Embed Size (px)
Citation preview
FLOW AROUND A ROTATING SHORT CYLINDER:
A COMPUTATIONAL STUDY
by
ABU SADEK SAIFUR RAHMAN, B.Sc.M.E., M.Sc.E.
A THESIS
IN
MECHANICAL ENGINEERING
Submitted to the Graduate Faculty of Texas Tech University in
Partial Fulfillment of the Requirements for
the Degree of
MASTER OF SCIENCE
IN
MECHANICAL ENGINEERING
Approved
August, 1996
ACKNOWLEDGMENTS
I would like to express my gratitude and thanks to my graduate advisor, Dr. S.
Parameswaran, for his advice and guidance in every minute detail of this thesis.
I would also like to thank my thesis committee members. Dr. J. W. Oler and Dr. T T.
Maxwell for their invaluable suggestions and cooperation.
Special thanks are due to Mr. Ramesh Andra and Mr. Thirumala Reddy for helping me
learn software packages.
My appreciation is extended to my friends and colleagues, specially, K. Elankumaran,
Ron Runyan, A. Kumar, S. Jayantha, K. Prabakaran for their help, support and
appreciation when I needed it.
My appreciation is also extended to Chrysler Corporation for financial support.
Lastly, I would like to thank my parents, whose support and encouragement has made
it possible for me to pursue my higher education.
11
TABLE OF CONTENTS
ACKNOWLEDGMENTS ii
ABSTRACT v
LIST OF TABLES vii
LIST OF FIGURES viii
NOMENCLATURE x
CHAPTER
I. INTRODUCTION 1
1.1 Importance of CFD Analysis 2
1.2 Applications of CFD Analysis 3
1.3 Objectives of the Study 4
n. LITERATURE REVIEW 5
m. MATHEMATICAL FORMULATION 14
3.1 Turbulence Model 14
3.1.1 Standard k-8 Model 15
3.2 Numerical Formulation 17
3.3 Solution Procedure 20
3.4 AIRFL03D Code 21
3.5 Multigrid Technique 22
IV. PRE-PROCESSING 23
4.1 Tasks in Pre-processing 23
iii
4.2 ICEM CFD/CAE for Grid Generation 24
4.3 ICEM DDN and MULCAD 24
4.4 Airflo3d and ICEM CFD/CAE Interfaces 25
V. POST-PROCESSING 39
VL RESULTS AND DISCUSSIONS 40
Vn. CONCLUSIONS AND RECOMMENDATIONS 59
7.1 Conclusions 59
7.2.Recommendations 59
REFERENCES 60
APPENDIX 62
IV
ABSTRACT
Despite wide spread interest in the aerodynamics of cars in recent years, the flow field
associated with the wheels has received relatively little attention, mainly due to difficulties
in obtaining an adequate simulation of the flow. Yet in many cases where aerodynamic
designs are important, flow around the wheels can play a major role in the behavior of the
vehicle. The obvious example is racing cars, which travel at high speeds with totally
exposed wheels. A detailed understanding of the flow should also help in dealing with the
hazard formed by entrainment and dispersal of spray from a wet road caused by trucks.
In the present study, AIRFL03D~a multi-grid based finite-volume code has been used
to predict numerically the flow around a short cylinder which resembles the flow around a
wheel. Comparisons are made for the flow around a stationary cylinder with that around
the same cylinder when rotating in order to highlight the specific effects of rotation. Lift
and drag are also calculated fi"om pressure distributions.
Standard k-e model was used in the AIRFL03D code. Although it has been reported
that the standard k-s model cannot accurately predict rotational flow, reasonable results
have been obtained for a certain range of wheel rotation.
ICEM^^ CFD/CAE a commercial preprocessing software has been used for model
generation as well as generation of the grid. EnSight^^ another commercial postprocessing
software has been used for the visualization of the analysis. The computational results
obtained show very good trends in the prediction of the flow field compared with previous
experimental results.
LIST OF TABLES
6.1 Comparison of experimental and computational resuhs of drag coefficients 53
6.2 Drag and lift coefficients for coarse grid for different spin ratios 55
6.3 Drag and lift coefficients for fine grid for different spin ratios 55
6.4 Comparison of lift coefficient for clockwise and counterclockwise rotation of the cylinder 56
6.5 Drag coefficient CD for different spin ratios for flow around a rotating cylinder in ground contact 58
M
LIST OF FIGURES
2.1 Experimental for setup flow around an exposed rotating wheel [8] 6
2.2 Experimental setup for flow around a 1:4 scaled dovm model of racing car [8]. ...7
2.3 General view of model in the Imperial College wind tunnel [12] 9
2.4 Flow patterns revealed by wool tufts[12] 10
2.5 Experimental setup for flow and pressure distribution of an isolated wheel [2] 12
3.1 A typical control volume that surrounds a node P and its neighboring nodes
N,S,EandW 19
4.1 Mesh configuration for grid elements of suspended short cylinder 27
4.2 Mesh configuration for grid elements of suspended short cylinder (front view) 28
4.3 Mesh configuration for grid elements of suspended short cylinder
(side view) 29
4.4 Mesh configuration of cylinder face 30
4.5 Mesh configuration for grid elements of suspended short cylinder
(top view) 31
4.6 Mesh configuration of four symmetry planes of suspended short cylinder 32
4.7 Six domains of suspended short cylinder 33 4.8 Mesh configuration for grid elements of short cylinder in ground proximity 34 4.9 Mesh configuration for grid elements of short cylinder in ground proximity
(front view) 35
4.10 Mesh configuration for grid elements of short cylinder in ground proximity (side view) 36
4.11 Symmetry planes of short cylinder in ground proximity 37
4.12 Five domains of short cylinder in ground proximity 38
6.1 Pressure contours for flow around a clockwise rotating cylinder 42
6.2 Pressure contours for flow around a counterclockwise rotating cylinder 43
6.3 Pressure contours for flow around a non-rotating cylinder 44
6.4 Particle traces for a flow around a counterclockwise rotating cylinder 45
6.5 Particle traces for a flow around a clockwise rotating cylinder 46
6.6 Particle traces for a flow around a non-rotating cylinder 47
6.7 Vector arrows for flow around a counterclockwise rotating cylinder 48
6.8 Vector arrows for flow around a clockwise rotating cylinder 49
6.9 Vector arrows for flow around a non-rotating cylinder 50
6.10 Vector arrows for flow around a clockwise rotating cylinder in ground contact 51
6.11 Vector arrows for flow around a counterclockwise rotating cylinder in ground contact 52
6.12 Comparison of experimental and computational results of drag coefficients 54
6.13 Comparison of lift coefficient for clockwise and counterclockwise rotation of the cylinder 57
Mil
NOMENCLATURE
ai constant
p density
8 dissipation rate of turbulence energy
|i dynamic viscosity
ap., aN, as, a \ finite-difference coefficients
(j) general variable
At time step
t time
E
k
P
Re
T
internal energy
kinetic energy of 1
static pressure
Reynolds number
temperature
u X component of the velocity
V y component of the velocity
w z component of the velocity
IX
CHAPTER I
INTRODUCTION
The problem of accurately simulating the flow field around a vehicle on a smooth
road in a wind tunnel has occupied many investigators during the last four decades. The
flow field associated with the wheel has received very little attention. But in many cases
where an ideal aerodynamic shape of a vehicle is needed, one cannot overlook the effect
of wheel rotation on the aerodynamics of the whole body. Moreover for racing cars which
travel at high speeds with totally exposed wheels, a detailed understanding of flow around
the exposed wheels is very important. A detailed understanding of the flow should also
help in dealing with the hazard formed by entrainment and dispersal of spray from wet
road.
