View
26
Download
0
Category
Tags:
Preview:
Citation preview
L
NASA / TM--1998-20663 7
Design and Performance Calculations of a
Propeller for Very High Altitude Flight
L. Danielle Koch
Lewis Research Center, Cleveland, Ohio
National Aeronautics and
Space Administration
Lewis Research Center
February 1998
::ii!ili!i_....
:iii!iiiiii_._
NASA Center for Aerospace Information
800 Elkridge Landing Road'Lin_icum Heights, MD 21090-2934.Price Code: A07
Available from.
National Technical Information Service
5287 Port Royal Road
Springfield, VA 221!2_)Price Code: A07
DESIGN AND PERFORMANCE CALCULATIONS OF A PROPELLER
FOR VERY HIGH ALTITUDE FLIGHT
by
L. DANIELLE KOCH
Submitted in partial fulfillment of the requirements
for the degree of Masters of Science in Engineering
Thesis Advisor: Dr. Eli Reshotko
Department of Mechanical and Aerospace Engineering
CASE WESTERN RESERVE UNIVERSITY
DESIGN AND PERFORMANCE CALCULATIONS OF A PROPELLER
FOR VERH HIGH ALTITUDE FLIGHT
:,ii!_:_iiii!il
'iiiii_
by
L. DANIELLE KOCH
ABSTRACT
Reported here is a design study of a propeller for a vehicle capable of subsonic
flight in Earth's stratosphere. All propellers presented were required to absorb 63.4
kW (85 hp) at 25.9 km (85,000 r) while aircraft cruise velocity was maintained at
Mach 0.40. To produce the final design, classic momentum and blade-element
theories were combined with two and three-dimensional results from the Advanced
Ducted Propfan Analysis Code (ADPAC), a numerical Navier-Stokes analysis code.
The Eppler 387 airfoil was used for each of the constant section propeller
designs compared. Experimental data from the Langley Low-Turbulence Pressure
Tunnel was used in the strip theory design and analysis programs written. The
experimental data was also used to validate ADPAC at a Reynolds numbers of 60,000
and a Mach number of 0.20. Experimental and calculated surface pressure
coefficients are compared for a range of angles of attack.
Since low Reynolds number transonic experimental data was unavailable,
ADPAC was used to generate two-dimensional section performance predictions for
Reynolds numbers of 60,000 and 100,000 and Mach numbers ranging from 0.45 to
vii
0.75. Surfacepressurecoefficientsarepresentedfor selectedanglesof attack, in
additionto thevariationof lift and drag coefficients at each flow condition.
A three-dimensional model of the final design was made which ADPAC used
to calculated propeller performance. ADPAC performance predictions were _iiiiii!
compared with strip-theory calculations at design point. Propeller efficiency
predicted by ADPAC was within 1.5% of that calculated by strip theory methods,
although ADPAC predictions of thrust, power, and torque coefficients were
approximately 5% lower than the strip theory results. Simplifying assumptions made
in the strip theory account for the differences seen.
iiiil
viii
ACKNOWLEDGEMENTS
!ii:_:
How fortunate I am to have so many blessings to count! For their patience
and guidance, I would like to thank Dr. Eli Reshotko and Dr. Christopher Miller. It
takes special skill to be a teacher, and I am sincerely grateful to have been able to
learn by your examples.
For their unfailing enthusiasm, I would like to thank Dave Bents and Tony
Colozza.of the ERAST team. It has been a long and bumpy road, and your optimism
has really made a difference.
For making financial support available, I would like to thank NASA, Jeff
Haas, Wayne Thomas, and Chuck Mehalie. While slightly beyond the boundaries of
my normal assigned duties, I believe that I am a better engineer because of the
experience gained through this thesis work.
ix
CONTENTS
ABSTRACT ................................................................................................................. vii
ACKNOWLEDGEMEI_S .......................................................................................... ix
NOMENCLATURE ...................................................................................................... xi
CHAPTER 1--Introduction ........................................................................................... 1
CHAPTER 2---Selection of Airfoil and Airfoil Performance Data .............................. 6
CHAPTER 3---Grid Study and ADPAC Validataion .................................................. 22
CHAPTER 4---Propeller Design Using Experimental Airfoil Data .......................... 42
CHAPTER 5---ADPAC Two-Dimensional Aerodynamic Predictions .................... 52
CHAPTER 6---Propeller Design and Analysis UsingTwo-Dimensional ADPAC Predictions ............................................ 86
CHAPTER 7---ADPAC Three-Dimensional Performance Calculations ................... 97
CHAPTER 8--Conclusion ....................................................................................... 114
REFERENCES ........................................................................................................ 116
NOMENCLATURE
....ii!!!!_'_ii!iiii!!i:i
a = speed of sound
C
Cd =
CI =
Cp
chord
drag coefficient = D/(qS)
lift coefficient = L/(qS)
pressure coefficient= ( )2 ,, 2+(r-OM (y)M,o 2 2 +(y -1)M _
CP =
CQ
CT =
power coefficient = P/(pn3d s)
torque coefficient = Q/(pn2d s)
thrust coefficient = T/(pn2d 4)
d = diameter
D = drag
e specific stored energy
advance ratio = V/(nd)
L = lift
M = Mach number = V/a
n = rotational speed
P = power
q ._. dynamic pressure = 0.5pV 2
Q = torque
xi
r = radius
Rtip = tip radius
T
= wing area
= thrust
ii!ili!!i_'
U x component of velocity
V y component of velocity
V freestream velocity
W z component of velocity
x = chordwise distance
ydistance from airfoil surface
dimensionless distance = (y/v)(XwJ9) °s
t_ = angle of attack
13 = twist angle
efficiency = (CT*J)/CP
dynamic viscosity
V kinematic viscosity
p = density
"l_wail = shear stress at the wallii,_i!_ i
xii
CHAPTER 1-INTRODUCTION
Background
Concern for the environment and determination to overcome a new challenge
can make very high altitude subsonic flight possible. Driven by the needs of the
atmospheric research community, a remotely piloted vehicle capable of flying
subsonically in the stratosphere is being developed by a consortium of federal,
industrial, and academic partners under NASA's Environmental Research Aircraft
and Sensor Technology (ERAST) program.
In-situ measurements at altitudes between 24.4 km (80,000 fi)and 30.5 km
(100,000 ft) are needed to further our understanding of the dynamics and chemistry
of Earth's atmosphere. These measurements would augment laboratory research, data
from samples of the lower stratosphere taken by the ER-2 aircraft, and measurements
from satellites and balloons. A better fundamental understanding of the atmosphere
can help us to make more responsible decisions in the way we choose to live, ,,v_._,rk_
and travel.
Undeniably, development of a suitable propulsion system is the most
formidable challenge. Currently, there are no existing propulsion systems capable of
meeting either the program's near term altitude goal of 25.3 km (83,000 ft) or
ultimate goal of 30.5 km (100,000 ft). Studies summarized by the ERAST program's
Leadership Team ( Ref. 1) suggest that the near term goal may be met by either a
modified gas turbine power plant or a turbocharged reciprocating combustion engine.
-:: :: : : : : ::.- :::::,:: :::::: ::::: ::::: : :::::::::::::::::::::::: ::: :: :: :: ::
Non-airbreathing or hybrid systems are the most likely candidates for propelling an
aircraft to the ultimate altitude goal.
For many of the conceptual aircraft being considered, power produced is
transferred to thrust by a propeller. Presented here is an aerodynamic design study of
a propeller to meet the near term ERAST vehicle requirements using the most readily
available computational tools, design and analysis methods, and experimental data.
Strip-theory design and analysis methods are used with two and three-dimensional
results from the Advanced Ducted Propfan Analysis Code-Version 7 (ADPAC), a
numerical Navier-Stokes analysis code, to develop a propeller design.
Propeller Requirements
Design is an iterative process. It begins with a carefully chosen set of
requirements that are based on the best results of any conceptual or experimental
studies done. The propeller requirements in Table 1 have been derived from the
Near-Term ERAST mission requirements shown in Table 2 and the expected
propulsion system performance (Ref. 1).
Table 1. Propeller Requirements
Altitude
Power
25.9 km
(85,000 ft)
63.4 kW
(85 hp)
Maximum Relative Mach Number 0.80
Cruise Mach Number 0.40
Table 2. ERAST Mission Requirements
Mission
Mission altitude
Operational Radius
Payload weight
Near-Term Goal
(1998 - 2000)
25.3 km
(83,000 ft)
1000 km
(539 nmi)
150 kg
(330 lbm)
Long-Term Goal
(2000 +)
30.5 km
( 100,000 ft)
4000 km
(2160 nmi)
225 kg
(496 lbm)
Payload accommodations Access to undisturbed free stream
Airspeed range 0.40 < M < 0.85
Operational Constraints
Crosswind Capability
Can operate in moderate turbulence
Operation in ambient air temperatures to -100 ° C
Takeoff and landing in moderate crosswinds
(minimum 15 knots)
Deployment To remote base of operations at airfields worldwide
Overview of the Design and Analysis Methods Used
Having a firm set of requirements, the designer must then decide upon a
method to meet them. The steps taken to arrive at the final design presented in this
thesis are briefly described below. Each step will be discussed in depth in the
chapters to follow.
Step 1. The Eppler 387 airfoil was chosen for the constant section propeller blade.
While this airfoil was considerably thicker than those typically used for propeller
sections, it was selected because it was known to have good perfomlance at low
Reynolds numbers. Experimental lift and drag data that could be used in the strip-
theory programs, as well as the surface static pressure data that could be used to
validate ADPAC was available for this airfoil.
;_;i:ep 2. A grid study was conducted to determine an acceptable computational mesh
density for the two-dimensional ADPAC performance calculations of the Eppler 387
airfoil. Having identified an appropriate mesh, ADPAC was validated by comparing
calculated surface pressure coefficients to experimental pressure coefficients for a
range of angles of attack.
Step 3. A strip-theory design program was written based on the procedures described
by Adkins and Liebeck (Ref. 2)° The low Reynolds number, low Mach number
experimentaldata from the Eppler 387 were incorporatedinto the programand a
seriesof propellersweredesigned.
Step4. The ADPAC codewas usedto calculatetwo-dimensionalairfoil section
performancefor higherMachnumberssinceno experimentaldatawerefoundfor this
regime. The Reynoldsnumber-Machnumbercombinationswere identified by the
resultsof Step3.
Step5. The resultsfrom Step4 were incorporatedinto the strip-theorydesignand
analysiscodes. Another setof propellerswasdesigned,examinedand comparedto
arrive at thefinal geometry. Off designperformancecalculationsweremadefor the
final propellerdesignwith thestrip-theoryanalysisprogram.
Step6. A three-dimensionalcomputationalmeshfor the final propellerdesignwas
made,andADPAC wasusedto makea three-dimensionalperformanceprediction.
TheADPAC resultwascomparedto thestrip-theoryresultat thedesignpoint.
CHAPTER 2
Selection of Airfoil and Airfoil Performance Data
The propeller designer's most critical decisions lie in the selection of blade
airfoil sections and airfoil performance data. Accuracy of a propeller design or
analysis conducted using strip theory methods will be compromised if any variation
of airfoil performance with Reynolds number and Mach number is not taken into
account. While the designer may be aided by modem numerical design and analysis
programs, results cannot be used with any confidence until calculated perfomaance is
in good agreement with experimental data.
With the renewed interest in high altitude remotely piloted vehicles,
sailplanes, and wind energy conversion, much research has been done to gain a better
understanding of the behavior of steady and unsteady, two and three dimensional
subsonic flows at low Reynolds numbers. Low Reynolds numbers are those below
10 6, as defined by Mueller in Refe_:ence 3, since the unpredic:tiblity of the boundary
layer and the effects of laminar separation and reattachment play an important role in
this regime. Results of this research has led to the development of many
computational tools to design and analyze airfoils in this regime. Even so, behavior
of the laminar boundary layer is still not completely understood and measurement and
modelling of the boundary layer over airfoils at low Reynolds numbers still presents a
challenge (Ref. 3)°
For subsonic flows, the laminar boundary layer over an airfoil at low
Reynoldsnumberhasbeenobservedto behavein threedifferentpattemsasreported
in Reference3. The laminarboundarylayer may either transition naturally to a
turbulentboundarylayer,mayfully separatefrom theairfoil surface,or mayseparate
andreattachto theairfoil surfaceformingalaminarseparationbubble.
Performanceis best if the laminarboundarylayer naturally transitionsto a
turbulent boundary layer before reaching the adversepressuregradient. With
increasedenergy, the turbulent boundary layer is able to withstand the adverse
pressuregradientandtheflow will beableto stayattachedto theairfoil surfacemuch
longeryieldinggoodlift anddragcharacteristics.
Full separationresultsin a severeperformancedegradation.The airfoil will
stall at high anglesof attackwhenthe laminarboundarylayer completelyseparates
from theairfoil surfacenearthe leadingedge. Full separationcanalsooccurat lower
anglesof attack if the laminarboundarylayer is unableto overcomean adverse
pressuregradient.
A separationbubbleis formedwhen the laminarboundarylayer, unableto
overcomean adversepressuregradient,separatesbut then reattachesto the airfoil
surfaceaftertransitioningto turbulent. Typically, the laminarshearlayerwill begin
transitioning immediately downstreamof the separationpoint. The separated
turbulentshearlayerwill thengrow quickly entrainingflow from thefreestreamuntil
it reattachesto the airfoil surface.Within the bubble is a region of slow moving
< , :NI i i:: ¸ ! i ::i:i ..... i ¸ i:::_!::!_ i!i !_i ii...... : : '_:_i:!iii Hi,!+ii?i,i ¸ ¸¸ !ii!?!?!i!:i̧ :_;ii!!!?i:!i_¸!i,:!!_!i!ii!!i!_<i!i_iiii!:i!!iii-_:'!ii!?_i'ii!i!!ii!!iii!ii!!ii_i?ii!7!!!?i'i!i!i!ii!!iiiiiii+iii!!!i!!illI_I!̧
reversed flow with the center of the vortex lying near the reattachment point. The
airfoil surface pressure remains nearly constant across the bubble region and increases
rapidly near the point where the flow reattaches.
The length of the separation bubble depends upon how rapidly the laminar
shear layer is able to transition. Generally, separation bubbles will lengthen as chord
Reynolds number is decreased. While not always clearly seen, increasing free stream
turbulence levels, airfoil surface roughness, and employing boundary layer tripping
devices have usually been effective in shortening the laminar separation bubble and
improving airfoil performance (Re£ 3). Increasing the adverse pressure gradient has
also been seen to reduce the length of the separation bubble by reducing the time
needed for transition (Ref. 4).
