge3738 edge3742 vertices
vertex3425 vertex3431
face link face641 face650 edges edge3578 edge3579 vertices
vertex3283 vertex3285
face link face650 face660 edges edge3579 edge3580 vertices
vertex3285 vertex3287
face link face660 face670 edges edge3580 edge3581 vertices
vertex3287 vertex3289
face link face670 face680 edges edge3581 edge3582 vertices
vertex3289 vertex3291
face link face680 face690 edges edge3582 edge3583 vertices
90
vertex3291 vertex3293
face link face690 face700 edges edge3583 edge3584 vertices
vertex3293 vertex3295
face link face700 face710 edges edge3584 edge3585 vertices
vertex3295 vertex3297
face link face710 face720 edges edge3585 edge3586 vertices
vertex3297 vertex3299
face link face720 face730 edges edge3586 edge3587 vertices
vertex3299 vertex3301
face link face730 face740 edges edge3587 edge3588 vertices
vertex3301 vertex3303
face link face740 face750 edges edge3588 edge3589 vertices
vertex3303 vertex3305
face link face750 face760 edges edge3589 edge3590 vertices
vertex3305 vertex3307
face link face760 face770 edges edge3590 edge3591 vertices
vertex3307 vertex3309
face link face770 face780 edges edge3591 edge3592 vertices
vertex3309 vertex3311
face link face915 face925 edges edge4899 edge4901 vertices
vertex4480 vertex4482
face link face925 face935 edges edge4901 edge4903 vertices
vertex4482 vertex4484
face link face935 face945 edges edge4903 edge4905 vertices
vertex4484 vertex4486
face link face945 face955 edges edge4905 edge4907 vertices
vertex4486 vertex4488
face link face955 face965 edges edge4907 edge4909 vertices
vertex4488 vertex4490
face link face965 face975 edges edge4909 edge4911 vertices
vertex4490 vertex4492
face link face975 face985 edges edge4911 edge4913 vertices
vertex4492 vertex4494
face link face985 face995 edges edge4913 edge4915 vertices
vertex4494 vertex4496
face link face995 face1005 edges edge4915 edge4917 vertices
vertex4496 vertex4498
face link face1005 face1015 edges edge4917 edge4919 vertices
vertex4498 vertex4500
face link face1015 face1025 edges edge4919 edge4921 vertices
vertex4500 vertex4502
face link face1025 face1035 edges edge4921 edge4923 vertices
vertex4502 vertex4504
face link face1035 face1045 edges edge4923 edge4925 vertices
vertex4504 vertex4506
face link face1045 face1055 edges edge4925 edge4927 vertices
vertex4506 vertex4508
face link face918 face928 edges edge4825 edge4828 vertices
vertex4436 vertex4439
face link face928 face938 edges edge4828 edge4831 vertices
vertex4439 vertex4442
face link face938 face948 edges edge4831 edge4834 vertices
vertex4442 vertex4445
face link face948 face958 edges edge4834 edge4837 vertices
vertex4445 vertex4448
face link face958 face968 edges edge4837 edge4840 vertices
91
vertex4448 vertex4451
face link face968 face978 edges edge4840 edge4843 vertices
vertex4451 vertex4454
face link face978 face988 edges edge4843 edge4846 vertices
vertex4454 vertex4457
face link face988 face998 edges edge4846 edge4849 vertices
vertex4457 vertex4460
face link face998 face1008 edges edge4849 edge4852 vertices
vertex4460 vertex4463
face link face1008 face1018 edges edge4852 edge4855 vertices
vertex4463 vertex4466
face link face1018 face1028 edges edge4855 edge4858 vertices
vertex4466 vertex4469
face link face1028 face1038 edges edge4858 edge4861 vertices
vertex4469 vertex4472
face link face1038 face1048 edges edge4861 edge4864 vertices
vertex4472 vertex4475
face link face1048 face1058 edges edge4864 edge4867 vertices
vertex4475 vertex4478
face link face911 face920 edges edge108 edge118 vertices
vertex88 vertex94
face link face920 face930 edges edge118 edge128 vertices
vertex94 vertex100
face link face930 face940 edges edge4783 edge4785 vertices
vertex4409 vertex4411
face link face940 face950 edges edge4785 edge4787 vertices
vertex4411 vertex4413
face link face950 face960 edges edge4787 edge4789 vertices
vertex4413 vertex4415
face link face960 face970 edges edge4789 edge4791 vertices
vertex4415 vertex4417
face link face970 face980 edges edge4791 edge4793 vertices
vertex4417 vertex4419
face link face980 face990 edges edge4793 edge4795 vertices
vertex4419 vertex4421
face link face990 face1000 edges edge4795 edge4797 vertices
vertex4421 vertex4423
face link face1000 face1010 edges edge4797 edge4799 vertices
vertex4423 vertex4425
face link face1010 face1020 edges edge4799 edge4801 vertices
vertex4425 vertex4427
face link face1020 face1030 edges edge4801 edge4803 vertices
vertex4427 vertex4429
face link face1030 face1040 edges edge4803 edge4805 vertices
vertex4429 vertex4431
face link face1040 face1050 edges edge4805 edge4807 vertices
vertex4431 vertex4433
LINKING THE TOP OF THE CHANEL OUTBOXES
face modify face1256 side vertex6322 vertex6321
face modify face1263 side vertex6322 vertex6321
face modify face1260 side vertex6397 vertex6396
92
face link face1256 face1260 edges edge6803 edge6923 vertices
vertex6322 vertex6397
face link face1256 face371 edges edge6774 edge2053 vertices
vertex6292 vertex1955 reverse
face link face371 face375 edges edge2053 edge2336 vertices
vertex1955 vertex2135
face link face1263 face378 edges edge6820 edge2228 vertices
vertex6322 vertex2071 reverse
face link face1263 face1273 edges edge6820 edge6823 vertices
vertex6322 vertex6324
face link face1273 face1283 edges edge6823 edge6826 vertices
vertex6324 vertex6326
face link face1283 face1293 edges edge6826 edge6829 vertices
vertex6326 vertex6328
face link face1293 face1303 edges edge6829 edge6832 vertices
vertex6328 vertex6330
face link face1303 face1313 edges edge6832 edge6835 vertices
vertex6330 vertex6332
face link face1313 face1323 edges edge6835 edge6838 vertices
vertex6332 vertex6334
face link face1323 face1333 edges edge6838 edge6841 vertices
vertex6334 vertex6336
face link face1333 face1343 edges edge6841 edge6844 vertices
vertex6336 vertex6338
face link face1343 face1353 edges edge6844 edge6847 vertices
vertex6338 vertex6340
face link face1353 face1363 edges edge6847 edge6850 vertices
vertex6340 vertex6342
face link face1363 face1373 edges edge6850 edge6853 vertices
vertex6342 vertex6344
face link face1373 face1383 edges edge6853 edge6856 vertices
vertex6344 vertex6346
face link face1383 face1393 edges edge6856 edge6859 vertices
vertex6346 vertex6348
face link face1393 face1403 edges edge6859 edge6862 vertices
vertex6348 vertex6350
face link face1256 face1265 edges edge6774 edge6776 vertices
vertex6292 vertex6294
face link face1265 face1275 edges edge6776 edge6778 vertices
vertex6294 vertex6296
face link face1275 face1285 edges edge6778 edge6780 vertices
vertex6296 vertex6298
face link face1285 face1295 edges edge6780 edge6782 vertices
vertex6298 vertex6300
face link face1295 face1305 edges edge6782 edge6784 vertices
vertex6300 vertex6302
face link face1305 face1315 edges edge6784 edge6786 vertices
vertex6302 vertex6304
face link face1315 face1325 edges edge6786 edge6788 vertices
vertex6304 vertex6306
face link face1325 face1335 edges edge6788 edge6790 vertices
vertex6306 vertex6308
face link face1335 face1345 edges edge6790 edge6792 vertices
vertex6308 vertex6310
face link face1345 face1355 edges edge6792 edge6794 vertices
vertex6310 vertex6312
93
face link face1355 face1365 edges edge6794 edge6796 vertices
vertex6312 vertex6314
face link face1365 face1375 edges edge6796 edge6798 vertices
vertex6314 vertex6316
face link face1375 face1385 edges edge6798 edge6800 vertices
vertex6316 vertex6318
face link face1385 face1395 edges edge6800 edge6802 vertices
vertex6318 vertex6320
face link face1260 face1270 edges edge6894 edge6896 vertices
vertex6353 vertex6356
face link face1270 face1280 edges edge6896 edge6898 vertices
vertex6356 vertex6359
face link face1280 face1290 edges edge6898 edge6900 vertices
vertex6359 vertex6362
face link face1290 face1300 edges edge6900 edge6902 vertices
vertex6362 vertex6365
face link face1300 face1310 edges edge6902 edge6904 vertices
vertex6365 vertex6368
face link face1310 face1320 edges edge6904 edge6906 vertices
vertex6368 vertex6371
face link face1320 face1330 edges edge6906 edge6908 vertices
vertex6371 vertex6374
face link face1330 face1340 edges edge6908 edge6910 vertices
vertex6374 vertex6377
face link face1340 face1350 edges edge6910 edge6912 vertices
vertex6377 vertex6380
face link face1350 face1360 edges edge6912 edge6914 vertices
vertex6380 vertex6383
face link face1360 face1370 edges edge6914 edge6916 vertices
vertex6383 vertex6386
face link face1370 face1380 edges edge6916 edge6918 vertices
vertex6386 vertex6389
face link face1380 face1390 edges edge6918 edge6920 vertices
vertex6389 vertex6392
face link face1390 face1400 edges edge6920 edge6922 vertices
vertex6392 vertex6395
LINKING THE BOTTOM OF THE CHANEL OUTBOXES
face link face375 face385 edges edge2440 edge2443 vertices
vertex2251 vertex2253
face link face385 face395 edges edge2443 edge2446 vertices
vertex2253 vertex2255
face link face395 face405 edges edge2446 edge2449 vertices
vertex2255 vertex2257
face link face405 face415 edges edge2449 edge2452 vertices
vertex2257 vertex2259
face link face415 face425 edges edge2452 edge2455 vertices
vertex2259 vertex2261
face link face425 face435 edges edge2455 edge2458 vertices
vertex2261 vertex2263
face link face435 face445 edges edge2458 edge2461 vertices
vertex2263 vertex2265
face link face445 face455 edges edge2461 edge2464 vertices
vertex2265 vertex2267
face link face455 face465 edges edge2464 edge2467 vertices
94
vertex2267 vertex2269
face link face465 face475 edges edge2467 edge2470 vertices
vertex2269 vertex2271
face link face475 face485 edges edge2470 edge2473 vertices
vertex2271 vertex2273
face link face485 face495 edges edge2473 edge2476 vertices
vertex2273 vertex2275
face link face495 face505 edges edge2476 edge2479 vertices
vertex2275 vertex2277
face link face505 face515 edges edge2479 edge2482 vertices
vertex2277 vertex2279
face link face378 face388 edges edge2245 edge2248 vertices
vertex2135 vertex2141
face link face388 face398 edges edge2248 edge2251 vertices
vertex2141 vertex2147
face link face398 face408 edges edge2251 edge2254 vertices
vertex2147 vertex2153
face link face408 face418 edges edge2254 edge2257 vertices
vertex2153 vertex2159
face link face418 face428 edges edge2257 edge2260 vertices
vertex2159 vertex2165
face link face428 face438 edges edge2260 edge2263 vertices
vertex2165 vertex2171
face link face438 face448 edges edge2263 edge2266 vertices
vertex2171 vertex2177
face link face448 face458 edges edge2266 edge2269 vertices
vertex2177 vertex2183
face link face458 face468 edges edge2269 edge2272 vertices
vertex2183 vertex2189
face link face468 face478 edges edge2272 edge2275 vertices
vertex2189 vertex2195
face link face478 face488 edges edge2275 edge2278 vertices
vertex2195 vertex2201
face link face488 face498 edges edge2278 edge2281 vertices
vertex2201 vertex2207
face link face498 face508 edges edge2281 edge2284 vertices
vertex2207 vertex2213
face link face508 face518 edges edge2284 edge2287 vertices
vertex2213 vertex2219
face link face371 face380 edges edge2185 edge2188 vertices
vertex2071 vertex2073
face link face380 face390 edges edge2188 edge2191 vertices
vertex2073 vertex2075
face link face390 face400 edges edge2191 edge2194 vertices
vertex2075 vertex2077
face link face400 face410 edges edge2194 edge2197 vertices
vertex2077 vertex2079
face link face410 face420 edges edge2197 edge2200 vertices
vertex2079 vertex2081
face link face420 face430 edges edge2200 edge2203 vertices
vertex2081 vertex2083
face link face430 face440 edges edge2203 edge2206 vertices
vertex2083 vertex2085
face link face440 face450 edges edge2206 edge2209 vertices
vertex2085 vertex2087
face link face450 face460 edges edge2209 edge2212 vertices
95
vertex2087 vertex2089
face link face460 face470 edges edge2212 edge2215 vertices
vertex2089 vertex2091
face link face470 face480 edges edge2215 edge2218 vertices
vertex2091 vertex2093
face link face480 face490 edges edge2218 edge2221 vertices
vertex2093 vertex2095
face link face490 face500 edges edge2221 edge2224 vertices
vertex2095 vertex2097
face link face500 face510 edges edge2224 edge2227 vertices
vertex2097 vertex2099
TOP SIDE BOX beginning of channel
face link face1649 face1633 edges edge97 edge3533 vertices
vertex4374 vertex3162 reverse
TOP SIDE BOXES
face link face1650 face1651 edges edge4749 edge4751 vertices
vertex4376 vertex4378
face link face1652 face1653 edges edge4753 edge4755 vertices
vertex4380 vertex4382
face link face1653 face1654 edges edge4755 edge4757 vertices
vertex4382 vertex4384
face link face1654 face1655 edges edge4757 edge4759 vertices
vertex4384 vertex4386
face link face1655 face1656 edges edge4759 edge4761 vertices
vertex4386 vertex4388
face link face1656 face114 edges edge4761 edge4763 vertices
vertex4388 vertex4390
face link face114 face1657 edges edge4763 edge4765 vertices
vertex4390 vertex4392
face link face1657 face1658 edges edge4765 edge4767 vertices
vertex4392 vertex4394
face link face1658 face1659 edges edge4767 edge4769 vertices
vertex4394 vertex4396
face link face1659 face1660 edges edge4769 edge4771 vertices
vertex4396 vertex4398
face link face1660 face1661 edges edge4771 edge4773 vertices
vertex4398 vertex4400
face link face1661 face1662 edges edge4773 edge4775 vertices
vertex4400 vertex4402
face link face1650 face1634 edges edge4900 edge8036 vertices
vertex4481 vertex3464 reverse
face link face1634 face1635 edges edge8036 edge8037 vertices
vertex3464 vertex3466
face link face1635 face1636 edges edge8037 edge8038 vertices
vertex3466 vertex3468
face link face1636 face1637 edges edge8038 edge8039 vertices
vertex3468 vertex3470
face link face1637 face1638 edges edge8039 edge8040 vertices
vertex3470 vertex3472
face link face1638 face1639 edges edge8040 edge8041 vertices
vertex3472 vertex3474
face link face1639 face6 edges edge8041 edge8042 vertices
96
vertex3474 vertex3476
face link face6 face1640 edges edge8042 edge8043 vertices
vertex3476 vertex3478
face link face1640 face1641 edges edge8043 edge8044 vertices
vertex3478 vertex3480
face link face1641 face1642 edges edge8044 edge8045 vertices
vertex3480 vertex3482
face link face1642 face1643 edges edge8045 edge8046 vertices
vertex3482 vertex3484
face link face1643 face1644 edges edge8046 edge8047 vertices
vertex3484 vertex3486
face link face1644 face1645 edges edge8047 edge8048 vertices
vertex3486 vertex3488
face link face1645 face1646 edges edge8048 edge8049 vertices
vertex3488 vertex3490
face link face1651 face1652 edges edge4751 edge4753 vertices
vertex4378 vertex4380
TOP SIDE BOX END OF CHANNEL
face link face1647 face1663 edges edge8050 edge99 vertices
vertex7433 vertex7435 reverse
TOP SIDE BOX BACK OF CHANNEL
face link face1648 face1664 edges edge12 edge8069 vertices
vertex8 vertex84 reverse
BOTTOM SIDE BOX
face link face1665 face1681 edges edge6773 edge2048 vertices
vertex6291 vertex1950 reverse
face link face1680 face1696 edges edge8071 edge8105 vertices
vertex7436 vertex7438 reverse
face link face1666 face1667 edges edge6894 edge6896 vertices
vertex6397 vertex6399
face link face1667 face1668 edges edge6896 edge6898 vertices
vertex6399 vertex6401
face link face1668 face1669 edges edge6898 edge6900 vertices
vertex6401 vertex6403
face link face1669 face1670 edges edge6900 edge6902 vertices
vertex6403 vertex6405
face link face1670 face1671 edges edge6902 edge6904 vertices
vertex6405 vertex6407
face link face1671 face209 edges edge6904 edge6906 vertices
vertex6407 vertex6409
face link face209 face1672 edges edge6906 edge6908 vertices
vertex6409 vertex6411
face link face1672 face1673 edges edge6908 edge6910 vertices
vertex6411 vertex6413
face link face1673 face1674 edges edge6910 edge6912 vertices
vertex6413 vertex6415
face link face1674 face1675 edges edge6912 edge6914 vertices
vertex6415 vertex6417
face link face1675 face1676 edges edge6914 edge6916 vertices
vertex6417 vertex6419
97
face link face1676 face1677 edges edge6916 edge6918 vertices
vertex6419 vertex6421
face link face1677 face1678 edges edge6918 edge6920 vertices
vertex6421 vertex6423
face link face1666 face1682 edges edge6894 edge8090 vertices
vertex6397 vertex2251 reverse
face link face1682 face1683 edges edge8090 edge8091 vertices
vertex2251 vertex2253
face link face1683 face1684 edges edge8091 edge8092 vertices
vertex2253 vertex2255
face link face1684 face1685 edges edge8092 edge8093 vertices
vertex2255 vertex2257
face link face1685 face1686 edges edge8093 edge8094 vertices
vertex2257 vertex2259
face link face1686 face1687 edges edge8094 edge8095 vertices
vertex2259 vertex2261
face link face1687 face1688 edges edge8095 edge8096 vertices
vertex2261 vertex2263
face link face1688 face1 edges edge8096 edge8097 vertices
vertex2263 vertex2265
face link face1 face1689 edges edge8097 edge8098 vertices
vertex2265 vertex2267
face link face1689 face1690 edges edge8098 edge8099 vertices
vertex2267 vertex2269
face link face1690 face1691 edges edge8099 edge8100 vertices
vertex2269 vertex2271
face link face1691 face1692 edges edge8100 edge8101 vertices
vertex2271 vertex2273
face link face1692 face1693 edges edge8101 edge8102 vertices
vertex2273 vertex2275
face link face1693 face1694 edges edge8102 edge8103 vertices
vertex2275 vertex2277
face link face1679 face1695 edges edge89 edge2227 vertices
vertex6320 vertex2039 reverse
MESHING BEGINS HERE
BOUNDARY LAYERS BEGINS HERE
BOUNDARY LAYER FOR THE bottom of plenum
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer1 face face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
98
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 edge edge97
edge4748 edge106 edge6946 edge6947 edge107 edge4749
edge4750 edge116 edge6972 edge6973 edge117 edge4751
edge4752 edge126 edge6998 edge6999 edge127 edge4753
edge4754 edge136 edge7024 edge7025 edge137 edge4755
edge4756 edge146 edge7050 edge7051 edge147 edge4757
edge4758 edge156 edge7076 edge7077 edge157 edge4759
edge4760 edge166 edge7102 edge7103 edge167 edge4761
edge4762 edge176 edge7128 edge7129 edge177 edge4763
edge4764 edge186 edge7154 edge7155 edge187 edge4765
edge4766 edge196 edge7180 edge7181 edge197 edge4767
edge4768 edge206 edge7206 edge7207 edge207 edge4769
edge4770 edge216 edge7232 edge7233 edge217 edge4771
edge4772 edge226 edge7258 edge7259 edge227 edge4773
edge4774 edge236 edge7284 edge7285 edge237 edge4775
edge4776 edge246 edge7310 edge7311 edge247 edge4777 add
MESHING THE PLENUM
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer2 face face4 face4 face5 face110
face110 edge edge99 edge8069 edge100 edge8052 edge98 add
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer4 face face1649 face1664 face1664
face1664 face1663 edge edge8052 edge98 edge100 edge8069
edge99 add
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer4 face face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face4 face2 face2 face2 face2 face2 face4
face5 face110 face110 edge edge9 edge3398 edge3399
edge3400 edge3401 edge3402 edge3403 edge3404 edge3406
edge3405 edge3407 edge3408 edge3409 edge3415 edge3410
edge3411 edge3412 edge3413 edge3414 edge3416 edge3417
edge3418 edge3419 edge3420 edge3421 edge3422 edge3423
edge3424 edge3425 edge3426 edge3427 edge3428 edge3429
edge3430 edge3431 edge3432 edge3433 edge3434 edge3435
edge3436 edge3437 edge3438 edge3439 edge3440 edge3441
edge3442 edge3443 edge3444 edge3445 edge3446 edge3447
99
edge3448 edge3449 edge3450 edge3451 edge3457 edge3452
edge3453 edge3454 edge3455 edge3456 edge3458 edge3459
edge3460 edge3461 edge3462 edge3463 edge3464 edge3465
edge3466 edge3467 edge3468 edge3469 edge3475 edge3481
edge3470 edge3471 edge3472 edge3473 edge3474 edge3476
edge3477 edge3478 edge3479 edge3480 edge3487 edge11
edge3482 edge3483 edge3484 edge3485 edge3486 edge8051
edge12 edge10 edge8034 add
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer5 face face1663 face1664 face1664
face1664 face1649 edge edge99 edge8069 edge100 edge98
edge8052 add
BOUNDARY LAYER OF THE HOLES
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer1 face face642 edge edge3534 add
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer7 face face117 face1600 edge edge4824
edge110 add
BONDARY LAYER OF THE CHANNEL
TARGET WALL BOUNDARY LAYER
BBBL
BBL
BBL
BBBL
BBL
BBL
BBBLLLLL
blayer create first $firstch growth $growthch rows $rowsch transition 1 trows 0
uniform
blayer attach b_layer8 face face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
100
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face105 face105 face106
face104 face104 edge edge2048 edge2049 edge2050 edge2051
edge2052 edge2053 edge2054 edge2055 edge2056 edge2057
edge2058 edge2059 edge2060 edge2061 edge2062 edge2063
edge2064 edge2065 edge2066 edge2072 edge2067 edge2068
edge2069 edge2070 edge2071 edge2084 edge2078 edge2073
edge2074 edge2075 edge2076 edge2077 edge2079 edge2080
edge2081 edge2082 edge2083 edge2090 edge2096 edge2085
edge2086 edge2087 edge2088 edge2089 edge2091 edge2092
edge2093 edge2094 edge2095 edge2102 edge2108 edge2097
edge2098 edge2099 edge2100 edge2101 edge2103 edge2104
edge2105 edge2106 edge2107 edge2114 edge2120 edge2109
edge2110 edge2111 edge2112 edge2113 edge2115 edge2116
edge2117 edge2118 edge2119 edge2126 edge2132 edge2121
edge2122 edge2123 edge2124 edge2125 edge2127 edge2128
edge2129 edge2130 edge2131 edge2133 edge2134 edge2136
edge2137 edge1 edge2135 edge8088 edge3 edge4 edge8105
edge2 add
blayer create first $firstch growth $growthch rows $rowsch transition 1 trows 0
uniform
blayer attach b_layer9 face face1681 face1696 face1696
face1696 face1695 edge edge2 edge8105 edge4 edge3
edge8088 add
blayer create first $firstch growth $growthch rows $rowsch transition 1 trows 0
uniform
blayer attach b_layer10 face face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face105 face105
face106 face104 face104 edge edge6743 edge101
edge7336 edge7337 edge102 edge6744 edge6745 edge111
edge7373 edge7374 edge112 edge6746 edge6747 edge121
edge7410 edge7411 edge122 edge6748 edge6749 edge131
edge7447 edge7448 edge132 edge6750 edge6751 edge141
edge7484 edge7485 edge142 edge6752 edge6755 edge6753
edge151 edge6754 edge7521 edge7522 edge152 edge161
101
edge6756 edge6757 edge7558 edge7559 edge162 edge171
edge7595 edge7596 edge172 edge6758 edge6759 edge181
edge7632 edge7633 edge182 edge6760 edge6761 edge191
edge7669 edge7670 edge192 edge6762 edge6763 edge6767
edge6765 edge201 edge7706 edge7707 edge202 edge6764
edge211 edge6766 edge7743 edge7744 edge212 edge6769
edge221 edge6768 edge7780 edge7781 edge222 edge6771
edge231 edge6770 edge7817 edge7818 edge232 edge241
edge7854 edge7855 edge242 edge6772 edge89 edge8070
edge91 edge92 edge8087 edge90 add
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer11 face face4 face5 face2 face5
face110 face2 edge edge8 edge8 edge6 edge7 edge7
edge5 add
blayer create first $firstch growth $growthch rows $rowsch transition 1 trows 0
uniform
blayer attach b_layer12 face face106 face104 face103 face105
edge edge87 edge87 edge85 edge88 add
BOUNDARY LAYERS ENDS HERE
edge picklink edge6948 edge6949
edge mesh edge6949 edge6948 successive ratio1 1 intervals $NumbNodes
edge picklink edge6950
edge mesh edge6950 successive ratio1 1 intervals ($NumbNodes2)
face mesh face1450 map
edge picklink edge6963 edge6947
edge mesh edge6947 edge6963 successive ratio1 1 intervals ($Numbtelnodes+$rows)
face mesh face912 map
edge picklink edge6961 edge6960 edge7889 edge7890
edge mesh edge7890 edge7889 edge6960 edge6961 successive ratio1 1
intervals ($NumbNodes)
edge picklink edge6959 edge7891
edge mesh edge7891 edge6959 successive ratio1 1 intervals ($NumbNodes2)
face mesh face1452 map
face mesh face1600 face117 map
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer12 face face2 face110 face5 face110
face2 face4 face5 face4 edge edge5 edge5 edge7
edge7 edge6 edge6 edge8 edge8 add
Meshing constants
$NumbNodes=5
$Numbtelnodes=6
$PLobnodes=5
$Chobnodes=5
$Plbenodes=($NumbNodes(4)+$rows)
$plsqnodes=($NumbNodes(3))
102
$Pllsnodes=($NumbNodes+$rows)
$Nojetcells=10
edge picklink edge3686 edge3402
edge mesh edge3686 edge3402 successive ratio1 1 intervals ($PLobnodes)
edge picklink edge6744 edge6864
edge mesh edge6864 edge6744 successive ratio1 1 intervals 5
face link face1260 face375 edges edge6923 edge2440 vertices
vertex6397 vertex2251 reverse
face modify face915 side vertex4479 vertex4480
face mesh face915 face918 face911 map size 1
face mesh face1260 face1263 face1256 map size 1
edge picklink edge8068 edge8053
edge mesh edge8068 edge8053 successive ratio1 1 intervals ($Plbenodes)
edge picklink edge8086 edge8071
edge mesh edge8071 edge8086 successive ratio1 1 intervals ($CHbenodes)
edge delete edge8053 edge8068 keepsettings onlymesh
edge mesh edge8053 edge8068 successive ratio1 1 intervals ($Plbenodes)
edge delete edge8090 keepsettings onlymesh
edge picklink edge8090
edge mesh edge8090 successive ratio1 1 intervals ($plsqnodes)
edge delete edge8054 keepsettings onlymesh
edge picklink edge8054
edge mesh edge8054 successive ratio1 1 intervals ($plsqnodes)
face mesh face1647 face1679 face1678 face1646 face1633
face1665 map
edge delete edge98 edge8087 keepsettings onlymesh
edge picklink edge8087 edge98
edge mesh edge98 successive ratio1 1 intervals ($Pllsnodes)
edge mesh edge8087 successive ratio1 1 intervals ($CHlsnodes)
face mesh face1648 face1680 map
COOPERING ALL THE JETS
volume mesh volume3 cooper source face1600 face1452 face117
face1514 face1512 face115 intervals ($Nojetcells)
volume mesh volume5 cooper source face1456 face1602 face124
face1518 face1520 face122 intervals ($Nojetcells)