Most of the early researches on aerodynamics of vehicles were experimental in
nature. But today the role of Computational Fluid Dynamics (CFD) in engineering
predictions has become so strong that numerical simulation of flow field around vehicles
has become very easy. This is due to the rapid development in computer hardware
resources and as well as efficient numerical algorithm.
In the present study, an attempt has been made to predict flow field around a short
cylinder using Computational Fluid Dynamics (CFD) procedures. The main problem of
CFD analysis or any numerical simulation is the difficuhies in generating an appropriate
body-fitted finite-volume grid for the complex geometries. ICEM^^ CFD/CAE, a
commercial preprocessor for model generation as well as grid generation, has been used in
the present work for this purpose. It is difficult for the human eye to comprehend tabular
results, so visualization of the analysis is also very important. EnSight™ a commercial
postprocessing software has been used in the present work for the visualization of the
analysis.
l.l Importance of CFD Analysis
The advent of powerful computers has led to the development of solutions to
many complex flow problems by Computational Fluid Dynamics (CFD) analysis over the
past few years, many commercial CFD packages have become available. Due to the
emergence of theses packages, CFD analysis or, a numerical approach to solve fluid flow
problems has become very popular. One of the reasons of the popularity of CFD is that it
provides important new technological capabilities that cannot easily be provided by
experimental facilities. Because of basic limitations, experiments suffer from wall
interference, flow angularity, Reynolds number limitations and insufficient technique for
local measurements. Numerical flow simulations, on the other hand, do not have these
fundamental limitations. Engineers are now using CFD to reduce the number of prototype
tests, cut manufacturing costs, and reduce overall time to market. CFD not only allows us
designs to be tested digitally earlier in the design process, but it also helps avoid the need
to divert significant amounts of time and resources to building and evaluating prototypes.
Engineers are also using CFD to gain insights into complex phenomenon and to perform
"what-if' analyses on more design ahematives. CFD allows the investigation and of
processes that are not understood fully and allows the discovery of significant flow
features that otherwise couldnot be uncovered -perhaps because of limitations on the
locations of measurement devices in the flow domain or flow-field disturbances caused by
the intrusion of measurement devices. CFD also helps to gain a much clear understanding
of the interactions between physical phenomena and their sensitivity to various operational
parameters. The ability to simulate and visualize such interactions often leads to new
concepts and new designs that even experienced engineers might not have anticipated.
Many revolutionary design ideas are not even explored because of the excessive costs and
time of doing experiments. CFD opens the door to performing quick, systematic screening
of large number of design concepts.
1.2 Applications of CFD Analysis
Computational Fluid dynamics (CFD) has wide applications in areas such as
aerospace, automobile and material manufacturing industries. Over the years, the types of
CFD applications have changed. Previously, codes were used to analyze individual
components in isolation, whereas they are now employed increasingly to study more-
complex system-level designs. For example, in the aerospace industry, codes were used to
look at general airflow characteristics of the combustor in an aero engine. Now, codes are
used to analyze all of the components of the combustor in the design phase. The
turbomachinery industry is also using CFD to analyze the most critical components. By
using CFD it has become possible to simulate chemical-vapor deposition. Engineers are
using it in the semiconductor industry to model an entire reactor that is depositing the
various substances to create the semiconductor wafers. The cooling of an electronic
device is very important for optimal performance. It is very difficult to design a ver>' small
fan for this purpose without knowing the flow properties around small objects like
resistors, capacitors, etc. By using CFD the flow around these tiny objects is easily
simulated. So, the bottom line is the application of CFD is indispensable for modem
design of anything where flow is involved.
1.3 Objectives of the Study
The objective of this work is to predict the flow around stationary and rotating
short cylinder which resembles the wheel of a car. This is done in order to highlight the
specific effects of rotation on the aerodynamics of a vehicle. This study is also aimed at
assessing the capability of standard k-e model in predicting the mean flow quantities.
CHAPTER II
LITERATURE REVIEW
The aerodynamic actions on a wheel have been measured in the case of airplane
wheels. They were non-rotating wheels, in a free airstream, that is far away from the
ground surface. So, it is clear that the results of these tests are not of practical use in the
case of automobile wheels. In this case, measurements were carried out only to determine
the driving moment necessary for the rotation of the wheel when the velocity of rotation is
such as to cancel the velocity of the air relative to the wheel in the proximity of the
contact area with the ground, that is in the case of rolling. But when a wheel of an
automobile is concerned, an evaluation of all the aerodynamic components (drag, lift, side-
force, rolling, pitching, and yawing moment) are very important.
Morelli [8] carried out two different tests in the wind tunnel of the Laboratory of
Aerodynamics of the "Politecnico di Torino" for the evaluation of the aerodynamic actions
on rolling wheels. He determined the aerodynamic actions on automobile wheels in two
conditions: isolated wheels (partially faired); and wheel as they are mounted on a racing
car. In his experiment, an automobile wheel was mounted in the center of the test section
of an wind tunnel (Figure 2.1). The ground was simulated by a plate parallel to the
airstream, having a specially shaped leading edge. The wind velocity was measured by an
anemometer at the working section of the tunnel. In the second part of his experiment, he
used a 1:4 scaled-down model of a racing car, the "Ferrari" F-l. He mounted the car in
the working section of the wind tunnel (Figure 2.2). The car was provided with four
Figure 2.1 : Experimental setup for flow around an exposed rotating wheel[8]
Figure 2.2 : Experimental setup for flow around a 1:4 scaled down model of racing car [8].
wheels. The wind tunnel tests were carried out at the same value of air speed for both
cases. In addition to these tests, the measurements were also taken with the standing
wheels to isolate the effect of rotation on the results.