Preliminary studies showed that at an altitude of 25.9 km (85,000 fi) propeller
blade Reynolds numbers could vary from 50,000 to 200,000 while relative free-
stream Mach numbers could range ffc,r;_ 0.40 to the design limit of 0.80. No
experimental data was found for this transonic low Reynolds number regime.
Experimental results were found for an Eppler 387 airfoil that had been tested at the
Langley Low-Turbulence Pressure Tunnel (LTPT) at Reynolds numbers of 60,000 to
460,000 and a Mach number range of 0.03 .to 0.13 (Ref. 5). Because of the high
quality of the experimental data, and the availability of airfoil surface pressure, lift,
and drag coefficients at each angle of attack, the Eppler 387 airfoil was chosen over
other airfoils with known good performance at low Reynolds numbers for tile
constantsectionpropeller. This sectionis much thicker than the transonic airfoils
normally chosen for propellers tip sections. The simplification of one airfoil for the
entire blade was made for academic purposes only, simplifying programming and
modelling.
The variation of the lift and drag coefficients for the Eppler 387 measured at
the Langley LTPT for Reynolds numbers of 60,000, 100,000 and 200,000 are shown
in Figures 1 and 2. At a Reynolds number of 60,000, laminar separation was not
always observed to be followed by turbulent reattachment. This phenomenon can be
seen in Figure 1, as the airfoil stalls around c_ = 3.00 ° and the boundary layer did not
reattach until an angle of attack of 7.50 °. In fact, both phenomena, separation with
and without reattachment, were observed at an angle of attack of 4.00 °. The
measurement techniques used were not able to resolve the unsteady nature of the flow
at this Reynolds number. This behavior may result from short separation bubbles
bursting, although further experimentation would be needed to prove this. McGhee,
Walker, iand Millard observed no hysteresis loops for this airfoil in the Langley LTPT
in a set of experiments designed to study hysteresis effects for Reynolds numbers
from 60,000 to 300,000.
Figures 3 through 5 show the variation of pressure coefficients on the airfoil
surface for Reynolds numbers ranging from 60,000 to 200,000 for an angle of attack
of 8.00 ° . From these figures and others reported in Reference 5, surface pressure
measurements and oil flow visualization techniques showed that the length of the
10
separationbubble decreasedas Reynolds number was increased. Oil flow
visualizationindicatedthat theboundarylayer naturallytransitionedfor a Reynolds
numberof 200,000anda = 8.O0°.
TheEppler387hasbeentestedin severalotherfacilitiesandthedatafrom the
Langley Low-TurbulencePressureTunnel have been used to validate numerous
airfoil designand analysiscodes. Comparisonsof theseresults shedlight on the
manychallengesstill faced. Reference5 presentsexperimentalresultsfrom testsof
two dimensionalmodelsof the Eppler387 in the Low TurbulenceWind Tunnel at
Delft andthe Model Wind Tunnelat Stuttgart. As reportedin Reference5 andseen
again in Figures6 through11 , observationsat Langley for a Reynoldsnumberof
60,000wereconfirmedin testsof anEppler387sectionin theLow TurbulenceWind
Tunnelat Delft, but notby testsin the:ModelWind Tunnelat Stuttgart. Reasonsfor
thesediscrepanciesarestill unknownbut havebeenassociatedwith differencesin
tunnel turbulencelevels, model quality, model mountingconfigurations,and force
measurementmethods.
TheEppler-Somerscode(Re£ 5) andDrela's XFOIL andISEScodes(Ref. 6,
7) areamongthe designandanalysiscodesthathavebeenvalidatedwith the Eppler
387 data takenat Langley. The XFOIL and ISES codesusean inviscid/viscous
interaction technique while the Eppler-Somerscode couples complex mapping,
potential flow and boundary,layer techniquestogetherto solve for the flow field
around an airfoil. Generalagreementbetweenthe calculatedand experimental
11
resultswasgoodfor eachof thesecodes,althoughagreementdegradedasReynolds
number decreased.This degradationis inherent to the techniqueused since as
Reynoldsnumberdecreasesandtheboundarylayerthickensthe interactionbetween
the inviscidandviscousregiongetsstrongerandthe boundarylayer approximations
becomelessaccurate(Ref. 8). At Reynoldsnumbersabove100,000thesecodesare
practicaldesigntoolsbecausetheycansolvefor anairfoil's performancequickly.
O4
! T T l
I3 'lu°!oU2°°3 _!'I
(D
(1,)
00_,D
o. c/c:/o H IIH
oooooo
ooo
H li fl
r_
01
ol
==
=o"
k_
e_
ee
em
13
w=-,4
°v==lo
O
ol,--{
1.4 I I I I I I
0.01
! ! I I I0.02 0.03 0.04 0.05 0.06
_- Re = 60,000 M = 0.05Re = 100,000 M = 0_08
-_ Re = 200,000 M ...._,.G6
Drag Coefficient, Cd
!0.07 0.08
Figure 2" Variation of Drag Coefficient with Reynolds Number as Measured at
the Langley Low-Turbulence Pressure "Funnel
14
-5 l I I I !
2, 0 "0 ...... 0
- l'-" ---0 ..... 0 ------0 ---0 __0___0 - 0
l l l l
0 0.. 0 0 -0-0 o
0 ......0 .....0 ......0---0-_-0 ....0-----0....0 .....0 .....0 .....o- 0 ----0 ....o o
2 I I I I I I l I I 1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 l
X/C-o- Langley Data, M = 0.05
Figure 3" Pressure Coefficient versus Non-Dimensional Chordwise Position,
Re = 60,000 and _ = 8.01°
-I-
0
:_>oooo
2
I I l I I I I I I
0
Laminar SeparationOil Flow Visualization
0 ....0 ......0 ......._....0 .......0 ..
Turbulent Reattachment
Oil Flow Visualization
0--. 0 0 -0 ....0
O- 0
0 ........0 ......0 .........0----0----0......0---0 ......0 ......0---0 ....0 -- O----0 .....O 0
l I I I I I i I I ,
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
-o- Langley Data_ M = 0.08X/C
o
Figure 4: Pressure Coefficient versus Non-Dimensional Chordwise Position,
Re = 100,000 and _ = 8.00 °
15
-5
-4
-2- O
--1 ""
0-
2
I I I i i i I i i
Natural Transition
Oil Flow Visualization
-O ........O-
0_0 ....0 -.
O. 0
0 .....0 ........0 ....0---0 ....O----O ....0-- -0 ....0 ....0 .....0 ....0 0 ....O- 0
I I I I I I I I I
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
-O- Langley Data, M = 0.06X/C
Figure 5" Pressure Coefficient versus Non-Dimensional Chordwise Position,
Re = 200,000 and t_ = 8.00 °
16
v=--4
°v==t
O
°_==l
1.3 I ! I !
-5
i _'
:/" i
// ,
_o /"
/ o ./
,/, .
,/' //'
/
_ //! /
I_1'_,///
i /
4-
I
I
\
\
I i I I0 5 10 15 20
_, degrees
-o- Langley Dats_:Tunnel Turbulence Level = 0.16%-+ Delft Data, Tuanei Turbulence Level = 0.03%->< StuttgartData, TunnelTurbulence Level - 0.08%
Figure 6- Comparison of Measured Lift Coefficients versus Angle of Attack
from Tests at Langley, Delft, and Stuttgart at Re = 60,000
17
v==-4
O
o¢=q
o
OL)
-I-,,,4
13 ! I I I i
--0.1
-0.2
, .. ,,
,?-.
<,
I !0.02 0.03 0.04
I I IO.O5 0.O6 0.07
Drag Coefficient, Cd-e- Langley Data, Tunnel Turbulence Intensity = 0.16%-x:. Dolt1 Data, Tunnel Turbul__::_=_IntcrL_ity= 0.03%--'_- Stuttgart Data, Tunnel Tur_en_ Intensity = 0.08%
0.08
Figure 7- Comparison of Measured Lift Coefficients versus Drag Coefficients
Tests at Langley, Delft, and Stuttgart at Re = 60,000
18
°p-¢
O
°v,-¢
Io4 I I I
0°2
./
/
/' I'
/..
/ /
/ / /
/.//I , ..
i / /
•/ ._. ;
/ , .
//._.
...../'//
_(÷ ..../'/ //
¢" ×/.'_ .;
, /
/? :.,I_/" //
.I.-.-4. _
//
/_" .-I-- "1--.._4.. .*I- ____.._, _.-I-" ._._q----_ "
.,,
-5
I I0 5
or, degrees
-o- Langley Data, Tunnel Turbulence Level = 006%Deltt Data, Tunnel Turbulence Level = 0.03%
-_ Stuttgart Data, Tunnel Turbulence Level = 0.08%
I10 15
Figure 8: Comparison of Measured Lift Coefficients versus Angle of Attack from
Tests at Langley, Delft, and Stuttgart at Re = 100,000
19
°v-_
O
°v-q
1.4
1.2 "-
1-
0.8-
0.6-
0.4-
0.2--
0-
-0.:
i I I
0.01
I !4
0.025 Drag Coefficient, Cd
-_- Langley Data, Tunnel Turbulence Level .... 9.06%
DeLft Data, Tunnel Turbulence Level = 0.03%
-_ Stuttgart Data, Tunnel Turbulence Level = 0.08%
I0.055 0.07
Figure 9: Comparison of Measured Lift Coefficients versus Drag Coefficients
Tests at Langley, Delft, and Stuttgart at Re = 100,000
20
O° _=,,I
O
OO
°_,=1 J/
+'!/
t
I I I-5 0 5 10
co, degrees
-_- Langley Data.. Tunnel Turbulence Level = 0.06%-_ DclR Data, Tunnel Turbulence Level = 0_03%
-_ Stuttgart Data, Tunnel Turbulence Level = 0.08%
!15 2O
Figure 10: Comparison of Measured Lift Coefficients versus Angle of Attack
from Tests at Langley, Delft, and Stuttgart at Re- 200,000
21
0 0.01 0.02 0.03 0.04
Drag Coefficient, Cd
-o- Langley Data, Tunnel Turbulence Level = 0.06%Delft Data, Tunnel Turbulence Level - 0.03%
-_ Stuttgart Data, Tunnel Turbulence Level = 0.08%
0.05 0.06
Figure 11- Comparison of Measured Lift Coefficients versus Drag Coefficients
Tests at Langley, Delft, and Stuttgart at Re = 200,000
CHAPTER 3
Grid Study and ADPAC Validation
ADPAC is a three-dimensional time-marching Euler/Navier-Stokes analysis
code that was originally developed to enable researchers to study the effects of
compressor casing and endwall treatments (Ref. 9). The code is flexible enough to
allow it to be used for analysis applications other than compressors. ADPAC geins
much of its flexibility from the use of a multiple-block grid system. This feature is
helpful when studying complicated geometries where it may not be possible to create
a single structured grid of the flowfield. The multiple-block grid system allows one
to create different grids for different areas of the flowfield. Special commands are
provided to allow the different blocks to communicate with each other.
While the code had been validated for several turbomachinery and non-
turbomachinery applications, ADPAC was unvalidated in the regime of interest for
the ERAST propeller. The two-dimensional Eppler 387 experimental data from the
I,angley LTPT were used for this validation.
The first task at hand was to conduct a grid study. The purpose of the grid
study is to identify the minimum computational mesh density for which a solution is
independent of the number of grid points. For subsonic low Reynolds number flow_:_
the grid must be sufficiently dense to resolve the boundaD '_layer and any separation
bubbles formed. Several 'C' grids of the flow field around the Eppler 387 geometry
were created. Measured coordinates from the Langley pressure model of the airfoil
22
23
"Level 3" grid had23,409points,andthe"Level 2" grid had5,945points. Eachgrid
extendedten chordlengthsupstream,downstream,above,and below the blade.The
minimum acceptablenumber of points is desiredto reduce computationaltime.
Increasingthe numberof grid points past that of the Level 4 meshwasconsidered
prohibitive. Views of the entirecomputationaldomainfor thethreetwo-dimensional
gridscanbe foundin Figures12through14. Figures15throl,gh 17showtheportion
of eachmeshcloseto the airfoil surfaceanddisplaythepackingof grid points in the
boundarylayerregion.
Two otherfiles arerequiredby ADPAC in orderto runa calculation,an input
file and a boundarydatafile. The input file containsparametersthat allow one to
scalethe non-dimensionalgrid. In the boundarydatafile, one canspecify theangle
of attackand how the boundariesof the grid are to be treated.A combinationof
parameterswithin the input andboundarydatafiles setthe flow conditions. For all
num_?,.rthe two-dimensionalairfoil performancecalculations,the freestreamMach _
was fixed on the horizontal straight sections of the outer boundary of the
computationalgrid. Total temperatureand total pressurewere fixed on the inlet
curved sectionof the outer boundary, and static pressure was fixed at the straight
vertical exit plane° A no-slip condition was imposed on the blade surface, forcing the
velocity at the blade to be zero. Because ADPAC is a compressible code, a freestream
Mach number of 0.20 was set. The Mach numbers for the experimental data were
generally below 0.10.
24
Eachgrid wasusedto calculatethe flow at Reynoldsnumbersof 60,000,
100,000and200,000while angleof attackwasnominally8.00°. Angle of attack was
set to match that given by the experiment. Figures 18 through 20 show the calculated
airfoil surface pressure coefficients plotted against the non-dimensionalized
chordwise position and compared to the experimental data. Good agreement between
the computations with the Level. 4 grid and the experimental data was seen even at a
Reynolds number of 60,000 which would have the longest separation bubble of all
three cases.
• Figure 21 shows a comparison of the calculated value of the lift coefficient as
a function of the inverse number of mesh points for each Reynolds number. As
Reynolds number increases, more grid lines must be packed towards the airfoil
surface to resolve the thinner boundary layer. The dimensionless distance of the grid
line away from the wall, y+, is defined by Schlichting in Reference 10 as:
+
y =
Y I "l_wallp
where y is the dimensional distance of the grid line away from the airfoil surface, x,,.,,,
is the shear stress at the wall, p is the fluid density, and v is the fluid kinematic
viscosity. The values of y+ for the first grid line of the Level 4 mesh at the quarter
chord point are 0.0624, 0.0915, and 0.1537 for Reynolds numbers of 60,000, 100,000,
and 200,000, respectively.