volume mesh volume7 cooper source face1460 face1604 face131
face1526 face1524 face129 intervals ($Nojetcells)
volume mesh volume9 cooper source face1464 face1606 face138
face1532 face1530 face136 intervals ($Nojetcells)
volume mesh volume11 cooper source face1468 face1608 face145
face1538 face143 face1536 intervals ($Nojetcells)
volume mesh volume13 cooper source face1472 face1610 face152
face1544 face1542 face150 intervals ($Nojetcells)
volume mesh volume15 cooper source face1476 face1612 face159
face1550 face1548 face157 intervals ($Nojetcells)
volume mesh volume17 cooper source face1480 face1614 face166
face1556 face1554 face164 intervals ($Nojetcells)
volume mesh volume19 cooper source face1484 face1616 face173
face1562 face171 face1560 intervals ($Nojetcells)
volume mesh volume21 cooper source face1488 face1618 face180
face1568 face1566 face178 intervals ($Nojetcells)
103
volume mesh volume23 cooper source face1492 face1620 face187
face1574 face1572 face185 intervals ($Nojetcells)
volume mesh volume25 cooper source face1496 face1622 face194
face1578 face1580 face192 intervals ($Nojetcells)
volume mesh volume27 cooper source face1624 face1500 face201
face1586 face1584 face199 intervals ($Nojetcells)
volume mesh volume29 cooper source face1504 face1626 face208
face1592 face1590 face206 intervals ($Nojetcells)
volume mesh volume31 cooper source face1628 face1508 face215
face1596 face1598 face213 intervals ($Nojetcells)
volume mesh volume30 cooper source face1506 face1052 face1594
face1397 intervals ($Nojetcells)
volume mesh volume28 cooper source face1502 face1042 face1588
face1387 intervals ($Nojetcells)
volume mesh volume26 cooper source face1498 face1032 face1582
face1377 intervals ($Nojetcells)
volume mesh volume24 cooper source face1494 face1022 face1576
face1367 intervals ($Nojetcells)
volume mesh volume22 cooper source face1490 face1012 face1570
face1357 intervals ($Nojetcells)
volume mesh volume20 cooper source face1486 face1002 face1564
face1347 intervals ($Nojetcells)
volume mesh volume18 cooper source face1482 face992 face1558
face1337 intervals ($Nojetcells)
volume mesh volume16 cooper source face1478 face982 face1552
face1327 intervals ($Nojetcells)
volume mesh volume14 cooper source face1474 face972 face1546
face1317 intervals ($Nojetcells)
volume mesh volume12 cooper source face1470 face962 face1540
face1307 intervals ($Nojetcells)
volume mesh volume10 cooper source face1466 face952 face1534
face1297 intervals ($Nojetcells)
volume mesh volume8 cooper source face1462 face942 face1528
face1287 intervals ($Nojetcells)
volume mesh volume6 cooper source face1458 face932 face1522
face1277 intervals ($Nojetcells)
volume mesh volume4 cooper source face1454 face922 face1516
face1267 intervals ($Nojetcells)
volume mesh cylinder cooper source face1450 face912 face1510
face1257 intervals ($Nojetcells)
window modify invisible mesh
volume mesh volume34 cooper source face1649 face1650 face1651
face1652 face1653 face1654 face1655 face1664 face1639
face1638 face1637 face1636 face1635 face1634 face1633
face1648 face1610 face1608 face1606 face1604 face1602
face1600 face1472 face962 face1468 face952 face1464
face942 face1460 face932 face1456 face922 face1452
face912 face915 face918 face911 face925 face928
face920 face935 face938 face930 face945 face948
face940 face955 face958 face950 face965 face968
face960 face694 face689 face684 face679 face674
face669 face664 face659 face654 face649 face644
face640 face697 face696 face692 face687 face686
face682 face677 face676 face672 face667 face666
104
face662 face657 face656 face652 face647 face646
face642 face695 face698 face690 face685 face688
face680 face675 face678 face670 face665 face668
face660 face655 face658 face650 face645 face648
face641 face152 face1470 face145 face1466 face138
face1462 face131 face1458 face124 face1454 face117
face1450 face1657 face1658 face1659 face1660 face1661
face1662 face1663 face788 face1656 face1474 face159
face1647 face1646 face1645 face1644 face1643 face1642
face1641 face1640 face1478 face1628 face1626 face1624
face1622 face1620 face1618 face1616 face1614 face1612
face1508 face1052 face1504 face1042 face1500 face1032
face1496 face1022 face1492 face1012 face1488 face1002
face1484 face992 face1480 face982 face1476 face972
face975 face978 face970 face985 face988 face980
face995 face998 face990 face1005 face1008 face1000
face1015 face1018 face1010 face1025 face1028 face1020
face1035 face1038 face1030 face1045 face1048 face1040
face1050 face114 face1058 face774 face769 face764
face759 face754 face749 face744 face739 face734
face729 face724 face719 face714 face709 face704
face699 face777 face776 face772 face767 face766
face762 face757 face756 face752 face747 face746
face742 face737 face736 face732 face727 face726
face722 face717 face716 face712 face707 face706
face702 face779 face784 face787 face775 face778
face770 face765 face768 face760 face755 face758
face750 face745 face748 face740 face735 face738
face730 face725 face728 face720 face715 face718
face710 face705 face708 face700 face782 face786
face785 face6 face780 face1055 face215 face1506
face208 face1502 face201 face1498 face194 face1494
face187 face1490 face180 face1486 face173 face1482
face166 intervals ($Plzdnodes)
volume delete body onlymesh
volume mesh body cooper source face1689 face1690 face1691
face1692 face1693 face1681 face1682 face1683 face1684
face1685 face1686 face1687 face1688 face1696 face1671
face1670 face1669 face1668 face1667 face1666 face1665
face1677 face1676 face1675 face1674 face1673 face1672
face1680 face199 face1584 face1377 face192 face1578
face1367 face185 face1572 face1357 face178 face1566
face1347 face171 face1560 face1337 face164 face1554
face1327 face157 face1548 face1317 face150 face1542
face1307 face143 face1536 face1297 face136 face1530
face1287 face129 face1524 face1277 face122 face1518
face1267 face115 face1512 face1257 face1380 face1383
face1375 face1370 face1373 face1365 face1360 face1363
face1355 face1350 face1353 face1345 face1340 face1343
face1335 face1330 face1333 face1325 face1320 face1323
face1315 face1310 face1313 face1305 face1300 face1303
face1295 face1290 face1293 face1285 face1280 face1283
face1275 face1270 face1273 face1265 face1260 face1263
face1256 face209 face374 face370 face384 face379
face394 face389 face404 face399 face414 face409
105
face424 face419 face434 face429 face444 face439
face454 face449 face464 face459 face474 face469
face484 face479 face494 face489 face377 face376
face372 face387 face386 face382 face397 face396
face392 face407 face406 face402 face417 face416
face412 face427 face426 face422 face437 face436
face432 face447 face446 face442 face457 face456
face452 face467 face466 face462 face477 face476
face472 face487 face486 face482 face497 face496
face492 face375 face378 face371 face385 face388
face380 face395 face398 face390 face405 face408
face400 face415 face418 face410 face425 face428
face420 face435 face438 face430 face445 face448
face440 face455 face458 face450 face465 face468
face460 face475 face478 face470 face485 face488
face480 face495 face498 face490 face1 face1586
face1582 face1580 face1576 face1574 face1570 face1568
face1564 face1562 face1558 face1556 face1552 face1550
face1546 face1544 face1540 face1538 face1534 face1532
face1528 face1526 face1522 face1520 face1516 face1514
face1510 face1403 face518 face1588 face1592 face1594
face1694 face1695 face1598 face1679 face1678 face515
face516 face510 face500 face508 face505 face213
face1596 face1397 face206 face1590 face1387 face517
face514 face512 face502 face506 face507 face509
face499 face504 face1400 face1395 face1385 face1390
face1393 intervals ($Chzdnodes)
BOUNDARY CONDITIONS
physics create Symmetry btype SYMMETRY face face2 face103
face211 face204 face197 face190 face183 face176
face169 face162 face155 face148 face141 face134
face127 face120 face112
physics create Wall btype SYMMETRY face face110 face5 face1649
face1664 face918 face915 face911 face925 face1650
face928 face920 face935 face938 face930 face1652
face1651 face948 face945 face940 face1653 face1654
face958 face955 face950 face1655 face965 face968
face960 face978 face975 face970 face1656 face114
face985 face988 face980 face995 face998 face990
face1657 face1005 face1008 face1000 face1658 face1015
face1018 face1010 face1659 face1028 face1025 face1020
face1035 face1660 face1038 face1030 face1045 face1661
face1048 face1040 face1055 face1662 face1058 face1050
face1663 face4 face1395 face1679 face1403 face1400
face1680 face1385 face1678 face1393 face1390 face1375
face1677 face1383 face1380 face1676 face1365 face1373
face1370 face1675 face1355 face1363 face1360 face1674
face1345 face1353 face1350 face1673 face1335 face1343
face1340 face1672 face1325 face1333 face1330 face209
face1315 face1323 face1320 face1671 face1305 face1313
face1310 face1670 face1295 face1303 face1300 face1669
106
face1285 face1293 face1290 face1668 face1275 face1283
face1280 face1667 face1265 face1273 face1270 face1666
face1256 face1263 face1260 face1665 face214 face91
face207 face85 face200 face79 face193 face73 face186
face67 face179 face61 face172 face55 face165 face49
face158 face43 face151 face37 face144 face31 face137
face25 face130 face19 face123 face13 face116 face8
physics modify Wall btype WALL face face110 face5 face1649
face1664 face918 face915 face911 face925 face1650
face928 face920 face935 face938 face930 face1652
face1651 face948 face945 face940 face1653 face1654
face958 face955 face950 face1655 face965 face968
face960 face978 face975 face970 face1656 face114
face985 face988 face980 face995 face998 face990
face1657 face1005 face1008 face1000 face1658 face1015
face1018 face1010 face1659 face1028 face1025 face1020
face1035 face1660 face1038 face1030 face1045 face1661
face1048 face1040 face1055 face1662 face1058 face1050
face1663 face4 face1395 face1679 face1403 face1400
face1680 face1385 face1678 face1393 face1390 face1375
face1677 face1383 face1380 face1676 face1365 face1373
face1370 face1675 face1355 face1363 face1360 face1674
face1345 face1353 face1350 face1673 face1335 face1343
face1340 face1672 face1325 face1333 face1330 face209
face1315 face1323 face1320 face1671 face1305 face1313
face1310 face1670 face1295 face1303 face1300 face1669
face1285 face1293 face1290 face1668 face1275 face1283
face1280 face1667 face1265 face1273 face1270 face1666
face1256 face1263 face1260 face1665 face214 face91
face207 face85 face200 face79 face193 face73 face186
face67 face179 face61 face172 face55 face165 face49
face158 face43 face151 face37 face144 face31 face137
face25 face130 face19 face123 face13 face116 face8
physics create Heat Fluxes btype WALL face face104 face106
face370 face379 face389 face372 face382 face392
face371 face380 face390 face378 face388 face398
face376 face386 face396 face374 face384 face394
face377 face387 face397 face375 face385 face395
face1681 face1682 face1683 face1684 face1696 face402
face412 face422 face432 face442 face400 face410
face420 face430 face440 face408 face418 face428
face438 face448 face406 face416 face426 face436
face446 face404 face414 face424 face434 face444
face407 face417 face427 face437 face447 face405
face415 face425 face435 face445 face1688 face1685
face1686 face1687 face452 face462 face472 face482
face492 face1693 face450 face460 face470 face480
face490 face1692 face458 face468 face478 face488
face498 face1 face456 face466 face476 face486 face496
face454 face464 face474 face484 face494 face457
face467 face477 face487 face497 face1691 face455
face465 face475 face485 face495 face1689 face1690
face518 face502 face512 face1695 face500 face510
face1694 face508 face506 face516 face504 face514
face507 face517 face515 face505
physics create Mass flow inlet btype SYMMETRY face face640 face649
107
face659 face642 face652 face662 face672 face641
face650 face660 face670 face648 face658 face668
face678 face646 face656 face666 face676 face644
face654 face664 face674 face647 face657 face667
face677 face645 face655 face665 face675 face1633
face1634 face1635 face1636 face1637 face1648 face679
face689 face699 face682 face692 face702 face712
face680 face690 face700 face710 face688 face698
face708 face718 face6 face686 face696 face706 face716
face684 face694 face704 face714 face687 face697
face707 face717 face685 face695 face705 face715
face1640 face1638 face1639 face719 face729 face739
face749 face722 face732 face742 face752 face762
face720 face730 face740 face750 face760 face728
face738 face748 face758 face768 face726 face736
face746 face756 face766 face724 face734 face744
face754 face764 face727 face737 face747 face757
face767 face725 face735 face745 face755 face765
face1645 face1641 face1642 face1643 face1644 face788
face769 face779 face772 face782 face770 face780
face778 face776 face786 face774 face784 face777
face787 face775 face785 face1647 face1646
physics create Outflow btype OUTFLOW face face105
108
REFERENCES
Al-Aqal O M A 2003 ldquoHeat transfer distributions on the walls of a narrow channel
with jet impingement and cross flowrdquo PhD Thesis University of Pittsburgh
Bunker Ronald S 2007 Gas Turbine Heat Transfer Ten Remaining Hot Gas Path
Challengesrdquo Journal of Turbomachinery April Vol 129 pp 193-201
Downs James P Landis Kenneth K 2009 ldquoTurbine Cooling Systems Design- Past
Present and Futurerdquo Proceedings of ASME Turbo Expo 2009 June 8-12 2009
GT2009-59991
Florschuetz LW Berry R A Metzger D E 1980 ldquoPeriodic streamswise variations of
heat transfer coefficients for inline and staggered arrays of circular jets with cross
flow of spent airrdquo ASME J of Heat Transfer 102 p 132-137
Florschuetz L W Truman C R Metzger D E 1981 ldquoStreamwise Flow and Heat
Transfer Distributions for Jet Array Impingement with Cross flowrdquo Journal of
Heat Transfer Vol 103 pp 337
Florschuetz L W Isoda Y 1983 ldquoFlow Distributions and Discharge Coefficient for
Jet Array Impingement With Initial Cross flowrdquo Journal of Engineering for
Power Vol 105 pp 296
Incropera Frank P DeWitt D P 2002 Fundamentals of Heat and Mass Transfer John
Wiley amp Sons Inc New Jersey pp 491-493
Liu Quan Kapat J May 2006 ldquoStudy of Heat Transfer Characteristics of Impinging
Air Jet Using Pressure and Temperature Sensitive Luminescent Paintrdquo UCF
Dissertation
109
Martin H 1977 ldquoImpinging jet flow heat and mass transferrdquo Advances in heat transfer
Vol 13
Ricklick Mark Kapat J December 2009 ldquoCharacterization of an Inline Row
Impingement Channel for Turbine Blade Cooling Applicationsrdquo UCF
Dissertation
Zuckerman N Lior N 2005 ldquoImpingement Heat transfer Correlations and Numerical
Modelingrdquo Journal of Heat Transfer Vol 127 pp 544
xi
Carnot Describing a Carnot cycle
Exit
Effective
Quantity Lost to the Environment
Reference Value
Wall Value
Base Line Value
1
CHAPTER ONE INTRODUCTION
11 Gas Turbine as a Heat Engine
Gas turbine is a form of heat engine where the hot reservoir is created by the
combustion of fuel and the cold reservoir is the open atmosphere It is well known that
the maximum efficiency of any heat engine is denoted as the Carnot efficiency
A more accurate cycle is used to describe the processes inside a gas turbine ndash the
Brayton Cycle The Brayton cycle as seen in Figure 1 is composed of four processes In
a gas turbine air is drawn in at state 1 it is compressed until it reaches state 2 The
compressed air is mixed with fuel and ignited as it passes through the combustor The hot
air then passes through the turbines where work is extracted The process from state 4 to
state 1 happens throughout the atmosphere therefore the Brayton cycle is an open loop
cycle as the same air is not continuously being fed through the motor
Figure 1 Brayton Cycle Flow Path and T-s Diagram (Adapted from UPTB Website)
The Brayton cycle has an isentropic efficiency similar to the carnot the Brayton
cycle efficiency is defined as
2
It can be seen that increasing the temperature at which air enters the first turbine
stage T3 increases the overall efficiency of the turbine Moreover increasing the
pressure ratio Pr also aids in the increase of the efficiency One of the hurdles of
increasing T3 is the fact that the post combustion gas is a few hundred degrees Celsius
above the melting point of the super alloys used to make the turbine stator vanes and
rotor blades For this reason it is important to cool the hot components of the gas turbine
in order to assure a reasonable life for the machine
12 Cooling of Hot Components
The transition duct that connects the combustor to the first stage turbine as well
as the first stage of the turbine are the parts that are subject to the harshest thermal
loadings and must therefore be cooled aggressively to maintain them in working
conditions for a long period of time Since the first stage guide vanes and rotor extrude
into the flow they are subject to the highest convection coefficients These heat transfer
coefficients can reach up to 4000 Wm2K (Downs 2009) Figure 2 shows the different
magnitudes of convection coefficient around the blade High heat transfer coefficients
occur where the air stagnates into the leading edge of the airfoil This high heat transfer
region is not only caused by the lack of a thermal boundary layer to protect the airfoil but
also because the effective heat transfer driving temperature is the recovery temperature
At the high Mach numbers that occur in turbines the ratio of total to static temperatures
is significant causing the leading edge to have the highest effective heat load Another
3
peak occurs on the suction side of the blade as the boundary layer created by the airfoil
switches from being a laminar boundary layer into a turbulent one Due to the nozzling
effect of the turbine rotor and stators the flow gathers speed toward the trailing edge of
the airfoil leading to higher convection coefficients on the pressure side of the airfoil
Figure 2 Thermal Loading Throughout a Turbine Blade (Daniels 1982)
Simple convection channels were implemented in the early nineteen sixties as
years passed the cooling techniques became more and more sophisticated allowing the
free stream temperature to increase to previously impossible levels Currently the use of
film cooling coupled with backside impingement leads the turbine cooling technology
The trend of allowable turbine inlet temperature is shown in Figure 3 from this figure it
can be seen that the allowable free stream temperature has increased around 600 degrees
in the past 50 years The addition of thermal barrier coatings also helps in the increase in
allowable combustion temperatures by creating an extra resistance that the heat needs to
move through as it moves from the combustion gasses into the coolant air It is impotatnt
to notice that as seen in Figure 4 the increase in turbine inlet temperatures is done with
the combined benefits of new alloys TBC and cooling technologies
4
Figure 3 Allowable Turbine Inlet Temperature vs Cooling Techniques over the Years (Clifford 1985)
Figure 4 Turbine Inlet Temperature Increase with the help of TBC New Super Alloys and Cooling
Technologies (Kapat and Kiesow Lectures 2010)
The cooling of inlet guide vanes can be done with the use of impingement inserts
inside the airfoils As air passes through the miniscule holes in the inserts a jet is formed
which then impinges on the wall of the airfoil producing one of the largest single phase
heat transfer coefficients This already impinged coolant air is then bled out as film
5
cooling as well as bled out through the trailing edge Figure 5 shows a stator vane with
the impingement insert in black the film cooling extraction as well as the trailing edge
bleed
Figure 5 Turbine Stator Cooled with Impingement Coupled with Film Cooling (Florschuetz 1980)
The cooling of turbine airfoils with the use of an impingement insert is only
possible in stationary components as the rotating ones are subject to centrifugal loadings
making it unfeasible to cool them with this setup Rotor blades are typically cooled with
serpentine passages that have heat transfer enhancing features such as ribs dimples and
other turbulators these serpentine passages are located in the mid chord of the blade On
the trailing edge a bank of pins are used to obtain high convective coefficients in the thin
region the coolant is the bled out to compensate for the boundary layer created around
the airfoil Rows of impingement holes cool the leading edge The spent air is then bled
out through showerhead cooling Figure 6 and Figure 7 show in detail the cooling
channels around two similar airfoils airfoils
6
Figure 6 Rotor Blade Cooling Configuration (Gladden 1988)
Figure 7 Cross-section of Turbine Airfoil with Cooling Channels (Han et al 1984)
7
The coolant air is bled out from the later stages of the compressor This air is
expensive as it has been compressed and not under gown the heat addition by
combustion It is imperative that the minimum amount of coolant is used in these cooling
configurations The cooling must also be as uniform as possible to reduce thermal
stresses within the blades leading to a higher component life Figure 8 shows freestream
metal and coolant temperatures of the flow blade and coolant air It can be seen that a
decrease of 25degrees in the surface temperature of the blade can provide an airfoil with
twice the working life Impingement cooling has great potential to provide high heat
transfer coefficients at a small flow rate Impingement of a jet onto a surface provides
high heat transfer coefficients due to a starting boundary layer as well as its high
turbulence When the jet is located around 3 diameters from the target surface the heat
transfer profile has two peaks one located at the stagnation region and the other located
between one and 3 diameters from the stagnation region As the jet is moved away from
the target wall the secondary peak diminishes leaving a profile with a maximum at the
stagnation region decreasing radialy
Figure 8 Relative Temperatures for Hot Gas Metal Temperature and Coolant Temperature (Cardwell 2005)
Cardwell N D 2005
8
Figure 9 shows a diagram of a jet impinging on a target surface The potential
core is the part of the jet that has not been affected by the surrounding stagnant fluid As
the jet moves towards the target wall its momentum diffuses into the surrounding fluid
decreasing the velocity at which it reaches the target wall and potentially decreasing the
corresponding heat transfer coefficient Studies have shown (Martin 1973 for example)
that the potential core may last anywhere between 7 to 10 diameters The successful
impingement of the potential core yields significantly higher heat transfer coefficients
than a fully diffused jet this comes however at a cost of higher pressure drop across the
jet plate as well as a highly non uniform heat transfer profile
Figure 9 (a) The Development of the Wall Jet (b) Jet Diffusion to Surroundings (Liu 2006)
9
CHAPTER TWO LITERATURE REVIEW
21 Impingement Literature Cornerstone
From the early days of simple convective cooling channels in turbine airfoils
studies have been done on modes of enhancing heat transfer coefficients while
maintaining a low pressure drop and minimum mass flow rate Heat transfer
characteristics of single round nozzle impingement were studied in the late 1960rsquos and
early 1970rsquos The collected works of many authors is combined into ldquoHeat and Mass
Transfer between Impinging Gas Jets and Solid Surfacesrdquo by Holger Martin 1977 The
paper collects works from multiple authors who studied single round nozzle impingement
effects on heat and mass transfer coefficients In this compilation non dimensional jet to
target spacing was studied they ranged from ZD=12-10 providing plots of Sherwood
number as a function of radius for four different jet to target spacings The local
Sherwood number was also given for a slot jet for HS ranging from 5 to 20 Studies on
impingement jet arrays were also gathered alongside an array of slot jets Correlations
were given for multiple setups present in the paper Circular jet arrays and slot arrays are
studied in detail with both analytical and experimental approaches The paper also
combines studies done on swirling jets turbulence enhancers on the target surface
impingement on concave surfaces and angle of attack variations Optimization studies
were also done to find the optimal spacing for round and slot jet arrays
Florschuetz studied the heat transfer characteristics of an array of jets impinging
on a flat surface This study was guided towards finding an optimal spacing for an array
for jets used to cool the midchord of turbine airfoils similar to that found in Figure 5 His
main contributions include a Nusselt number correlation as a function of jet to target
10
spacing jet Reynolds number and other flow and geometric parameters He found that an
increase in hole spacing and channel height resulted in a decrease of heat transfer He
also provided a one dimensional jet mass flux and channel mass flux correlations
His Nusselt number correlation takes the form of
Where A B and n are dependent by the two different types of arrays inline or staggered
Liu studied new techniques in temperature and pressure measurements of a single
slot jet with the use of temperature sensitive paint or TSP and pressure sensitive paint or
PSP In his work both measurement techniques are explained in detail Since TSP is the
only tool from that study currently used in this work it will be explained further in the