The most characteristic aerodynamic effect of a rolling wheel found was the
downward directed lift. He found that when the wheel was rotating, the drag was
increased by approximately 10% over the drag when wheel was not rotating. He
postulated that this increment of drag was due to the dowrtward lift, i.e., induced drag.
Stapleford and Carr [12] carried out another experiment on the aerodynamic
characteristics of exposed rotating wheels in the model wind tunnels at MIRA and
Imperial College. A model consisting of a very slender body with four wheels (Figure 2.3),
spaced at typical track to wheel base proportion, was used to examine the characteristics
of exposed wheels and to establish satisfactory methods of simulating these in the wind
tunnel. To determine the effects of a moving ground surface, they used the Imperial
College wind tunnel, where such a facility is provided.
They found that stationary wheels develop a large lift force when brought into
contact with the ground. This lift force was reduced, however, by rotation of the wheels,
which caused a negative (downward) lift component that became very large when a
clearance existed under the wheels.They found that the aerodynamic drag of an exposed
wheel increased by either rotation or proximity to the ground surface. They also found
that the provision of a moving ground surface does not appear to affect these forces
significantly and that an adequate simulation can be provided without rotation by
Figure 2.3 ; General view of model in the Imperial College wind tunnel [12].
Figure 2.4 : Flow patterns revealed by wool tufts [12]. (a) Stationary wheels, gaps open. (b) Rotating wheels, gaps open. (c) Stationary wheels, gaps sealed. (d) Rotating wheels , gaps sealed
10
mounting the wheels at a distance from the ground equal to between zero and 5 percent of
their diameter.
Fackrell and Harvey [2] carried out a detailed study of the air flow around an
isolated road wheel (Figure 2.5). The forces on the wheel were obtained by integrating
pressure measurements thus permitting a fiill simulation of a rotating wheel in contact with
the ground to be carried out. The effect of wheel width and thread pattern were
investigated.
In their experiment, they found that, a small gap under a wheel produces a negative
lift force. This lift force increases when the wheel is rotating or when the floor is moving.
They attributed this phenomena to the venturi effect. When air finds a gap under the
wheel it starts rushing through the gap. Thus when the velocity increases, pressure drops
and resuhs in a negative lift. They also added that the air flow under the wheel will be
increased by the rotation of the wheel and/or movement of the floor.
Fackrell and Harvey [2] in another experiment carried out an investigation of the
air flow around two wheel profiles typical of those used on racing cars. They compared
the flow around a stationary wheel with that around the same wheel when rotating in
order to highlight the specific effects of rotation. The lift and drag forces were obtained
from the pressure distribution over the wheels. In their investigation, they found that the
separation position is fiarther forward on the rotating wheel than on the stationary one.
Griffiths and Ma [3] investigated the differential boundary-layer separation effects
in the flow over a rotating cylinder. They attempted to examine the negative Magnus force
11
Figure 2 5 Experimental setup for flow and pressure distribution of an isolated wheel [3]
12
very closely. They carried out wind tunnel tests at the University of Wales using a 6 inch
diameter and 12 inch long cylinder, fitted with circular end plates and rotating at speeds up
to 3000 rpm in air speeds up to 130 ft/sec. The experimental results indicated that a
lateral force opposite in direction to the normal Magnus force can act on a body rotating
in stream of fluid near the critical Reynolds number. They noted that this negative force
arises from the fact that different effective Reynolds numbers and hence different flow
regimes may exist on each side of the body so that the boundary layer remains attached
longer over one side than the other.
13
CHAPTER III
MATHEMATICAL FORMULATION
In practical situations, flows are almost always turbulent. This means that the fluid
motion is highly random, unsteady and three-dimensional. The following discussions in
this chapter cover the theory of turbulence, the equations to be solved for the current
study, the numerical formulation, and then a brief account" of the algorithm used to solve
the flow field. This chapter also covers a discussion on the incompressible flow-solver
AIRFL03D developed by S. Parameswaran which employs the standard k-e model of
Launder and Spalding [6] and SIMPLE algorithm of Patanker and Spalding [10].
3.1 Turbulence Model
Turbulence is the fluctuating, disorderly motion of fluid a particle. Turbulent
motion can be described by the Navier-Stokes equations. However, the turbulent motion
contains elements which are much smaller than the extent of the flow domain. To resolve
the motions of these elements in a numerical procedure, the mesh size of the numerical
grid should be even smaller than the smallest eddies of the turbulent motion. Therefore, a
huge number of grid points is needed to cover the flow domain which is beyond the
capability of the present-day computers. Hence it is not feasible to solve Navier-Stokes
equations directly.
Osborne Reynolds first suggested a statistical approach of solving the equations
which describe turbulent flow. Here the equations are averaged over a time scale, which is
14
long compared with that of the turbulent motion. Unfortunately, the time averaging
procedure introduces additional unknowns in the mean flow equations. This means that
the equations no longer constitute a closed system. So, a "turbulence modeling" is
necessary to make the system of equations closed. A model of turbulence means a set of
equations which, when solved with the mean flow equations, allows calculations of the
relevant correlations and so simulates the behavior of the real fluid in important respects.
Many different turbulence models have been developed over the last 30 years. They are
zero-equation mixing length model, one-equation model and the well known two-equation
k-8 model. Among these models, the standard k-e by Launder and Spalding has been
widely used due to its simplicity and capability to produce realistic predictions.
3.1.1 Standard k-e Model
In the standard k-e model, the governing equations are derived from the Reynolds-
averaged Navier-Stokes equation with an eddy viscosity approximation. The differential
equations governing the unsteady, incompressible, turbulent flow in three space
dimensions are expressed in Cartesian tensor notation as follows:
Continuity
^ = 0; dx,
Momentum
ai. a / \ 1 r9p d \ fc\ c)u^ . — ( u u ) = — + — iy^ff — - + — - >
di dx^ ' ^' p ^ , dy. \dy. 5xJ
15
Here the effective kinetic viscosity, Veff, is taken as the sum of the molecular and
turbulent viscosity as given by:
Energy
p — = V.(kVT) + (t)
where t is the time, p is the density, p is the pressure field, Ui and T are the mean velocity
and mean temperature, respectively and (j) is the dissipation function. The eddy viscosity Vt
is related to the turbulent kinetic energy k and its rate dissipation e by
V t = - ^ —
where C^ is the model constant and k and e are obtained from a two-equation turbulence
model of Launder and Spalding [13].