25
Accompanyingeach solution is a set of convergenceplots. Figures 22
through24 containtwo convergenceplots for eachsolution: the Root Mean Square
(RMS) Error, andtheNumberof Separatedpointsat eachiteration. TheRootMean
SquareErrorwasdefinedto be thesumof thesquaresof theresidualsof all the cells
in the mesh, the residualbeing the sum of the changesof the five conservative
variables,p, pu, pv, pw, andpe. TheADPAC definition of a separatedpoint wasa
cell whosevaluefor Vxwasnegative.Generally,for the low Machnumbercases,the
calculationwas run until the numberof separatedpoints seemedto be constantand
theresidualswerereducedby atleastthreeordersof magnitude.
The Level 4 grid was thenusedfor a seriesof calculationsat a Reynolds
numberof 60,000andanglesof attackrangingfrom -2.94° to 12.00°. The Level 4
grid was chosenbecauseof the good agreementbetween the surfacepressures
calculatedby ADPAC andthe experimentaldataat a Reynoldsnumberof 60,000
(Fig. 18). Lift coefficientswerecalculatedfor eachangleof attackandcanbe seen
comparedto the Langleyresultsin Figure25. Pressurecoefficientdistributionsare
presentedin Figures26 through31 for eachof the coloredpoints in Figure 25.
Figures32 through37 are the correspondingconvergencehistoriesfor eachof the
selectedADPAC calculations. Sincethe viscousdragresult wasunavailablefrom
ADPAC, it wasestimatedby calculatingskin friction dragonbothsidesof aflat plate
drag(Ref. 10):
26
Cd=1.328
The total of the viscous plus pressure drag coefficients were then plotted against the
Langley data and are shown in Figure 38.
There was generally good agreement between the ADPAC calculated values
and the experimental values. Examination of the plots shows that ADPAC, like many
other numerical analysis codes, was unable to predict the laminar stall that was
measured at Langley at angles of attack from 3.00 ° to 7.50 ° . The marked increase in
measured drag in this region was also unpredicted by this version of ADPAC. For
angles of attack less than 8.01 ° there is not good agreement between the calculated
and experimental data near the trailing edge with ADPAC predicting recompression
farther upstream than was seen in experiments in the Langley LTPT (Fig. 26 - 29).
Agreementbetween the ADPAC prediction and the experimental results at the trailing
edge improves at ar_gles of attack of 8.01 o and greater (Fig. 30 - 31).
27
=J=
/!!/
!!r/
,, ,.,_
i
Figure 12: Entire Level 2 Computational Mesh of the Eppler 387 Airfoil
Figure 13" Entire Level 3 Computational Mesh for the Eppler 387 Airfoil
29
Figure 16" Portion of Level 3 Mesh Close to the Airfoil Surface
Figure 17" Portion of Level 4 Computational Mesh Close to the Airfoil Surface
30
-5 I I I I I I I ! I
0 ,_ ........ _..____,_.____._:_ __,_.... ___-___,--__-_----__---=--_----"_
1 "_"_i "_'__
2 I I I I I I ! I0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
o Langley Data, M = 0.05
Lovol 4 Mosh, M = 0.20
-- Lovol 3 Mesh, M = 0.20
-- Lovol 2 Mesh, M = 0.20
X/C
Figure 18: Pressure Coefficient vs. Non-dimensional Chordwise Position and
Different Computational Mesh Densities, Re - 60,000 and _ = 8.01 °
-5 I I I I I I I ! i
4i _
3
-2!_::_. ___ ___
1 I I I I I IT_
20 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
O Langloy Data, M = 0.08
Lovel 4 Mesh, M = 0.20
-- Lovel 3 Mesh, M = 0.20
- " Lovel 2 Mesh, M = 0.20
X/C
Figure 19: Pressure Coefficient vs. Non-dimensional Chordwise Position and
Different Computational Mesh Densities, Re- 100,000 and _ - 8.00 °
31
<> Langley Data, M = 0.06
Level 4 Mesh, M = 0.20
Level 3 Mesh, M = 0.20
- Level 2 Mesh, M = 0.20
X/C
Figure 20: Pressure Coefficient vs. Non-dimensional Chordwise Position and
Different Computational Mesh Densities, Re = 200,000 and _= 8.00 °
rj
1.5 n
1 --
0.5 --
o
--o- Re = 60,000
+- Re = 100,000
-_ Re = 200,000
l/(Number of Mesh Points)
0.001
Figure 21- Calculated Lift Coefficient vs. Inverse of Number of Computational
Mesh Points at ot - 8.01°
32
-2 It-O
12: -4 ¸
rj3
o
_) -8
Q
..J
-I0
4000
Q O
Z_
I I I I I I I
<h
...... _..- . -.
u
i I I I I I I
0 500 1 000 ! 500 2000 2500 3000 3500
Level 4 Convergence
.... Level 3 Convergence
.... Level 2 Convergence
Iteration Number
4000
.
0 500
i I I I I I
/ ......../
/
/
........ :S < .............................................................................
I I .! I I !
1000 1500 2000 2500 3000 35004000
Level 4 Convergence
.... Level 3 Convergence
Level 2 Convergence
Iteration Number
Figure 22- Comparison of the Convergence Histories, Re = 60,000 M = 0.2
-2 I I I I I I
t_
r,,r.l
0
e_ -8
0
.-I
c¢I
x 6.
-I0
4000
2000
I I I I I
500 1 000 1500 2000 2500
I I
3000 3500
Level 4 Convergence
-- Level 3 Convergence
Level 2 Convergence
Iteration Number
I I I I I I I
I_&]<<-- ..... ,-"
0 50O 1000
/
/
I I I I I
1500 2000 2500 3000 3500
I
Level 4 Convergence
'- Level 3 Convergence
.... Level 2 Convergence
Iteration Number
4000
Figure 23: Comparison of the Convergence Histories, Re = 100,000 M = 0.2
40O0
33
L--
r_t3
C/3
O
r_q
L.
r./3
-2 I I I
-'-,_. _,_
'-. i'!):),._.._.,_...._
I I I-I0
0 500 1000 1500
I I I I i I
I I I I I I
2000 2500 3000 3500 4000 4500 5000
Level 4 Convergence
--- Level 3 Convergence- Level 2 Convergence
Iteration Number
3000 I I I I I I I
2000 / _"_-
//yJ
j_
...................................._..................................0IJ ......... i I , I _ _ I
0 500 1 000 1500 2000 2500 3000 3500
I
!
4O00 4500
Level 4 Convergence
-- Level 3 Convergence
Level 2 Convergence
Iteration Number
5000
Figure 24: Comparison of the Convergence Histories, Re = 200,000 M = 0.2
"::::t"
! i i i i l t__
IO 'lu0!__0o3 U!l
(Dr.,,_
o¢.-,I,::5It
o It ._
g3
r +f
r_
6Jl
0
_----,,,_
tt
0
r_
!j_ee
¢,q
e_
35
-5
-4
-3
I i I i I I I I I
o 0 o o o o o
I I I I I I I I I
O.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
o Langley Data, M = 0.05
ADPAC Calculation, M = 0.20X/C
Figure 26" Pressure Coefficient vs. Non-dimensional Chordwise Position,
Re = 60,000 tx = 4.00 °
I I I I I I I I I
0-0 0---0....0--_-0.......-0....0--'--0----0.....0---0 ....0 0 0
0_ - ..... 0 0
G¢oo._---o--o_o -o_---o ---o--o---o---o-o::---:_---
I I I I I I I I .......I I
0.1 0.2 0.3 0.4 0.5 0_6 0.7 0.8 0.9
O Langley Data, M = 0.05
ADPAC Calculation, M = 0.20
X/C
Figure 27: Pressure Coefficient vs. Non-dimensional Chordwise Position,
Re = 60,000 c_ = 4.99 °
36
-4-
-3_
-2-
-l
0
l
! I i I
-_:£00 0 0
,-
0 0
<Z__. 0
i I i I I
0 o o o 0 o 0 o o o
o _0 0 0 ___0___0 _.0_ 0 0- - 0-_--
2 I I I I I I I I I
0 O. 1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
o Langley Data, M = 0.05
ADPAC Calculation, M = 0.20
X/C
Figure 28: Pressure Coefficient vs. Non-dimensional Chordwise Position,
Re = 60,000 a = 6.01°
I I I I I I i I i
-2_O
O- -0 -0 ...._ .....0 ....0 -0--0- 0 0 0
0
0 0 0 0O-
_O__O--O--_O----O_-_----O----O--O----O--O---O-----O----O----O
if
2 I I I I I I ! ! I ,0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
X/Co Langley Data, M = 0.05
ADPAC Calculation, M = 0.20
-.$-__.:_
Figure 29" Pressure Coefficient VSoNon-dimensional Chordwise Position,
Re- 60,000 tx = 7.00 °
37
-5 I I I I
_2I%o<_. _ o
__|,.m
I I I I I
--0 .... O_0 _ O 0
o--o.....o o ---_----
I I l I I I I I I I
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
X/Co Langley Data, M = 0.05
ADPAC Calculation, M = 0.20
Figure 30" Pressure Coefficient vs. Non-dimensional Chordwise Position,
Re = 60,000 t_ = 8.01°
o
I I I I I I I I
I I I I I l I I ,
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
o Langley Data, M = 0.05
ADPAC Calculation, M -0.20
X/C
Figure 31" Pressure Coefficient vs. Non-dimensional Chordwise Position,
Re = 60,000 c_ = 9.00 °
oo
%
! g
I °- g"l O0
- i -
- i -i
/
eet
/ °< "-_
//0
o
t-,
Z§ =
c_
J0_] SI_IOI l]0l
I
1
- //
/
(\
\
\
",.,\
'l I .......
1I-tt
L-
g g oo oeq --,
%
slu!0d p01_.1_d0Sj0 J0qtunN
-' O
oG", II
oo ¢'q
II
g oo X,D,,O
g..
Egzo
.o ;;_"_ g.," O
....,O_..,
,, =¢De_
o g:lo
I.
o =Io oo
" L)
o .<o
_ gh
° gl
I.=
om_
i I
..
l'
/
-3
5i
_ I ..-----7 i"
J0_t SI_ O[ i]0"I
,, Ez
.o
IN¢J
0 "-'0e_
[ I J '
m
-\
-._ ..
I [ "=--:o° § g °0 oeel _ ,-,I
g
oo
0o
ob-_-_
z
0._
L.
oN
m
\ ooo
ooo
"_7.
o
slu!0dp01_J_d0sj0 ._0qtunN
0
o'xO',,
II
¢.q
!i
II
e,,
I.o
'4_
om
=
¢12
I....¢D
=OL)L).,¢gh
.<oo
¢DI.
olmal
39
O
I:::
0'2
O
O
-4
-6
-I0
I I I I I I I
I I I I ! I I
0 I000 2000 3000 4000 5000 6000
IterationNumber
7000 8ooo
r._......
O
C_t...
c_
r./D
o
l..,,
E
Z
4000
2000
I I I i i I !
/.
/
I I I ! I ! !
0 1000 2000 3000 4000 5000 6000 7000Iteration Number
8000
Figure 34" ADPAC Convergence History, Re = 60,000 M = 0.20 c_ = 6.01°
O -4
o"2
-6O
O -8
-10
I I i I i i i I
I I I I I I I I
1000 2000 3000 4000 5000 6000 7000 8000
Iteration Number
9ooo
°..O
O"2
OL.
E
Z
4ooo
2000
I I I I I i I I
,- t-_---._.__._... __.... .
i
/
:
/
/
/£
//
! I I I I I I !
1000 2000 3000 4000 5000 6000 7000 8000Iteration Number
9000
Figure 35" ADPAC Convergence History, Re = 60,000 M = 0.20 ct = 7.00 °
4O
O
C_O
C)
...,9
O
O
CL_
Z
2L-4
-6 L_"_,..,,
0 500
I l
I I
1000 1500
I I I i
l I I
2000 2500 3000
IterationNumber
I
3500 4ooo
4000
2000
!,:l.:lj\:<.
'
/
//
/
./
J
I I I i [
I I I ! I ! I
500 i 000 ! 500 2000 2500 3000 3500Iteration Number
4000
Figure 36: ADPAC Convergence History, Re = 60,000 M = 0.20 _ = 8.01°
-2 i I
0
C/2
0
E
Z
i.i0 -4
_2
-6
_0Q -8
-10
I I i I I
I I I I I I
1000 2000 3000 4000 5000 6000
Iteration Number
60OO I I I I i I I
4OOO
2000
,/
m ./
I
/..
/
/
./
: I I I
0 1000 2000 3000
I
7000
I I I !
4000 5000 6000 7000Iteration Number
8000
8000
Figure 37" ADPAC Convergence History, Re = 60,000 M = 0,,20 tx = 9.00 °
41
L)
°v,-I
O
OL)
• v=,,l
1.4
1.3
1.2
I i i I i I I i i
- <>_----o-<>--_<>----
\<>
4"
| --
0.9--
0.8--
0.7--
40.6-- '
t/
0.5-- _
/
0.4 '
I!,,,
0.3 It"
0.2 -!_
t/
0"F
//
/
/
/
0
/' •
o' "oo----_
//
/,o
/
0/
B
\
/
@
t /,, .4.- 4" /
/
t"
'4- ....
' 0
I I ! I I ! I I !
0.03 0.04 0.05 0.06 0.07 0.08 0.09 O. 1 O. ! I
Drag Coefficient, Cd-o- Langley Data, M = 0.05
-t-- ADPAC Calculation, M = 0.20
0,12
Figure 38: Comparison of Measured and Calculated Drag Coefficient versus
Lift Coefficient for Re = 60,000
CHAPTER 4
Propeller Design Using Experimental Airfoil Data
Fundamentals of propeller theory were established by Glauert as early as 1926
(Ref. 11). Primarily because of the absence of computers, solutions of Glauert's
analysis theory could only be obtained after making a number of simplifying
assumptions. While the basic theory has remained the same, Adkins and Liebeck ::,
have recently removed most of the assumptions, establishing iterative design and -
analysis procedures which, with the aid of a computer, can solve for the geometry or
performance of a propeller quickly.
Glauert used a combination of momentum and blade element theory to model
the propeller. In the momentum theory, the flow upstream and downstream of the
propeller is considered to be a potential flow, that is, the fluid is assumed to be
inviscid, incompressible, and irrotational. The propeller is thought of to have a large
number of blades so that it could be represented as an 'actuator disc.' Further,
Glauert assumed that the axial velocity passing through the actuator disc is
continuous, and the pressure over the surface of the disc is constant although it
increases discontinuously after passing through the disc.