experimental setup section
11
22 Relevant Impingement Channel Studies
Al-Aqal 2003 studied three different types of impingement channels The use of
TLC was implemented in this work to obtain heat transfer distributions for the target
wall The three different configurations varied the number of holes in the streamwise and
spanwise directions The first channel had a single row of 6 streamwise jets the second
consisted of 2 rows of 12 streamwise holes summing up to a total of 24 holes The last
channel is a triple spanwise row with 18 streamwise jets This last geometry is the most
similar to the one present in the current study The third geometry will be used to
compare results There are differences however the total width of the channel is of 16
diameters as opposed to 8 in this study The streamwise jet spacing is also different Al-
Aqal used an XD of 65 compared to XD = 5 in this study The jet to target plate
spacings are similar on two occasions as he studied a ZD=4 6 and 8 while this work
uses a ZD = 6 8 and 10 Average jet Reynolds numbers also fall within the range of this
study as they range between 5000 and 33000 The author provides span averaged plots
for all cases and Reynolds numbers convenient when comparing the results
Ricklick 2009 studied a channel similar to the one found in this study His
channel was composed of a single row of 15 jets with a YcD = 4 XD = 5 and 15 and
ZD = 1 3 and 5 Two channels were tested one was pressure fed while the other was fed
by suction TSP was used to gather temperature data of all four wetted surfaces on the
pressure channel and two surfaces on the suction channel Since the maximum jet Mach
number was less than 03 the flow was assumed to be incompressible leading to the
conclusion that both channels contain identical flow patterns Thin foil heaters were used
to create the required heat flux for the channel Besides channel geometry Reynolds
12
numbers and heater geometry Ricklicksrsquo experimental setup is identical to the one
presented in this work The author also provided an ample comparison of his results to
literature He provided thermal performances of the entire channel at different Reynolds
numbers and channel heights
A small CFD study was also done A paved mesh was created on the target wall
with finer mesh near the impingement locations The resulting y+ at the wall was higher
than one yielding potentially faulty heat transfer values however this is acceptable since
the CFD was used as a tool to better understand the flow physics and help understand the
experimental heat transfer profiles
23 Computational Studies on Impingement Channels
El-Gabry did a numerical study of jet impingement with cross flow Two different
turbulence models were compared in their ability to predict surface Nusselt number The
Yang-Shih and standard k-ε models were used to compute the flow generated by jets
angled at 30 60 and 90 degrees with cross flow The computational results were
compared to previous experimental work by El-Gabry Comparisons to experimental
results at ZD = 1 and 2 90deg injection angle between Yang-Shih and standard k-ε The
error in the average Nu from the experimental results and both turbulence models were
calculated It was found that the Yang-Shih model behaved well at low Reynolds
numbers with the average Nusselt number being 5 off from the experimental value
while the standard k-ε was off my 94 As jet Reynolds number was increased the error
of the standard k-ε model dropped to as low as 39 while the error from the Yang-shih
model increased to -76 The span average plots show the experimental data Nusselt
number alongside the span averages of the results acquired by the Yang-Shih and
13
standard k-ε models High Nusselt numbers occur at the impingement location decreasing
thereafter after another impingement location is found The frequencies of these
variations are all the same for the experimental and the two numerical solutions The
amplitude of fluctuations between the impingement locations and the areas in between
are much larger for both of the numerical results however the Yang-Shih model over
predicts at the high Reynolds number for the ZD=2 case Since the amplitude of
fluctuations is greater for the CFD solutions it is important to note that even though the
error in average Nusselt number is not great the actual differences in the profile are much
greater upwards of 20 difference of heat transfer coefficients between the experimental
and numerical heat transfer peaks Other variations were studied (Injection angles for
example) but will not be discussed as their importance to the current study is minimal
Zuckerman compared a much wider set of turbulence models in their ability to
successfully predict Nusselt numbers caused by jet impingement The models tested were
k ndash ε k-ω Reynolds Stress Model algebraic stress models shear stress transport and
lastly the υ2f turbulence model DNS runs are extremely time consuming to run
therefore LES was run on its behalf to provide results for the unsteady turbulence
models The paper summarizes all the different models used their computational cost
impingement heat transfer coefficient and their ability to predict the second peak in heat
transfer As expected DNSLES provide the best prediction of both stagnation and
secondary peak heat transfer coefficient however this comes at a large computational
cost The k ndash ε and k-ω provide poor heat transfer results for the stagnation region where
they can have 30 error from the correct value The Realizable k ndash ε model provides
14
better heat transfer results while still maintaining a low computational cost The highest
accuracy to cost ratio was achieved by the υ2f model where it predicts the heat transfer
coefficient for the surface with a minimum of 2 error while not being as expensive as
the other unsteady models such as DNS and LES Ideally the CFD portion of this work
would be run with the υ2f model however since the code used to run the simulation
FLUENT does not have the υ2f model a realizable k ndash ε model will be used with
enhanced wall functions for both thermal and velocity gradients
15
CHAPTER THREE EXPERIMENTAL SETUP AND TECHNIQUES
31 Temperature Measurements with TSP
Temperature sensitive paint or TSP provides the capability of measuring
temperatures over the painted area This measurement technique supersedes the
advantages of other temperature measurement devices such as thermocouples because it
provides the user with data over a large area rather than point temperatures given by
thermocouples
Uni-Coat TSP is purchased from ISSI It is very robust to different working
conditions Calibration done on one batch of paint can be used for multiple cans as the
product is highly consistent The paint is calibrated in a dark booth a painted coupon is
placed on the hot side of a thermoelectric heat pump working on the Peltier effect
thermal paste is used to minimize contact resistance between the hot side and the TSP
coupon Calibrated thermocouples are placed in between the TSP and the thermoelectric
heat pump A reference temperature and picture are taken and the calibration commences
At least 5 or 6 data points should be taken to form the calibration Intensity ratios are
taken between the hot and cold pictures They are then plotted versus their corresponding
temperature
The paint consists of fluorescent molecules suspended in a binder These
molecules with a certain wavelength of light will be exited to a higher energy level The
molecules then can dissipate some of the energy by transferring it vibrationally to its
neighboring binder particles and dissipate the remainder of the energy by radiating it as a
photon as the molecule comes down to its original ground state Since the amount of
16
energy that the particle can transmit to others through vibration is directly proportional on
temperature and the total initial energy is fixed by measuring the ratio of the intensity at
a known temperature (reference picture) and intensity of the unknown temperature
feeding it through the correlation the unknown temperature can be found to an
uncertainty of 1 K Figure 10 shows a simplified Jablonski diagram adapted from the
suppliers website The blue arrows signify the blue light used to excite the luminescent
molecule Tris(22rsquo-bipyridyl) Ruthenium(II) Chloride Hexahydrate with a shellac binder
in our case The shellac binder is impermeable to oxygen opposite of that found in PSP
due to PSP relying on the presence of oxygen for it to function Once the particle is
excited it can give off the energy in two different ways one is by emitting it back out as
another photon of the same energy and therefore wavelength The second mode of the
particle to lose its energy is through vibrational relaxation This second process is directly
dependent on the temperature ie the higher the temperature the higher the probability
for it to lose energy to its surroundings Once it loses some energy to the surrounding
particles it releases the remainder of the energy as a photon of less energy of that which
excited it originally hence why a long pass filter is installed in the CCD camera For a
more descriptive explanation of the way TSP works refer to Liu 2006
17
Figure 10 Simplified Jablonski Diagram (Adapted from ISSI Website)
Throughout the past two years there have been numerous projects at CATER that
have used TSP Painting surfaces with TSP should be done carefully by someone who
has experience with spray painting since every single can costs $500 A single can should
be able to paint an area the size of an acrylic plate that is 36rdquo wide and 24rdquotallThe
sidewalls and the target wall of the impingement channel were painted with the use of
less than one can Painting on different surfaces is difficult for example when painting
Rohacell the paint canister can be held very close to the surface while spraying due to
the surface being somewhat porous and rough however when painting straight onto
metal heater strips the can should be placed as far back as possible for the first run
Ideally for the first pass through only a slight mist should be applied If the can is being
held too close to the surface the paint will run Figure 11 shows a set of heater strips that
has been painted too closely leading the paint to drip down Ideally the paint would be
applied to the surface in as many coats as possible Of course this would be time
18
demanding and impractical therefore with the knowledge that I have gained through the
multiple TSP paintings on different surfaces I have compiled a list of TSP dos and
donrsquots
Dos
Clean the surface to be painted with acetone or break parts cleaner Break
parts cleaner is preferable over acetone as it does not leave an oily residual
after cleaning
Paint the first coat as thin as possible Most of the surface should not be
covered There should be an even mist of miniscule TSP circles This will
give the later coats something to attach to
When positioning the test section to paint make sure to wipe it one last
time as small dust particles may have attached to the surface
Stop if you see small bumps in the paint This is caused by dust particles
collecting all the paint around it while it is still wet due to surface tension
Clean the surface and repaint This should be noticeable in the first few
coats If you see this pattern happening do not continue thinking it will be
covered by future coats What will happen is the problem will get worse
and worse ultimately the surface will have to be cleaned again and
repainted
When painting test sections try to paint the smallest section as possible
This will not only save paint but will make it very simple for the post
processing code to crop out the unpainted areas
19
Let the finished painted surface to sit at least for 90 minutes after the last
coat before baking There have been problems when baking steel and
acrylic test sections with the paint cracking while baking right after the
last coat Normally the finished surface is left to dry overnight and baked
first thing in the morning
For test sections that are too large to be baked in the oven the heat gun
may be used Carefully place a thermocouple in a central location with
blue painters tape The heating should be uniform and should not take
more than 20 minutes of continuous blowing When the thermocouple
reaches 80-90 C the plate can be assumed to be baked To introduce a
factor of safety in the baking it does not hurt to bake it longer than it
normally takes
Once the test section is mounted and ready to run cover it with cloth that
does not let any light through This will protect the paint for further uses
This is especially important on test sections that can be used multiple
times like the ones found in this study
When the test is running turn off the LED lights This light is the most
damaging to the TSP as it degrades the quality of the fluorescent
molecules
If there is a particular head of the TSP can that you prefer over others you
can remove it once the can is empty It is difficult to get used to a single
kind of nozzle being able to transfer it from can to can is a must if
painting consistency is to be kept
20
Donrsquots
Do not clean a test section that has already been used with too much
acetone The acetone is volatile evaporating quickly cooling the test
section rapidly If this test section has had heaters attached to it and run
previously the acrylic will crack due to uneven stresses inside of it
If paint is dripping stop painting immediately Clean the surface and start
over Hold the can far from the surface in order for it not to drip
Do not use TSP to teach new apprentices undergrads or graduate students
how to paint Regular spray paint is two orders of magnitude lower in cost
while the painting process is exactly the same
Do not paint with the doors closed The paint contains carcinogens that
can harm the lungs Always use a respirator and keep the room well
ventilated In-situ painting and baking has not been tried however it may
be a real option if the test section is difficult to disassemble and easily
accessible to painting and baking
If there is a can of paint that contains too little paint for the test section
that needs to be painted try to find a new can The mixing of two different
cans of TSP can be dangerous at times however it has been noticed over
the years that ISSI provides a very robust and dependable product that
does not vary significantly from batch to batch
21
Figure 11 Heater Strips Painted with TSP Too Closely
32 Experimental Setup of Suction Channel
The impingement channel is fed under suction As seen in Figure 12 air enters
through the plenum it crosses the jet plate as it gains speed to form the jets
which then impinge on the target wall The flow then passes through a venturi
flow meter and finally through the blower into the atmosphere A bypass valve is
used to control the flow rate of the impingement channel
22
Figure 12 Flow Loop of Impingement Channel
The impingement channel consists of 15 streamwise rows of 3 spanwise jets each The
total width of the channel YcD is of 8 diameters while the streamwise spacing between
the rows is XD=5 the spanwise distance between the holes is of YD=2 Figure 13shows
the top view of the jet plate The plate is counter bored to ensure that a nearly flat
velocity profile of the jet is achieved Figure 14 shows the front view of the channel Z is
denoted as the distance between the jet and target plates Side walls are interchangeable
to change the height of the channel to 6 8 and 10 diameters Two thirds of the
streamwise rows can be covered to change the XD from 5 to 15
Figure 13 Top View of Jet Plate
23
Figure 14 Front View of Impingement Channel
The target and sidewalls had heaters made specifically for them in a serpentine
style This was necessary to increase the resistance as the VARIACs used to power them
only had a maximum current output of 20 amps The heater strips are two diameters
wide at each end copper tape with conductive adhesive was used to connect the leads to
the power supply The heater consists of 50 micron thick steel sheet sandwiched between
two pieces of Kapton tape The heater is attached to the painted surface with the use of
double sided Kapton tape The target test section can be seen in Figure 15 also seen in
this figure are the two Teflon gaskets lined on the sides of the target plate With the target
wall bolted onto the sidewall the gasket is compressed generating a strong seal
Figure 15 Target Wall Test Section with Heater Leads
24
For this study the test matrix shown in Table 1 will be run Target and side wall
data will be taken at three different impingement heights at two different Reynolds
numbers of 7500 and 15000 denoted by A and B respectively A streamwise jet spacing
study is also done by testing the target and side wall heat transfer at an XD=15 for the
low impingement height channel
Table 1 Test Matrix
XD ZD Wall Re
5
10 TW
7500
15000
SW 7500
15000
8 TW
7500
15000
SW 7500
15000
6 TW
7500
15000
SW 7500
15000
15 6 TW
7500
15000
SW 7500
15000
33 Data Processing and Reduction
As described previously when taking temperature measurements with the use of TSP
reference temperatures are noted and a reference picture is taken The experiment is the
run once the experiment reaches steady state a new set of 4 pictures is taken Given the
calibration curve temperatures are backed out
25
Given the amount of heat generated inside the heater
Dividing by the heated area to get heat flux
Heat loss tests were run to consider how much of the heat flux generated by the heaters
goes through the backside instead of into the flow It was found that 25 of the heat flux
leaks out to the atmosphere through the acrylic In order to account for this heat leakage
it must be subtracted from the calculated value to become
Where Ah is the effective heated area given by
Where Aunheated is an estimate of how much unheated area is between the heater strips (~
3 of the total area)
To obtain heat transfer coefficient
Where Tref is the reference temperature Typically set in literature to be the jet
temperature
To obtain the average Reynolds number for the jets the total mass flow rate is used
Where Dj is the jet diameter and μ is dynamic viscosity (1983kgm s at 300K)
26
Pressure measurements were taken at the sidewall after the last jet entered the channel
These pressure measurements were used to determine the thermal performance of the
tallest two channels (ZD = 8 and 10)
The thermal performance at constant pumping power is found by using the equation
Where h is the average heat transfer coefficient for the target wall of them impingement
channel and ho is the heat transfer coefficient obtained by passing the same amount of
flow through a smooth duct ie the Dittus-Boelter correlation The friction factor f is
found with the use of
Where Ppl is the plenum static pressure assumed to be atmospheric and Plast jet is
the pressure read after the last jet V is the volumetric flow rate divided by the cross-
sectional area of the duct after the last impingement row The hydraulic diameter of the
channel is set to be
The baseline friction factor was calculated with the use of the Moody chart the hydraulic
diameter and the total mass flow rate though the channel Thermal performance at
constant pressure drop was also calculated with
27
34 Uncertainty Analysis
A simple uncertainty analysis was done to estimate the error in calculation of the
heat transfer coefficient from the given outputs of the test data From the bare basic
measurements for voltage area current temperature of thermocouples and temperature
profiles of paint a simple uncertainty analysis can be done to estimate the error for the
calculated heat transfer coefficient Figure 16 shows the different sources of error in the
calculation of heat transfer coefficient The effective uncertainty was calculated by taking
the root of the sum of the squares of all the individual percentage errors The
experimental uncertainty for heat transfer coefficient was of 703 This error may be
reduced by acquiring higher temperatures of the TSP reading current with a more
accurate ammeter or reading reference temperatures with the use of a thermopile instead
of a single thermocouple
Figure 16 Heat Transfer Coefficient Uncertainty Tree
28
35 Lateral Conduction Analysis
To take into account the lateral conduction occurring inside the heater foil while
the test is running two simple 1D conduction and convection equations were used to
quantify the amount of heat moving through the heater laterally and the amount of heat
convecting into the air The lateral conduction is expected to be at a maximum at the
places where there are large spatial variations of surface temperature which is why the
ZD = 6 XD = 5 case at high Re is chosen to be studied Figure 17 shows the
temperature distribution of the aforementioned case Four cold spots can be seen by their
distinct blue and yellow color located at the stagnation regions The maximum
temperature gradient occurs between the third jet impingement and the middle region
between jets The temperature difference was seen to be of 13degC The distance in between
these two temperatures is of 25D=01875m The corresponding heat flux between these
two points was calculated to be 13000Wm2 with ksteel~20Wm K A region of 1cm by
1cm was then created and the amount of heat calculated through conduction and
convection were compared To acquire the amount of heat removed through conduction
a heat flux of 13000Wm2 was imposed through an area of 01m by 00005m this
equaled to 00277 W The amount of heat moved through convection was calculated by
multiplying the heat flux used during the test by the area of the square 0001m2 the
resulting heat moving through the heater onto the air is 6 W Since the heat moving
through to the air is two orders of magnitudes larger than the heat moving laterally the
effective lateral conduction can be neglected
29
Figure 17 Temperature Profile of First Five Impingement Rows
A second order approach was also taken to quantify the amount of lateral
conduction in the heater The temperature gradient was taken from high peaks in heat
transfer caused by the second row of impingement of the same ZD=6 XD=5 channel at
high Re Figure 18 shows the high heat transfer coefficients created by the second row of
jets A quadratic curve fit was obtained by for this small region so that a continuous
equation of heat transfer coefficients as a function of streamwise distance was quantified
30
Figure 18 Detailed View of First Heat Transfer Peak with a Polynomial Curve Fit
The net heat gained by a differential volume from lateral conduction is the
difference in the temperature gradient at the entrance and the exit multiplied by the
thermal conductivity and cross sectional area Using this method shown in Figure 19 the
net change in convective heat transfer due to lateral conduction can be studied
Figure 19 Control Volume Heat Transfer Analysis
By taking the difference between the out flowing heat trough the right side and
the inflowing heat from the left side a net gain or loss can be found Figure 20 shows the
y = -470630x2 + 31244x - 14842Rsup2 = 09934
300
310
320
330
340
350
360
370
380
0 001 002 003 004 005
HTC
(W
m2K
)
x (m)
Heat Transfer Peak
Poly (Heat Transfer Peak)
31
difference in magnitude between the out flowing heat through convection seen in red and
the net inflow of heat from lateral conduction in blue From these calculations it was also
found that the amount of heat moving through lateral conduction is tow orders of
magnitude smaller than the amount of heat moving out through convection leading to the
belief that even at high temperature gradients lateral conduction does not play an
important role in the ongoing heat transfer processes in the impingement channel A more
detailed calculation of this work can be seen in appendix A
Figure 20 Heat Loss through Convection and Lateral Conduction
002 003 004 0051 10
5
1 104
1 103
001
qconv x( )
qnet x( )
x x
32
CHAPTER FOUR HEAT TRANSFER RESULTS
41 Heat Transfer Validation
In order to obtain confidence in our experimental setup an experiment was made
to test something that has already been published in literature A smooth channel was the
obvious choice as it was easy to setup by taking off the end cap and blocking all the holes
with smooth blue painters tape on the flow side and metal tape on the plenum side to
ensure no leaks into the channel from the jet plate The smooth channel has been studied
widely and multiple correlations exist one of these equations is the Dittus-Boelter
correlation (Incropera 2007) The test was run using the ZD=6 side wall so that the
hydraulic diameter was a minimum Figure 21 shows the span averaged results versus
non dimensional distance into the channel
Figure 21 Validation Spanwise Averaged Results
0
10
20
30
40
50
60
0 1 2 3 4 5 6 7 8 9
HTC
(W
m2K
)
XDc
Span Avg
Dittus Boelter
33
The plot shows decreasing heat transfer coefficient with increasing XDc due to
the developing thermal boundary layer The span average does not reach the Dittus-
Boelter due to it not being fully developed in the limited space it is given Typical flows
can take up to 60 diameters to achieve a fully developed profile with the current setup
the maximum length of the channel was of 9 diameters The profile however seems to