In the AIRFL03D code, which has been used for this study, the standard k-e
model has been used to predict the turbulent flow. This model characterizes the turbulent
flow by two quantities: the kinetic energy of turbulence, k and the dissipation rate of
turbulent energy, e. In this model, the turbulent viscosity, Vt is determined from k and e.
The k - equation:
dk a / , \ d Vj ok
a ax/ ^ ^ axj + (u,k) = - '-—- + G - p 8
The e - equation:
16
cfe a Vj ae
di ax, ^ ^ ax a ax
where,
au. I au, au.^
k
G=v,^^ ^ + J
axji^ax. dKj
and C,=l.44, C2=l.92, C^=0.09, ak=1.0, a,=l.22 are empirical constants.
3.2 Numerical Formulation
The numerical formulation of the set of equations to be solved is described in this
section. Previously the three basic equations, the momentum, continuity and energy
equations are discretized to facilitate their numerical solution. The momentum equation is
solved to obtained the velocity field. An estimated pressure field is used to solve for the
initial velocity field. Then the continuity equation has been used to check for any
continuity errors. Apart from these equations, a pressure-correction equation is introduced
to solve for the actual pressure field. The corrected pressure field obtained from the
pressure-correction equation is used to update the velocity field. The energy equation is
solved only after the continuity equation is satisfied by the velocity field Except for the
pressure correction equation, all equations are solved by the Stones [13] algorithm.The
pressure correction equation has been solved by the conjugate gradient method.
A typical control volume that surrounds a node P and its neighboring nodes N,S,E,
and W are shown in Figure 3.1. The general discretized form of the momentum equation
17
to solve for the velocity field in the three directions of the flow field as given b>
Parameswaran.
/ x n + l . J . n \
p.voip.^ '^^ ' ^+(F;( | )" - ' )^- (F; ( | )"^ ' )^ _ (pn n+i ^ - ( F ^ T ^ ' ) ^
^VoU ^ ^ ^ VVol w
+
+ VVoU ^ ' ' W o l ,
t b
+ S,.Volp
where Fl, F2, and F3 are the convective fluxes, across the east, north, and top cell faces, a
is the area of any of the six cell faces and Vol. of a general cell.
«i>r'
r:'
v:'
J.n+1 = <t>P
J.n+1 = < P E
Jvn+l = q>P
J. n+l
xn+l = q>p
J.n+1
if F," > 0
if F," < 0
if V; > 0
if F2" < 0
if F3" > 0
if F3" < 0
The quantities in the above equations have been derived according to the
upwinding differencing scheme. The superscript n and n+l refer to the old and the new
time levels. The subscript in general refers to the location in the physical plane.
The pressure correction equation is obtained from the momentum and continuity
equations. The convective fluxes, Fl, F2, and F3 at the cell faces are computed from the
18
NW e
w •
w
SW ^
N •
n 1 1
P _ • _
S ^ •
NE •
E •
e
SE •
Figure 3.1: Control volume for node P and the surrounding control volumes.
19
velocity projections along the coordinate direction at the cell faces. All velocity
projections except the one which is not parallel to the cell face are computed from the
cartesian components stored at the nodes either side of the face. The velocity projection in
the direction connecting the adjacent nodes is computed from momentum balance.
3.3 Solution Procedure
The solution to the coupled momentum and continuity equations is achieved by
carrying out the following steps:
1. The momentum equations are solved to yield the intermediate velocity
field u*, V* and w* with the existing pressure field.
2. The new fluxes Fi*, F2* and F3* are computed from the velocity
components at the cell faces. The velocity projection along a direction is
calculated from momentum balance.
3. The continuity error 8p is calculated for each cell from the newly
calculated fluxes Fi*, F2* and F^*. The pressure correction equation is
assembled and solved to yield a new pressure field p*.
4. A new velocity field u**, v** and w** is obtained from the momentum
equation by replacing the old pressure field with the newly calculated p* field.
5. A new set of fluxes Fj**, F2** and F?** is calculated from the new
pressure field p* and the velocity field u**, v** and w**.
6. The pressure correction equation is solved to get an improved pressure field,
p**.
20
7. Steps 4-6 are repeated until the momentum and the continuity equations satisf>'
a preset tolerance
8. The set of equations for production k*, dissipation e* and the energy e* are
solved.
3 4 AIRFL03D Code
The AIRFL03D code is intended to model fluid flow in or around three-
dimensional complex geometries with or without heat transfer. The flow can be either
steady or unsteady. The program solves the transport equations for three dimensional,
unsteady incompressible flows together with two equation model for turbulence (the k-e
model). For steady state problems, the solution is obtained by marching in time until the
solution remains unchanged.
The code employs the well-known iterative SIMPLE (Semi-Implicit Method for
Pressure Linked Equations) algorithm.The algorithm is based on the predictor-corrector
method. The predictor step involves the assumption of an initial pressure field to solve for
an approximate velocity field. Then in the corrector step the algorithm implicitly solves
for the actual pressure field based on the predicted velocity field and then applies
corrected pressure field to update the velocity field. The corrector step is repeated for a
preset number of pressure corrections and each time the velocity field is updated. The
number of pressure corrections may be varied to attain different order of accuracy for the
continuity error. The continuity error is calculated after each corrector step and the
procedure is stopped after a preset value of accuracy in the continuity has been reached.
21
3.5 Multi-grid technique
In this study, a multi-grid based AIRFL03D code was applied. In the multi-grid
technique only the lowest level grid is generated by the user with the aid of ICEMCFD, a
preprocessing software package. The next level grid is created without any user input. The
initial guess at that grid level is obtained from the solution at the lowest level using multi-
grid principles. The basic Full Approximation Scheme-Full Multi Grid (FAS-FMG)
algorithm of Achi Brandt [1] has been used in the solution of pressure correction equation.
In the multi-grid technique in this study, each cell was divided into eight cells and
accordingly each cell face was divided into four cell faces. The main reasons for using this
technique is to minimize CPU time.
22
CHAPTER IV
PRE-PROCESSING
All the tasks that take place before the actual calculations are called 'pre
processing'. Pre-processing is the generation of all the input data required by a solver for
a specific fluid flow. This is the most important component of the CFD analysis for flow
in/or around complex geometries. Today, there are many software packages available in
the market to ease the work of a design engineer.