Glauert used a blade element theory to get more detailed information on the
performance of the propeller blades. In this theory, flow past any blade airfoil section
is assumed to be two-dimensional and the lift at each section results from the
circulation of flow around the blade. Trailing vortices are shed from the blade and
42
43
passdownstreamin a helicalvortexsheet,andinterferencefrom these vortices cause
the rise in axial and radial velocities through the propeller. Forces on the blade
elements can be resolved, and once integrated over the length of the blade, ultimately
yield propeller thrust, power, and efficiency.
Strip-theories other than Glauert's momentum-blade element theory exist,
differing only in the way in which the induced velocities are found (Ref. 12). It was
Adkins and Liebeck (Ref. 2), however, who published algorithms for iterative design
and analysis procedures in which nlany of the simplifying assumptions were
eliminated. Specifically, Adkins and Liebeck's procedures eliminated the small angle
assumption, and the lightly loaded assumption in the Prandtl approximation for
momentum loss due to radial flow. Their procedures continue to neglect contraction
of the wake. If the vortex sheet is assumed to form a rigid helical surface, the Betz
condition for minimum energy loss will be met. A design will be optimized when
viscous as well as momentum losses are minimized. To do this, the designer should
specify that each section operate at an angle of attack corresponding to the maximum
lift-to-drag ratio.
Adkins and Liebeck give eleven steps describing the iterative design
procedure in Reference 2. Briefly, the parameters specified at the beginning of a
design are: power, hub and tip radii, rotational speed, flight velocity, number of
blades, number of radial stations along the blade, and either a lift coefficient or chord
length distribution along the blade. The program iterates to find blade twist angles,
44
chordor lift coefficient distributions (depending on which was specified in the input),
radial and axial interference factors, Reynolds number, and relative Mach number.
A Reynolds number distribution was specified for the initial propeller designs
(Fig. 39). This ensured that the two-dimensional airfoil experimental data available
to the design program would be representative of the blade sections. The program
used sim,91e conditional statements to apply the experimental data from the Langley
tests shown in Figures 1 and 2. For chord Reynolds number equal to or exceeding
100,000, the experimental data for Reynolds number of 100,000 was used, while the
experimental data for Reynolds number of 60,000 was used if the chord Reynolds
number was below 100,000.
Several designs were produced using the specified Reynolds number
distribution. The propeller diameter and number of blades were varied until the
maximum lift coefficient along the blade did not exceed 80% of the maximum
experimental lift coefficient for the section. For a two-bladed propeller, these criteria
were met when the diameter was increased to 6.8 m (22.3 ft). A 4.6 m (15o 1 ft) three-
bladed propeller and a 3.5 m (11.5 ft) four-bladed propeller also met these
requirements. Of the three designs, the three-bladed propeller was the most feasible.
While there are several benefits to a two-bladed design, the extremely large diameter
required raises manufacturing question, s that would be avoided in the smaller three-
bladed design. The three-bladed design yielded better efficiency than the even
smaller four-bladed design because of the decreased disk loading. Efficiencies of the
45
three-bladedpropeller and the four-bladedpropeller were 85.3% and 81.5%,
respectively. Comparisonsof the propellergeometriescanbe found in Figures40
_ough 42.
Examinationof the blade twist distributionsfor all threedesigns(Fig. 40)
showeda 'hook' in thecurveasthebladewastwistedthroughthe stalledportion of
the lift curve for the experimental data at the Reynolds number of 60,000 (Fig. 1).
Since viscous losses were not minimized in these designs, the three-bladed design
was optimized by relaxing the requirement that section lift coefficient be less than
80% of the maximum and specifying a constant lift coefficient corresponding to the
maximum lift-to-drag ratio point in the experimental data set (Fig. 43 - 44). Blade
twist, chord, lift coefficient, and chord Reynolds number distributions can be found in
Figures 45 through 47. While this eliminated the 'hook' in the twist distribution
(Fig. 40), it was clear that the lift coefficients near the hub would have to be
decreased in order to increase the chordlengths of the inboard sections. The exercise
of refining the hub sections was deferred to the next design trials.
The design studies using the Langley experimental data were useful in several
ways. These studies showed that the specified Reynolds number distribution did
yield a reasonable propeller geometry. With refinement, chordlengths of the inboard
sections could be improved and the hook in the twist distribution curve could be
eliminated. Knowing the Reynolds number and relative Mach number distribution
over the blade would help to account for compressibility effects that were so far
46
neglectedin the presentdesigns. As will be shownin the next chapter,ADPAC
wouldbeusedto makeperformancepredictionsfor theEppler387 airfoil operatingat
thesetransoniclow Reynoldsnumberconditions. Finally, the designstudieswere
usefulin identifying feasiblevaluesfor thepropellerdiameterandnumberof blades.
47
1.6-105 I I I I I I I I
1.4"10 5
"_ 1.2"I05
:::1
Z
1"105
¢D
8" 104
./
//
/
/"/'
/:
.-. //
///
/
//
/
6.1o 4 , I I
0.I 0.2 0.3
//
//
/
,/
/
I l l I0.4 0.5 n
r/Rtip
-,...,.,,
\,.
_ -\
\
I0.7 0.8 0.9 1
Figure 39: Design Reynolds Number vs. Non-dimensional Radial Position
9O
80 D
70--
60--
50--
40--
3O
I i I i i I I I I
<_L,
I I I .
0 0.I 0.2 0.3
_,:-'-...._
0.4 0.5 0.6 0.7 0.8 0.9 1
r/R.tip
-o- Blade Twist Angle, 2 Bladed Propeller, Rtip = 3.4 m
_'- Blade Twist Angle, 3 Bladed Propeller, Rtip - 2.3 m
+ Blade Twist Angle, 4 Bladed Propeller, Rtip = 1.75 m
Figure 40" Blade Twist A_gle (degrees) vs. Non-dhnensional Radial Position,
Designed Using Langley 2-D Experimental Data Only
48
t.,O
0.8
0.6 m
0.4
0.2
I I I I I I I I I
I I
0.1 0.2
.1[ --_" ._.
I I I ! I,
0.3 0.4 0.5 0.6 0.7
-e- Chord, 2 Bladed Propeller, Rtip = 3.4 m r/Rtip
_ Chord, 3 Bladed Propeller, Rtip = 2.3 m
-+- Chord, 4 Bladed Propeller, Rtip = 1.75 m
u
! ! _-LJ
0.8 0.9 1
Figure 41- Chord (meters) vs. Non-dimensional Radial Position,
Designed Using Langley 2-D Experimental Data Only
O
OO
rj
° _,,,I
1.2
0.8
0.6
0.4
0.2
I i I
/ °.
//.,// ." /al_..
._/ . . / / "
I I I
0 0.1 0.2 0.3
i I I I ' ' I I ]
/..-" z<.-_ //
I I I ! I I
0.4 0.5 0.6 0.7 0.8 0.9
r/Rtip
-e- Lift Coefficient, 2 Bladed Propeller, Rtip = 3.4 m
'< LiR Coefficient, 3 Bladed Propeller, Rtip = 2.3 m
+ Lift Coefficient, 4 Bladed Propeller, Rtip = 1.75 m
Figure 42: Lift Coefficient vs. Non-dimensional Radial Position,
Designed Using Langley 2-D Experimental Data Only
50
1.2
1.18
_D0,.._ 1.160
0 1.14
1.12
1.1
I I I i I i I I
I ! ! I ! ! ! !0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
r/Rtip
Figure 44- Lift Coefficient vs. Non-dimensional Radial Position, Three Bladed
Design, Tip Radius = 2.3 m, Langley 2-D Experimental Data Only
90
80
70
60
50
400.1
I I I I i I i i
<>
<>
<>
<><>
<>! ! I ! ..... ! ! I I. °oc_
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
r/Rtip
Figure 45- Blade Twist Angle (degrees) vs. Non-dimensional Radial Position,
Three Bladed Design, Tip Radius = 2.3 m, Langley 2-D Data Only
51
O
L)
0.8
0.6
0.4
0.1
I I i i i l I I
O •
O -O
"oI ! ! ! I ! ! !
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
r/Rtip
Figure 46: Chord (meters) vs. Non-dimensional Radial Position, Three Bladed
Design, Tip Radius = 2.3 m, Langley 2-D Experimental Data Only
1.5' 105 I i I I i i I i
1.10 5
r.,_ ¸
o
_, 1o4
_ loooo
.<>
.............................___o.,_:::i........................................................__.__..._._ooo,./
.0 0
//
I l I I l I l I
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
r/Rtip
Figure 47: Reynolds Number vs. Non-dimensional Radial Position, Three Bladed
Design, Tip Radius = 2.30 m, Langley 2-D Data Only
CHAPTER 5
ADPAC Two-Dimensional Aerodynamic Predictions
ADPAC two-dimensional results were combined with the strip theory design
program in an effort to account for compressibility effects so far neglected. To do so,
the blade was divided into four segments. The specified propeller Reynolds number
distribution and the resulting Mach number distribution were used to identify an
average value of the Reynolds number and the Mach number for each segment
(Figure 48). These values are listed in Table 3.
Table 3. Reynolds Number-Mach Number Combinations
Segment Reynolds Number Mach Number
1 60,000 0.45
2 100,000 0.55
3 100,000 0.65
4 60,000 0.75
The Level 4 computational mesh of the Eppler 387 (Figures 14 and 15) was
used to generate section performance predictions for a range of angles of attack for
each of the Reynolds number-Mach number combinations in Table 3. Surface
pressure coefficients were compared to Langley experimental data that had been
corrected for the elevated relative Mach number using the Prandtl-Glauert
compressibility correction (Ref. 13)
(f_P corrected --"
Cpo
52
53
whereCpo is the value of the incompressible pressure coefficient and M_ is the free
stream Mach number. The pressure coefficients calculated with ADPAC were in
turn integrated to yield lift and pressure drag coefficients. The total drag coefficient
was found by adding the viscous drag component once again estimated by drag on
both sides of a flat plate given by Schlichting in Reference 10"
Lift and drag curves are found in Figures 49 through 52. Plots of the surface pressure
coefficients and corresponding ADPAC convergence history plots for angles of attack
of 4 °, 5 °, 6 °, 7 °, 8 °, and 9 ° are given for Segment 1 in Figures 53 through 64,
Segment 2 in Figures 65 through 76, Segment 3 in Figures 77 through 88, and
Segment 4 in Figures 89 through 100. Where appropriate, the number of supersonic
points at each iteration are included in the convergence history plots.
An examination of the Segment 1 results at Re = 60,000 and M = 0.45 shows
that agreement between the ADPAC calculated values and the corrected Langley data
is generally good. The calculated suction side pressure recoveries are sharper than the
corrected data would suggest for low angles of attack. Just as was seen in the code
validation, ADPAC did not predict a laminar stall at angles of attack between 5.00 °
and 6.49 ° . For angles of attack between 7.51 ° and 12.00 ° , there appears to be
periodic shedding of the separated shear layer, similar to that reported by Pauley, et.
al. in Reference 4. Figure 101 shows the pressure distribution over the airfoil at an
angle of attack at 8.01 ° and the streamlines shown in Figure 102 for the same
54
conditionindicatemultiple separationandreattac_ent points nearthetrailing edge
of thesuctionside. Theseresults,aswell asall of theotherADPAC resultspresented
here,arenot time-accurate,but representthe steadystateflow solutionachievedwith
local time stepping.Thelocal time steppingtechniqueadvanceseachcell in time by
an incrementequal to the maximum allowabletime step for that cell. Generally,
largercellsawayfrom aboundary,layerwill havealargertime stepthansmallercells
closerto asolid surface.
Examinationof the resultsin Segment2 for a Reynoldsnumberof 100,000
anda Machnumberof 0.55showsthattherewasalsogenerallygoodagreementfor
anglesof attackrangingfrom -2.88° to 4.00°. Shockwavesnearthe leadingedgeare
seenin theADPAC predictionsfor anglesof attackgreaterthan6.00°. Full stall is not
predictedat 14.04°. The Prandtl-Glauert correction is inadequate for these conditions
and an experiment would be needed to validate these predictions.
As Mach number is i_creased from 0.55 in Segment 2 to 0.65 in Segment 3,
more differences are seen between the corrected experimental data and the ADPAC
predictions. Shock waves are seen for all angles of attack above 3.00 ° , and like in
Segment 2, full stall of the airfoil at 14°04 ° is not predicted by ADPAC.
Representative of the tip sections, Segment 4 with a Reynolds number of
60,000 and a Mach number of 0.75 shows gross differences between the corrected
Langley data and the ADPAC predictions as would be expected from the inaccuracy
of the Prandtl-Glauert correction at these conditions. ADPAC solutions indicate that
55
theairfoil is unableto producea strongleadingedgesuctionasaresult of the shock
wavesseenateveryangleof attack.
56
1.5 I ' l i i • _. I I 0.89i1.4-- 0.25 + 0._5 + --
..
: d- -I-1.3-
.p1.2-
1ol- -+ [Segment2 ] [Segment3 ] _
........................................................................................................... + .......... -_0.9-- +
n
.......... 0 .....
-Isegme°t'i
........ 0 .....
@
^ _.00
-I-ra
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0I ! I . I I !
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
-O- Relative Mach Number
+- Reynolds Number/100,000
Figure 48" Segmented Reynolds Number and Mach Number Distributions
:: .: :: : :.:::_::.:i:i ..... ._: =============================
57
4,..t
_D.vu{
O
(D
1.4
1.3
1.2
l.l
l
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0--"
"-0.1
I I i I i I
>{ " 0/"/
I Ol /
//.. .. I" -
//_< d" _"".- t-/
/ y,- +1-/_ // ./
,,." ,_
,, .,," _%>
/ o_
//
•• /_//
•• _i///
t, '" L /
¢
.//_
///'/
//
//
/
/" O/"
// o .,-.........
-/'O00. ,// " /
/ _ /":." o
..
o.__.