have an asymptote at the Dittus-Boelter correlation value leading to the belief that if the
channel was longer that value given by the correlation would be reached One important
factor to take into account in determining whether the experimental setup is validated is
the fact that the Dittus-Boelter correlation has an uncertainty near 30 Since the span
average at high XDc is well within 30 from the calculated value it is safe to assume
that the current experimental setup is validated
42 Heat Transfer Results
Heat transfer results are compared based on variations in channel height and
average jet Reynolds number As discussed earlier there are numerous other parameters
also affecting the heat transfer in these channels As these parameters are changed flow
structures within the channel are expected to be altered as well as discussed in the
literature Two of the major contributors to heat transfer in these channels are the
successful jet impingement and the resulting cross flow The same domain is captured in
both the local and averaged results
Figure 22 through Figure 25 highlights the heat transfer distribution for the cases
with a jet to jet spacing of 5 diameters in the streamwise direction and of 2 in the
spanwise direction It is evident that the smallest channel height (ZD=6) performs the
best at all Reynolds numbers on all surfaces It is also interesting to note the similarity
34
in the target wall profiles between case 528A and B where the curves are very similar
other than the obvious offset due to the change of the Reynolds number At this large
spacing we also see the degradation of the jets a few diameters downstream of each
impingement location The downstream shifts of the peaks are evident after the second
and third row of jets Also evident in these plots is the deflection of the impinging jet and
the wall jets from the cross flow The cross flow is forced to flow around the jet
deflecting the spread of the wall jet in the downstream direction Impingement locations
are also very evident at low XD however as XD and therefore the cross flow increase
the magnitude of the peaks start decreasing and eventually level out to pure internal flow
Figure 22 Target Wall Heat Transfer Coefficient Distributions
35
Figure 23 Span-averaged Target Wall Heat Transfer Distribution
36
Figure 24 Side Wall Heat Transfer Coefficient Distributions
37
Figure 25 Span-averaged Side wall Heat Transfer Distribution
Figure 23 and Figure 25 show similar details with impingement peaks clearly
diminishing and shifting in the downstream direction The cross flow clearly has some
negative influence on these geometries when compared to the more traditional
impingement highest on the order of 1 to 5 jet diameters The heat transfer profiles of the
target wall for all heights seen in Figure 22 and Figure 24 show the rapid decay in heat
transfer after the third jet This can be explained by understanding that the first jet does
not have any cross flow to deflect it the second jet only has the first jet worth of
momentum deflecting it downstream however since the channel is so tall the
momentum of the cross flow after the first and second jet are not enough to greatly
disturb the incoming jets After the third jet however the cross flow builds up enough
momentum to greatly affect the integrity of the jets downstream causing the span-
0
20
40
60
80
100
120
140
160
2 12 22 32 42 52 62 72
HTC
(W
m2K
)
XD
5210B_SW 528A_SW Jet Location
526A_TW 526B_TW
38
averaged heat transfer to rapidly drop The point at which the crossflow starts taking a
considerable effect occurs around XD =35 The target wall profile of the ZD=10
channel shows the outside jets on the second row of jet deflecting downstream It can be
conjectured that the bending of the outside jets downstream is caused by the wall jet
created by the first row of jets separating from the side wall and deflecting the outside
jets of the following rows of jets The heat transfer profile for the ZD case excludes the
first jet due to shadows being present when the data was taken
Also evident from this spanwise averaged data is the increase in heat transfer
with increases in Reynolds numbers and decreases in impingement height Results tend
to be the closest from case to case at the first impingement jet This is a reasonable
result as the effects of cross flow have little to no effect at the first few impingement
locations The impact of the jet would then be the driving force at these locations and
would be similar between cases except if the potential core is not reaching the target
surface The potential core of a jet tends to last between 6 and 10 diameters from its
origin It can be seen that the difference in heat transfer coefficient in the first two jets for
the ZD=8 and ZD=10 channel is much different than the corresponding difference
between the ZD=6 and ZD=8 heights This decreased difference between the heights of
the peaks may be attributed to the potential core reaching the target wall at the heights of
6 and 8 diameters leading to similar profiles and may not be reaching the surface at the
height of 10 diameters The heat transfer values of the peaks diminish in the downstream
direction The range of fluctuation also drops that is the profile becomes more uniform
at large XD This drop in fluctuation is more visible at the tallest channel height
(ZD=10) and less pronounced at the smallest channel This is due to the jet in the small
39
channel having to travel a shorter distance to impinge on the target plate leaving the
crossflow less time for it to deflect the jet as opposed to the tall channel where the jet has
to travel almost twice the distance as the ZD=6 channel for it to impinge on the target
wall This effect cannot be solely explained by the built up cross flow in the channel
Mixing loses also take part in the degradation of the stagnation size of the downstream
jets The mixing losses have much greater effect on the taller channels due to the same
reason that the cross flow has a higher impact on them too the jets have to travel a large
distance before hitting the target plate leading the stagnant or moving surrounding air to
be a sink of its downward momentum for a longer time and distance than the respective
smaller channels The heat transfer coefficient of the side wall was also analyzed
Similar effects are expected on the side wall due to the expected impact of the wall jet
As expected the strength of the cross flow is not enough to prevent wall jets from
successfully impacting the side wall at small XD jet locations however the crossflow
takes dominance at around XD=25 Also evident in these plots is the concentration of the
wall jet impact to the bottom of the channel on the order of 1-2 diameters in height It is
interesting to note that for the 5210B case in Figure 24 as the first jet diffuses outward
it impacts the sidewall at a height of ZD=6 The height at which the diffused jet affects
the sidewall heat transfer coefficient decreases as the crossflow increases The stagnation
regions are also deflected in the downstream direction similar to the target surface
results These effects are most evident in the 5210B Similar characteristics can be
explained from the spanwise-averaged plots shown in Figure 25 These results again
clearly show the effects of increasing the impingement height and increases in Reynolds
number As the height is increased the effect of the wall jet is significantly reduced
40
partially due to the increased surface area much of which is not affected by the wall jet
The diminishing effect of the cross flow accumulation is also evident in these plots as the
heat transfer peaks decrease in the downstream direction
43 XD Comparisons
The streamwise jet spacing was changed from XD=5 to 15 by covering two out
of three rows of jets This was done by covering the impingement holes inside the
channel with smooth blue painters tape and sealing the plenum side of the jet plate with
metal tape to ensure no leakage The profile is expected to be less uniform than the case
where XD=5 due to the large spreading of the high heat transfer peaks Due to the large
separation between the rows of jets there is a lower amount of downward momentum
than the equivalent XD=5 geometry for this reason it is expected to see a lower heat
transfer peak due to the jets momentum diffusing out faster to the stagnant air decreasing
the effective impingement velocity Figure 26 shows the target wall heat transfer
distribution Similar to the XD=5 profile it can be seen that the heat transfer due to the
jet impingement drastically reduces after the third jet This phenomenon leads us to
believe that at both Reynolds numbers the cross flow generated by the first three jets is
powerful enough to effectively deflect the fourth jet downstream diminishing its heat
transfer performance The similarity seen in Figure 26 between high and low Reynolds
number implies that the downstream deflection of the jets is not dependent on the jet
Reynolds numbers
41
Figure 26 XD=15 Target Wall Heat Transfer Profile
42
Figure 27 XD=15 Span-averaged Target Wall Heat Transfer Distribution
On the span averaged plots seen in Figure 27 the downstream deflection of the
jets is evident however as described previously the shifts in the peaks of heat transfer
occur at the same xD for both Reynolds numbers The amplitude of fluctuation of heat
transfer coefficients for the high Reynolds number case is larger than that of the low
Reynolds number Both profiles seem to start to level off at the end of the impingement
channel with the lowest span average being located just before the fourth jet at both
Reynolds numbers
A comparison of target wall heat transfer coefficients between XD =15 and 5 is
shown in Figure 28 At first glance it is clearly visible that the XD=15 average heat
transfer coefficient is smaller than its XD=5 counterpart This is also noticed by Ricklick
where he showed average HTC profiles for larger XD to be smaller than those at lower
XD (Ricklick 2009) This may occur due to there not being as high downward
0
50
100
150
200
250
300
350
0 20 40 60 80
HTC
(W
m2
K)
XD
Low Re
High Re
Impingement Location
43
momentum for the XD=15 case as compared to the XD=5 due to the lack of close jets
The stagnant air around the spaced out jets is taking away more of its momentum
decreasing the effective impingement Reynolds number Also important to notice is the
fact that since the XD=5 case has three times the flow impinged into it the cross flow
velocity and therefore Reynolds number will be three times as large increasing the heat
transfer coefficient
Figure 28 Target Wall Span-average Comparison of XD=5 and 15 at High Re
The side walls also show similar patterns to their XD=15 counterparts Strong
wall jet impingement can be seen on the side wall at low xD and zD Figure 29 shows
areas where the wall jet generated by the target wall impinges on the sidewall Similar to
the profile seen in Figure 24 the high heat transfer region reaches upward in the z
direction up to a height of 4-5 diameters for the first jet This high heat transfer stagnation
region decreases as xD increases to the point where the wall jet created by the last jet is
negligible when coupled with pure channel flow
0
50
100
150
200
250
300
350
400
0 10 20 30 40 50 60 70 80
HTC
(W
m2K
)
XD
XD = 5 XD = 15 Jet Location
- Blocked for XD =15
44
Figure 29 Side Wall Heat transfer Coefficient Profile
The span averaged plot seen in Figure 30 shows a nearly flat profile with peaks
located at the stagnation regions of the wall jets Thw downstream deflection for the
XD=15 case is much more pronounced than the one for the XD=5 case This is due to
the jet not being constrained by the wall jets generated by the previous and latter
impingement locations In the XD=15 case the wall jet is free to move downstream
more so than the XD=5 due to it not being disturbed by anything other than the cross
flow
45
Figure 30 XD=15 Side Wall Span-averaged Heat Transfer Coefficients
44 3D Comparison of the Heat Transfer Profiles
In order to further understand the targetsidewall interactions both heat transfer profiles
were positioned in an isometric view representative of the channel One important thing
to note is that both target and side wall profiles are not on the same scale This form of
data display is only qualitative way to describe the heat transfer profiles Figure 31 shows
the 3D profile of the XD=5 ZD=6 case The both stagnation regions of the jet onto the
target wall and the wall jet into the sidewall can be seen to occur at the same location for
the first three streamwise rows After the fourth and fifth row the wall jet diminishes in
magnitude Also visible in this view is the increasing heat transfer at low zD towards the
end of the channel of the side wall The constant input of mass and downward momentum
into the channel causes the cross flow generated by the previous jets to be squeezed into
the lower third of the channel increasing the velocity and the heat transfer of the target
wall
0
20
40
60
80
100
120
0 20 40 60 80
HTC
(W
m2K
)
XD
Low Re High Re Jet Locations
46
Figure 31 3D Heat Transfer Profile for ZD=6 XD=5
Similar patterns are seen in the taller ZD=8 channel seen in Figure 32 The wall jet
generate by the third streamwise row of jets is been deflected downward more than its
ZD=6 counterpart This can be attributed to the fact that the jet located at the ZD=8
channel has lost much of its momentum and is more easily bent downstream by the cross
flow generated by the first two jets The ZD=8 sidewall shows similar increasing heat
transfer at high xD however the increase is not as drastic as the one found in the ZD=6
channel This is caused due to the extra two diameters the jets have to cover to impinge
on the surface since the ZD=8 channel is one third larger than the ZD=6 one the flow
has to have more area to flow through The last few jets only deflect the cross flow
downward about 4 diameters this leaves two diameters for the flow to pass through on
the ZD=6 channel causing the velocity to increase rapidly and therefore increasing the
heat transfer coefficient at the low zD Since the ZD=8 channel has four remaining
47
diameters for the flow to move through it does not deflect it as much as the ZD=6
channel does only increasing the cross flow velocity and resulting heat transfer
coefficient slightly over the area at low zD and high xD
Figure 32 3D Heat Transfer Profile for ZD=8 XD=5
The 3D heat transfer profile for ZD=6 and xD=15 channel seen in Figure 33 shows
similar details to those seen in the XD=5 channels The stagnation regions of the jet and
wall jet occur at the same x location for the first three rows of jets the wall jet generated
by the fourth row of jets is deflected downstream only generating as small region of high
convective coefficients at the side wall The region located at the top right corner of the
side wall is colored red signifying high heat transfer however this area is generated by
the heaters providing non uniform heat flux at this location This region of high heat
transfer coefficients also occur at xD=0-4 of the target wall where the heater coil bends
48
Figure 33 3D Heat Transfer Profile for ZD=6 XD=15
45 Thermal Performance Calculations
Thermal performance calculations were done on the two tallest channels (ZD=8 and 10)
The pumping power was calculated for both channels at two Reynolds numbers Figure
34 shows the ratio of pressures required to pull the same amount of flow through as
smooth duct as opposed to through the jet plate The ZD=10 channel at high Reynolds
number requires the largest pressure as seen in the Figure however in order to pull the
same amount of flow rate through it requires a smaller pressure difference due to the
large cross section
49
Figure 34 Pressure Drop Ratio with Respect to Smooth Channel
Next the heat transfer enhancement was calculated A total area averaged heat
transfer coefficient was taken for the target wall and compared to the smooth channel
Dittus-Boelter value while using the same total mass flow rate Figure 35 shows an
average heat transfer enhancement of four times that of a smooth channel Similar trends
were noticed in the literature (Ricklick 2009) of decreasing heat transfer enhancement
with an increase of jet Reynolds number Ricklick also showed an increase in heat
transfer enhancement with an increase of jet to target spacing similar to the one seen in
Figure 35
0
10
20
30
40
50
60
528A_TW 528B_TW 5210A_TW 5210B_TW
PP
o
50
Figure 35 Heat Transfer Enhancement
Thermal performances at constant pressure drop were then calculated by dividing
the heat transfer enhancement by the pressure increase As seen in Figure 36 all the
values fall well below 1 making the impingement channel an unfeasible mode of heat
transfer enhancement when a constant pressure is supplied
Figure 36 Thermal Performance at Constant Pressure Drop
0
05
1
15
2
25
3
35
4
45
528A_TW 528B_TW 5210A_TW 5210B_TW
hh
o
0
002
004
006
008
01
012
014
528A_TW 528B_TW 5210A_TW 5210B_TW
(hh
o)
(PP
o)
51
The thermal performance at constant pumping drop was calculated in the same
way that the constant pressure drop was calculated the only difference being the pressure
ratio term was raised to the one third power As seen in Figure 37 the thermal
performances at constant pumping power are all higher than unity this signifies that if a
surface needs to be cooled with the supply of a constant pumping power the
impingement channel is a feasible option Similar to the figure literature (Ricklick 2009)
showed a decrease of thermal performance with an increase of channel height and
Reynolds number
Figure 37 Thermal Performance at Constant Pumping Power
0
02
04
06
08
1
12
14
528A_TW 528B_TW 5210A_TW 5210B_TW
(hh
o)
(PP
o)1
3
52
CHAPTER FIVE COMPUTATIONAL FLUID DYNAMICS
51 Problem Setup
In order to further enhance the understanding of the heat transfer profiles showed
previously a computational study was performed Even though CFD does not yield
accurate quantitative results it produces good qualitative data that can be used to explain
the flow physics in the channel and therefore increase the understanding of the patterns
seen previously The channel was meshed with the use of GAMBIT Due to the
symmetry the channel was split in half in the streamwise direction All horizontal
surfaces (parallel to the target wall) were divided into 6 different regions that are later on
going to be meshed individually The six regions are seen in Figure 38 section 1 is
located at the center of every jet also referred to as ldquojet centerrdquo This region was created
to reduce the squewness of the elements near the center of the jet by allowing the mesh to
be completely linear with a squewness of zero Section two complements section 1 to
complete the impingement hole The half impingement hole located at the symmetry wall
contains the same exact region 2 however it only has one half of the jet center Section 3
was made in order to bring the polar geometry of the holes to match the cartesian aspect
of the remainder of the channel With the addition of section 3 to the channel the only
remaining sections are square or rectangular regions Region 4 lies in between
streamwise rows of jets Section 5 is located at the entrance and the exit of the channel
These sections are not square in contrast with section 4 The last remaining section is
located near the side wall of the channel extending from the beginning to the exit of the
channel
53
Figure 38 Horizontal Plane of Impingement Channel Geometry
All the faces of sections 1 and 2 are linked throughout the channel and the
plenum however in order to have greater control of the mesh in the plenum and the
channel the remaining sections 3 4 5 and 6 are not linked to every single similar face
instead they are only linked to similar faces in either the plenum or the channel
Boundary layer spacing number of rows and growth factor are placed around the
channel In order to maintain a y+ of less than unity the first cell spacing of the boundary
layer inside the channel was set to be 000001 m (01mm) This first cell spacing yielded
y+
values varying between zero and 9 at the target side and front end wall Figure 39
shows a contour of y+ values on the heated walls The maximum values occur near the
impingement locations as expected due to large shear caused by the steep velocity
gradient normal to the wall On the downstream direction the y+ also increases due to the
increase of flow rate and therefore the increased skin friction on the wall At the
impingement location of the first jet the y+ is close to zero due to the velocity having its
direction mostly normal to the surface yielding no shear
54
Figure 39 Target Side and Front End Wall y+ Values
Once the faces were linked edge meshes were created on the sides of the jet center
Section 2rsquos inner edge was also meshed using a different parameter than the one used for
the jet center in order to allow for more freedom when trying to refine the mesh These
two edge meshes is followed by meshing all of section 2 faces alongside all the jet
centers Once these were complete section 3rsquos inner edge was meshed with different
parameters for the channel and plenum Sections 4 and 5 sides that connected with the
face made by section 6 were meshed so that their spacing was similar again the plenum
and channel were meshed separately for increased control of mesh density in both of
these areas The upstream-most edge of section 6 was meshed so that the spacing is
similar to the edge mesh in sections 4 and 5 this was done in order to have aspect ratios
of the wall be as close as possible to unity Sections 3 4 5 and 6 were meshed on both
the channel and the plenum With the entire target wall plane meshed these surface
meshes are coopered upwards to connect to the opposite wall The vertical spacing has
55
also been set up differently between the channel and the plenum The holes and the
plenum were also coopered The finished mesh was then exported as a msh file
Boundary conditions were set in GAMBIT once the mesh was imported into
Fluent values were set to every face depending on their location and purpose Figure 40
shows the four different boundary conditions Face 1 (blue) was set to be a mass flow
inlet The flow rate is half of the total flow rate at a given jet Reynolds number due to it
being only half of the entire domain Face 2 (yellow) is a symmetry plane face 3 (red) is
a pressure outlet at zero gauge pressure The rest of the faces in the channel denoted by
the number 4 (white) are set to walls The target side and front end wall had a heat flux
applied to them equal to 10000Wm2
Figure 40 Finished Mesh with Boundary Conditions
The model was imported into Fluent It was scaled down by a factor of 1000 due to it
being made in GAMBIT in millimeters The energy model was turned on The Realizable
k-ε model was used with enhanced wall functions on both the pressure and thermal
gradients The boundary conditions were set as discussed previously the mass flow inlet
was set to the specific flow rate normal to the surface the heat fluxes were set on the
56
heated walls the outflow gauge pressure was set to zero Two important reference values
characteristic length and reference temperature were set to be the diameter of the jet
(0075m) and 300K respectively The spatial discretization parameters were set to second
order upwind for momentum turbulent kinetic energy turbulent dissipation rate and
energy The under-relaxation factors were set to default Four monitors were created to
aid in the determination of convergence two of them read Nusselt numbers at the
stagnation region of the first and last jet the remaining two read the exit velocity at the
first and last jet The continuity x y and x velocities and energy equations residuals
were set to be 1E-6 while k and ε residuals were set to 1E-4 The solution was initialized
on the all zones at 1ms in the positive x direction The solution was set to autosave every
100 iterations while keeping only the two newest dat files The calculation was then run
for a maximum of 7000 iterations
A grid independence study was done on the domain to find the optimal size of
mesh that provides the correct solution while minimizing the compute time Two
monitors were set to check for grid independence both of them were vertex maximum
One of them read the Nusselt number at the impingement location of the first center jet
while the second one measures the velocity at the exit of the last jet Four different mesh
sizes were run to the convergence criterion explained before their sizes were 900000
15 million 28 million and 43 million cells
57
Figure 41 Grid Independence Study
It can be seen in Figure 41 that the difference between the 28 and 43 million cell
meshes are very small a difference of under 006 for velocity and 7 for Nusselt
number It can be safe to assume that the 28 million cell mesh is large enough to provide
a mesh independent solution The GAMBIT journal file used to create this mesh is
attached to the appendix The results shown hereafter are the ones obtained by the 28
million cell mesh
Figure 42 Residual Plots for the 26M Cell Run
67
69
71
73
75
77
79
81
83
85
485
4855
486
4865
487
4875
488
4885
489
0 1 2 3 4 5
Nu
sse
lt N
um
be
r
Cell Ammount (Millions)
Grid Independence Study
Velocity
Nusselt Number
58