4.1 Tasks in pre-processing
The following are the tasks a pre-processing software package does for any kind
of CFD analysis:
1. Define control volumes for which conservation laws are applied.
2. Define the boundaries of the geometry.
3. Apply the boundary conditions.
4. Specify the initial conditions.
5. Set the fluid properties.
6. Set the numerical control parameter.
In carrying out these tasks, the user has to interact with the computer in some way and so
the pre-processing program usually has a graphical interface, so that parameters can be set
and the resulting changes seen quickly. Usually, the most difficult task in pre-processing
phase is the generation of the control volumes.
23
4.2 ICEM CFD/CAE for Grid Generation
In the present flow problem ICEM CFD/CAE has been used to take care of the
pre-processing task. This commercial software package is an interactive computer
graphics code developed to simplify the task of generating the computational mesh
especially for computational fluid dynamics (CFD) solvers. It has the advantage of
creating geometry as well as mesh. ICEM DDN is the module which can be used to create
complex geometry. ICEM MULCAD is the module used to generate the mesh and assign
boundary conditions. ICEM CFD/CAE has several advantages over the commercial finite
element pre-processing software package PATRAN. It does not have any limitation to the
number of the cells one can apply to a domain (for PATRAN the limit is 1111 hexagonal
element per hyper patch).
4 3 ICEM DDN and MULCAD
The geometry to be meshed must be created by ICEM DDN. It is very important
to keep in mind while creating the DDN geometry that MULCAD can utilize only lines or
B-spline curves as edge entities and project upon only B-spline surfaces. So, all non B-
spline curves must be converted to B-spline curves. The same is also true for surfaces.
That is, after creating a non B-spline surface by whatever means, it has to be converted to
a B-spline surface using B-spline conversion icons in DDN. Since, the user has to decide
in DDN what kind of topology he wants to get finally from the module mulcad, it is
important that he prepares the geometry for allowed topology type. In this analysis the
24
interface between ICEM and Airflo3d is mainly designed to generate an internally
structured mesh. In other words inside the domains, which are 3-D volume sections of the
flow field, the mesh should be structured, which means one should be able to draw
consistent ijk directions for each domain. It is important to remember that a domain
should be internally structured (or single block), which means that parallel vertices (edges
of the domain) must be all the same type like i-direction, or j-direction. Otherwise,
Padamm, which is a sub processor of ICEM to generate mesh for a given topology, will
fail to run, with an error massage like "unable to find the origin for domain number."
On the other hand, being structured inside the domain does not mean that ijk
directions should be the same globally. Hence one can use "Multi-Block Mesh" by having
a topology that requires altering ijk directions from one domain to another. If the mesh is
by nature a multi-block mesh, ICEM will automatically create multi-block mesh topology
to fulfill the task, given that domains are internally structured.
4.4 Airflo3d and ICEM CFD/CAE Interfaces
Airflo3d_ICEM interface is the program which converts the output of ICEM
CFD/CAE into Airflo3d readable format. Airflo3d is the solver which has been used for
the numerical solution. To analyze the flow around a rotating wheel where a rotary motion
of wall planes are involved, another interface program rotnn.f has been developed. This
interface assigns velocity to moving wall planes. The output from this interface is read by
modified Airflo3d. Actually, in modified Airflo3d a small modification has been made in
the read and write statements so that it can read and v^te variable moving wall velocity
25
instead of fixed wall velocity. See the Appendix for a listing Figures 4.1-4.2 show the
mesh configuration for grid elements of both suspended and grounded rotating short
cylinder.
26
r
N 4\
<r
•a c >%
c o
j=i CO
T3
•o C
8.
o CO
c e
13
•c 00
c o
. ^ H
Cd u, 3 bO
in c o o
J3 CO
U
U.
27
c o
c • ^
o t: o CO •o O
T3 C
CO 3 CO
Ci-i
O CO
c
13
•c
c o • ^ 4—1
a D bO c o o
J C CO U
:s <N Tt (U
bO
28
CO
c
•a c
» ^
t: o JIZ
•a c u a, CO
CO
c/) <_• C
6 13 •a C 00
a c o
•a a
5 i;3 c o o
CO
i-i
3
29
X
^
-a c * u c o
• ^ «^ cd 3 bO c o o
JZ CO O
u 3 to
30
—
—
—
—-
—
---
—
—
—
—
-
— -
—
—
- - •
—
-
- -
—
—
I
—
—
-
-—
—
-
- - -
—
—
—
- —
—
—
1 1.
—
J<
--
— -
—
-'
•
X
?•
(Top
vie
w
Und
er
hort
cy
Its o
f sus
pend
ed s
el
emer
rid
oo U l o
uz, io
n *^ cd
figur
c o
£shc
:s
u
Figu
i
31
o T3 C
• ^
o
o CO
-o O c a. CO 3 CO
C o •a cd Ul 3 bO C o o
JZ
N
< -Ul 3 bO
32
•o c o
o JZ t/i
-o c 4> Ou, CO 3 ( /}
o (A
a
o
CO
r-
V-i
3 bO
33
•3 2 a. a 3 o Ul bO C
N
X .N
•a c
'>> o t: o
Cui
o i2 c
13
c bo
o 4_*
2 a c o o
JZ CO (L>
OO
3 bO
34
0\
a
35
ii > o
00
•3 o Ul
ex, c 3
2 bO
c c
t: o t/5
i2 c B
JO 1 3
•c bO
o cd Ul 3 bO
c o o Xi
Ul 3 bO
36
2 a
PU
37
X 2 ex,
T3 C 3
2 bO C Ul 4>
•o a •^ ">»
o t: o x: CO
(4-1
o CO
C
•a 6 o > • •
'*' Ul a
38
CHAPTER V
POST-PROCESSING
Post-processing is the ability to visualize the results of variables from a
computational analysis. A CFD analysis or in any numerical analysis produces a large
quantity of tabular output which is very difficult to interpret without graphical post
processing. EnSight is the post-processing software which has been used in the present
analysis. EnSight is a post-processing software in which scalar variables (such as
temperature, pressure, etc.) and vector variables (such as velocity) can be read and
displayed in a number of different ways.
EnSight is an advanced and fiill-featured engineering postprocessor available. It
was originally developed for, and has been continually refined to meet the needs of the
most demanding computational engineers in the world The EnSight graphical user
interface (GUI) provides access to a vast array of fiinctionality. The GUI is consequently
large and seemingly complex. It is, however organized in a hierarchical fashion, with
dialog windows (accessed via manus) containing functionally grouped commands. The
design of most of the main dialogs also permits information hiding, so one can hide
sections of the interface that is used infrequently.