I
//
o I I I I I--4 --2 0 2 4 6
cz, angle of attack, degreeso Re =60,000M = 0.2
LeastSquaresPolynomialFitofRe = 60,000M = 0.2Re =60,000M = 0.45
_ LeastSquaresPolynomialFitofRe =60,000M = 0.45* Re = 60,000 M = 0.75
.... Least Squares Polynomial Fit of Re = 60,000 M -- 0.75
I I8 10
Figure 49: Comparison of ADPAC Predicted Lift Coefficients at
Re = 60,000 and M = 0.20, 0.45, 0.75
_ : : ::?-: _: ":: Y::: :_ : " ?::_::::::- .... :/": :"/:Y ,, /:i_ i: ::i : :71:?!: I::I:::i:UZI_:I:L ::i:?:!?:::.... I"Y!:::!::¸ "_i:::::i:L U::III!:I:":i:::Y::Z_:::I__L:;: :?Z:i:iG::!!_ii_i_:_!:i/i:!::!!::i:!:!:!:::L:::!:i::ii:!_::?::iiii::!i!i;::¸::!:::ii:::Z:ii!:_:::::_:_::'::i::_:::::::i::::::_
58
C
t,-m
0.18
0.16
0.14
0.12
0.08
0.06
0.04
0.02
-4
I-
I I8 I0 12
I I I I I"2 0 2 4 6
or, angle of attack, degreesRe = 60,000 M = 0.2Least Squares Polynomial Fit of Re = 60,000 M = 0.2Re = 60,000 M = 0.45Least Squares Polynomial Fit of Re = 60,000 M = 0.45Re = 60,000 M = 0.75
' Least Squares Polynomial Fit of Re = 60,000 M = 0.75
Figure 50: Comparison of ADPAC Predicted Drag Coefficients vs Angle ofAttack at Re - 60,000 and M = 0.20, 0.45, 0.75
59
¢)-v.-¢
¢)O
°_
1.4 I I I I I I
0.7
0.6
0.5
/ ,,,/
,,I/./ ,,
_I ,//"/:/
/
/,{
//
//
I /N:'
//
// /
o Re=I00,000M=0.55
I I I I4 6 8 I0
or, angle of attack, degrees
Least Squares Polynomial Fit of Re = 100,000 M = 0.55)< Re = 100,000 M = 0.65
Least Squares Polynomial Fit of Re = 100,000 M =0.65
\\
Figure 51" Comparison ofADPAC Predicted LiftCoefficientsat
Re = 100,000 and M = 0.55,0.65
60
O
O
0.2
0.18
0.16
0.14
0.12
0.08
0.06
0.04
0.02
I I' I I I I I I I
//
X /,,
/ .....(>
/ ,/
/ /.
/L,. '°.._
! I I I ! I I,
-4 -2 0 2 4 6 8 10
(z, angle of attack, degreeso Re = 100,000 M = 0.55
Least Squares Polynomial Fit of Re = 100,000 M - 0.55
Re = 100,000 M = 0.65
-- Least Squares Polynomial Fit of Re = 100,000 M = 0.65
t/
/
//
/
/ o/:
///
//.
/:
///
/./
o .,/o./
/"
/
/.
!
II
II
//
/
/
//
//"
/'
/
.'/.
,/
I I12 14 16
Figure 52: Comparison of ADPAC Predicted Drag Coefficients vs Angle ofAttack at Re = 100,000 and M = 0.55, 0.65
61
I I I I I I I i I
! ! ! I ! I ! ! ! '
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 I
O Corrected Langley Data
ADPAC Calculation, M = 0.45
X/C
Figure 53- Pressure Coefficient vs. Non-dimensional Chordwise Position,
Re = 60,000 t_ = 4.00 °
I I I I I I I I i
I I I ! ! I ! I !
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0 Corrected Langley Data
.... ADPAC Calculation, M = 0.45
X/C
Figure 54" Pressure Coefficient vs. Non-dimensional Chordwise Position,
Re = 60,000 tx = 4.99 °
62
I i I I I I I I I
_0 0 0> 0 0 0 0 0 0 0 0
o_om
0 0 0 0 0
__.
9_ ....0 0 __0 ....O_
0 0
O:......0---
I I I I I I I I I J
O.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0 Corrected Langley Data
ADPAC Calculation, M = 0.45
X/C
Figure 55" Pressure Coefficient vs. Non-dimensional Chordwise Position,
Re = 60,000 _ = 6.01 °
I I i I I I I i i
--_.._
--0.....0 ....0 ......0 ......0 --0 ...0- 0 0
0
O_ 0 O_ 0 0
_ _---^_-e_------_-_O-----O----0--0- -0---70-- 0----0---0---0 --0 "-_- :-__ V V V V --
I J........ I I I I I I I
0 0. I O._ 0.3 0.4 0.5 0.6 0.7 0.8 0.9
O Corrected Langley Data
ADPAC Calculation, M = 0.45
X/C
Figure 56: Pressure Coefficient VSoNon-dimensional Chordwise Position,
Re- 60,000 ct = 7.00 °
63
-5 I I I I I l l I I
0......0__ 0
-----0-----0-_0_._0- ',0 0 -_| i-,- \\ . . _
"'' 0 " \ /0
o- ,.° °""° "/° ° o°
_o-o---°--°--°--°--° ......o......o--o- --o--o -o--o-_o-'-o---o-- ---I u
2 I I I I I I I I I0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
o Corrected Langley Data
ADPAC Calculation, M = 0.45
X/C
Figure 57 • Pressure Coefficient vs. Non-dimensional Chordwise Position,
Re = 60,000 _ = 8.01°
-5 i I i I i I I I I
--4
--3 _
-2 -- ----..... --..... "'" 0
- | -- _ .f"_"_"- --
0- o_ o \o /o_o_ o..8......--¢_......O---0 ....0---0 ....0---0---0- .....0-- 0----0-----0-----0....._ 0-- -0....0
2 I ! I ! ! I ! ! I0 0.I 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
o Corrected Langley Data
ADPAC Calculation, M = 0.45
X/C
Figure 58" Pressure Coefficient vs. Non-dimensional Chordwise Position,
Re- 60,000 cx = 9.00 °
64
0
f._
r./2
.,.,,,,i
o -6
i I I I i I
I I I ! I I ! !
500 1000 1500 2000 2500 3000 3500 4000
Iteration Number
4500
3000
2000
1000
I I , _.._ I I i I I I..... .
.
- //
/
/
/
/ -._ -- _ - -._,__Y
,; J
0 500
-..._
I I I I I I I
1000 1500 2000 2500 3000 3500 4000
Iteration Number
4500
Figure 59: ADPAC Convergence History, Re = 60,000 M = 0.45 c_ =4.00 °
t/-Ir.,o -4
_o -6O
-8
4OOO
t_
1.4
..t_ 2000
Or)
I I I i I I i I
it
I
0 500
I_'_............. __.._.. ,,---... , .
_ __ ...... _,' _ ..... ,--_, _,,..........................................
I I I I I I
1000 1500 2000 2500 3000 3500
Iteration Number
I ! I I i I i i
I
4O00
//
/
/,/
,/
/
4500
,_ I ! I ! I ! I !
0 500 i000 1500 2000 2500 3000 3500 4000
Iteration Number
4500
Figure 60: ADPAC Convergence History, Re = 60,000 M = 0.45 a =4.99 °
65
gr-Io'2
O,
-g_o
CCJ
4000
2OO0
I I I I i I
\\
\\-.
I2OO
I400
I I600 800
Iteration Number
! I
1000 1200
I I I I I I
.I-"
::I
/7 /f
p-
//:
/
/..i:
/- ....t
00 200 400 600 800 ! 000 1200
Iteration Number
1400
1400
Figure 61" ADPAC Convergence History, Re = 60,000 M = 0.45 Gt=6.01°
t-.O
I=: -4
O
-6
4000
c_
L_.
2ooozg.
r._
I I I I I I I I
I
.-_.o
.",'. -.-.- .........................
I ! I ! ! ! ! !1000 !500 2000 2500 3000 3500 4000
Iteration Number
0 500 450O
I I I I I I I I
--.--. _
,, ----- _....._.,_,_ ._
/.
t/
//
,/
/t
/
/XA ...... 'f
,:I I I I I ! I I !0 500 1000 1500 2000 2500 3000 3500 4000
Iteration Number4500
Figure 62" ADPAC Convergence History, Re = 60,000 M = 0.45 tz =7.00 °
66
O
I.r-1r./2
O
_0
O
-2 I I
I I !-8
0 500 Io00 1500
I i I I I
r--. _--
I ! I 1
2O00 25000 3OOO 35OO
IterationNumber
4ooo
4000
I-,
2oooO_
n
..,
/
,/
i: ":._''' " "-
0 500
I I
/
i i I 1
.-.
I I I ! I 1
1000 1500 2000 2500 3000 3500
Iteration Number
4000
Figure 63" ADPAC Convergence History, Re- 60,000 M = 0.45 c_ = 8.01°
O
I::
O'2
O
O
-3 i 1 I
m
!.,.
TL
I I i I I
I I I-70 500 1000 1500
t. .....
I ! I ! !_
2000 2500 3000 3500 4000
Iteration Number
4500
L..
Z _ca,
r,t)
6000
4000
2000
0
I I I
i' _''.--, ...... ,
f "-,..
(,,,,,'
I"
J
/
--._..
I I I I I
I I I I I I I I
500 1000 ! 500 2000 2500 3000 3500 4000Iteration Number
45oo
Figure 64- ADPAC Convergence History, Re = 60,000 M = 0.45 tx = 9.00 °
67
-3
-2
I I I I I t i i i
I I I I I I I I I0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
O Corrected Langley Data
ADPAC Calculation, M = 0.55
X/C
Figure 65" Pressure Coefficient vs. Non-dimensional Chordwise Position,
Re = 100,000 tx = 4.00 °
L)
-4-
-3
-2 t..-
"1
o
1
I i I I i i I i 1
-0---0 ....0 .........0 .....-0-_-_0 .__/
7 o o
.......... O__ 0 ....
00_-0---_0----0 0 0_0 0 0------0---0_-----0 ---0
0 0 --0----0 --0 0 --_0- -
l l l I , l l l l I I
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 I
X/C
m
m
!i
0 Corrected Langley Data
ADPAC Calculation, M = 0.55
Figure 66: Pressure Coefficient vs. Non-dimensional Chordwise Position,
Re - 100,000 tx = 5.01°
68
I I I I I I i i I
o o
I I I I I I I I I
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
X/Co Corrected Langley Data
ADPAC Calculation, M = 0.55
Figure 67: Pressure Coefficient vs. Non-dimensional Chordwise Position,
Re- 100,000 ct = 6.00 °
I I I I I I I I I
_210%OOOo O --0
•--o....o....o ......o-_o ,, o--| _ -..._
o
- .o ....o- --o -o -o . o-o ---o- -0-
o------°----(r---°---°_-°----°_--°---:° _-o----o-- o----o---_ ....o- -o--o- -............oO
2 .............. i ....... I I I I I I I !0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
X/Co Corrected Langley Data
ADPAC Calculation_ M = 0.55
Figure 68- Pressure Coefficient vs. Non-dimensional Chordwise Position,
Re = 100,000 tx = 7.00 °
69
I I I I I I I I I
-,0
......___.o.....o o o
o- __o____. ° _o-.._o_o_
--¢).....o---O-----O.....0----0---0-- 0---0-- "-0---0-- --0-----0--0
0 .....0.-__0-----0 ---0 -
I I I I I I I I I I
0 0. ! 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
X/Co Corrected Langley Data
ADPAC Calculation, M = 0.55
Figure 69" Pressure Coefficient vs. Non-dimensional Chordwise Position,
Re = 100,000 cz = 8.00 °
-5
-2'-"
0--
1
I I I I I I I I I
"0
.....o o --oo
o-o
o
... o _..o._ o. -o_ --o_ -o_ --oo- -o ---
-.._-^----^----¢,,.----o---o---o---o- -o-- o----o----o --o .---o--_ v vv--
I I I I I I I I I
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
o Corrected Langley Data
ADPAC Calculation, M = 0.55
X/C
Figure 70" Pressure Coefficient vs. Non-dimensional Chordwise Position,
Re = 100,000 t_ = 9.00 °
....... :> ::: :: : :: ..... :::: ........ :'? .... .... • • Y!:/:;i, _ • • Y: .... ?!Y , :Y i:: ¸.:: ¸: : ......... ::!:::::......... : ::::::yi ¸,A:>::Yi:i!?::,:i.>; :::::/: :!:::::II:I::U̧ ?i:::::::::!:?::!i::(i/::i:Y:::,!!:::i::i:::!:::¸!!i:::ili:::il/,!!/:!:i!Y:::!i!::!i!:iii::::::::i:::::!:hli:!
7O
0
Q
I I I I I I I
I I I I I I I
500 1000 1500 2000 2500 3000 3500
Iteration Number
4000
Z _t_
r./2
3000
2000
lO00
I I I I I I I
//i
/
/
/
/
,-?...... I I l I I I i
0 500 1000 1500 2000 2500 3000 3500Iteration Number
4000
Figure 71" ADPAC Convergence History, Re - 100,000 M - 0.55 _ - 4.00 °
I--4O
r.P2
_U2O
-6
I I I I I I I
m
L]i
o.,
...... ----,-........
'_.,__ '-_ .,,.._ ../
! I I I ! 1 I
500 1000 1500 2000 2500 3000 3500 4000
Iteration Number
ta_
3000
2000
1000
I I I I I I I
//
/
//
//
/
_L I I
0 500 1000
I I I I _L..._
1500 2000 2500 3000 ."__,00 4000
Iteration Number
Figure 72" ADPAC Convergence History, Re = 100,000 M = 0.55 c_ = 5.01°
71
i.,,o
-21 i I i i i i Iu,.] L
° •-8 I ! I I I I
,I. ,4000.
400 I I i i i i i=
OL.
._'_ 200 ;_,,,
0 "" I I I I I I I.1., .4000.
400O I I I I I I i
_._O '
_,., /_'-----.
.__ 2000 ,, .................................
Z o'J ,/
m I ! I ! I I I0
0 500 1000 i 500 2000 2500 3000 3500 4000Iteration Number
Figure 73" ADPAC Convergence History, Re = 100,000 M = 0.55 cz = 6.00 °
-2 I Ii..,O
-4
-6 _.,.--, .... _ ..... _. _ jr--
O
-8 I I,.lj
.,..,=
°,.,
r_
I i 1 I I
I ! ! ! !
IO00/ I I I I I I
k500 /..__i "_
o I ""I f I ! \r -/,-L
.400q
.400(
_l 4000] I i I i I I I
_ 2000 // ....... "- ...................
O '
m i ! I I I ! !0
0 500 1000 1500 2000 2500 3000
Iteration Number3500 4000
Figure 74" ADPAC Convergence History, Re = 100,000 M = 0.55 _ = 7.00 °
¢,q
.._=
lt
i -F1
'L
t
/
I
1it -J
o"OO
......... i ...........
'h/
.,r
../"
'k.,
),,
I
,
"-,..)
/
.=_ ¢
/
_.j _
_<t .....q ...... I --0
0 0
_°-u_ISPf'd01 i_°q s)u!od 0!uosaodnsjo aoqtun N
O
t
\,
1
t
("
_ 1 ..
/)
/f'
\.
° § °oo
slu!od pole.led:) Sjo JoqtunN
Oot¢-)('-4 l,=.
(1.)