For future reference Figure 42 shows the residuals of the 26M cell calculation
Up until around 4400 iterations the residuals were increasing shortly thereafter the
residuals started decreasing until it converged just after 5500 iterations All runs for the
differently sized meshes had the same residual patters with the peak of residuals and
point of convergence happening at different iterations
52 CFD Results
As describe previously all the results shown here are for the mesh containing 28 million
elements Figure 43 shows the total pressure contours It can be seen that the plenum
portion is at a constant total pressure Once the jets form since there are very small losses
in the jets due to the wall friction the total pressure still remains constant Only when the
jets enter the channel and start mixing with the cross flow is that they start losing the total
pressure head It is important to notice how the first two jets have the total pressure close
to the plenum arriving at the target wall This implies a successful impingement of the
undisturbed potential core As we move downstream the total pressure is lost quite
rapidly as the jets interact with the cross flow
Figure 43 Total Pressure Contours
59
Similar details can be drawn out from Figure 44 it can be seen that the first three
jets successfully impinge on the target wall while the rest of the downstream ones are
deflected by the cross flow As mentioned by Ricklick the velocity magnitude of the last
jet is larger than that of the first jet due to there being a lower static pressure at the end of
the channel providing it with a steeper pressure gradient hence higher velocity
Figure 44 Velocity Magnitude Contours
Turbulent kinetic energy was plotted in Figure 45 it is expected to have the
highest turbulent kinetic energy near the exit of the holes where the stagnant air is in
contact with the fast moving jet The mixing between the two regimes causes very
energetic eddies to form potentially enhancing the target and side wall heat transfer
coefficient As cross flow builds up towards the end of the channel the turbulent kinetic
energy increases due to larger overall velocities and fluctuations between the cross flow
and jets
60
Figure 45 Turbulent Kinetic Energy Contours
As Ricklick showed in his work the static temperature rise is quite small for such a small
channel It can be seen in Figure 46 that the driving temperature for heat transfer is that of
the plenum It is important to notice that a wall heat flux of 10000 Wm2 was used as the
boundary condition Not even in the most powerful tests would we ever use heat fluxes
that high they normally range between 2500 to a maximum of 7000 Wm2 A heat flux of
10000 Wm2 will increase the temperature at a faster rate than what it is normally used in
experimental testing
Figure 46 Static Temperature Contours
61
Figure 47 Target and Side Wall Heat Transfer Coefficient Contours
Figure 47 shows the target and sidewall heat transfer profiles Peaks can be seen at the
first three locations similar to that seen in Figure 22 The trend decreases rapidly to
eventually become a slowly increasing heat transfer profile due to the increase of mass
flow through the channel The sidewall provides the same results clear peaks in heat
transfer where the wall jets impinge on the sidewall seen in Figure 48 in more detail The
sidewall also shows a recirculation zone in between the first row of jets and the end wall
This is caused by the wall jet from the first row hitting the back wall moving upwards in
a circular pattern and coming back down when it encounters the first impingement row
Figure 48 Closer View of First few Rows of Impingement HTC Contours
62
Figure 49 Pathlines Generating from the First Row of Jets
Figure 49 helps explain the low heat transfer region between the first row of jets and
the end wall Pathlines are generated at the exit of each hole in the first row As the
air impinges on the surface half of it moves downstream and the other half movers
upstream to this recirculation zone where it circulates for a period of time before
reuniting with the remainder of the flow to move downstream The wall jet that
moves towards the second row of jets encounters the wall jet created by the second
row of jets causing the pathlines to drastically move upwards On the side of the
channel the pathlines behave erratically with no clear pattern clearly signifying the
highly turbulent and chaotic flow structure of this impingement channel
63
CHAPTER SIX CONCLUSIONS
It has been seen from this analysis that the side walls provide significant heat
transfer in an impingement channel especially at the relatively smaller channel
height This is primarily the result of successful impact of the wall jet with the side
walls It was shown that the tallest channel (ZD=10) has the most uniform profile with
low heat transfer coefficients when compared to the other channels The peaks of the
ZD=6 and 8 channels have a very similar profile which may indicate the successful
impingement of the potential core of the jet on the target surface As XD increases the
peaks diminish and a positive slope profile is attained by the increase of cross flow
velocity as more and more jets are introduced Tall impingement channels provide the
user with a heat transfer profile that is more uniform than those provided with the use of a
smaller channel while still maintaining higher convective coefficients when compared to
a smooth flow scenario The downstream shift of the wall jets is found to be independent
of Reynolds number and heavily dependent on streamwise position It was also found that
at XD=15 the wall jets decay faster than their XD=5 counterparts From the 3D heat
transfer profiles it was seen that the cross flow generated by multiple upstream jets is
deflected downward decreasing its effective flow area increasing its velocity hence
providing higher convective coefficients at the side wall at high xD and low zD
64
APPENDICES
Appendix A
Lateral Conduction Consideration
Thickness of foil heater Heat flux
Sample volume width
Volumetric heat generation
Volume of sample volume
Temperature profile from the first row of impingement ONLY valid for 02ltxlt045
t 50m k 20W
m K qflux 6000
W
m2
1mm
V 2
t qvol
qflux
t
T x( ) 298Kqflux
470630 x2
31244x 14842 W
m2K
N 15
x 02045 02
N 102 047
002 003 004 005314
315
316
317
318
319
320
T x( )
x
A t
qnet x( ) A kxT x
m
d
d xT x( )
d
d
1
m
002 003 004 0050
5 105
1 104
15 104
2 104
qnet x( )
x
65
Now comparing the net heat gained by lateral conduction to heat generated and convected out
It can be seen that the lateral conduction into the sample volume is two orders of magnitude smaller than the heat removed by convection
qgen qvol V 6 103
W
qconv x( ) 2
qflux qnet x( )
002 003 004 0051 10
5
1 104
1 103
001
qconv x( )
qnet x( )
x x
66
Appendix B
This is the journal file run on gambit to generate the geometry faces links
boundary layer face and volume meshes as well as the boundary conditions
set diameter
$d=75
$zc=6($d)
$xc=80($d)
$yc=4($d)
$y=2($d)
$x=5($d)
$zp=5($d)
$ztot=($zc)+($d)+($zp)
$jcf=(13)
$ocf=2
Boundary layer constants
$first=01
$growth=12
$rows=4
Meshing constants
$NumbNodes=5
$Numbtelnodes=6
$PLobnodes=5
$Chobnodes=5
$Plbenodes=($NumbNodes(4)+$rows)
$plsqnodes=($NumbNodes(3))
$Pllsnodes=($NumbNodes+$rows)
$Nojetcells=10
$Chzdnodes=($zc$Nojetcells)($d)
$Plzdnodes=($zp$Nojetcells)($d)
Boundary layer constants for channel
$firstch=001
$growthch=12
$rowsch=8
$CHbenodes=($NumbNodes(4)+$rowsch)
$CHlsnodes=($NumbNodes+$rowsch)
volume create body width ($xc) depth ($yc) height ($ztot) offset ($xc2) ($yc2) ($ztot2) brick
volume create cylinder height ($ztot) radius1 ($d2) radius3 ($d2) offset ($x) 0 ($ztot2) zaxis frustum
volume cmove cylinder multiple 1 offset 0 ($y) 0
volume cmove cylinder volume3 multiple 14 offset ($x) 0 0
volume create jetplate width ($xc) depth ($yc) height ($d)offset ($xc2) ($yc2) ($d2+$zc) brick
volume split body volumes jetplate connected
volume split jetplate volumes cylinder volume3 volume4 volume5
volume6 volume7 volume8 volume9 volume10 volume11
volume12 volume13 volume14 volume15 volume16 volume17
67
volume18 volume19 volume20 volume21 volume22 volume23
volume24 volume25 volume26 volume27 volume28 volume29
volume30 volume31 connected
face create jetcenter width ($jcf$d) height ($jcf$d) offset ($x) 0 0 xyplane rectangle
face create jetcircle radius ($d2) xyplane circle
face move jetcircle offset ($x) 0 0
face create outbox width ($ocf$d) height ($ocf$d) offset ($x) 0 0 xyplane rectangle
face split outbox connected faces jetcircle jetcenter
face split jetcircle connected faces face1
face split outbox connected faces face1
face cmove jetcenter outbox jetcircle face222 face223 multiple 1 offset 0 ($y) 0
face cmove jetcenter outbox jetcircle face222 face223 face224 face225 face226
face227 face228 multiple 14 offset ($x) 0 0
volume delete jetplate lowertopology
face split face1 connected keeptool faces jetcircle jetcenter outbox
face222 face223 face224 face225 face226 face227
face228 face229 face230 face231 face232 face233
face234 face235 face236 face237 face238 face239
face240 face241 face242 face243 face244 face245
face246 face247 face248 face249 face250 face251
face252 face253 face254 face255 face256 face257
face258 face259 face260 face261 face262 face263
face264 face265 face266 face267 face268 face269
face270 face271 face272 face273 face274 face275
face276 face277 face278 face279 face280 face281
face282 face283 face284 face285 face286 face287
face288 face289 face290 face291 face292 face293
face294 face295 face296 face297 face298 face299
face300 face301 face302 face303 face304 face305
face306 face307 face308 face309 face310 face311
face312 face313 face314 face315 face316 face317
face318 face319 face320 face321 face322 face323
face324 face325 face326 face327 face328 face329
face330 face331 face332 face333 face334 face335
face336 face337 face338 face339 face340 face341
face342 face343 face344 face345 face346 face347
face348 face349 face350 face351 face352 face353
face354 face355 face356 face357 face358 face359
face360 face361 face362 face363 face364 face365
face366 face367 face368
face move jetcircle jetcenter outbox face222 face223 face224
face225 face226 face227 face228 face229 face230
face231 face232 face233 face234 face235 face236
face237 face238 face239 face240 face241 face242
face243 face244 face245 face246 face247 face248
face249 face250 face251 face252 face253 face254
face255 face256 face257 face258 face259 face260
face261 face262 face263 face264 face265 face266
face267 face268 face269 face270 face271 face272
face273 face274 face275 face276 face277 face278
face279 face280 face281 face282 face283 face284
face285 face286 face287 face288 face289 face290
face291 face292 face293 face294 face295 face296
face297 face298 face299 face300 face301 face302
face303 face304 face305 face306 face307 face308
face309 face310 face311 face312 face313 face314
68
face315 face316 face317 face318 face319 face320
face321 face322 face323 face324 face325 face326
face327 face328 face329 face330 face331 face332
face333 face334 face335 face336 face337 face338
face339 face340 face341 face342 face343 face344
face345 face346 face347 face348 face349 face350
face351 face352 face353 face354 face355 face356
face357 face358 face359 face360 face361 face362
face363 face364 face365 face366 face367 face368 offset 0
0 $ztot
THIS SPLITS THE TOP PLENUM FACE WITH THE FACES CREATED IN THE BOTTOM
face split face6 connected keeptool faces jetcircle jetcenter outbox
face222 face223 face224 face225 face226 face227
face228 face229 face230 face231 face232 face233
face234 face235 face236 face237 face238 face239
face240 face241 face242 face243 face244 face245
face246 face247 face248 face249 face250 face251
face252 face253 face254 face255 face256 face257
face258 face259 face260 face261 face262 face263
face264 face265 face266 face267 face268 face269
face270 face271 face272 face273 face274 face275
face276 face277 face278 face279 face280 face281
face282 face283 face284 face285 face286 face287
face288 face289 face290 face291 face292 face293
face294 face295 face296 face297 face298 face299
face300 face301 face302 face303 face304 face305
face306 face307 face308 face309 face310 face311
face312 face313 face314 face315 face316 face317
face318 face319 face320 face321 face322 face323
face324 face325 face326 face327 face328 face329
face330 face331 face332 face333 face334 face335
face336 face337 face338 face339 face340 face341
face342 face343 face344 face345 face346 face347
face348 face349 face350 face351 face352 face353
face354 face355 face356 face357 face358 face359
face360 face361 face362 face363 face364 face365
face366 face367 face368
THIS MOVES THE FACES THAT WE ARE USING TO PLIT THE BOTTOM PLENUM SURFACE
face move jetcircle jetcenter outbox face222 face223 face224
face225 face226 face227 face228 face229 face230
face231 face232 face233 face234 face235 face236
face237 face238 face239 face240 face241 face242
face243 face244 face245 face246 face247 face248
face249 face250 face251 face252 face253 face254
face255 face256 face257 face258 face259 face260
face261 face262 face263 face264 face265 face266
face267 face268 face269 face270 face271 face272
face273 face274 face275 face276 face277 face278
face279 face280 face281 face282 face283 face284
face285 face286 face287 face288 face289 face290
face291 face292 face293 face294 face295 face296
face297 face298 face299 face300 face301 face302
69
face303 face304 face305 face306 face307 face308
face309 face310 face311 face312 face313 face314
face315 face316 face317 face318 face319 face320
face321 face322 face323 face324 face325 face326
face327 face328 face329 face330 face331 face332
face333 face334 face335 face336 face337 face338
face339 face340 face341 face342 face343 face344
face345 face346 face347 face348 face349 face350
face351 face352 face353 face354 face355 face356
face357 face358 face359 face360 face361 face362
face363 face364 face365 face366 face367 face368 offset 0
0 -$zp
SPLITS THE BOTTOM FACE OF THE PLENUM WITH THE FACES THAT ARE USED TO SPLIT
face split face114 connected keeptool faces jetcircle jetcenter
outbox face222 face223 face224 face225 face226 face227
face228 face229 face230 face231 face232 face233
face234 face235 face236 face237 face238 face239
face240 face241 face242 face243 face244 face245
face246 face247 face248 face249 face250 face251
face252 face253 face254 face255 face256 face257
face258 face259 face260 face261 face262 face263
face264 face265 face266 face267 face268 face269
face270 face271 face272 face273 face274 face275
face276 face277 face278 face279 face280 face281
face282 face283 face284 face285 face286 face287
face288 face289 face290 face291 face292 face293
face294 face295 face296 face297 face298 face299
face300 face301 face302 face303 face304 face305
face306 face307 face308 face309 face310 face311
face312 face313 face314 face315 face316 face317
face318 face319 face320 face321 face322 face323
face324 face325 face326 face327 face328 face329
face330 face331 face332 face333 face334 face335
face336 face337 face338 face339 face340 face341
face342 face343 face344 face345 face346 face347
face348 face349 face350 face351 face352 face353
face354 face355 face356 face357 face358 face359
face360 face361 face362 face363 face364 face365
face366 face367 face368
COPIES THE FACES THAT WE USED TO SPLIT TO BOTTOM OF THE PLENUM TO THE TOP OF
THE CHANNEL
face cmove jetcircle jetcenter outbox face222 face223 face224
face225 face226 face227 face228 face229 face230
face231 face232 face233 face234 face235 face236
face237 face238 face239 face240 face241 face242
face243 face244 face245 face246 face247 face248
face249 face250 face251 face252 face253 face254
face255 face256 face257 face258 face259 face260
face261 face262 face263 face264 face265 face266
face267 face268 face269 face270 face271 face272
face273 face274 face275 face276 face277 face278
face279 face280 face281 face282 face283 face284
70
face285 face286 face287 face288 face289 face290
face291 face292 face293 face294 face295 face296
face297 face298 face299 face300 face301 face302
face303 face304 face305 face306 face307 face308
face309 face310 face311 face312 face313 face314
face315 face316 face317 face318 face319 face320
face321 face322 face323 face324 face325 face326
face327 face328 face329 face330 face331 face332
face333 face334 face335 face336 face337 face338
face339 face340 face341 face342 face343 face344
face345 face346 face347 face348 face349 face350
face351 face352 face353 face354 face355 face356
face357 face358 face359 face360 face361 face362
face363 face364 face365 face366 face367 face368 multiple 1 offset 0
0 -$d
NAME OF COPIED NEW FACES
face1104 face1105 face1106 face1107 face1108 face1109 face1110 face1111
face1112 face1113 face1114 face1115 face1116 face1117 face1118 face1119
face1120 face1121 face1122 face1123 face1124 face1125 face1126 face1127
face1128 face1129 face1130 face1131 face1132 face1133 face1134 face1135
face1136 face1137 face1138 face1139 face1140 face1141 face1142 face1143
face1144 face1145 face1146 face1147 face1148 face1149 face1150 face1151
face1152 face1153 face1154 face1155 face1156 face1157 face1158 face1159
face1160 face1161 face1162 face1163 face1164 face1165 face1166 face1167
face1168 face1169 face1170 face1171 face1172 face1173 face1174 face1175
face1176 face1177 face1178 face1179 face1180 face1181 face1182 face1183
face1184 face1185 face1186 face1187 face1188 face1189 face1190 face1191
face1192 face1193 face1194 face1195 face1196 face1197 face1198 face1199
face1200 face1201 face1202 face1203 face1204 face1205 face1206 face1207
face1208 face1209 face1210 face1211 face1212 face1213 face1214 face1215
face1216 face1217 face1218 face1219 face1220 face1221 face1222 face1223
face1224 face1225 face1226 face1227 face1228 face1229 face1230 face1231
face1232 face1233 face1234 face1235 face1236 face1237 face1238 face1239
face1240 face1241 face1242 face1243 face1244 face1245 face1246 face1247
face1248 face1249 face1250 face1251 face1252 face1253
THIS SPLITS THE TOP OF THE CHANNEL WITH THE NEW COPIED FACES
face split face209 connected keeptool faces face1104 face1105 face1106 face1107
face1108 face1109 face1110 face1111 face1112 face1113 face1114 face1115
face1116 face1117 face1118 face1119 face1120 face1121 face1122 face1123
face1124 face1125 face1126 face1127 face1128 face1129 face1130 face1131
face1132 face1133 face1134 face1135 face1136 face1137 face1138 face1139
face1140 face1141 face1142 face1143 face1144 face1145 face1146 face1147
face1148 face1149 face1150 face1151 face1152 face1153 face1154 face1155
face1156 face1157 face1158 face1159 face1160 face1161 face1162 face1163
face1164 face1165 face1166 face1167 face1168 face1169 face1170 face1171
face1172 face1173 face1174 face1175 face1176 face1177 face1178 face1179
face1180 face1181 face1182 face1183 face1184 face1185 face1186 face1187
face1188 face1189 face1190 face1191 face1192 face1193 face1194 face1195
face1196 face1197 face1198 face1199 face1200 face1201 face1202 face1203
face1204 face1205 face1206 face1207 face1208 face1209 face1210 face1211
face1212 face1213 face1214 face1215 face1216 face1217 face1218 face1219
face1220 face1221 face1222 face1223 face1224 face1225 face1226 face1227
71
face1228 face1229 face1230 face1231 face1232 face1233 face1234 face1235
face1236 face1237 face1238 face1239 face1240 face1241 face1242 face1243
face1244 face1245 face1246 face1247 face1248 face1249 face1250 face1251
face1252 face1253
THIS UNITES THE RECTANGLE OUTSIDE FACES AND THE SEMICIRCLE SO THAT IT MAKES
A RECTANGLE WIHOUT THE CENTERJET
face unite faces jetcircle face223 real
face unite faces face222 outbox real
face unite faces face228 face226 real
face unite faces face225 face227 real
face unite faces face231 face233 real
face unite faces face232 face230 real
face unite faces face236 face238 real
face unite faces face237 face235 real
face unite faces face241 face243 real
face unite faces face242 face240 real
face unite faces face248 face246 real
face unite faces face245 face247 real
face unite faces face253 face251 real
face unite faces face252 face250 real
face unite faces face256 face258 real
face unite faces face257 face255 real
face unite faces face263 face261 real
face unite faces face260 face262 real
face unite faces face268 face266 real
face unite faces face265 face264 real
face unite faces face265 face267 real
face unite faces face273 face271 real
face unite faces face272 face270 real
face unite faces face276 face278 real
face unite faces face277 face275 real
face unite faces face281 face283 real
face unite faces face282 face280 real
face unite faces face286 face288 real
face unite faces face287 face285 real
face unite faces face291 face293 real
face unite faces face292 face290 real
face unite faces face296 face298 real
face unite faces face297 face295 real
face unite faces face301 face303 real
face unite faces face302 face300 real
face unite faces face306 face308 real
face unite faces face307 face305 real
face unite faces face316 face318 real
face unite faces face312 face310 real
face unite faces face311 face313 real
face unite faces face315 face317 real
face unite faces face321 face323 real
face unite faces face322 face320 real
face unite faces face326 face328 real
face unite faces face327 face325 real
face unite faces face331 face333 real
face unite faces face332 face330 real
face unite faces face336 face338 real
72
face unite faces face337 face335 real
face unite faces face347 face345 real
face unite faces face346 face348 real
face unite faces face342 face340 real
face unite faces face341 face343 real
face unite faces face356 face358 real
face unite faces face357 face355 real
face unite faces face352 face350 real
face unite faces face351 face353 real
face unite faces face361 face363 real
face unite faces face366 face368 real
face unite faces face360 face362 real
face unite faces face365 face367 real
SPLITTING ALL THE FACES OF THE CIRCLES IN THE BOTTOM OF THE PLENUM
face split face912 connected keeptool faces face222
face split face117 connected keeptool faces face228
face split face117 connected keeptool faces face225
face split face922 connected keeptool faces face232
face split face124 connected keeptool faces face236
face split face124 connected keeptool faces face237
face split face932 connected keeptool faces face242
face split face131 connected keeptool faces face248
face split face131 connected keeptool faces face245
face split face942 connected keeptool faces face252
face split face138 connected keeptool faces face256
face split face138 connected keeptool faces face257
face split face952 connected keeptool faces face260
face split face145 connected keeptool faces face268
face split face145 connected keeptool faces face265
face split face962 connected keeptool faces face272
face split face152 connected keeptool faces face276
face split face152 connected keeptool faces face277
face split face972 connected keeptool faces face282
face split face159 connected keeptool faces face286
face split face159 connected keeptool faces face287
face split face982 connected keeptool faces face292
face split face166 connected keeptool faces face296
face split face166 connected keeptool faces face297
face split face992 connected keeptool faces face302
face split face173 connected keeptool faces face306
face split face173 connected keeptool faces face307
face split face1002 connected keeptool faces face312
face split face180 connected keeptool faces face316
face split face180 connected keeptool faces face315
73
face split face1012 connected keeptool faces face322
face split face187 connected keeptool faces face326
face split face187 connected keeptool faces face327
face split face1022 connected keeptool faces face332
face split face194 connected keeptool faces face336
face split face194 connected keeptool faces face337
face split face1032 connected keeptool faces face342
face split face201 connected keeptool faces face346
face split face201 connected keeptool faces face347
face split face1042 connected keeptool faces face352
face split face208 connected keeptool faces face356
face split face208 connected keeptool faces face357
face split face1052 connected keeptool faces face360
face split face215 connected keeptool faces face366
face split face215 connected keeptool faces face365
THIS UNITES THE RECTANGLE OUTSIDE FACES AND THE SEMICIRCLE SO THAT IT MAKES
A RECTANGLE WIHOUT THE CENTERJET
face unite faces face1104 face1108 real
face unite faces face1107 face1106 real
face unite faces face1113 face1111 real
face unite faces face1112 face1110 real
face unite faces face1118 face1116 real
face unite faces face1117 face1115 real
face unite faces face1123 face1121 real
face unite faces face1122 face1120 real
face unite faces face1128 face1126 real
face unite faces face1127 face1125 real
face unite faces face1133 face1131 real
face unite faces face1132 face1130 real
face unite faces face1138 face1136 real
face unite faces face1137 face1135 real
face unite faces face1143 face1141 real
face unite faces face1142 face1140 real
face unite faces face1148 face1146 real
face unite faces face1147 face1145 real
face unite faces face1153 face1151 real
face unite faces face1152 face1150 real
face unite faces face1158 face1156 real
face unite faces face1157 face1155 real
face unite faces face1163 face1161 real
face unite faces face1162 face1160 real