EnSight cannot read the output file of AIRFL03D solver, res.bin, without
modification of format. A FORTRAN interface program airflo3d_ensight.f converts the
res.bin file to EnSight readable format. This program creates a geometry file, result file,
and other necessary files according to the requirements of EnSight.
39
CHAPTER VI
RESULTS AND DISCUSSIONS
In this study, the flow around a rotating short cylinder has been predicted
computationally. The computed results are presented in the following pages by vector
arrows, particle traces and pressure contours. The computational results were obtained for
the Reynolds number in the turbulent region. It was found that when a short cylinder
rotates about its axis, the pressure distribution around the cylinder does not remain
symmetrical about the flow direction. This effect can be visualized from the figures
showing the pressure contours. In the pressure contours plot presented in Figure 6.1, it
has been found that when the wheel is rotating in a clockwise direction, a low pressure
(blue color contours) region exists on the upper surface of the cylinder. This low pressure
on the upper surface of the cylinder causes an upward lift or positive lift. But, in the
pressure contour plot Figure 6.2, where the cylinder is rotating in a counterclockwise
manner, the low pressure (blue color contours) region shows up on the lower surface of
the cylinder. Due to this a down ward lift or negative lift has been found This type of lift
forces are due to the 'Magnus Effect'. The pressure contours for non-rotating cylinder
has been shown in the Figure 6.3.
The computational study was extended for different spin ratios. It was found that
when spin ratio was increased, coefficient of drag CD also increased. The increased drag is
due the induced drag which arises due to the presence of lift force Figures 6.4, 6.5 and
6.6 illustrate characteristic particle traces. It was found that the particles were first being
40
PRESSURE CONTOURS
FLOW AROUND A CLOCKWISE ROTATING CYLINDER
pressure 3.0343e-01
8.8705e-02
-1.2603e-01
-3.4076e-Dl
-5.5549e-01
I
Figure 6.1: Pressure contours for flow around a clockwise rotating cylinder.
41
PRESSURE CONTOURS
FLOW AROUND A COUNTERCLOCKWISE ROTATING CYLINDER
pressure 3.a397e-01
1.00246-01
-1 .03498-01
-3 .0722e-01
-5.1D95e-01
Figure 6.2 Pressure contours for flow around a counterclockwise rotating cylinder.
42
PRESSCJRjE CONTOURS
FLOW AROUND A NON-ROTATING dfc>4NDER \
pressure 3.2455e-01
1.7652e-ai
2.8500e-02
-1.1952e-01
-2.6755e-01
I
Figure 6.3: Pressure contours for flow around a non-rotating cylinder.
43
PARTICLE TRACE S
uelocity 1.29B6B^0a
i.a278»>ao
7.5597e-01
FLOW AROUND A COUNTER CLOCKWISE ROTATING CYLINDER
4.8414e-01
2.1230e-01
Figure 6.4 : Particle traces for flow around a counterclockwise rotating cylmder
44
PARTICLE TRACES
FLOW AROUND A CLOCKWISE ROTATING CYLINDER
L^elocity 1.2918e«00
2.1411e-01
Figure 6.5 : Particle traces for flow around a clockwise rotating cyUnder.
45
PARTICLE TRACES
velocity 1.2B18e«00
I.OOBOe^OO
7.3012B-01
FLOW AROUND A NON-ROTATING CYLINDER
4.5426e-01
1.7841e-01
Figure 6.6 : Particle traces for flow around a non-rotating cylinder.
46
earned along the direction of rotation and then released. These figures clearly depict the
ability of the present computational study in predicting rotational flow. Figures 6.7-6.9
show the vector arrows around the short cylinder. In Table 6.1 a comparison of
experimental and computational resuhs of drag coefficients has been presented.
In this study, a small lift was found (Table 6.2 and Table 6.3) even when the wheel
was nonrotating. This might be due to some possible unsteadiness in the field
The flow around a rotating wheel in contact with the ground plane has also been
predicted in this computational study. The computation was also carried out for different
spin ratios. Here also (Figure 6.10 and Figure 6.11), the computational study captured all
the global features. Table 6.4 shows the comparison of lift coefficient for clockwise and
counterclockwise rotation of the cylinder. The predicted drag has been presented in Table
6.5.
In Figure 6.12, a comparison has been made between present computational results
and the available experimental results of drag coefficients. It was found that up to a spin
ratio of 2.0 the computational and experimental results are almost same. Beyond the spin
ratio of 2.0, the experimental drag coefficient increases rapidly. This might be the
limitation of the standard k-e model. But for automobile wheel the spin ratio is 1.0. So,
standard k-e model can easily be used to predict flow around a rotating wheel
Although, no numerical study has been found on the flow around a cylinder, the
results of other experimental studies carried out by diflferent people also agree with the
resuhs of this computational study.
47
• • •»—
. . ^ • ^ VECTOR ARROWS
' • - • ' .
^ *- * » >
< « « « « 4 « « « 4
ue loc i ty ^ 2.'12f2e400'
j » j r .»•
> . ^ k
t f f r / r
t
f ^ / / / /*
1 ,4
^ X *
.^ /*
_* / •
.-* * .--r
«
--» --•
1. 66496 tOX)
-• -•• •
1.?0a6e4fl0
7.523Se-dl
FLOWAROUND A COWmSRCCOfcKWlSEllOfATr G CYLINDER ' ^ „^„„ „ • -•^^^__^„„-^ «-* . -^ -^ _ , . 2 .9608e-a i
Figure 6.7 : Vector arrows for flow around a counterclockwise rotating cylinder.
48
*• • — » — • • • - • «r -••
r^VECTOR ARROWS "
- • — • — • - >
yelpcity"' be •DO
R.OW AROUND A.'CL6ci5wSE'ROTi5^MGC^i^£ER^ ^ -. . ^
> • ^ » -? . 6 3 5 7 B - B 1
Figure 6.8 : Vector arrows for flow around a clockwise rotating cylinder.
49
VECTOR ARROWS . .
FLOW AROUND A NON-ROTAT!NO-CYLINDER
1.8311e-01
Figure 6.9 • Vector arrows for flow around a non-rotating cyUnder.
50
.VECXOR ARROWS
*-^ -^
Melocity 1.3000e«a0
I.OIBOetOO
7.3596e-01
4
L, FLOW AROUND A CLOCKWISE ROTATING CYLINDER IN GROUND CONTACT
4.5394e-01 * •
>
1.7192e-01
Figure 6 10; Vector arrows for flow around a clockwise rotating cylinder in ground contact
51
VECTOR ARROWS
r
• . * •
FLOW AROUND A COUNTER CLOCKWISE ROTATING CYUNDER IN GROUND CONTACT.