E
Z
§._gg.=(1.,)
.....
oo
0
00
II
It
e-,
II
o
Im
o
.<
<oo
om
]
I -
?
i -?
._:
[I
1
./.<
_ i,,-"I
a0aa/tSI,kr'dOI _0q
..... •
1'
// .-
//i
- [ -
\
/"1)
- I -/.
- 1 -
(.
0 0 0 '_
slu!od o!uos_adnsjo aoqtun N
r
/m
/
¢t
f
\
/
o o o
slu!od p01eaed0s20 aoqtunN
ooo 0
".
o
o
(I.)
E= II
t-0._
t... "--
o.4,,,,,)
._-
e_
o
- ¢D;;).
OL)
o
w-)
o®
¢D
0.0
73
-5i i i i i i i i i
_CCO0 0 ....¢ _ _0=____ "
> , " o o/ o
/- 0 O --
o o o --o o o------o--o--o------o--o--o--o--o--o--o - o o --:--_--_
I I l l I l t l I
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0 Corrected Langley Data
ADPAC Calculation, M = 0.65
X/C
Figure 77: Pressure Coefficient vs. Non-dimensional Chordwise Position,
Re = 100,000 ct = 4.00 °
I I i i I I I I I
-3-
-2 _
_¢oo oo---o
-| - /
/
/
0-
/6>0_0 0 0 0
1>
0 0 "\0 0 0 0
..--. __
.-- _ ___
-0 ....0 0 ....0__--
0 0 "---0 0 0 0 0 0 0 O-- -0-------0_0 ....0-'--0-
I I I l I l I t I q
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0 Corrected Langley Data
ADPAC Calculation, M = 0.65
X/C
Figure 78- Pressure Coefficient vs. Non-dimensional Chordwise Position,
Re = 100,000 ot = 5.01°
74
-4"-"
I I i ! I I I i I
-_O_o O
_- ...... --_
/
--/
>,/
. " ..\_
0 0 _0 0 0 0 O
\,_/': 0
..........-- -0 . 0-- -0- -0 ....O- 0 ....
0 -_----0 0 0 0--0---0_0 ----0-_0-" 0 0 0
I l
0.1 0.2
I I ! I I ! I
0.3 0.4 0.5 0.6 0.7 0.8 0.9
X/Co Corrected Langley Data
ADPAC Calculation, M = 0.65
Figure 79- Pressure Coefficient vs. Non-dimensional Chordwise Position,
Re = 100,000 o_= 6.00 °
-5 I I I I I I I I I
-4
- o_ _ o_ --0 0 ......0--7_-
0 ' 0--0-----0-----0_- 0 0 .....0--
-3
-2 / 0 0 0 0 -0 0 0 • 0 0 0 0
'" ....0 -0_
..---_-o---6_,__o -0 o-- o o o o-....._._ :
lr_O_" _ i ......
2 I I i i I I I
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
o Corrected Langley Data
ADPAC Calculation, M = 0.65
X/C
Figure 80- Pressure Coefficient VSoNon-dimensional Chordwise Position,
Re = 100,000 tx = 7.00 °
....... . : ..... ...... :: .... : : ::: :: :: :... : : : : : . ..... ..... . .... ::: ..... , ......: :: : _ . :::: :: :::: : .: :: ::: ::::::::::::::::::::::::::::
75
-5 I I i I I I I I I
-4
.... -....... -----_____._O___O_ -i / o
,......
(_<:_0 0 0 0
0 0
00
0.................. 0 o
o°---°- o
0 O----_---<S ....o-- o ......o --o- -o- o _ o
I I I I I l I I I
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
o Corrected Langley Data
ADPAC Calculation, M = 0.65
X/C
Figure 81" Pressure Coefficient vs. Non-dimensional Chordwise Position,
Re = 100,000 _ = 8.00 °
I I I i I I I I I
>
0
-%_oo
m
o0 -"'0"
o'- 0
-" 0
_o o o o o o o o o
oo o
.... 0._o__o__
o ---o.....-0-- o-- o----o- -
0 0 - 0 ---_
-0....0 0 0
I I l I I I I I I
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
o Corrected Langley Data
ADPAC Calculation, M = 0.65
X/C
Figure 82- Pressure Coefficient vs. Non-dimensional Chordwise Position,
Re = 100,000 o_= 9.00 °
76
,. -2 I
r_ -4 __
-6
O
-8,.1,
i I I
! I I
25OO
i i
! I25oo
4000 I
t,.,
_ 20oo s _---_
¢') "'J' ]r/_ 0 "
500
_ -._../ ----..
i I i
I ! I1000 1500 2000
Iteration Number2500
Figure 83" ADPAC Convergence History, Re = 100,000 M = 0.65 ¢x= 4.00 °
I,-4O
I=tzd
Q
I I I I I I I
! ! ! ! 1 I !•4000,
o
"_ot_G,)
2000 [ I F I I I |
c,--.,,
1000 .......",___._j_.._j..-.."-,-...._J"........_ .........._,._-...._._j.-_..__....... ...........--.
o I I I I I I I•1, •4ooo.
_.)
ra_
4000 I I I I I I I
,,.._._J'-- _,.._.,/_'".,..._.__ -......._ __.. . ....-,
2000 .t"c -''" ';'(.... ".......... "--_'" ............. "-""........_
0 I I I ! ! I I0 500 1000 1500 2000 2500 3000 3500 4000
Iteration Number
Figure 84: ADPAC Convergence History, Re = 100,000 M = 0.65 ct = 5.01°
..... I .... 1.........
i
i3
I/
I -
/!
r--"
g¢'4
i .... o°
f
(
t-
aoaa_tSI_ OI i_0l s]u!od o!uosaodn S slu!od po]_aedosjo aoqmn N jo aoqtun N
t__D
E
z
o.=og.
0
_D
II
_D
il
II
o
o_
¢D
g_
o00,<
,<oe
g0
00
i-!
!
IIi
!
_J
)?
o"00
0
I o
/
1
JoJJ] SIAr_0I go1 slu!o d o!uosa0dns s]u!od po]_a_dos3o aaqtunN jo aoqtunN
0
r-:II
_D
0o II0
¢'q _D
z II
t_
o
- :=
0
o0o 0
0,<
,<
g0
1,1
._
O'Qt_
OOOOoo
_p
¢3¢3
et_
mmo
o
,,B
¢'D
II
II
oxLXa
II
O
_g
=z
C_"t,,}
Q
O
NumberofSeparated Points
Number ofSupersonic Points
Log 10 RMS Error
l-
I-
/i-
fi-
l)
0
0
!
i
f,o
0
o0
/,/il
I
1
I
,.
I
i.
o•
mm_•
II
II
II
0
_ o
xg
g
Number of
Separated Points
| _ i ....
Number of
Supersonic Points
0
m
m
,-..0
0
I
"1
(
t_/
........ l .....
Log 10RMS Error
I i
,.,,,...
.,,.,
....l .............lm
oo
79
-5 I I i i I i i I I
-4
-3
-2
_<>oo ......?........°-_>-_ ....c--o--;_o--_.o___o....-, o_ <>o- O
0 ;'_ ...... ----- -O-
"-0_0 0 0_0----'0----0_---0- -0--0--0- --0-- 0 --00 0 00
2 I I I I I ! I ! !
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
O Corrected Langley Data X/C
ADPAC Calculation, M = 0.75
Figure 89" Pressure Coefficient vs. Non-dimensional Chordwise Position,
Re = 60,000 tx = 4.00"
I I I i i i i i I
7>
/
"7
°--0 o o
o 0 0 0
0 0 0 0 o. 0 0 0 0 0 o o o_,
_.
0 _-0---0---0--0- --0--0--0---0 0 -0 --
, I I i I I I l I I
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
O Corrected Langley Data
ADPAC Calculation, M = 0.75
X/C
Figure 90: Pressure Coefficient vs. Non-dimensional Chordwise Position,
Re = 60,000 t_ = 4.99 °
80
-2
I I I _ I I I i I
_0> ..........-.... "0--_-00
>
[;
0 0 0 0 0 0 ....0 0 0 0 0 0
o---o-----6---o----o_o---o--o--o---o---o- -o....o ....o.--o
l I I I I I I I I
0 0.1 0.2 0.3 0,4 0.5 0.6 0.7 0.8 0.9
o Corrected Langley Data
ADPAC Calculation, M = 0.75
X/C
o o
o "-o-:-_
Figure 91" Pressure Coefficient vs. Non-dimensional Chordwise Position,
Re = 60,000 t_ = 6.01 °
-2
I I I I I I I I I
i __ 0 0 0 0 0 0 0 0 0-! --'-f .... - ........ 0
V ...."...._ - -0---0--_- -0
0 .....o-
I___oo o o o o o o
2L,. ! ! ! I I 1 ! ! !0 0.1 0.2 0.3 0.4 0,5 0.6 0.7 0.8 0,9
o Corrected Langley Data
_- ADPAC Calculation, M = 0.75
X/C
Figure 92" Pressure Coefficient vs. Non-dimensional Chordwise Position,
Re = 60,000 t_ = 7.00 °
oo
_0o
o o
,<>o
o o
o o
0 oi
O_ 0
0 0
/
° !o
/o
o
o
-" " I ' 'I' I..... I .... |..... i ............
oo
o o
o
? o!
o
oj o
og
/
0
0 --"
0
o
0
o I o- o l o -
J , I 0
oP°̂°°_ J _::::::::::,...........-A'___
0
0
0
0
(-,,.
II
>.,,.o
o_O_
o 0
0om
o_
o
Im
o
oo_
0
E_o_
o
o_
Deml
_Do_eo
o
t_
t_
De
o
II
II
---Itji
g_II
_D_D
O
o
oo
o
oo
o
oo
_g0
z
_-go
o
Number of
Separated Points
Number of
Supersonic Points
to .1_
g
ii -
l-
_ I ......... g
to
oo
g
Log 10RMS Error
d,I
/J
/
-//
I
De
_DtJIee
¢3o
t_
_mle
o
II
II
--dLXl
II
O
o
g
g
N,-.,,
'-.I
__.
0
z
'-1
t_
g-Q
O
Number of
Separated Points
0 00 00 0
I0
0
Number of
Supersonic Points
....,
g
i
tti
g
Log 10RMS Error
I
Il
-IJ
ooIx9
Imme
t_kDO0ee
0"Q¢'D
t_
lame
oml
t_
II
II
...dL#I
g_II
",,4
O
0
--t
z
-'I O
Number of
Separated Points
l,d
Q0
1
I
,,
¢
(I:L
(?
_ 1i
J
(1
_______1______
Number of
Supersonic Points
o
............I!
..,,-
r
Log 10RMS Error
oo _, £.
f
t..¸
m
,,
.,
.,
...
..
ee
_,
_m
II
II
II
0
a"
z°
Number of
Separated Points
I
t1_
J ._
........... _ | ,,
oo
Number of
Supersonic Points
..... i .... ,
;. ; | ..............
Log 10RMS Error
oo
I
1 ,., i
ooL_
-a'-oo
I I ¸,' ¢_ IO
.I
... ._ ...
: I,
[ ',
t., t
(.,, _ ,,,p 0o _ g o
i0.I.I_[ S_ 0 [ _0"I slu't°d °!u°s't°dnsjo J0qmnN
m
I I
L
i
J
l-- i
]
f
0 0 0 00 0 0
slu!od poleaedosjo Joqtun N
1-
°_t/%t"q
x
¢...,
O t-0,2
eq --
o
odII
It3
i
II
_D
II
o
ella
_D
1,1_D
OL_L_<
o •
o_o_
t_J0ellm
I
J
t
.
O
oo
........ I :: I ....... i...... "--- o
i
I
L
r
I
i
nI
I'
,r
../.
o o
¢,,,i ,,-,
gL.¢J
E
oxo I::::
_.o_¢'3L..¢J
_0LI;:[ S_[_[ 0[ _°'I slu!od o.tuosJodnsjo aoqmn N
slu!od poleJedosjo Joqtun N
O
i
Ox
It
It%
II
o.,
_D
II¢.2
1,1O
ollm
_D_J01,1
L_L_.<
.<oe
_D
emll
85
Figure 101- Pressure Distribution for Re = 60,000 M - 0.45 cx= 8.01 °
Figure 102" Streamlines Over the Suction Surface of the Airfoil,
Re = 60,000 M = 0.45, _= 8.01 °
CHAPTER 6
Propeller Design and Analysis Using Two-Dimensional ADPAC Predictions
The designs in Chapter 4 using only the low speed Langley data neglected the
effects of compressibility. Even the Prandtl-Glauert compressibility corrections are
inadequate for the tip sections. To account for the compressibility effects, the
resulting lift and drag curves for each of the conditions listed in Table 3 were
incorporated into the strip theory design and analysis programs (Figures 49 through
52). Again, simple conditional statements were used to apply these predicted values
along the length of the blade.
The first design exercise was to see what effect elevated Mach numbers would
have on the propellers designed using only the Langley experimental data. Keeping
the number of blades, diameter, and Reynolds number distribution the same as was
used for the initial designs, new designs were made. The new twist, chord, and lift
coefficient distributions can be found in Figures 103 through 105.
Examination of the twist distribution still show a 'hook' near the tip. In these
designs, though, this 'hook' results from the degradation in performance as Mach
number is increased, rather than from the laminar stall found in the Langley data at
low angles of attack. Efficiencies of the three and four-bladed propellers using the
ADPAC predictions were 80.3% and 76.4%. These values are roughly 5% less than
the efficiencies predicted for the low speed designs using the low speed Langley data
alone.
86
87
To optimize the design, a lift coefficient distribution asymptotically reaching
the average maximum lift-to-drag ratio point along the blade was specified (Fig. 106).
This was done to increase the chordlengths of the inboard sections, as was seen to be
necessary in Chapter 4. The resulting propeller twist, chord, Reynolds number, and
relative Mach number distributions can be found in figures 107 through 110.
Efficiency for this propeller at design point was 85.1%. This propeller was
considered to be the final design.
The strip-theory analysis program was used to generate off-design propeller
performance predictions for the final design. Input to the analysis program includes
the propeller geometry, advance ratio, pitch angle, cruise Mach number, and altitude.
The program iterates to find the induced velocities and induced angle of attack. From
this information, the lift coefficient distribution along the blade can be found and
propeller thrust, power, and torque coefficients as well as efficiency can be calculated.
Among the many tests of programming integrity, performance calculated by the
design program should and did exactly match that calculated by the analysis program
at design point.