face unite faces face1168 face1166 real
face unite faces face1167 face1165 real
face unite faces face1173 face1171 real
face unite faces face1172 face1170 real
face unite faces face1178 face1176 real
face unite faces face1177 face1175 real
face unite faces face1183 face1181 real
74
face unite faces face1182 face1180 real
face unite faces face1186 face1188 real
face unite faces face1187 face1185 real
face unite faces face1193 face1191 real
face unite faces face1192 face1190 real
face unite faces face1198 face1196 real
face unite faces face1197 face1195 real
face unite faces face1203 face1201 real
face unite faces face1202 face1200 real
face unite faces face1206 face1208 real
face unite faces face1207 face1205 real
face unite faces face1213 face1211 real
face unite faces face1212 face1210 real
face unite faces face1216 face1218 real
face unite faces face1217 face1215 real
face unite faces face1221 face1223 real
face unite faces face1222 face1220 real
face unite faces face1228 face1226 real
face unite faces face1227 face1225 real
face unite faces face1233 face1231 real
face unite faces face1232 face1230 real
face unite faces face1238 face1236 real
face unite faces face1237 face1235 real
face unite faces face1243 face1241 real
face unite faces face1242 face1240 real
face unite faces face1248 face1246 real
face unite faces face1247 face1245 real
face unite faces face1253 face1251 real
face unite faces face1252 face1250 real
SPLITTING ALL THE FACES OF THE CIRCLES IN THE TOP OF THE CHANNEL
face split face1257 connected keeptool faces face1107
face split face115 connected keeptool faces face1113
face split face115 connected keeptool faces face1112
face split face1267 connected keeptool faces face1117
face split face122 connected keeptool faces face1123
face split face122 connected keeptool faces face1122
face split face1277 connected keeptool faces face1127
face split face129 connected keeptool faces face1133
face split face129 connected keeptool faces face1132
face split face1287 connected keeptool faces face1137
face split face136 connected keeptool faces face1143
face split face136 connected keeptool faces face1142
face split face1297 connected keeptool faces face1147
face split face143 connected keeptool faces face1153
face split face143 connected keeptool faces face1152
face split face1307 connected keeptool faces face1157
face split face150 connected keeptool faces face1163
face split face150 connected keeptool faces face1162
75
face split face1317 connected keeptool faces face1167
face split face157 connected keeptool faces face1173
face split face157 connected keeptool faces face1172
face split face1327 connected keeptool faces face1177
face split face164 connected keeptool faces face1183
face split face164 connected keeptool faces face1182
face split face1337 connected keeptool faces face1187
face split face171 connected keeptool faces face1193
face split face171 connected keeptool faces face1192
face split face1347 connected keeptool faces face1197
face split face178 connected keeptool faces face1203
face split face178 connected keeptool faces face1202
face split face1357 connected keeptool faces face1207
face split face185 connected keeptool faces face1213
face split face185 connected keeptool faces face1212
face split face1367 connected keeptool faces face1217
face split face192 connected keeptool faces face1221
face split face192 connected keeptool faces face1222
face split face1377 connected keeptool faces face1227
face split face199 connected keeptool faces face1233
face split face199 connected keeptool faces face1232
face split face1387 connected keeptool faces face1237
face split face206 connected keeptool faces face1243
face split face206 connected keeptool faces face1242
face split face1397 connected keeptool faces face1247
face split face213 connected keeptool faces face1253
face split face213 connected keeptool faces face1252
face split face1452 connected keeptool faces face224
face split face1456 connected keeptool faces face234
face split face1460 connected keeptool faces face244
face split face1464 connected keeptool faces face254
face split face1468 connected keeptool faces face264
face split face1472 connected keeptool faces face274
face split face1476 connected keeptool faces face284
face split face1480 connected keeptool faces face294
face split face1484 connected keeptool faces face304
face split face1488 connected keeptool faces face314
face split face1492 connected keeptool faces face324
face split face1496 connected keeptool faces face334
face split face1500 connected keeptool faces face344
face split face1504 connected keeptool faces face354
face split face1508 connected keeptool faces face364
DELETING ALL THE FACES USED TO MAKE THE CUTS
face delete jetcircle face222 face228 face225 jetcenter
76
face224 face231 face232 face236 face237 face229
face1456 face241 face242 face239 face248 face244
face245 face253 face249 face252 face254 face256
face257 face263 face259 face260 face268 face264
face265 face273 face272 face269 face276 face277
face274 face281 face282 face286 face279 face287
face284 face291 face292 face296 face297 face289
face294 face301 face299 face302 face306 face307
face304 face311 face312 face316 face315 face309
face314 face321 face322 face326 face327 face319
face324 face331 face332 face329 face336 face334
face337 face341 face342 face339 face346 face344
face347 face351 face352 face349 face356 face354
face357 face361 face359 face360 face366 face364
face365 lowertopology
face delete face1104 face1105 face1107 face1113 face1112
face115 face234 face1118 face1114 face1117 face1123
face1122 face122 face1138 face1128 face1127 face1124
face1133 face1132 face129 face1134 face1137 face1143
face136 face1142 face1148 face1144 face1147 face1153
face143 face1152 face1158 face1154 face1157 face1163
face150 face1162 face1168 face1164 face1167 face1173
face157 face1172 face1178 face1174 face1177 face1183
face164 face1182 face1186 face1184 face1187 face1193
face171 face1192 face1198 face1194 face1197 face1203
face178 face1202 face1206 face1204 face1207 face1213
face185 face1212 face1216 face1214 face1217 face1221
face192 face1222 face1228 face1224 face1227 face1233
face199 face1232 face1238 face1234 face1237 face1243
face206 face1242 face1248 face1244 face1247 face1253
face213 face1252 lowertopology
face delete face1109 face1119 face1129 face1139 face1149 face1159
face1169 face1179 face1189 face1199 face1209 face1219
face1229 face1239 face1249 lowertopology
face create CP1 width 600 height 75 offset 300 (225+($d)2) 0 xyplane rectangle
face create CP2 width 600 height 75 offset 300 (225+($d)2) ($zc) xyplane rectangle
face create CP3 width 600 height 75 offset 300 (225+($d)2) ($zc+$d) xyplane rectangle
face create CP4 width 600 height 75 offset 300 (225+($d)2) ($zc+$d+$zp) xyplane rectangle
face split face6 connected faces CP4
face split face114 connected faces CP3
face split face209 connected faces CP2
face split face1 connected faces CP1
GEOMETRY IS FINISHED
face modify face912 side vertex6437 vertex6436
77
face modify face1600 side vertex7302 vertex7303
face modify face117 side vertex6446 vertex6447
face modify face646 side vertex3312
face modify face646 side vertex3313
face modify face647 side vertex3432 vertex3433
face modify face372 side vertex2040 vertex2041
face modify face376 side vertex2100 vertex2101
face modify face377 side vertex2221 vertex2220
LINKING ALL THE JET CENTERS
face link face1450 face640 edges edge6949 edge3518 vertices
vertex6437 vertex3253 reverse
face link face1450 face1257 edges edge6949 edge7340 vertices
vertex6437 vertex6797 reverse
face link face1257 face370 edges edge7340 edge2139 vertices
vertex6797 vertex2041 reverse
face link face1257 face1454 edges edge7340 edge6975 vertices
vertex6797 vertex6461 reverse
face link face1454 face649 edges edge6975 edge3519 vertices
vertex6461 vertex3255 reverse
face link face1454 face1267 edges edge6975 edge7377 vertices
vertex6461 vertex6831 reverse
face link face1267 face379 edges edge7377 edge2141 vertices
vertex6831 vertex2043 reverse
face link face1267 face1458 edges edge7377 edge7001 vertices
vertex6831 vertex6485 reverse
face link face1458 face659 edges edge7001 edge3520 vertices
vertex6485 vertex3257 reverse
face link face1458 face1277 edges edge7001 edge7414 vertices
vertex6485 vertex6865 reverse
face link face1277 face389 edges edge7414 edge2143 vertices
vertex6865 vertex2045 reverse
face link face1277 face1462 edges edge7414 edge7027 vertices
vertex6865 vertex6509 reverse
face link face1462 face669 edges edge7027 edge3521 vertices
vertex6509 vertex3259 reverse
face link face1462 face1287 edges edge7027 edge7451 vertices
vertex6509 vertex6899 reverse
face link face1287 face399 edges edge7451 edge2145 vertices
vertex6899 vertex2047 reverse
face link face1287 face1466 edges edge7451 edge7053 vertices
vertex6899 vertex6533 reverse
face link face1466 face679 edges edge7053 edge3522 vertices
vertex6533 vertex3261 reverse
face link face1466 face1297 edges edge7053 edge7488 vertices
vertex6533 vertex6933 reverse
face link face1297 face409 edges edge7488 edge2147 vertices
vertex6933 vertex2049 reverse
face link face1297 face1470 edges edge7488 edge7079 vertices
vertex6933 vertex6557 reverse
face link face1470 face689 edges edge7079 edge3523 vertices
vertex6557 vertex3263 reverse
face link face1470 face1307 edges edge7079 edge7525 vertices
vertex6557 vertex6967 reverse
face link face1307 face419 edges edge7525 edge2149 vertices
78
vertex6967 vertex2051 reverse
face link face1307 face1474 edges edge7525 edge7105 vertices
vertex6967 vertex6581 reverse
face link face1474 face1317 edges edge7105 edge7562 vertices
vertex6581 vertex7001 reverse
face link face1474 face699 edges edge7105 edge3524 vertices
vertex6581 vertex3265 reverse
face link face1317 face429 edges edge7562 edge2151 vertices
vertex7001 vertex2053 reverse
face link face1317 face1478 edges edge7562 edge7131 vertices
vertex7001 vertex6605 reverse
face link face1478 face1327 edges edge7131 edge7599 vertices
vertex6605 vertex7035 reverse
face link face1478 face709 edges edge7131 edge3525 vertices
vertex6605 vertex3267 reverse
face link face1327 face439 edges edge7599 edge2153 vertices
vertex7035 vertex2055 reverse
face link face1327 face1482 edges edge7599 edge7157 vertices
vertex7035 vertex6629 reverse
face link face1482 face719 edges edge7157 edge3526 vertices
vertex6629 vertex3269 reverse
face link face1482 face1337 edges edge7157 edge7636 vertices
vertex6629 vertex7069 reverse
face link face1337 face449 edges edge7636 edge2155 vertices
vertex7069 vertex2057 reverse
face link face1337 face1486 edges edge7636 edge7183 vertices
vertex7069 vertex6653 reverse
face link face1486 face1347 edges edge7183 edge7673 vertices
vertex6653 vertex7103 reverse
face link face1347 face459 edges edge7673 edge2157 vertices
vertex7103 vertex2059 reverse
face link face1486 face729 edges edge7183 edge3527 vertices
vertex6653 vertex3271 reverse
face link face1347 face1490 edges edge7673 edge7209 vertices
vertex7103 vertex6677 reverse
face link face1490 face1357 edges edge7209 edge7710 vertices
vertex6677 vertex7137 reverse
face link face1490 face739 edges edge7209 edge3528 vertices
vertex6677 vertex3273 reverse
face link face1357 face469 edges edge7710 edge2159 vertices
vertex7137 vertex2061 reverse
face link face1357 face1494 edges edge7710 edge7235 vertices
vertex7137 vertex6701 reverse
face link face1494 face1367 edges edge7235 edge7747 vertices
vertex6701 vertex7171 reverse
face link face1494 face749 edges edge7235 edge3529 vertices
vertex6701 vertex3275 reverse
face link face1367 face479 edges edge7747 edge2161 vertices
vertex7171 vertex2063 reverse
face link face1367 face1498 edges edge7747 edge7261 vertices
vertex7171 vertex6725 reverse
face link face1498 face1377 edges edge7261 edge7784 vertices
vertex6725 vertex7205 reverse
face link face1377 face489 edges edge7784 edge2163 vertices
vertex7205 vertex2065 reverse
face link face1498 face759 edges edge7261 edge3530 vertices
79
vertex6725 vertex3277 reverse
face link face1377 face1502 edges edge7784 edge7287 vertices
vertex7205 vertex6749 reverse
face link face1502 face1387 edges edge7287 edge7821 vertices
vertex6749 vertex7239 reverse
face link face1387 face499 edges edge7821 edge2165 vertices
vertex7239 vertex2067 reverse
face link face1387 face1506 edges edge7821 edge7313 vertices
vertex7239 vertex6773 reverse
face link face1502 face769 edges edge7287 edge3531 vertices
vertex6749 vertex3279 reverse
face link face1506 face1397 edges edge7313 edge7858 vertices
vertex6773 vertex7273 reverse
face link face1506 face779 edges edge7313 edge3532 vertices
vertex6773 vertex3281 reverse
face link face1397 face509 edges edge7858 edge2167 vertices
vertex7273 vertex2069 reverse
LINKING ALL THE COMPLETE JETCENTERS
face link face1452 face644 edges edge7891 edge3773 vertices
vertex7303 vertex3433
face link face1452 face115 edges edge7891 edge7364 vertices
vertex7303 vertex6819
face link face1452 face1456 edges edge7891 edge7900 vertices
vertex7303 vertex7311
face link face1456 face654 edges edge7900 edge3774 vertices
vertex7311 vertex3435
face link face1456 face122 edges edge7900 edge7401 vertices
vertex7311 vertex6853
face link face1456 face1460 edges edge7900 edge7909 vertices
vertex7311 vertex7319
face link face1460 face1464 edges edge7909 edge7918 vertices
vertex7319 vertex7327
face link face1460 face129 edges edge7909 edge7438 vertices
vertex7319 vertex6887
face link face1460 face664 edges edge7909 edge3775 vertices
vertex7319 vertex3437
face link face1464 face674 edges edge7918 edge3776 vertices
vertex7327 vertex3439
face link face1464 face136 edges edge7918 edge7475 vertices
vertex7327 vertex6921
face link face1464 face1468 edges edge7918 edge7927 vertices
vertex7327 vertex7335
face link face1472 face1468 edges edge7936 edge7927 vertices
vertex7343 vertex7335
face link face1468 face143 edges edge7927 edge7512 vertices
vertex7335 vertex6955
face link face1468 face684 edges edge7927 edge3777 vertices
vertex7335 vertex3441
face link face1472 face694 edges edge7936 edge3778 vertices
vertex7343 vertex3443
face link face1472 face150 edges edge7936 edge7549 vertices
vertex7343 vertex6989
face link face1472 face1476 edges edge7936 edge7945 vertices
80
vertex7343 vertex7351
face link face1476 face1480 edges edge7945 edge7954 vertices
vertex7351 vertex7359
face link face1476 face157 edges edge7945 edge7586 vertices
vertex7351 vertex7023
face link face1476 face704 edges edge7945 edge3779 vertices
vertex7351 vertex3445
face link face1480 face714 edges edge7954 edge3780 vertices
vertex7359 vertex3447
face link face1480 face164 edges edge7954 edge7623 vertices
vertex7359 vertex7057
face link face1480 face1484 edges edge7954 edge7963 vertices
vertex7359 vertex7367
face link face1484 face171 edges edge7963 edge7660 vertices
vertex7367 vertex7091
face link face1484 face724 edges edge7963 edge3781 vertices
vertex7367 vertex3449
face link face1480 face1488 edges edge7954 edge7972 vertices
vertex7359 vertex7375
face link face1488 face178 edges edge7972 edge7697 vertices
vertex7375 vertex7125
face link face1488 face734 edges edge7972 edge3782 vertices
vertex7375 vertex3451
face link face1488 face1492 edges edge7972 edge7981 vertices
vertex7375 vertex7383
face link face1492 face744 edges edge7981 edge3783 vertices
vertex7383 vertex3453
face link face1492 face185 edges edge7981 edge7734 vertices
vertex7383 vertex7159
face link face1492 face1496 edges edge7981 edge7990 vertices
vertex7383 vertex7391
face link face1496 face754 edges edge7990 edge3784 vertices
vertex7391 vertex3455
face link face1496 face192 edges edge7990 edge7771 vertices
vertex7391 vertex7193
face link face1496 face1500 edges edge7990 edge7999 vertices
vertex7391 vertex7399
face link face1500 face1504 edges edge7999 edge8008 vertices
vertex7399 vertex7407
face link face1504 face1508 edges edge8008 edge8017 vertices
vertex7407 vertex7415
face link face1500 face199 edges edge7999 edge7808 vertices
vertex7399 vertex7227
face link face1500 face764 edges edge7999 edge3785 vertices
vertex7399 vertex3457
face link face1504 face774 edges edge8008 edge3786 vertices
vertex7407 vertex3459
face link face1508 face784 edges edge8017 edge3787 vertices
vertex7415 vertex3461
face link face1504 face206 edges edge8008 edge7845 vertices
vertex7407 vertex7261
face link face1508 face213 edges edge8017 edge7882 vertices
vertex7415 vertex7295
linking the jetcenters of the bottom of the channel one of them has to be reversed but the otherones are not
81
face link face115 face374 edges edge7364 edge2394 vertices
vertex6819 vertex2221 reverse
face link face374 face384 edges edge2394 edge2396 vertices
vertex2221 vertex2223
face link face384 face394 edges edge2396 edge2398 vertices
vertex2223 vertex2225
face link face394 face404 edges edge2398 edge2400 vertices
vertex2225 vertex2227
face link face404 face414 edges edge2400 edge2402 vertices
vertex2227 vertex2229
face link face414 face424 edges edge2402 edge2404 vertices
vertex2229 vertex2231
face link face424 face434 edges edge2404 edge2406 vertices
vertex2231 vertex2233
face link face434 face444 edges edge2406 edge2408 vertices
vertex2233 vertex2235
face link face444 face454 edges edge2408 edge2410 vertices
vertex2235 vertex2237
face link face454 face464 edges edge2410 edge2412 vertices
vertex2237 vertex2239
face link face464 face474 edges edge2412 edge2414 vertices
vertex2239 vertex2241
face link face474 face484 edges edge2414 edge2416 vertices
vertex2241 vertex2243
face link face484 face494 edges edge2416 edge2418 vertices
vertex2243 vertex2245
face link face494 face504 edges edge2418 edge2420 vertices
vertex2245 vertex2247
face link face504 face514 edges edge2420 edge2422 vertices
vertex2247 vertex2249
UP TO THIS POINT ALL THE FACES ARE CONNCTED SUCCESSFULLY
LINKING THE FIRST THREE JET TELEPHONES
face link face912 face117 edges edge6950 edge6960 vertices
vertex6437 vertex6446 reverse
face link face912 face1600 edges edge6950 edge7890 vertices
vertex6437 vertex7303 reverse
face link face912 face372 edges edge6950 edge2168 vertices
vertex6437 vertex2041
face link face117 face376 edges edge6959 edge2304 vertices
vertex6447 vertex2101 reverse
face link face1600 face377 edges edge7890 edge2423 vertices
vertex7303 vertex2221 reverse
face link face372 face382 edges edge2168 edge2169 vertices
vertex2041 vertex2043
face link face377 face387 edges edge2423 edge2424 vertices
vertex2221 vertex2223
face link face376 face386 edges edge2304 edge2306 vertices
vertex2101 vertex2103
face link face387 face397 edges edge2424 edge2425 vertices
vertex2223 vertex2225
face link face386 face396 edges edge2306 edge2308 vertices
82
vertex2103 vertex2105
face link face382 face392 edges edge2169 edge2170 vertices
vertex2043 vertex2045
face link face382 face392 edges edge2169 edge2170 vertices
vertex2043 vertex2045
face link face382 face392 edges edge2169 edge2170 vertices
vertex2043 vertex2045
face link face382 face392 edges edge2169 edge2170 vertices
vertex2043 vertex2045
face link face397 face407 edges edge2425 edge2426 vertices
vertex2225 vertex2227
face link face392 face402 edges edge2170 edge2171 vertices
vertex2045 vertex2047
face link face396 face406 edges edge2290 edge2291 vertices
vertex2104 vertex2106
face link face407 face417 edges edge2426 edge2427 vertices
vertex2227 vertex2229
face link face417 face427 edges edge2427 edge2428 vertices
vertex2229 vertex2231
face link face427 face437 edges edge2428 edge2429 vertices
vertex2231 vertex2233
face link face437 face447 edges edge2429 edge2430 vertices
vertex2233 vertex2235
face link face447 face457 edges edge2430 edge2431 vertices
vertex2235 vertex2237
face link face457 face467 edges edge2431 edge2432 vertices
vertex2237 vertex2239
face link face467 face477 edges edge2432 edge2433 vertices
vertex2239 vertex2241
face link face477 face487 edges edge2433 edge2434 vertices
vertex2241 vertex2243
face link face487 face487 edges edge2434 edge2434 vertices
vertex2243 vertex2243
face link face487 face487 edges edge2434 edge2434 vertices
vertex2243 vertex2243
face link face487 face487 edges edge2434 edge2434 vertices
vertex2243 vertex2243
face link face487 face497 edges edge2434 edge2435 vertices
vertex2243 vertex2245
face link face497 face507 edges edge2435 edge2436 vertices
vertex2245 vertex2247
face link face507 face517 edges edge2436 edge2437 vertices
vertex2247 vertex2249
face link face406 face416 edges edge2291 edge2292 vertices
vertex2106 vertex2108
face link face416 face426 edges edge2292 edge2293 vertices
vertex2108 vertex2110
face link face426 face436 edges edge2293 edge2294 vertices
vertex2110 vertex2112
face link face436 face446 edges edge2294 edge2295 vertices
vertex2112 vertex2114
face link face446 face456 edges edge2295 edge2296 vertices
vertex2114 vertex2116
face link face456 face466 edges edge2296 edge2297 vertices
vertex2116 vertex2118
face link face466 face476 edges edge2297 edge2298 vertices
83
vertex2118 vertex2120
face link face486 face496 edges edge2299 edge2300 vertices
vertex2122 vertex2124
face link face476 face486 edges edge2298 edge2299 vertices
vertex2120 vertex2122
face link face496 face506 edges edge2300 edge2301 vertices
vertex2124 vertex2126
face link face506 face516 edges edge2301 edge2302 vertices
vertex2126 vertex2128
face link face392 face402 edges edge2142 edge2144 vertices
vertex2044 vertex2046
face link face402 face412 edges edge2171 edge2172 vertices
vertex2047 vertex2049
face link face412 face422 edges edge2172 edge2173 vertices
vertex2049 vertex2051
face link face422 face432 edges edge2173 edge2174 vertices
vertex2051 vertex2053
face link face432 face442 edges edge2174 edge2175 vertices
vertex2053 vertex2055
face link face442 face452 edges edge2175 edge2176 vertices
vertex2055 vertex2057
face link face452 face462 edges edge2176 edge2177 vertices
vertex2057 vertex2059
face link face462 face472 edges edge2177 edge2178 vertices
vertex2059 vertex2061
face link face472 face482 edges edge2178 edge2179 vertices
vertex2061 vertex2063
face link face482 face492 edges edge2179 edge2180 vertices
vertex2063 vertex2065
face link face492 face502 edges edge2180 edge2181 vertices
vertex2065 vertex2067
face link face502 face512 edges edge2181 edge2182 vertices
vertex2067 vertex2069
LINKING THE TELEPHONES OF THE BOTTOM OF THE PLENUM
face link face912 face922 edges edge6950 edge6976 vertices
vertex6437 vertex6461
face link face922 face932 edges edge6976 edge7002 vertices
vertex6461 vertex6485
face link face932 face942 edges edge7002 edge7028 vertices
vertex6485 vertex6509
face link face942 face952 edges edge7028 edge7054 vertices
vertex6509 vertex6533
face link face952 face962 edges edge7054 edge7080 vertices
vertex6533 vertex6557
face link face962 face972 edges edge7080 edge7106 vertices
vertex6557 vertex6581
face link face972 face982 edges edge7106 edge7132 vertices
vertex6581 vertex6605
face link face982 face992 edges edge7132 edge7158 vertices
vertex6605 vertex6629
face link face992 face1002 edges edge7158 edge7184 vertices
vertex6629 vertex6653
face link face1002 face1012 edges edge7184 edge7210 vertices
vertex6653 vertex6677
84
face link face1012 face1022 edges edge7210 edge7236 vertices
vertex6677 vertex6701
face link face1032 face1042 edges edge7262 edge7288 vertices
vertex6725 vertex6749
face link face1042 face1052 edges edge7288 edge7314 vertices
vertex6749 vertex6773
face link face117 face124 edges edge6960 edge6986 vertices
vertex6446 vertex6470
face link face124 face131 edges edge6986 edge7012 vertices
vertex6470 vertex6494
face link face131 face138 edges edge7012 edge7038 vertices
vertex6494 vertex6518
face link face138 face145 edges edge7038 edge7064 vertices
vertex6518 vertex6542
face link face145 face152 edges edge7064 edge7090 vertices
vertex6542 vertex6566
face link face152 face159 edges edge7090 edge7116 vertices
vertex6566 vertex6590
face link face159 face166 edges edge7116 edge7142 vertices
vertex6590 vertex6614
face link face166 face173 edges edge7142 edge7168 vertices
vertex6614 vertex6638
face link face173 face180 edges edge7168 edge7194 vertices
vertex6638 vertex6662
face link face180 face187 edges edge7194 edge7220 vertices
vertex6662 vertex6686
face link face187 face194 edges edge7220 edge7246 vertices
vertex6686 vertex6710
face link face194 face201 edges edge7246 edge7272 vertices
vertex6710 vertex6734
face link face1022 face1032 edges edge7236 edge7262 vertices
vertex6701 vertex6725
face link face1032 face1042 edges edge7262 edge7288 vertices
vertex6725 vertex6749
face link face201 face208 edges edge7271 edge7297 vertices
vertex6735 vertex6759
face link face208 face215 edges edge7297 edge7323 vertices
vertex6759 vertex6783
face link face1600 face1602 edges edge7890 edge7899 vertices
vertex7303 vertex7311
face link face1602 face1604 edges edge7899 edge7908 vertices
vertex7311 vertex7319
face link face1604 face1606 edges edge7908 edge7917 vertices
vertex7319 vertex7327
face link face1606 face1608 edges edge7917 edge7926 vertices
vertex7327 vertex7335
face link face1608 face1610 edges edge7926 edge7935 vertices
vertex7335 vertex7343
face link face1610 face1612 edges edge7935 edge7944 vertices
vertex7343 vertex7351
face link face1612 face1614 edges edge7944 edge7953 vertices
vertex7351 vertex7359
face link face1614 face1616 edges edge7953 edge7962 vertices
vertex7359 vertex7367
face link face1616 face1618 edges edge7962 edge7971 vertices