•
•
f
velocity 2.2721e*00
1.7859e«00
^ 1.2^97e*D0
8.1351e-01
3.2731e-01
Figure 6.11: Vector arrows for flow around a counterclockwise rotating cylinder in ground contact
52
Table 6.1 : Comparison of experimental and computational results of drag coefficients.
Spin Ratio , coD/2V
0
0.5
1.0
1.5
2
2.5
3.0
Experimental
0.85
0.87
0.90
0.95
1.1
1.75
2.2
Computational
0.90
0.93
0.96
0.99
1.01
1.06
1.10
53
2.5
c '.2 1.5 +
o
^ 1 (0
0.5
1
• Experimental B Computational
0.5 1.5 2
Spin Ratio
2.5
Figure 6.12 : Comparison of experimental and computational resuhs of drag coefficients.
54
Table 6.2 : Drag and Lift coefficients for coarse grid for different spin ratios.
S. R.
0DD/2V
0
1
5
10
c.w. CD
0.934
0.939
0.974
1.037
CL
0.000
0.010
0.038
0.102
c.c.w. CD
0.934
- 0.939
0.974
1.032
CL
0.005
0.000
-0.026
-0.081
Table 6.3 ; Drag and Lift coefficients for fine grid for different spin ratios.
S. R.
03D/2V
0
1
5
10
C.W.
CD
0.982
0.983
1.011
1.129
CL
0.024
0.037
0.115
0.322
CC.W.
CD
0.982
0.983
1.003
1.068
CL
0.024
0.012
-0.047
-0.169
55
Table 6.4 : Comparison of lift coefficient for clockwise and counterclockwise rotation of the cylinder.
Spin Ratio
0
1
3
5
7
9
Clockwise rotation
0.024
0.037
0.077
0.115
0.22
0.322
Counterclockwise rotation
0.024
0.012
-0.018
-0.047
-0.105
-0.169
56
c «
O U
0.35 -
0.3
0.25 -0.2
0.15
0.1
0.05 E
n yj
-0.05 ^
-0.1
-0.15
-0.2
1
) 1
- -
• Clockwise rotation HCountercl(x;k\Msc rotation
•
1 t t
2 3 4 fi 8
Spin Ratio
Figure 6.14 : Comparison of lift coefficient for clockwise and counterclockwise rotation of the cylinder.
57
Table 6.5 : Drag coefficient Cofor different Spin Ratios
Spin Ratio
0
1
2
3
4
Drag Coefficient
1.220
1.299
1.320
1.33
1.340
58
CHAPTER VII
CONCLUSION AND RECOMMENDATIONS
6.1 Conclusion
A finite-volume method has been described for calculating incompressible flow
around a rotating wheel. The numerical model captures most of the global features
observed in the experiments. For low spin ratios the predicted drag or lift coefficients
agree reasonably well with the experimental values. For high spin ratios computational
results vary significantly from the experimental results. But, for a spin ratio of one such as
occurs on automobile wheels, experimental results and computational resuhs are close.
From the present study, it can be concluded that the standard k-s model can also
predict rotational flow.
6.2 Recommendations
A complete aerodynamic study of a car with rotating wheel can be performed by
using newly developed interface and fi-om that the effect of wheel rotation on drag or lift
can directly be predicted.
The effect of ground movement on aerodynamics can also be predicted
simultaneously with the effect of wheel rotation.
The reasons behind the variation of drag and lift coefficient fi-om experimental
values at high spin ratios should also be analyzed in the fiiture studies.
59
REFERENCES
1 Brandt, A.," 1984 Multigrid Guide with Applications to Fluid Dynamics," Monograph, GMD-Studie 85, GMD-FIT, Postfach 1240, D-5205, St. Augustin 1, Germany, 1985. Also available from Secretary, Department of Mathematics, University of Colorado at Denver, Colorado 80204-5300.
2. Fackrell, J. E. and Harvey J. K., "The aerodynamics of an isolated road wheel," proceedings of the second AlAA Symposium on Aerodynamics Sposts & Competition Automobiles, May 11, 1974, Los Angeles, California.
3. Griffith, R. T., and Ma, C. Y. "Differential Boundary-Layer Separation Effect in the Flow over a Rotating Cylinder," Roy Aeronaut. Soc. J.. Vol. 73, pp. 524-526, June, 1969.
4. Ilker Kirish and Siva Parameswaran, "A Multigrid Based Computational Procedure to Predict Internal Flow with Heat Transfer," Proceedings of 30th 1995 National Heat Transfer Conference, Volume 9.
5. Issa, R. I., "Solution of the Implicitly Discretized Fluid Flow Equations by Operator Splitting," J. Comput. Phys., Vol. 62, pp. 40-65, 1986.
6. Launder, B. E. and Spalding, D. B. Mathematical Models of Turbulence, Academic Press, London, 1972.
7. Mendu, L. N. "Computation of Fluid Flow with Multi-Grid and Multi-Block Algorithms," Ph.D. Dissertation, Texas Tech University, 1995.
8. Morelli.A, "Aerodynamic Actions on an Automobile Wheel," Fifth Paper at the First Symposium on Road Vehicle Aerodynamics, City University London, 1969.
9. Parameswaran S., Srinivasan A. and Sun R., "Numerical Aerodynamics Simulation of Steady and Transient Flows Around Two-Dimensional Bluff Bodies Using the non-staggered Grid System," Numerical Heat Transfer. Part A, Vol. 21, pp. 443-461, 1992.
10. Patankar, S.V. and Spalding, D.B.," A Calculation Procedure for Heat, Mass and Momentum Transfer in Three Dimensional Parabolic Flows," Int. J. of Heat and MassTransf, Vol. 15, pp. 1787-1806, 1972.
60
11. Patankar, S. V., Numerical Heat Transfer and Fluid Flow, Hemisphere, Washington, D.C., 1990.
12. Stapleford, W.R. and G.W.Carr, "Aerodynamic Characteristics of Exposed rotating wheels," Motor Industry Research Association Report No. 1970/2, 1970
13. Stone, H. L. "Iterative solution of Implicit Approximations of Muhi-dimensional Partial Differential Equations," SIAM Journal of Numerical Analysis, vol 5, pp. 530-545, 1968.