The off-design performance maps were created by changing the advance ratio
and pitch angle of the propeller. Variations of the propeller efficiency, thrust, power,
and torque coefficients for a range of pitch angles are shown in figures 111 through
114. At design point, the value of the advance ratio is 1.814 and the blade twist angle
at the 75% radial position is 42.52 ° .
88
Examinationof theoff-design performance curves for the propellers indicates
that there may be some merit to operating the propeller at a slightly higher pitch angle
than that at the design point. While maintaining the design advance ratio of 1.814,
increasing the pitch angle so that the angle at the 75% radial position is 45 °, a 25%
increase in thrust can be realized for a penalty of 5% in efficiency. Operating at this
point may be desirable if sufficient engine power is available. Increasing the pitch
setting past this point may not be recommended since the blade begins to stall when
the angle at the 75% radial station reaches 50 ° as shown in Figure 115. To decrease
the advance ratio while maintaining a constant cruise velocity may not yield the
predicted increase in thrust since as tip speeds increase, shock waves will affect a
larger portion of the blade degrading perfo_ance. A comparison of the design point
conditions and those for this high thrust case can be found in Table 4. Actual
performance for both cases will vary from the predicted values as the blades twist in
operation. A structural analysis would need to be conducted to understand the
propeller's performance more fully°
89
Table4. Comparisonof theDesignPointandMaximumThrustPoint
Efficiency
DesignPointPitchAngleat 75%R=
42.52°
0.8509
Maximum Thrust Point
Pitch Angle at 75%R =
45.00 °
0.8107
Thrust Coefficient 0.1411 0.1780
Power Coefficient 0.3007 0.3983
Torque Coefficient 0.0479 0.0634
Thrust
Power
Torque
450.9 N
(101.3 lbs)
63.4 kW
(85 hp)
703.7 N-m
(519.0 ft-lbs)
1.814Advance Ratio
569.0 N
(127.9 lbs)
83.9 kW
(112.6 hp)
932.1 N-m
(687.5 ft-lbs)
1.814
90
8O
7O
6O
5O
4O
30'
i I I
.-...
-...\
I I I I I I
I I I I I I I0 0.1 0.2 0.3 0.4 0.'i 0.6 0.7
r/Rtip
-o- Blade Twist Angle, 2 Bladed Propeller, Rtip - 3.4 m
_ Blade Twis Angle, 3 Bladed Propeller, Rtip = 2.3 m
-+ Blade Twist Angle, 4 Bladed Propeller, Rtip = 1.75 m
! I0.8 0.9 l
Figure 103: Blade Twist Angle (degrees) vs. Non-dimensional Radial Position,
Designed Using ADPAC Predicted Values Only
I-iO
r..)
0.8
0.6
0.4
0.2
I I I I I i I I i
-_- Chord, 2 Blade<_ Propeller, Rtip = 3.4 m
_ Chord, 3 Bladed Propeller, Rtip = 2.3 m
-+- Chord, 4 Bladed Propeller, Rtip = 1.75 m
! I I I
0.3 0.4 0.5 0.6
r/Rtip
I !0.7 0.8 0.9
Figure 104: Chord (meters) vs. Non-dimensional Radial Position,
Designed Using ADPAC Predicted Values Only
\
\.\ ,, ,\
-.,
..
- III
u.
!.
', ,
_._-__
R', I
J,u0!0K40OD _,2!'1
¢:h _c,i,-;"._ II II II
d
O O O
888
o ,._t
0em
em
o
m
@om
ellll
@
em
E@
ellll
Ii
em
o
OO
O
O
¢.qo
o
O
f_
oelm
em
O
m
em
¢d
L_
em
em
92
80
70
60
50
40
<>I i I I I I I I
\O\
""O-
" O L.,_.
! I30 I ! ! ! I !0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
r/Rtip
Figure 107: Blade Twist Angle (degrees) vs. Non-dimensional Radial Position,
Designed Using ADPAC Predicted Values Only
O
L)
0.8
0.6
0.4
0.2 - <>
0.1
I I I I I I I i
O-- O ........O ........... O .....
I .... ! ! ! I I !0.2 0.3 0.4 0.5 0.6 0.7 0.8
r/Rtip
I0.9 I
Figure 108: Chord (meters) vs. Non-dimensional Radial Position,
Designed Using ADPAC Predicted Values Only
93
,.Q
1.51050
.
I I i
\.
0
1.105
o0
_:_ 5.104 0
I ! I ! I ! ! I0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
r/Rtip
0.|
\\
\
\t>10000
O
6000
Figure 109" Reynolds Number vs. Non-dimensional Radial Position,
Designed Using ADPAC Predicted Values Only
2:
0.8
0.7
0.6
0.5
0.4
I i I I i i I 1
rio_O _
A
,_I-O .... _J I
0.l 0.2 0.3
O
O
/
fJ
I I I I ! !0.4 0.5 0.6 0.7 0.8 0.9
r/Rtip
m
0 o0
Figure 110" Relative Mach Number vs. Non-dimensional Radial Position,
Designed Using ADPAC Predicted Values Only
94
¢j
0.9
0.8
0.7
0.6
0.5
I I I I I I I
1.7
l I I1.8 1.9 2
"'" ''",.....,
\,
I I2.1 2.2
Advance Ratio, JBeta at 75% R = 45.00 degrees
_' Beta at 75% R = 42.52 degrees--Design Point
-_ Beta at 75% R = 40.00 degrees
_<
K
I I2.3 2.4 2.5
Figure 111" Propeller Efficiency versus Advance Ratio for a Range of Pitch
Angles
0.25
0.2
"_ 0.15_D
0.!O
4--1r_
d_ 0.05
[..,
I I I I I I I
I I I2.2 2.3 2.4 2.5
-'<- Beta at 75% R = 45.00 degrees Advance Ratio, J
÷ Beta at 75% R = 42.52 degrees- Design Point
-_ Beta at 75% R = 40°00 degrees
Figure 112: Thrust Coefficient versus Advance Ratio for a Range of Pitch Ang es
95
L_4_
.p,q
O
O@
L_
O
0.5
04
0.3
0.2
0.1
I I I I I I I
T:_L. -.
-...
"U
I I I I I
.7 1.8 19 2 2.1 2.2
Advance Ratio, J--x- Beta at 75% R = 45.00 degrees
+ Beta at75% R = 42.52 degrees-Design Point
-o- Beta at 75% R. = 40.00 degrees
! 1
2.3 2.4 2.5
Figure 113: Power Coefficient versus Advance Ratio for a Range of Pitch Angles
0.08
0 /0.06
o_
0
0.0400
rjtD
0.02
I I i I I I I
-_ 'B°--.. "4-. -....
"B
"'0_.
--....
"13
"-x...-...g...
"'._
1.7
I I I I I I I1.8 1.9 2 2.1 2.2 2.3 2.4 2.5
Advance Ratio, JBeta at 75% R. = 45.00 degrees
÷ Beta at 75% R = 42,52 degrees - Design Point
-_ Beta at 75% R = 40.00 degrees
Figure 114: Torque Coefficient versus Advance Ratio for a Range of Pitch
Angles
96
o _,..I
O
O
• _,,MI
1.5 I I I I
s
/o
.....' - - o
/K ...p'" X
/' ..
,.
_. I I k0.5 I
_,- --O - <)-- - - " -0 - <_
, / |
' I' I -
X ,K--_
/.---._'" I I
X ..... -I,-" .... I
.- _.--'I" .... I' 'Ir_o,
11 _ _ ---.a-_D .... ---B---I_|
I' I
/ I
1.5 2 2.5
Radius, meters-_- Beta at 75% R - 45.00 degrees÷" Beta at 75% R = 42.52 degrees - Design Point
-a- Beta at 75% R = 40.00 degrees
-_" Beta at 75% R = 50.00 degrees
Figure 115: Lift Coefficient Distributions for a Range of Pitch Angles
CHAPTER 7
ADPAC Three-Dimensional Performance Calculations
A three-dimensional model of the propeller was made from the twist and
chord distributions (Fig. 107-108) calculated using Adkins' and Liebeck's strip theory
design methods (Ref. 5). Views of the propeller's solid surfaces can be seen in
Figures 116 and 117. The computational mesh of the flowfield around the propeller
extends one radius upstream of the propeller, one radius downstream, and one radius
radially outward from the blade tip, The entire mesh contains 4,157,138 grid points.
The hub surface was modelled as a simple cylinder. The blade suction and pressure
surfaces were established as "no-slip" surfaces while the cylindrical hub was
established as a "slip" surface. Total temperature and total pressure were fixed on the
vertical inlet plane, and freestream static pressure was fixed at the vertical exit plane.
The freestream Mach number was fixed on the cylindrical outer boundary of the
computational grid.
A program called TCGRID written by Roderick V. Chima (Ref. 14) was used
to create a fine "C" grid around one propeller blade as well as a somewhat coarser
"H" grid farther upstream of the blade. Since TCGRID was originally intended to
generate meshes for turbomachinery blading, it was a challenge to create an
appropriate mesh for such a large blade with this program. The two grid blocks made
with TCGRID were modified so that the final mesh consisted of ten separate grid
blocks. As shown in Figure 118, the fine "C" grid block was broken into four
97
98
separateblocks (Blocks 1-4),andthecoarseinlet block is shownin yellow asBlock
5. The fine meshwas retainedfor Block 1 closestto the blade,while themeshwas
coarsenedby eliminating everyothergrid line from the original fine meshto yield
Blocks 2 through4. The coarsemeshwasbrokenat the comersof the "C" grid to
avoid possibleproblemswithin ADPAC concemingstretchingratios,or the relative
sizeof neighboringcomputationalcells. Figure 119is aview forward looking aft of
thecomputationaldomainsurroundingoneof thethreepropellerblades. Figures120 •
through122showtheportion of the computationalmeshnearthe inlet block region,
near the blade hub, and near the exit region, respectively. SeparateFORTRAN
programswere written to extend the mesh radially outwards creating Blocks 6
through10(Fig. 123).
Therearemany featureswhich aredesiredof a computationalmesh_some
for physical reasonsand some to comply with the ADPAC program format.
Physically,thereagainshouldbeenoughgrid pointspackedcloseto thebladesurface
sothat theboundarylayercanbe resolved.Thegrid shouldalsoextendwell into the
free streamaheadof the blade,behind the blade,and radially outward. It is also
recommendedthat thegridlinesfollow thetrailing edgeangleof thebladesectionsso
that separationandanyvorticesthat maybe shedcanbeseen. The challengewhen
creatinga meshis meetingall theserequirementswhile keepingthe numberof grid
points to a minimum to reducecomputationaltime. Practically, the upstreamand
downstreamextentsof the meshweresacrificedin orderto addgrid points closerto
99
the blade surface. Even so, the three-dimensional mesh is much coarser than the two-
dimensional meshes seen earlier. Values for y+ of the first grid line above the blade
surface at approximately the quarter chord location were 2.266 for the section at
r/Rtip = 0.406, 2.692 for the section at r/Rtip = 0.666, and 3.671 at r/Rtip = 0.905.
For a mesh to be suitable for an ADPAC three-dimensional calculation,
stretching ratios for the cells should be around 1.3. TCGRID did not contain input
parameters to vary stretching ratios directly, so this requirement was met by adding
grid points until the stretching ratios near the tip were within acceptable bounds.
ADPAC uses a multigrid method to speed convergence. This technique generates
intermediate solutions by coarsening the mesh by eliminating grid points. Three
levels of multigrid are recommended and can be achieved if the number of cells in
each direction for each block are divisible by four. Coordinates for the leading edge
and trailing edge of the blade must also meet this criterion if the multigrid technique
is to be used. If an "H" grid is used for an inlet block, the upstream edge of the "C"
grid must be square and must not overlap the inlet block cells. Finally, coordinates of
all grid blocks must be ordered to form a left-handed coordinate system.
ADPAC was used to calculate the steady state viscous flow over the rotating
propeller blade at the design conditions. The convergence history plots are shown in
Figure 124. After over 2500 iterations, the solution was considered to be converged
because the RMS error had decreased by three orders of magnitude and the number of
separated points was constant. Figure 125 shows three blade sections near the hub,
100
midspan,and tip of the blade where the pressure and Mach number contours are
shown in Figures 126 through 131. The ADPAC solution at the design point
indicated no separation bubbles that had been seen in the low Reynolds number low
Mach number two-dimensional cases studied earlier. Full separation near the trailing
edge was seen, along with a shock wave along approximately one quarter of the blade ......
near the tip. The area of supersonic flow is more clearly seen in Figures 132 and 133.
Efficiency, as well as thrust, power, and torque coefficients were calculated and
compared to results obtained from strip theory calculations. The comparisons can be
in Table 5 or graphically in Figures 134 through 137.
Table 5. Comparison of Strip Theow and ADPAC Results at Design Point
Efficiency
Thrust Coefficient
Power Coefficient
Torque Coefficient
Thrust
Power
Torque
Strip Theory Result at
the Design Point
0.8509
0.1411
0.3007
0.04785
450.9 N
(101.3 lbs)
63.4 kW
(85 hp)
703.7 N-m
(519.0 ft-lbs)
ADPAC Result at the
Design Point
0.8624
0.1355
0.2850
0.04536
433.0 N
(97.3 lbs)
60.1 kW
(80.6 hp)
667.0 N-m
(491.9 fi-lbs)
101
power, and torque coefficients were approximately 5% lower. This difference can be
attributed to several factors. First, because of the simplistic application of the two-
dimensional low Reynolds number transonic predictions, the strip theory design did
not account for the shock from r/Rtip of approximately 0.75 to 0.90. Secondly, the
three-dimensional mesh was considerably less dense than the two-dimensional
meshes and may be below the value for which the solution is independent of the
number of grid points. Finally, the tip vortices as shown in Figure 138, were not
taken into account in the strip theory design and analysis programs. The tip vortex
from one blade and the blade wake can also be seen in the Mach number distribution
at the exit of the computational domain shown in Figure 139.
102
Figure 116: The Three-Bladed Propeller and Extended Hub Surface, Side View
Figure 117: Front View of Three-Bladed Propeller
103
BIock t
Block 2Block 3
Block 4
Figure 118: Computational Mesh Blocks and Solid Surfaces, Axial View
i¸¸
Figure 119: Forward Looking Aft View of Propeller Blade and ComputationalMesh Blocks
105
Figure 122- Magnified View of Trailing Edge Region
Figure 123: View of Computational Mesh Upstream and Above the Blade Tiw--
Forward Looking Aft
106
O,--1
-4
-{
-8'
I I I i I
, I I0 500 1000
I I I1500 2000 2500 3000
._ 2-i0 4O
_ 1.104r_
o
z 0
I I I i I
..-..