vertex7367 vertex7375
85
face link face1618 face1620 edges edge7971 edge7980 vertices
vertex7375 vertex7383
face link face1620 face1622 edges edge7980 edge7989 vertices
vertex7383 vertex7391
face link face1622 face1624 edges edge7989 edge7998 vertices
vertex7391 vertex7399
face link face1624 face1626 edges edge7998 edge8007 vertices
vertex7399 vertex7407
face link face1626 face1628 edges edge8007 edge8016 vertices
vertex7407 vertex7415
LINKING ALL THE TELEPHONES OF THE TOP OF THE CHANNEL
face link face912 face1510 edges edge6950 edge7339 vertices
vertex6437 vertex6797 reverse
face link face117 face1512 edges edge6959 edge7349 vertices
vertex6447 vertex6807
face link face1600 face1514 edges edge7890 edge7363 vertices
vertex7303 vertex6819
face link face1510 face1516 edges edge7339 edge7376 vertices
vertex6797 vertex6831
face link face1516 face1522 edges edge7376 edge7413 vertices
vertex6831 vertex6865
face link face1522 face1528 edges edge7413 edge7450 vertices
vertex6865 vertex6899
face link face1528 face1534 edges edge7450 edge7487 vertices
vertex6899 vertex6933
face link face1534 face1540 edges edge7487 edge7524 vertices
vertex6933 vertex6967
face link face1540 face1546 edges edge7524 edge7561 vertices
vertex6967 vertex7001
face link face1546 face1552 edges edge7561 edge7598 vertices
vertex7001 vertex7035
face link face1552 face1558 edges edge7598 edge7635 vertices
vertex7035 vertex7069
face link face1558 face1564 edges edge7635 edge7672 vertices
vertex7069 vertex7103
face link face1564 face1570 edges edge7672 edge7709 vertices
vertex7103 vertex7137
face link face1570 face1576 edges edge7709 edge7746 vertices
vertex7137 vertex7171
face link face1576 face1582 edges edge7746 edge7783 vertices
vertex7171 vertex7205
face link face1582 face1588 edges edge7783 edge7820 vertices
vertex7205 vertex7239
face link face1588 face1594 edges edge7820 edge7857 vertices
vertex7239 vertex7273
face link face1512 face1518 edges edge7350 edge7387 vertices
vertex6806 vertex6840
face link face1518 face1524 edges edge7387 edge7424 vertices
vertex6840 vertex6874
face link face1524 face1530 edges edge7424 edge7461 vertices
vertex6874 vertex6908
face link face1530 face1536 edges edge7461 edge7498 vertices
vertex6908 vertex6942
face link face1536 face1542 edges edge7498 edge7535 vertices
86
vertex6942 vertex6976
face link face1542 face1548 edges edge7535 edge7572 vertices
vertex6976 vertex7010
face link face1548 face1554 edges edge7572 edge7609 vertices
vertex7010 vertex7044
face link face1554 face1560 edges edge7609 edge7646 vertices
vertex7044 vertex7078
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vertex7078 vertex7112
face link face1566 face1572 edges edge7683 edge7720 vertices
vertex7112 vertex7146
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vertex7146 vertex7180
face link face1578 face1584 edges edge7757 edge7794 vertices
vertex7180 vertex7214
face link face1584 face1590 edges edge7794 edge7831 vertices
vertex7214 vertex7248
face link face1590 face1596 edges edge7831 edge7868 vertices
vertex7248 vertex7282
face link face1514 face1520 edges edge7363 edge7400 vertices
vertex6819 vertex6853
face link face1520 face1526 edges edge7400 edge7437 vertices
vertex6853 vertex6887
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vertex6887 vertex6921
face link face1532 face1538 edges edge7474 edge7511 vertices
vertex6921 vertex6955
face link face1538 face1544 edges edge7511 edge7548 vertices
vertex6955 vertex6989
face link face1544 face1550 edges edge7548 edge7585 vertices
vertex6989 vertex7023
face link face1550 face1556 edges edge7585 edge7622 vertices
vertex7023 vertex7057
face link face1556 face1562 edges edge7622 edge7659 vertices
vertex7057 vertex7091
face link face1562 face1568 edges edge7659 edge7696 vertices
vertex7091 vertex7125
face link face1568 face1574 edges edge7696 edge7733 vertices
vertex7125 vertex7159
face link face1574 face1580 edges edge7733 edge7770 vertices
vertex7159 vertex7193
face link face1580 face1586 edges edge7770 edge7807 vertices
vertex7193 vertex7227
face link face1586 face1592 edges edge7807 edge7844 vertices
vertex7227 vertex7261
face link face1592 face1598 edges edge7844 edge7881 vertices
vertex7261 vertex7295
LINKING ALL THE TELEPHONES OF THE TOP OF THE PLENUM
face link face912 face642 edges edge6950 edge3489 vertices
vertex6437 vertex3253 reverse
face link face642 face647 edges edge3489 edge3744 vertices
vertex3253 vertex3433
face link face117 face646 edges edge6959 edge3638 vertices
vertex6447 vertex3313
87
face link face642 face652 edges edge3489 edge3491 vertices
vertex3253 vertex3255
face link face652 face662 edges edge3491 edge3493 vertices
vertex3255 vertex3257
face link face662 face672 edges edge3493 edge3495 vertices
vertex3257 vertex3259
face link face672 face682 edges edge3495 edge3497 vertices
vertex3259 vertex3261
face link face682 face692 edges edge3497 edge3499 vertices
vertex3261 vertex3263
face link face692 face702 edges edge3499 edge3501 vertices
vertex3263 vertex3265
face link face702 face712 edges edge3501 edge3503 vertices
vertex3265 vertex3267
face link face712 face722 edges edge3503 edge3505 vertices
vertex3267 vertex3269
face link face722 face732 edges edge3505 edge3507 vertices
vertex3269 vertex3271
face link face732 face742 edges edge3507 edge3509 vertices
vertex3271 vertex3273
face link face742 face752 edges edge3509 edge3511 vertices
vertex3273 vertex3275
face link face752 face762 edges edge3511 edge3513 vertices
vertex3275 vertex3277
face link face762 face772 edges edge3513 edge3515 vertices
vertex3277 vertex3279
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vertex3279 vertex3281
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vertex3312 vertex3314
face link face656 face666 edges edge3655 edge3657 vertices
vertex3314 vertex3316
face link face666 face676 edges edge3657 edge3659 vertices
vertex3316 vertex3318
face link face676 face686 edges edge3659 edge3661 vertices
vertex3318 vertex3320
face link face686 face696 edges edge3661 edge3663 vertices
vertex3320 vertex3322
face link face696 face706 edges edge3663 edge3665 vertices
vertex3322 vertex3324
face link face706 face716 edges edge3665 edge3667 vertices
vertex3324 vertex3326
face link face716 face726 edges edge3667 edge3669 vertices
vertex3326 vertex3328
face link face726 face736 edges edge3669 edge3671 vertices
vertex3328 vertex3330
face link face736 face746 edges edge3671 edge3673 vertices
vertex3330 vertex3332
face link face746 face756 edges edge3673 edge3675 vertices
vertex3332 vertex3334
face link face756 face766 edges edge3675 edge3677 vertices
vertex3334 vertex3336
face link face766 face776 edges edge3677 edge3679 vertices
vertex3336 vertex3338
face link face776 face786 edges edge3679 edge3681 vertices
88
vertex3338 vertex3340
face link face647 face657 edges edge3744 edge3746 vertices
vertex3433 vertex3435
face link face657 face667 edges edge3746 edge3748 vertices
vertex3435 vertex3437
face link face667 face677 edges edge3748 edge3750 vertices
vertex3437 vertex3439
face link face677 face687 edges edge3750 edge3752 vertices
vertex3439 vertex3441
face link face687 face697 edges edge3752 edge3754 vertices
vertex3441 vertex3443
face link face697 face707 edges edge3754 edge3756 vertices
vertex3443 vertex3445
face link face707 face717 edges edge3756 edge3758 vertices
vertex3445 vertex3447
face link face717 face727 edges edge3758 edge3760 vertices
vertex3447 vertex3449
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vertex3449 vertex3451
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vertex3451 vertex3453
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vertex3453 vertex3455
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vertex3455 vertex3457
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vertex3457 vertex3459
face link face777 face787 edges edge3770 edge3772 vertices
vertex3459 vertex3461
face link face647 face1600 edges edge3685 edge6963 vertices
vertex3345 vertex6449
LINKING OUTBOXES ON THE PLENUM
face modify face911 side vertex4404 vertex4405
face modify face918 side vertex4405 vertex4404
face link face911 face915 edges edge4778 edge4898 vertices
vertex4374 vertex4434
face link face915 face645 edges edge4899 edge3833 vertices
vertex4480 vertex3463 reverse
face link face911 face641 edges edge4779 edge3578 vertices
vertex4405 vertex3283 reverse
face link face918 face648 edges edge4825 edge3686 vertices
vertex4436 vertex3347 reverse
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vertex3463 vertex3465
face link face655 face665 edges edge3834 edge3835 vertices
vertex3465 vertex3467
face link face665 face675 edges edge3835 edge3836 vertices
vertex3467 vertex3469
face link face675 face685 edges edge3836 edge3837 vertices
vertex3469 vertex3471
face link face685 face695 edges edge3837 edge3838 vertices
89
vertex3471 vertex3473
face link face695 face705 edges edge3838 edge3839 vertices
vertex3473 vertex3475
face link face705 face715 edges edge3839 edge3840 vertices
vertex3475 vertex3477
face link face715 face725 edges edge3840 edge3841 vertices
vertex3477 vertex3479
face link face725 face735 edges edge3841 edge3842 vertices
vertex3479 vertex3481
face link face735 face745 edges edge3842 edge3843 vertices
vertex3481 vertex3483
face link face745 face755 edges edge3843 edge3844 vertices
vertex3483 vertex3485
face link face755 face765 edges edge3844 edge3845 vertices
vertex3485 vertex3487
face link face765 face775 edges edge3845 edge3846 vertices
vertex3487 vertex3489
face link face775 face785 edges edge3846 edge3847 vertices
vertex3489 vertex3491
face link face648 face658 edges edge3686 edge3690 vertices
vertex3347 vertex3353
face link face658 face668 edges edge3690 edge3694 vertices
vertex3353 vertex3359
face link face668 face678 edges edge3694 edge3698 vertices
vertex3359 vertex3365
face link face678 face688 edges edge3698 edge3702 vertices
vertex3365 vertex3371
face link face688 face698 edges edge3702 edge3706 vertices
vertex3371 vertex3377
face link face698 face708 edges edge3706 edge3710 vertices
vertex3377 vertex3383
face link face708 face718 edges edge3710 edge3714 vertices
vertex3383 vertex3389
face link face718 face728 edges edge3714 edge3718 vertices
vertex3389 vertex3395
face link face728 face738 edges edge3718 edge3722 vertices
vertex3395 vertex3401
face link face738 face748 edges edge3722 edge3726 vertices
vertex3401 vertex3407
face link face748 face758 edges edge3726 edge3730 vertices
vertex3407 vertex3413
face link face758 face768 edges edge3730 edge3734 vertices
vertex3413 vertex3419
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vertex3419 vertex3425
face link face778 face788 edges edge3738 edge3742 vertices
vertex3425 vertex3431
face link face641 face650 edges edge3578 edge3579 vertices
vertex3283 vertex3285
face link face650 face660 edges edge3579 edge3580 vertices
vertex3285 vertex3287
face link face660 face670 edges edge3580 edge3581 vertices
vertex3287 vertex3289
face link face670 face680 edges edge3581 edge3582 vertices
vertex3289 vertex3291
face link face680 face690 edges edge3582 edge3583 vertices
90
vertex3291 vertex3293
face link face690 face700 edges edge3583 edge3584 vertices
vertex3293 vertex3295
face link face700 face710 edges edge3584 edge3585 vertices
vertex3295 vertex3297
face link face710 face720 edges edge3585 edge3586 vertices
vertex3297 vertex3299
face link face720 face730 edges edge3586 edge3587 vertices
vertex3299 vertex3301
face link face730 face740 edges edge3587 edge3588 vertices
vertex3301 vertex3303
face link face740 face750 edges edge3588 edge3589 vertices
vertex3303 vertex3305
face link face750 face760 edges edge3589 edge3590 vertices
vertex3305 vertex3307
face link face760 face770 edges edge3590 edge3591 vertices
vertex3307 vertex3309
face link face770 face780 edges edge3591 edge3592 vertices
vertex3309 vertex3311
face link face915 face925 edges edge4899 edge4901 vertices
vertex4480 vertex4482
face link face925 face935 edges edge4901 edge4903 vertices
vertex4482 vertex4484
face link face935 face945 edges edge4903 edge4905 vertices
vertex4484 vertex4486
face link face945 face955 edges edge4905 edge4907 vertices
vertex4486 vertex4488
face link face955 face965 edges edge4907 edge4909 vertices
vertex4488 vertex4490
face link face965 face975 edges edge4909 edge4911 vertices
vertex4490 vertex4492
face link face975 face985 edges edge4911 edge4913 vertices
vertex4492 vertex4494
face link face985 face995 edges edge4913 edge4915 vertices
vertex4494 vertex4496
face link face995 face1005 edges edge4915 edge4917 vertices
vertex4496 vertex4498
face link face1005 face1015 edges edge4917 edge4919 vertices
vertex4498 vertex4500
face link face1015 face1025 edges edge4919 edge4921 vertices
vertex4500 vertex4502
face link face1025 face1035 edges edge4921 edge4923 vertices
vertex4502 vertex4504
face link face1035 face1045 edges edge4923 edge4925 vertices
vertex4504 vertex4506
face link face1045 face1055 edges edge4925 edge4927 vertices
vertex4506 vertex4508
face link face918 face928 edges edge4825 edge4828 vertices
vertex4436 vertex4439
face link face928 face938 edges edge4828 edge4831 vertices
vertex4439 vertex4442
face link face938 face948 edges edge4831 edge4834 vertices
vertex4442 vertex4445
face link face948 face958 edges edge4834 edge4837 vertices
vertex4445 vertex4448
face link face958 face968 edges edge4837 edge4840 vertices
91
vertex4448 vertex4451
face link face968 face978 edges edge4840 edge4843 vertices
vertex4451 vertex4454
face link face978 face988 edges edge4843 edge4846 vertices
vertex4454 vertex4457
face link face988 face998 edges edge4846 edge4849 vertices
vertex4457 vertex4460
face link face998 face1008 edges edge4849 edge4852 vertices
vertex4460 vertex4463
face link face1008 face1018 edges edge4852 edge4855 vertices
vertex4463 vertex4466
face link face1018 face1028 edges edge4855 edge4858 vertices
vertex4466 vertex4469
face link face1028 face1038 edges edge4858 edge4861 vertices
vertex4469 vertex4472
face link face1038 face1048 edges edge4861 edge4864 vertices
vertex4472 vertex4475
face link face1048 face1058 edges edge4864 edge4867 vertices
vertex4475 vertex4478
face link face911 face920 edges edge108 edge118 vertices
vertex88 vertex94
face link face920 face930 edges edge118 edge128 vertices
vertex94 vertex100
face link face930 face940 edges edge4783 edge4785 vertices
vertex4409 vertex4411
face link face940 face950 edges edge4785 edge4787 vertices
vertex4411 vertex4413
face link face950 face960 edges edge4787 edge4789 vertices
vertex4413 vertex4415
face link face960 face970 edges edge4789 edge4791 vertices
vertex4415 vertex4417
face link face970 face980 edges edge4791 edge4793 vertices
vertex4417 vertex4419
face link face980 face990 edges edge4793 edge4795 vertices
vertex4419 vertex4421
face link face990 face1000 edges edge4795 edge4797 vertices
vertex4421 vertex4423
face link face1000 face1010 edges edge4797 edge4799 vertices
vertex4423 vertex4425
face link face1010 face1020 edges edge4799 edge4801 vertices
vertex4425 vertex4427
face link face1020 face1030 edges edge4801 edge4803 vertices
vertex4427 vertex4429
face link face1030 face1040 edges edge4803 edge4805 vertices
vertex4429 vertex4431
face link face1040 face1050 edges edge4805 edge4807 vertices
vertex4431 vertex4433
LINKING THE TOP OF THE CHANEL OUTBOXES
face modify face1256 side vertex6322 vertex6321
face modify face1263 side vertex6322 vertex6321
face modify face1260 side vertex6397 vertex6396
92
face link face1256 face1260 edges edge6803 edge6923 vertices
vertex6322 vertex6397
face link face1256 face371 edges edge6774 edge2053 vertices
vertex6292 vertex1955 reverse
face link face371 face375 edges edge2053 edge2336 vertices
vertex1955 vertex2135
face link face1263 face378 edges edge6820 edge2228 vertices
vertex6322 vertex2071 reverse
face link face1263 face1273 edges edge6820 edge6823 vertices
vertex6322 vertex6324
face link face1273 face1283 edges edge6823 edge6826 vertices
vertex6324 vertex6326
face link face1283 face1293 edges edge6826 edge6829 vertices
vertex6326 vertex6328
face link face1293 face1303 edges edge6829 edge6832 vertices
vertex6328 vertex6330
face link face1303 face1313 edges edge6832 edge6835 vertices
vertex6330 vertex6332
face link face1313 face1323 edges edge6835 edge6838 vertices
vertex6332 vertex6334
face link face1323 face1333 edges edge6838 edge6841 vertices
vertex6334 vertex6336
face link face1333 face1343 edges edge6841 edge6844 vertices
vertex6336 vertex6338
face link face1343 face1353 edges edge6844 edge6847 vertices
vertex6338 vertex6340
face link face1353 face1363 edges edge6847 edge6850 vertices
vertex6340 vertex6342
face link face1363 face1373 edges edge6850 edge6853 vertices
vertex6342 vertex6344
face link face1373 face1383 edges edge6853 edge6856 vertices
vertex6344 vertex6346
face link face1383 face1393 edges edge6856 edge6859 vertices
vertex6346 vertex6348
face link face1393 face1403 edges edge6859 edge6862 vertices
vertex6348 vertex6350
face link face1256 face1265 edges edge6774 edge6776 vertices
vertex6292 vertex6294
face link face1265 face1275 edges edge6776 edge6778 vertices
vertex6294 vertex6296
face link face1275 face1285 edges edge6778 edge6780 vertices
vertex6296 vertex6298
face link face1285 face1295 edges edge6780 edge6782 vertices
vertex6298 vertex6300
face link face1295 face1305 edges edge6782 edge6784 vertices
vertex6300 vertex6302
face link face1305 face1315 edges edge6784 edge6786 vertices
vertex6302 vertex6304
face link face1315 face1325 edges edge6786 edge6788 vertices
vertex6304 vertex6306
face link face1325 face1335 edges edge6788 edge6790 vertices
vertex6306 vertex6308
face link face1335 face1345 edges edge6790 edge6792 vertices
vertex6308 vertex6310
face link face1345 face1355 edges edge6792 edge6794 vertices
vertex6310 vertex6312
93
face link face1355 face1365 edges edge6794 edge6796 vertices
vertex6312 vertex6314
face link face1365 face1375 edges edge6796 edge6798 vertices
vertex6314 vertex6316
face link face1375 face1385 edges edge6798 edge6800 vertices
vertex6316 vertex6318
face link face1385 face1395 edges edge6800 edge6802 vertices
vertex6318 vertex6320
face link face1260 face1270 edges edge6894 edge6896 vertices
vertex6353 vertex6356
face link face1270 face1280 edges edge6896 edge6898 vertices
vertex6356 vertex6359
face link face1280 face1290 edges edge6898 edge6900 vertices
vertex6359 vertex6362
face link face1290 face1300 edges edge6900 edge6902 vertices
vertex6362 vertex6365
face link face1300 face1310 edges edge6902 edge6904 vertices
vertex6365 vertex6368
face link face1310 face1320 edges edge6904 edge6906 vertices
vertex6368 vertex6371
face link face1320 face1330 edges edge6906 edge6908 vertices
vertex6371 vertex6374
face link face1330 face1340 edges edge6908 edge6910 vertices
vertex6374 vertex6377
face link face1340 face1350 edges edge6910 edge6912 vertices
vertex6377 vertex6380
face link face1350 face1360 edges edge6912 edge6914 vertices
vertex6380 vertex6383
face link face1360 face1370 edges edge6914 edge6916 vertices
vertex6383 vertex6386
face link face1370 face1380 edges edge6916 edge6918 vertices
vertex6386 vertex6389
face link face1380 face1390 edges edge6918 edge6920 vertices
vertex6389 vertex6392
face link face1390 face1400 edges edge6920 edge6922 vertices
vertex6392 vertex6395
LINKING THE BOTTOM OF THE CHANEL OUTBOXES
face link face375 face385 edges edge2440 edge2443 vertices
vertex2251 vertex2253
face link face385 face395 edges edge2443 edge2446 vertices
vertex2253 vertex2255
face link face395 face405 edges edge2446 edge2449 vertices
vertex2255 vertex2257
face link face405 face415 edges edge2449 edge2452 vertices
vertex2257 vertex2259
face link face415 face425 edges edge2452 edge2455 vertices
vertex2259 vertex2261
face link face425 face435 edges edge2455 edge2458 vertices
vertex2261 vertex2263
face link face435 face445 edges edge2458 edge2461 vertices
vertex2263 vertex2265
face link face445 face455 edges edge2461 edge2464 vertices
vertex2265 vertex2267
face link face455 face465 edges edge2464 edge2467 vertices
94
vertex2267 vertex2269
face link face465 face475 edges edge2467 edge2470 vertices
vertex2269 vertex2271
face link face475 face485 edges edge2470 edge2473 vertices
vertex2271 vertex2273
face link face485 face495 edges edge2473 edge2476 vertices
vertex2273 vertex2275
face link face495 face505 edges edge2476 edge2479 vertices
vertex2275 vertex2277
face link face505 face515 edges edge2479 edge2482 vertices
vertex2277 vertex2279
face link face378 face388 edges edge2245 edge2248 vertices
vertex2135 vertex2141
face link face388 face398 edges edge2248 edge2251 vertices
vertex2141 vertex2147
face link face398 face408 edges edge2251 edge2254 vertices
vertex2147 vertex2153
face link face408 face418 edges edge2254 edge2257 vertices
vertex2153 vertex2159
face link face418 face428 edges edge2257 edge2260 vertices
vertex2159 vertex2165
face link face428 face438 edges edge2260 edge2263 vertices
vertex2165 vertex2171
face link face438 face448 edges edge2263 edge2266 vertices
vertex2171 vertex2177
face link face448 face458 edges edge2266 edge2269 vertices
vertex2177 vertex2183
face link face458 face468 edges edge2269 edge2272 vertices
vertex2183 vertex2189
face link face468 face478 edges edge2272 edge2275 vertices
vertex2189 vertex2195
face link face478 face488 edges edge2275 edge2278 vertices
vertex2195 vertex2201
face link face488 face498 edges edge2278 edge2281 vertices
vertex2201 vertex2207
face link face498 face508 edges edge2281 edge2284 vertices
vertex2207 vertex2213
face link face508 face518 edges edge2284 edge2287 vertices
vertex2213 vertex2219
face link face371 face380 edges edge2185 edge2188 vertices
vertex2071 vertex2073
face link face380 face390 edges edge2188 edge2191 vertices
vertex2073 vertex2075
face link face390 face400 edges edge2191 edge2194 vertices
vertex2075 vertex2077
face link face400 face410 edges edge2194 edge2197 vertices
vertex2077 vertex2079
face link face410 face420 edges edge2197 edge2200 vertices
vertex2079 vertex2081
face link face420 face430 edges edge2200 edge2203 vertices
vertex2081 vertex2083
face link face430 face440 edges edge2203 edge2206 vertices
vertex2083 vertex2085
face link face440 face450 edges edge2206 edge2209 vertices
vertex2085 vertex2087
face link face450 face460 edges edge2209 edge2212 vertices
95
vertex2087 vertex2089
face link face460 face470 edges edge2212 edge2215 vertices
vertex2089 vertex2091
face link face470 face480 edges edge2215 edge2218 vertices
vertex2091 vertex2093
face link face480 face490 edges edge2218 edge2221 vertices
vertex2093 vertex2095
face link face490 face500 edges edge2221 edge2224 vertices
vertex2095 vertex2097
face link face500 face510 edges edge2224 edge2227 vertices
vertex2097 vertex2099
TOP SIDE BOX beginning of channel
face link face1649 face1633 edges edge97 edge3533 vertices
vertex4374 vertex3162 reverse
TOP SIDE BOXES
face link face1650 face1651 edges edge4749 edge4751 vertices
vertex4376 vertex4378
face link face1652 face1653 edges edge4753 edge4755 vertices
vertex4380 vertex4382
face link face1653 face1654 edges edge4755 edge4757 vertices
vertex4382 vertex4384
face link face1654 face1655 edges edge4757 edge4759 vertices
vertex4384 vertex4386
face link face1655 face1656 edges edge4759 edge4761 vertices
vertex4386 vertex4388
face link face1656 face114 edges edge4761 edge4763 vertices
vertex4388 vertex4390
face link face114 face1657 edges edge4763 edge4765 vertices
vertex4390 vertex4392
face link face1657 face1658 edges edge4765 edge4767 vertices
vertex4392 vertex4394
face link face1658 face1659 edges edge4767 edge4769 vertices
vertex4394 vertex4396
face link face1659 face1660 edges edge4769 edge4771 vertices
vertex4396 vertex4398
face link face1660 face1661 edges edge4771 edge4773 vertices
vertex4398 vertex4400
face link face1661 face1662 edges edge4773 edge4775 vertices
vertex4400 vertex4402
face link face1650 face1634 edges edge4900 edge8036 vertices
vertex4481 vertex3464 reverse
face link face1634 face1635 edges edge8036 edge8037 vertices
vertex3464 vertex3466
face link face1635 face1636 edges edge8037 edge8038 vertices
vertex3466 vertex3468
face link face1636 face1637 edges edge8038 edge8039 vertices
vertex3468 vertex3470
face link face1637 face1638 edges edge8039 edge8040 vertices
vertex3470 vertex3472
face link face1638 face1639 edges edge8040 edge8041 vertices
vertex3472 vertex3474
face link face1639 face6 edges edge8041 edge8042 vertices
96
vertex3474 vertex3476
face link face6 face1640 edges edge8042 edge8043 vertices
vertex3476 vertex3478
face link face1640 face1641 edges edge8043 edge8044 vertices
vertex3478 vertex3480
face link face1641 face1642 edges edge8044 edge8045 vertices
vertex3480 vertex3482
face link face1642 face1643 edges edge8045 edge8046 vertices
vertex3482 vertex3484
face link face1643 face1644 edges edge8046 edge8047 vertices
vertex3484 vertex3486
face link face1644 face1645 edges edge8047 edge8048 vertices
vertex3486 vertex3488
face link face1645 face1646 edges edge8048 edge8049 vertices
vertex3488 vertex3490
face link face1651 face1652 edges edge4751 edge4753 vertices
vertex4378 vertex4380
TOP SIDE BOX END OF CHANNEL
face link face1647 face1663 edges edge8050 edge99 vertices
vertex7433 vertex7435 reverse
TOP SIDE BOX BACK OF CHANNEL
face link face1648 face1664 edges edge12 edge8069 vertices
vertex8 vertex84 reverse
BOTTOM SIDE BOX
face link face1665 face1681 edges edge6773 edge2048 vertices
vertex6291 vertex1950 reverse
face link face1680 face1696 edges edge8071 edge8105 vertices
vertex7436 vertex7438 reverse
face link face1666 face1667 edges edge6894 edge6896 vertices
vertex6397 vertex6399
face link face1667 face1668 edges edge6896 edge6898 vertices
vertex6399 vertex6401
face link face1668 face1669 edges edge6898 edge6900 vertices
vertex6401 vertex6403
face link face1669 face1670 edges edge6900 edge6902 vertices
vertex6403 vertex6405
face link face1670 face1671 edges edge6902 edge6904 vertices
vertex6405 vertex6407
face link face1671 face209 edges edge6904 edge6906 vertices
vertex6407 vertex6409
face link face209 face1672 edges edge6906 edge6908 vertices
vertex6409 vertex6411
face link face1672 face1673 edges edge6908 edge6910 vertices
vertex6411 vertex6413
face link face1673 face1674 edges edge6910 edge6912 vertices
vertex6413 vertex6415
face link face1674 face1675 edges edge6912 edge6914 vertices
vertex6415 vertex6417
face link face1675 face1676 edges edge6914 edge6916 vertices
vertex6417 vertex6419
97
face link face1676 face1677 edges edge6916 edge6918 vertices
vertex6419 vertex6421
face link face1677 face1678 edges edge6918 edge6920 vertices
vertex6421 vertex6423
face link face1666 face1682 edges edge6894 edge8090 vertices
vertex6397 vertex2251 reverse
face link face1682 face1683 edges edge8090 edge8091 vertices
vertex2251 vertex2253
face link face1683 face1684 edges edge8091 edge8092 vertices
vertex2253 vertex2255
face link face1684 face1685 edges edge8092 edge8093 vertices
vertex2255 vertex2257
face link face1685 face1686 edges edge8093 edge8094 vertices
vertex2257 vertex2259
face link face1686 face1687 edges edge8094 edge8095 vertices
vertex2259 vertex2261
face link face1687 face1688 edges edge8095 edge8096 vertices
vertex2261 vertex2263
face link face1688 face1 edges edge8096 edge8097 vertices
vertex2263 vertex2265
face link face1 face1689 edges edge8097 edge8098 vertices
vertex2265 vertex2267
face link face1689 face1690 edges edge8098 edge8099 vertices
vertex2267 vertex2269
face link face1690 face1691 edges edge8099 edge8100 vertices
vertex2269 vertex2271
face link face1691 face1692 edges edge8100 edge8101 vertices
vertex2271 vertex2273
face link face1692 face1693 edges edge8101 edge8102 vertices
vertex2273 vertex2275
face link face1693 face1694 edges edge8102 edge8103 vertices
vertex2275 vertex2277
face link face1679 face1695 edges edge89 edge2227 vertices
vertex6320 vertex2039 reverse
MESHING BEGINS HERE
BOUNDARY LAYERS BEGINS HERE
BOUNDARY LAYER FOR THE bottom of plenum
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer1 face face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
98
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 edge edge97
edge4748 edge106 edge6946 edge6947 edge107 edge4749
edge4750 edge116 edge6972 edge6973 edge117 edge4751
edge4752 edge126 edge6998 edge6999 edge127 edge4753
edge4754 edge136 edge7024 edge7025 edge137 edge4755
edge4756 edge146 edge7050 edge7051 edge147 edge4757
edge4758 edge156 edge7076 edge7077 edge157 edge4759
edge4760 edge166 edge7102 edge7103 edge167 edge4761
edge4762 edge176 edge7128 edge7129 edge177 edge4763
edge4764 edge186 edge7154 edge7155 edge187 edge4765
edge4766 edge196 edge7180 edge7181 edge197 edge4767
edge4768 edge206 edge7206 edge7207 edge207 edge4769
edge4770 edge216 edge7232 edge7233 edge217 edge4771
edge4772 edge226 edge7258 edge7259 edge227 edge4773
edge4774 edge236 edge7284 edge7285 edge237 edge4775
edge4776 edge246 edge7310 edge7311 edge247 edge4777 add
MESHING THE PLENUM
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer2 face face4 face4 face5 face110
face110 edge edge99 edge8069 edge100 edge8052 edge98 add
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer4 face face1649 face1664 face1664
face1664 face1663 edge edge8052 edge98 edge100 edge8069
edge99 add
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer4 face face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face2 face2 face2 face2 face2 face2 face2
face2 face4 face2 face2 face2 face2 face2 face4
face5 face110 face110 edge edge9 edge3398 edge3399
edge3400 edge3401 edge3402 edge3403 edge3404 edge3406
edge3405 edge3407 edge3408 edge3409 edge3415 edge3410
edge3411 edge3412 edge3413 edge3414 edge3416 edge3417
edge3418 edge3419 edge3420 edge3421 edge3422 edge3423
edge3424 edge3425 edge3426 edge3427 edge3428 edge3429
edge3430 edge3431 edge3432 edge3433 edge3434 edge3435
edge3436 edge3437 edge3438 edge3439 edge3440 edge3441
edge3442 edge3443 edge3444 edge3445 edge3446 edge3447
99
edge3448 edge3449 edge3450 edge3451 edge3457 edge3452
edge3453 edge3454 edge3455 edge3456 edge3458 edge3459
edge3460 edge3461 edge3462 edge3463 edge3464 edge3465
edge3466 edge3467 edge3468 edge3469 edge3475 edge3481
edge3470 edge3471 edge3472 edge3473 edge3474 edge3476
edge3477 edge3478 edge3479 edge3480 edge3487 edge11
edge3482 edge3483 edge3484 edge3485 edge3486 edge8051
edge12 edge10 edge8034 add
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer5 face face1663 face1664 face1664
face1664 face1649 edge edge99 edge8069 edge100 edge98
edge8052 add
BOUNDARY LAYER OF THE HOLES
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer1 face face642 edge edge3534 add
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer7 face face117 face1600 edge edge4824
edge110 add
BONDARY LAYER OF THE CHANNEL
TARGET WALL BOUNDARY LAYER
BBBL
BBL
BBL
BBBL
BBL
BBL
BBBLLLLL
blayer create first $firstch growth $growthch rows $rowsch transition 1 trows 0
uniform
blayer attach b_layer8 face face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
100
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face105 face105 face106
face104 face104 edge edge2048 edge2049 edge2050 edge2051
edge2052 edge2053 edge2054 edge2055 edge2056 edge2057
edge2058 edge2059 edge2060 edge2061 edge2062 edge2063
edge2064 edge2065 edge2066 edge2072 edge2067 edge2068
edge2069 edge2070 edge2071 edge2084 edge2078 edge2073
edge2074 edge2075 edge2076 edge2077 edge2079 edge2080
edge2081 edge2082 edge2083 edge2090 edge2096 edge2085
edge2086 edge2087 edge2088 edge2089 edge2091 edge2092
edge2093 edge2094 edge2095 edge2102 edge2108 edge2097
edge2098 edge2099 edge2100 edge2101 edge2103 edge2104
edge2105 edge2106 edge2107 edge2114 edge2120 edge2109
edge2110 edge2111 edge2112 edge2113 edge2115 edge2116
edge2117 edge2118 edge2119 edge2126 edge2132 edge2121
edge2122 edge2123 edge2124 edge2125 edge2127 edge2128
edge2129 edge2130 edge2131 edge2133 edge2134 edge2136
edge2137 edge1 edge2135 edge8088 edge3 edge4 edge8105
edge2 add
blayer create first $firstch growth $growthch rows $rowsch transition 1 trows 0
uniform
blayer attach b_layer9 face face1681 face1696 face1696
face1696 face1695 edge edge2 edge8105 edge4 edge3
edge8088 add
blayer create first $firstch growth $growthch rows $rowsch transition 1 trows 0
uniform
blayer attach b_layer10 face face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face103 face103
face103 face103 face103 face103 face105 face105
face106 face104 face104 edge edge6743 edge101
edge7336 edge7337 edge102 edge6744 edge6745 edge111
edge7373 edge7374 edge112 edge6746 edge6747 edge121
edge7410 edge7411 edge122 edge6748 edge6749 edge131
edge7447 edge7448 edge132 edge6750 edge6751 edge141
edge7484 edge7485 edge142 edge6752 edge6755 edge6753
edge151 edge6754 edge7521 edge7522 edge152 edge161
101
edge6756 edge6757 edge7558 edge7559 edge162 edge171
edge7595 edge7596 edge172 edge6758 edge6759 edge181
edge7632 edge7633 edge182 edge6760 edge6761 edge191
edge7669 edge7670 edge192 edge6762 edge6763 edge6767
edge6765 edge201 edge7706 edge7707 edge202 edge6764
edge211 edge6766 edge7743 edge7744 edge212 edge6769
edge221 edge6768 edge7780 edge7781 edge222 edge6771
edge231 edge6770 edge7817 edge7818 edge232 edge241
edge7854 edge7855 edge242 edge6772 edge89 edge8070
edge91 edge92 edge8087 edge90 add
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer11 face face4 face5 face2 face5
face110 face2 edge edge8 edge8 edge6 edge7 edge7
edge5 add
blayer create first $firstch growth $growthch rows $rowsch transition 1 trows 0
uniform
blayer attach b_layer12 face face106 face104 face103 face105
edge edge87 edge87 edge85 edge88 add
BOUNDARY LAYERS ENDS HERE
edge picklink edge6948 edge6949
edge mesh edge6949 edge6948 successive ratio1 1 intervals $NumbNodes
edge picklink edge6950
edge mesh edge6950 successive ratio1 1 intervals ($NumbNodes2)
face mesh face1450 map
edge picklink edge6963 edge6947
edge mesh edge6947 edge6963 successive ratio1 1 intervals ($Numbtelnodes+$rows)
face mesh face912 map
edge picklink edge6961 edge6960 edge7889 edge7890
edge mesh edge7890 edge7889 edge6960 edge6961 successive ratio1 1
intervals ($NumbNodes)
edge picklink edge6959 edge7891
edge mesh edge7891 edge6959 successive ratio1 1 intervals ($NumbNodes2)
face mesh face1452 map
face mesh face1600 face117 map
blayer create first $first growth $growth rows $rows transition 1 trows 0
uniform
blayer attach b_layer12 face face2 face110 face5 face110
face2 face4 face5 face4 edge edge5 edge5 edge7
edge7 edge6 edge6 edge8 edge8 add
Meshing constants
$NumbNodes=5
$Numbtelnodes=6
$PLobnodes=5
$Chobnodes=5
$Plbenodes=($NumbNodes(4)+$rows)
$plsqnodes=($NumbNodes(3))
102
$Pllsnodes=($NumbNodes+$rows)
$Nojetcells=10
edge picklink edge3686 edge3402
edge mesh edge3686 edge3402 successive ratio1 1 intervals ($PLobnodes)
edge picklink edge6744 edge6864
edge mesh edge6864 edge6744 successive ratio1 1 intervals 5
face link face1260 face375 edges edge6923 edge2440 vertices
vertex6397 vertex2251 reverse
face modify face915 side vertex4479 vertex4480
face mesh face915 face918 face911 map size 1
face mesh face1260 face1263 face1256 map size 1
edge picklink edge8068 edge8053
edge mesh edge8068 edge8053 successive ratio1 1 intervals ($Plbenodes)
edge picklink edge8086 edge8071
edge mesh edge8071 edge8086 successive ratio1 1 intervals ($CHbenodes)
edge delete edge8053 edge8068 keepsettings onlymesh
edge mesh edge8053 edge8068 successive ratio1 1 intervals ($Plbenodes)
edge delete edge8090 keepsettings onlymesh
edge picklink edge8090
edge mesh edge8090 successive ratio1 1 intervals ($plsqnodes)
edge delete edge8054 keepsettings onlymesh
edge picklink edge8054
edge mesh edge8054 successive ratio1 1 intervals ($plsqnodes)
face mesh face1647 face1679 face1678 face1646 face1633
face1665 map
edge delete edge98 edge8087 keepsettings onlymesh
edge picklink edge8087 edge98
edge mesh edge98 successive ratio1 1 intervals ($Pllsnodes)
edge mesh edge8087 successive ratio1 1 intervals ($CHlsnodes)
face mesh face1648 face1680 map
COOPERING ALL THE JETS
volume mesh volume3 cooper source face1600 face1452 face117
face1514 face1512 face115 intervals ($Nojetcells)
volume mesh volume5 cooper source face1456 face1602 face124
face1518 face1520 face122 intervals ($Nojetcells)
volume mesh volume7 cooper source face1460 face1604 face131
face1526 face1524 face129 intervals ($Nojetcells)
volume mesh volume9 cooper source face1464 face1606 face138
face1532 face1530 face136 intervals ($Nojetcells)
volume mesh volume11 cooper source face1468 face1608 face145
face1538 face143 face1536 intervals ($Nojetcells)
volume mesh volume13 cooper source face1472 face1610 face152
face1544 face1542 face150 intervals ($Nojetcells)
volume mesh volume15 cooper source face1476 face1612 face159
face1550 face1548 face157 intervals ($Nojetcells)
volume mesh volume17 cooper source face1480 face1614 face166
face1556 face1554 face164 intervals ($Nojetcells)
volume mesh volume19 cooper source face1484 face1616 face173
face1562 face171 face1560 intervals ($Nojetcells)
volume mesh volume21 cooper source face1488 face1618 face180
face1568 face1566 face178 intervals ($Nojetcells)
103
volume mesh volume23 cooper source face1492 face1620 face187
face1574 face1572 face185 intervals ($Nojetcells)
volume mesh volume25 cooper source face1496 face1622 face194
face1578 face1580 face192 intervals ($Nojetcells)
volume mesh volume27 cooper source face1624 face1500 face201
face1586 face1584 face199 intervals ($Nojetcells)
volume mesh volume29 cooper source face1504 face1626 face208
face1592 face1590 face206 intervals ($Nojetcells)
volume mesh volume31 cooper source face1628 face1508 face215
face1596 face1598 face213 intervals ($Nojetcells)
volume mesh volume30 cooper source face1506 face1052 face1594
face1397 intervals ($Nojetcells)
volume mesh volume28 cooper source face1502 face1042 face1588
face1387 intervals ($Nojetcells)
volume mesh volume26 cooper source face1498 face1032 face1582
face1377 intervals ($Nojetcells)
volume mesh volume24 cooper source face1494 face1022 face1576
face1367 intervals ($Nojetcells)
volume mesh volume22 cooper source face1490 face1012 face1570
face1357 intervals ($Nojetcells)
volume mesh volume20 cooper source face1486 face1002 face1564
face1347 intervals ($Nojetcells)
volume mesh volume18 cooper source face1482 face992 face1558
face1337 intervals ($Nojetcells)
volume mesh volume16 cooper source face1478 face982 face1552
face1327 intervals ($Nojetcells)
volume mesh volume14 cooper source face1474 face972 face1546
face1317 intervals ($Nojetcells)
volume mesh volume12 cooper source face1470 face962 face1540
face1307 intervals ($Nojetcells)
volume mesh volume10 cooper source face1466 face952 face1534
face1297 intervals ($Nojetcells)
volume mesh volume8 cooper source face1462 face942 face1528
face1287 intervals ($Nojetcells)
volume mesh volume6 cooper source face1458 face932 face1522
face1277 intervals ($Nojetcells)
volume mesh volume4 cooper source face1454 face922 face1516
face1267 intervals ($Nojetcells)
volume mesh cylinder cooper source face1450 face912 face1510
face1257 intervals ($Nojetcells)
window modify invisible mesh
volume mesh volume34 cooper source face1649 face1650 face1651
face1652 face1653 face1654 face1655 face1664 face1639
face1638 face1637 face1636 face1635 face1634 face1633
face1648 face1610 face1608 face1606 face1604 face1602
face1600 face1472 face962 face1468 face952 face1464
face942 face1460 face932 face1456 face922 face1452
face912 face915 face918 face911 face925 face928
face920 face935 face938 face930 face945 face948
face940 face955 face958 face950 face965 face968
face960 face694 face689 face684 face679 face674
face669 face664 face659 face654 face649 face644
face640 face697 face696 face692 face687 face686
face682 face677 face676 face672 face667 face666
104
face662 face657 face656 face652 face647 face646
face642 face695 face698 face690 face685 face688
face680 face675 face678 face670 face665 face668
face660 face655 face658 face650 face645 face648
face641 face152 face1470 face145 face1466 face138
face1462 face131 face1458 face124 face1454 face117
face1450 face1657 face1658 face1659 face1660 face1661
face1662 face1663 face788 face1656 face1474 face159
face1647 face1646 face1645 face1644 face1643 face1642
face1641 face1640 face1478 face1628 face1626 face1624
face1622 face1620 face1618 face1616 face1614 face1612
face1508 face1052 face1504 face1042 face1500 face1032
face1496 face1022 face1492 face1012 face1488 face1002
face1484 face992 face1480 face982 face1476 face972
face975 face978 face970 face985 face988 face980
face995 face998 face990 face1005 face1008 face1000
face1015 face1018 face1010 face1025 face1028 face1020
face1035 face1038 face1030 face1045 face1048 face1040
face1050 face114 face1058 face774 face769 face764
face759 face754 face749 face744 face739 face734
face729 face724 face719 face714 face709 face704
face699 face777 face776 face772 face767 face766
face762 face757 face756 face752 face747 face746
face742 face737 face736 face732 face727 face726
face722 face717 face716 face712 face707 face706
face702 face779 face784 face787 face775 face778
face770 face765 face768 face760 face755 face758
face750 face745 face748 face740 face735 face738
face730 face725 face728 face720 face715 face718
face710 face705 face708 face700 face782 face786
face785 face6 face780 face1055 face215 face1506
face208 face1502 face201 face1498 face194 face1494
face187 face1490 face180 face1486 face173 face1482
face166 intervals ($Plzdnodes)
volume delete body onlymesh
volume mesh body cooper source face1689 face1690 face1691
face1692 face1693 face1681 face1682 face1683 face1684
face1685 face1686 face1687 face1688 face1696 face1671
face1670 face1669 face1668 face1667 face1666 face1665
face1677 face1676 face1675 face1674 face1673 face1672
face1680 face199 face1584 face1377 face192 face1578
face1367 face185 face1572 face1357 face178 face1566
face1347 face171 face1560 face1337 face164 face1554
face1327 face157 face1548 face1317 face150 face1542
face1307 face143 face1536 face1297 face136 face1530
face1287 face129 face1524 face1277 face122 face1518
face1267 face115 face1512 face1257 face1380 face1383
face1375 face1370 face1373 face1365 face1360 face1363
face1355 face1350 face1353 face1345 face1340 face1343
face1335 face1330 face1333 face1325 face1320 face1323
face1315 face1310 face1313 face1305 face1300 face1303
face1295 face1290 face1293 face1285 face1280 face1283
face1275 face1270 face1273 face1265 face1260 face1263
face1256 face209 face374 face370 face384 face379
face394 face389 face404 face399 face414 face409
105
face424 face419 face434 face429 face444 face439
face454 face449 face464 face459 face474 face469
face484 face479 face494 face489 face377 face376
face372 face387 face386 face382 face397 face396
face392 face407 face406 face402 face417 face416
face412 face427 face426 face422 face437 face436
face432 face447 face446 face442 face457 face456
face452 face467 face466 face462 face477 face476
face472 face487 face486 face482 face497 face496
face492 face375 face378 face371 face385 face388
face380 face395 face398 face390 face405 face408
face400 face415 face418 face410 face425 face428
face420 face435 face438 face430 face445 face448
face440 face455 face458 face450 face465 face468
face460 face475 face478 face470 face485 face488
face480 face495 face498 face490 face1 face1586
face1582 face1580 face1576 face1574 face1570 face1568
face1564 face1562 face1558 face1556 face1552 face1550
face1546 face1544 face1540 face1538 face1534 face1532
face1528 face1526 face1522 face1520 face1516 face1514
face1510 face1403 face518 face1588 face1592 face1594
face1694 face1695 face1598 face1679 face1678 face515
face516 face510 face500 face508 face505 face213
face1596 face1397 face206 face1590 face1387 face517
face514 face512 face502 face506 face507 face509
face499 face504 face1400 face1395 face1385 face1390
face1393 intervals ($Chzdnodes)
BOUNDARY CONDITIONS
physics create Symmetry btype SYMMETRY face face2 face103
face211 face204 face197 face190 face183 face176
face169 face162 face155 face148 face141 face134
face127 face120 face112
physics create Wall btype SYMMETRY face face110 face5 face1649
face1664 face918 face915 face911 face925 face1650
face928 face920 face935 face938 face930 face1652
face1651 face948 face945 face940 face1653 face1654
face958 face955 face950 face1655 face965 face968
face960 face978 face975 face970 face1656 face114
face985 face988 face980 face995 face998 face990
face1657 face1005 face1008 face1000 face1658 face1015
face1018 face1010 face1659 face1028 face1025 face1020
face1035 face1660 face1038 face1030 face1045 face1661
face1048 face1040 face1055 face1662 face1058 face1050
face1663 face4 face1395 face1679 face1403 face1400
face1680 face1385 face1678 face1393 face1390 face1375
face1677 face1383 face1380 face1676 face1365 face1373
face1370 face1675 face1355 face1363 face1360 face1674
face1345 face1353 face1350 face1673 face1335 face1343
face1340 face1672 face1325 face1333 face1330 face209
face1315 face1323 face1320 face1671 face1305 face1313
face1310 face1670 face1295 face1303 face1300 face1669
106
face1285 face1293 face1290 face1668 face1275 face1283
face1280 face1667 face1265 face1273 face1270 face1666
face1256 face1263 face1260 face1665 face214 face91
face207 face85 face200 face79 face193 face73 face186
face67 face179 face61 face172 face55 face165 face49
face158 face43 face151 face37 face144 face31 face137
face25 face130 face19 face123 face13 face116 face8
physics modify Wall btype WALL face face110 face5 face1649
face1664 face918 face915 face911 face925 face1650
face928 face920 face935 face938 face930 face1652
face1651 face948 face945 face940 face1653 face1654
face958 face955 face950 face1655 face965 face968
face960 face978 face975 face970 face1656 face114
face985 face988 face980 face995 face998 face990
face1657 face1005 face1008 face1000 face1658 face1015
face1018 face1010 face1659 face1028 face1025 face1020
face1035 face1660 face1038 face1030 face1045 face1661
face1048 face1040 face1055 face1662 face1058 face1050
face1663 face4 face1395 face1679 face1403 face1400
face1680 face1385 face1678 face1393 face1390 face1375
face1677 face1383 face1380 face1676 face1365 face1373
face1370 face1675 face1355 face1363 face1360 face1674
face1345 face1353 face1350 face1673 face1335 face1343
face1340 face1672 face1325 face1333 face1330 face209
face1315 face1323 face1320 face1671 face1305 face1313
face1310 face1670 face1295 face1303 face1300 face1669
face1285 face1293 face1290 face1668 face1275 face1283
face1280 face1667 face1265 face1273 face1270 face1666
face1256 face1263 face1260 face1665 face214 face91
face207 face85 face200 face79 face193 face73 face186
face67 face179 face61 face172 face55 face165 face49
face158 face43 face151 face37 face144 face31 face137
face25 face130 face19 face123 face13 face116 face8
physics create Heat Fluxes btype WALL face face104 face106
face370 face379 face389 face372 face382 face392
face371 face380 face390 face378 face388 face398
face376 face386 face396 face374 face384 face394
face377 face387 face397 face375 face385 face395
face1681 face1682 face1683 face1684 face1696 face402
face412 face422 face432 face442 face400 face410
face420 face430 face440 face408 face418 face428
face438 face448 face406 face416 face426 face436
face446 face404 face414 face424 face434 face444
face407 face417 face427 face437 face447 face405
face415 face425 face435 face445 face1688 face1685
face1686 face1687 face452 face462 face472 face482
face492 face1693 face450 face460 face470 face480
face490 face1692 face458 face468 face478 face488
face498 face1 face456 face466 face476 face486 face496
face454 face464 face474 face484 face494 face457
face467 face477 face487 face497 face1691 face455
face465 face475 face485 face495 face1689 face1690
face518 face502 face512 face1695 face500 face510
face1694 face508 face506 face516 face504 face514
face507 face517 face515 face505
physics create Mass flow inlet btype SYMMETRY face face640 face649
107
face659 face642 face652 face662 face672 face641
face650 face660 face670 face648 face658 face668
face678 face646 face656 face666 face676 face644
face654 face664 face674 face647 face657 face667
face677 face645 face655 face665 face675 face1633
face1634 face1635 face1636 face1637 face1648 face679
face689 face699 face682 face692 face702 face712
face680 face690 face700 face710 face688 face698
face708 face718 face6 face686 face696 face706 face716
face684 face694 face704 face714 face687 face697
face707 face717 face685 face695 face705 face715
face1640 face1638 face1639 face719 face729 face739
face749 face722 face732 face742 face752 face762
face720 face730 face740 face750 face760 face728
face738 face748 face758 face768 face726 face736
face746 face756 face766 face724 face734 face744
face754 face764 face727 face737 face747 face757
face767 face725 face735 face745 face755 face765
face1645 face1641 face1642 face1643 face1644 face788
face769 face779 face772 face782 face770 face780
face778 face776 face786 face774 face784 face777
face787 face775 face785 face1647 face1646
physics create Outflow btype OUTFLOW face face105
108
REFERENCES
Al-Aqal O M A 2003 ldquoHeat transfer distributions on the walls of a narrow channel
with jet impingement and cross flowrdquo PhD Thesis University of Pittsburgh
Bunker Ronald S 2007 Gas Turbine Heat Transfer Ten Remaining Hot Gas Path
Challengesrdquo Journal of Turbomachinery April Vol 129 pp 193-201
Downs James P Landis Kenneth K 2009 ldquoTurbine Cooling Systems Design- Past
Present and Futurerdquo Proceedings of ASME Turbo Expo 2009 June 8-12 2009
GT2009-59991
Florschuetz LW Berry R A Metzger D E 1980 ldquoPeriodic streamswise variations of
heat transfer coefficients for inline and staggered arrays of circular jets with cross
flow of spent airrdquo ASME J of Heat Transfer 102 p 132-137
Florschuetz L W Truman C R Metzger D E 1981 ldquoStreamwise Flow and Heat
Transfer Distributions for Jet Array Impingement with Cross flowrdquo Journal of
Heat Transfer Vol 103 pp 337
Florschuetz L W Isoda Y 1983 ldquoFlow Distributions and Discharge Coefficient for
Jet Array Impingement With Initial Cross flowrdquo Journal of Engineering for
Power Vol 105 pp 296
Incropera Frank P DeWitt D P 2002 Fundamentals of Heat and Mass Transfer John
Wiley amp Sons Inc New Jersey pp 491-493
Liu Quan Kapat J May 2006 ldquoStudy of Heat Transfer Characteristics of Impinging
Air Jet Using Pressure and Temperature Sensitive Luminescent Paintrdquo UCF
Dissertation
109
Martin H 1977 ldquoImpinging jet flow heat and mass transferrdquo Advances in heat transfer
Vol 13
Ricklick Mark Kapat J December 2009 ldquoCharacterization of an Inline Row
Impingement Channel for Turbine Blade Cooling Applicationsrdquo UCF
Dissertation
Zuckerman N Lior N 2005 ldquoImpingement Heat transfer Correlations and Numerical
Modelingrdquo Journal of Heat Transfer Vol 127 pp 544