,.,-,, _",,-,,.,,.,__ ._,__"'_ "'_--._...-..._.,___
0 5O0 1000
I I I1500 2000 2500
Iteration
3OO0
Figure 124: Convergence History for the Three-Dimensional ADPACCalculation
!
r/Rtip = r/Rtip = r/Rtip =0.406 0.666 0.905
Figure 125" Hub, Midspan, and Tip Sections
107
Pressure Ratio, Ps/Pt
1.2500
0.7$00
. ,9.2500
i
Figure 126: Pressure Ratio Contours for r/Rtip = 0.406
\
Math Number \_l,
/
Figure 127- Mach Number Contours for r/Rtip - 0.0406
108
i
/
/,- . _. _ ./
!/ / .......l_mre Ralio, PI/Pt
<!/ /
i .\_-J ,: \ ,
.! \. ./
:: ",. /
Figure 128: Pressure Ratio Contours for r/Rtip = 0.666
Maeh Number
1=5000
0.7500
0.0000
....k.
/Figure 129: Mach Number Contours for r/Rtip = 0.666
110
Figure 132: Suction Surface Pressure Distribution
Figure 133: Mach Number Distribution Over the Suction Side of the Blade
III
0.9
0.8
o
o., _,,=a
[.T-1
0.7
0.6
0.5
\
'.\
\
'\
,\
I I I I
I.g !.9 2 2.1
I, ,,
2.2
Advance Ratio, J-_- Beta at 75% R = 45.00 degrees
+ Beta at 75% R = 42.52 degrees-Design Point
Beta at 75% R = 40.00 degrees
o ADPAC 3-D Calculation at the Design Point
I I I
_-..,--,-...._.....
4"
\
I I2.3 2.4 2.5
Figure 134: Comparison of Strip Theory and ADPAC Calculations of Efficiency
aJ®p=q
QJO
4--t
0.25
0.2
0.15
0.1
0.05
I I I I I I I
I I I1.7 1.8 i.9 2
Advance Ratio, JBeta at 75% R = 45.00 degrees
+ Beta at 75% R = 42.52 degrees - Design Point
-_ Beta at 75% R = 40°00 degrees
o ADPAC 3-D Calculation at the Design Point
Figure 135: Comparison of Strip Theory and ADPAC Calculations of ThrustCoefficient
112
r,..)
0
r,..)
0
0.5
0.4
0.3
0.2
0.I
I I I I I .i i
_-rl
1.7
I I I I I I !
1.8 !.9 2 2.1 2.2 2.3 2.4 2.5
Advance Ratio, J--'<- Beta at 75% R = 45.00 degrees
_ Beta at 75% R = 42.52 degrees-Design Point
-o Beta at 75% R = 40.00 degrees
o ADPAC 3-D Calculation at the Design Point
Figure 136: Comparison of Strip Theory and ADPAC Calculations of PowerCoefficient
CY
4--t
O_.vm
O
0.08
0.06
0.04
0.02
I i i I i I I
==. _
B..
13
I I I I
1.7 1.8 1.9 2 2.1
I ! , !
2.2 2.3 2.4
Advance Ratio, J-_ Beta at 75% R = 45.00 degrees
t Beta at 75% R = 42.52 degrees - Design Point
-e- Beta at 75% R = 40.00 degrees
o ADPAC 3-D Calculation at the Design Point
iI
!-,i
2.5
Figure 137: Comparison of Strip Theory and ADPAC Calculations of Torque
Coefficient
111
0.9
0.8
I I ! I
o
oI,,_
o
Er.l.l
0.7
0.6
0.5
Q,
:\
\
\i
I I I I
1.8 1.9 2 2.1
-_- Beta at 75% R = 45.00 degrees
o
I2.2
Advance Ratio, J
Beta at 75% R = 42.52 degrees-Design Point
Beta at 75% R = 40.00 degrees
ADPAC 3-D Calculation at the Design Point
I I I
•"'" "4- _, -• \
\
4"
I I2.3 2.4 2.5
Figure 134: Comparison of Strip Theory and ADPAC Calculations of Efficiency
0.25
0.2
0.15
O
E0.1
0
rj)
0.05
I I I I I i i
Advance Ratio, J-3<-- Beta at 75% R = 45.00 degrees
4- Beta at 75% R = 42.52 degrees- Design Point
-o Beta at 75% R = 40.00 degrees
o ADPAC 3-D Calculation at the Design Point
Figure 135: Comparison of Strip Theory and ADPAC Calculations of ThrustCoefficient
112
0o
g.,
o
0.5
0.4
0.3
0.2
O.l
I I I I I .I I
I ! I I I I !1.7 1.8 1.9 2 2.1 2.2 2.3 2.4
Advance Ratio, J-'_ Beta at 75% R = 45.00 degrees
_ Beta at 75% R = 42.52 degrees-Design Point-o Beta at 75% R = 40.00 degreeso ADPAC 3-D Calculation at the Design Point
2.5
Figure 136" Comparison of Strip Theory and ADPAC Calculations of Power
Coefficient
CY
4-a
Oo
0.08
0.06
0.04
0.02
I I i f' I I I
I I I I ! I , I1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5
Advance Ratio, J-_ Beta at 75% R = 45.00 degrees
_' Beta at 75% R = 42.52 degrees - Design Point
-e- Beta at 75% R = 40.00 degrees
o ADPAC 3-D Calculation at the Design Point
Figure 137" Comparison of Strip Theory and ADPAC Calculations of TorqueCoefficient
113
........ :.........
Figure 138: Tip Vortex Streamlines
Exit Plane Math Number
O.3OOO O.4OOO O..._H)O
Figure 139: Pressure Distribution at the Exit Plane of the ComputationalDomain
CHAPTER 8--CONCLUSION
Comparison of the strip theory design and analysis results with those from
ADPAC, a numerical Navier-Stokes analysis code, sheds light on the strengths and
weaknesses of both techniques. Propeller efficiency predicted by ADPAC was
within 1.5% of that calculated with the strip theory methods at the design point while
ADPAC predictions of thrust, power, and torque coefficients were approximately 5%
lower than the strip theory results.
The main advantage to the strip theory design and analysis methods is speed.
Since design is an iterative process, the designer must be able to change conditions
easily and determine the propeller's geometry quickly and Adkins' and Liebeck's
procedures prove to be a useful tool. Results from strip theory analyses can be
obtained quickly as well, a necessity when calculating performance at many off-
design conditions in order to create a propeller map. Despite the simplifying
assumptions made, reasonable accuracy was achieved with Adkins' and Liebeck's
strip theory methods.
The main advantages of using ADPAC was the elimination of simplifying
assumptions required to make the performance calculation and the visualization of
results. Shocks and tip vortices ignored in the strip theory analysis were clearly seen
in viewing the ADPAC results. However, the improvement in the analysis required a
substantial amount of time to Ieam how to run the code, to create appropriate meshes,
and to post-process the output files. This time is in addition to that required to
114
115
actually run the calculation. Thethree-dimensionalmeshconsumeda greatamount
of time sinceapproximately22 hourswere neededto complete100 iterationson a
dedicatedworkstationwith anR8000processor.
In conclusion,thefusion of two dimensional strip theory design and analysis
methods with ADPAC, a three-dimensional Navier-Stokes yielded a good first-
generation propeller design for a vehicle capable of subsonic flight in Earth's
stratosphere. Lift and drag coefficients for the Eppler 387 at low Reynolds number
transonic conditions were generated with ADPAC since experimental results were
unavailable for this regime. Examination of the three-dimensional results showed
that the Eppler 387 was not a suitable airfoil for at least the tip sections of the
propeller because of the shock waves seen on the suction surface of the relatively
thick outboard sections. Improvements can be made to this design by combining two-
dimensional airfoil ADPAC results for other airfoils into the strip theory design and
analysis methods (if experimental data is unavailable), making a full three-
dimensional prediction only after several design iterations are made.
REFERENCES
[1 ] ERAST Leadership Team. 1996. A Review of Remotely Piloted Aircraft (RPA)
Technology Required for High Altitude Civil Sciences Missions.
Washington, D.C.: NASA, Office of Aeronautics (Code R), Office of Mission
to Planet Earth (Code Y). Photocopied.
[2] Adkins, C.N. and R.H. Liebeck. 1983. Design of Optimum Propellers. New York"
American Instintue of Aeronautics and Astronautics. AIAA-83-0190.
[3] Mueller, To J. 1985. Low Reynolds Number Vehicles. Neuilly-Sur-Seine, France:
Advisory Group for Aerospace Research and Development. NTIS,
AGARDograph No. 288.
[4] Pauley, LoL. and P. Moin and WoC. Reynolds. 1989. The Instability of Two-
Dimensional Laminar Separation. In Low Reynolds Number Aerodynamics:
Proceedings of the Conference in Notre Dame, Indiana. June 5-7, 1989 by
Springer-Verlag, 82-92. New York: Springer-Verlag.
[5] McGhee, R.J. and B.J. Walker and B.F. Millard. 1988. Experimental Results for
the Eppler 387 Airfoil at Low Reynolds Numbers in the Langley Low-
Turbulence Pressure Tunnel. Washington, D.C. NASA TM-4062.
[6] Drela, M.1989. XFOIL: An Analysis and Desing System for Low Reynolds
Number Airfoils. In Low Reynolds Number Aerodynamics: Proceedings of
the Conference in Notre Dame, Indiana, June 5-7. 1989. By Springer-
Verlag. 1-12. New York" Springer-Verlag
[7] Drela, M. 1992. Transonic Low-Reyonlds Number Airfoils. Journal of Aircraft.
Volo 29 No. 6 (Nov.-Deco) ° 1106-1113.
[8] Coiro, D.Po and CodeNicola. 1989. Prediction of Aerodynamic Performance of
Airfoils in Low Reynolds Number Flows. In Low Reynolds Number
Aerodynamics: Proceedings of the Conference in Notre Dame, Indiana. June
5-7, 1989. By Springer-Verlag. 13-23, New York: Springer-Verlag.
[9] Hall, E.Jo and D.A. Top and R.A. Delaney. Task 7-ADPA C Users
Manual.Cleveland: NASA Lewis Research Center, NASA CR-195472.
[ 10] Schlichting, H. 1960. Boundary Layer Theory. New York: McGraw-Hill.
116
117
[11] Glauert,H. 1926.The Elements of Aerofoil and Airscrew Theory, Cambridge"
The University Press.
[ 12] McCormick, B.W. 1979. Aerodynamics, Aeronautics, and Flight Mechanics,
New York: John Wiley and Sons.
[ 13] Anderson, J.D. 1989. Introduction to Flight. New York: McGraw-Hill Book
Company.
[ 14] Chima, R.V. 1990. TCGRID. Cleveland: NASA Lewis Research Center.
REPORT DOCUMENTATION PAGE ! FormApprovedOMB No. 0 704-0188
Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources,gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of thiscollection of information, including suggestions for reducin_ this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 JeffersonDavis Highway, Suite 1204, Arlington, VA 22202-4302, and to the Office of Management and Budget, Paperwork Reduction Project (0704-0188), Washington, DC 20503.
1. AGENCY USE ONLY (Leave blank)
4. TITLE AND SUBTITLE
2. REPORT DATE
February 1998
3. REPORT TYPE AND DATES COVERED
Technical Memorandum
5. FUNDING I_IUMBERS
Design and Performance Calculations of a Propeller for Very High Altitude Flight
6. AUTHOR(S)
L. Danielle Koch
7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)
National Aeronautics and Space Administration
Lewis Research Center
Cleveland, Ohio 44135-3191
9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)
National Aeronautics and Space Administration
Washington, DC 20546-0001
WU-529-10-I 3--00
8. PERFORMING ORGANIZATIONREPORT NUMBER
E-11102
10. SPONSORING/MONITORING
AGENCY REPORT NUMBER
NASA TMm1998-206637
11. SUPPLEMENTARY NOTES
This report was submitted as a thesis in partial fulfillment of the requirements for the degree of Masters of Science in
Engineering to Case Western Reserve University, Cleveland, Ohio, January 1998. Responsible person, L. Danielle Koch,
organization code 7565, (216) 433-5656.
12a. DISTRIBUTION/AVAILABILITY STATEMENT
Unclassified- Unlimited
Subject Categories: 02 and 07 Distribution: Nonstandard
12b. DISTRIBUTION CODE
14. SUBJECT TERMS
Propeller; High-altitude; Low Reynolds number aerodynamics; ADPAC
17. SECURITY CLASSIFICATION
OF REPORT
Unclassified
NSN 754_)-01-280-5500
18. SECURITY CLASSIIT:ICATIONOF THIS PAGE
Unclassifiedm
19. SECURITY CLASSIFICATION
OF ABSTRACT
Unclassified
15. NUMBER OF PAGES
]3016. PRICE CODE
A0720. LIMITATION OF ABSTRACT
Standard Form 298 (Rev. 2-89)
Prescribed by ANSI Std. Z39-18298-102
This publication is available from the NASA Center for AeroSpace Information, (301) 621--0390.
13. ABSTRACT (Maximum 200 words)
Reported here is a design study of a propeller for a vehicle capable of subsonic flight in Earth's stratosphere. All propellers presented
were required to absorb 63.4 kW (85 hp) at 25.9 km (85,000 ft) while aircraft cruise velocity was maintained at Mach 0.40. To produce
the final design, classic momentum and blade-element theories were combined with two and three-dimensional results from the
Advanced Ducted Propfan Analysis Code (ADPAC), a numerical Navier-Stokes analysis code. The Eppler 387 airfoil was used for each
of the constant section propeller designs compared. Experimental data from the Langley Low-Turbulence Pressure Tunnel was used in
the strip theory design and analysis programs written. The experimental data was also used to validate ADPAC at a Reynolds numbers of
60,000 and a Mach number of 0.20. Experimental and calculated surface pressure coefficients are compared for a range of angles of
attack. Since low Reynolds number transonic experimental data was unavailable, ADPAC was used to generate two-dimensional section
performance predictions for Reynolds numbers of 60,000 and 100,000 and Mach numbers ranging from 0.45 to 0.75. Surface pressure
coefficients are presented for selected angles of attack, in addition to the variation of lift and drag coefficients at each flow condition. A
three-dimensional model of the final design was made which ADPAC used to calculated propeller performance. ADPAC performance
predictions were compared with strip-theory calculations at design point. Propeller efficiency predicted by ADPAC was within 1.5% of
that calculated by strip theory methods, although ADPAC predictions of thrust, power, and torque coefficients were approximately 5%
lower than the strip theory results. Simplifying assumptions made in the strip theo_'y account for the differences seen.
Recommended