14. Thom, A. "Experiment on the Flow Past a Rotating Cylinder," A R C . R & M 1410, 1931.
15. Wolf-Heinrich Hucho, Aerodynamics of Road Vehicles, Butterworth-Heinemann, Reprint 1990.
61
APPENDIX
COMPUTER CODE
c c C THIS PROGRAM READS airflo3d.dat FILE FROM ICEMCFD_AIRFL03D C C INTERFACE & ASSIGNS THE VELOCITIES AT EACH ROTATING C C WALL-CELL FACE. C C C C#####################################################//////////////////#######
INCLUDE 'FLWSD.H'
CHARACTER OTITLE*80,TITLE*80,UNITS*20,SELECT*80,USRUNIT*20 CHARACTER*6 NAME
REALFACTOR,XDIST,YDIST,ZDIST,CONSTANT,VEL,RAD,CONS
COMMON /ADDRES/ NEARCL(6,NCMAX),LDTHRF(6,NCMAX)
COMMON /FIELDS/ U(-NBMAX:NCMAX,3),TE(-NBMAX:NCMAX), + P(-NBMAX:NCMAX),E(-NBMAX:NCMAX), + ED(-NBMAX.NCMAX)
COMMON /PROPS/ VIS(-NBMAX:NCMAX),DEN(-NBMAX:NCMAX), + DIVU(-NBMAX:NCMAX),TEMP(NCMAX)
COMMON /OLD/ DENVO(NCMAX),EDO(NCMAX),TEO(NCMAX)
COMMON /AXES/ NAXIS,NAXPOS(MAXAXS),NSURR(MAXXPS,MAXAXS), + IASURX(MAXSUR,MAXXPS,MAXAXS),IBAXIS(MAXXPS,MAXAXS)
COMMON /SYMPL/ NSYMPL,NCSYMP(MAXSMP), + IASYMP(MAXSMC,MAXSMP),IBSYMP(MAXSMC,MAXSMP), -I- LDAFSP(MAXSMC,MAXSMP)
COMMON /MATRIX/ ACOEF(NCMAX,6),AZERO(NCMAX,3) MATRIX ELEMENTS FOR VELOCITY TRANSPORT COMMON /PCORR/ AU(NCMAX,3),SUU(NCMAX,3),PSU(NCMAX),
+ SUPRES(NCMAX), PSW(-NBMAX:NCMAX) EQUIVALENCE (PSW(1),GEN(1)) DIMENSION GEN(NCMAX)
COMMON /FLUX/ CNVFLX(6,NCMAX)
62
COMMON /GEOMl/ VOL(NCMAX) DIMENSION DELT(5),ENDT(5),NAME(5),PRANNO(5)
c COMMON /GEOM2/ XCORN(MAXVTX,3),ICORN(MAXVTX,8) C GRVELV^GRID CONVECTION VOLUMES
COMMON /WORK/ WORK1(0:NCMAX,9)
IREAD=10 IWRITE=11 OPEN(IREAD,FILE='airflo3d.bin',STATUS='OLD',FORM='UNFORMATTED') OPEN(IWRITE,FILE='rot.bin',STATUS='NEW',FORM='UNFORMATTED') OPEN(l,FILE='GHE_C.DAT',STATUS='NEW)
C DATA FACTOR/1000.0/ C DATA CONSTANT/0.0/
WRlTE(*,*)Type 1 for rotating 0 for non-rotating' READ(*,*)CONSTANT WRITE(*,*)T)pe user unit* WRlTE(*,*)T>pe 1000 for mm' WRITE(*,*)T>pe 100 for cm' READ(*,*)FACTOR WRITE(*,*)'T)pe X distance bet\veen LOCAL and GLOBAL origins ' READ(*,*)XDIST WRITE(*,*)'Type Y distance between LOCAL and GLOBAL origins' READ(*,*)YDIST WRITE(*,*)'T}pe Z distance bet\veen LOCAL and GLOBAL origins' READ(*,*)ZDIST WRITE(*,*)*Type the free stream velocity in m/sec.' READ(*,*)VEL WRITE(*.*)'Type the radius of the wall face (wheel) in meter.' READ(*,*)RAD WRITE(*.*)'T3'pe Spin RaUo' READ(*,*)CONS
READ (IREAD) OTITLE READ (IREAD) NTIME,IUNITS,(DELT(I),ENDT(I),I=1,NTIME) READ (IREAD) IVAR,(NAME(I),PRANN0(I),I=1,IVAR)
C CONVERGENCE READ (IREAD) MAXCCP,EPSP
C TURBULENCE PARAMETERS READ (IREAD) C1,C2,C3.CMU,CMU25.CMU75
C BULK FLUID PARAMETERS READ (IREAD) CVFL,VISREF
C ADDRESSING AND GRID DATA READ (IREAD) NC,((NEARCL(IF,IC),IF=1,6),IC=1,NC) READ (IREAD) ((LDTHRF(IF,IC),1F=1,6),IC=1,NC) READ (IREAD) ((ICORN(IC,IV),IC=l.NC).IV=l,8)
63
BOUNDARY DATA READ (IREAD) NB,NW,NAXIS,NSYMPL,NFRSTPL,NVELS
WALLS IF (NW.NE.O) THEN
READ (IREAD) (IAWALL(IW),IW=1,NW) READ (IREAD) (IBWALL(IW),IW=1,NW) READ (IREAD) (LDATB(IW),IW-1,NW) READ (IREAD) (IWV(IW),IW=1,NW) READ (IREAD) (TWALL(IW),IW=1,NW) READ (IREAD) (VELWAL(I), 1=1,3)
ENDIF
AXES IF (NAXIS.NE.O) THEN
READ (IREAD) (NAXP0S(LX:),LX-1,NAXIS) READ (IREAD) ((NSURR(IXP,IX),IXP=l,NAXPOS(IX)),IX-l,NAXIS) READ (IREAD) (((IASURX(ISN,IXP,IX),ISN=1,NSURR(DCP,DC)),
+ IXP-1,NAXP0S(IX)),IX=1,NAXIS) READ (IREAD) ((IBAXIS(IXP,IX),IXP=l,NAXPOS(IX)),IX=l,NAXIS)
ENDIF
SYMMETRY PLANES IF (NSYMPL.NE.O) THEN
READ (IREAD) (NCSYMP(IS),IS-1,NSYMPL) READ (IREAD) ((IASYMP(ISP,IS),ISP=1,NCSYMP(IS)),
+ IS=1,NSYMPL) READ (IREAD) ((IBSYMP(ISP,IS),ISP-1,NCSYMP(IS)),
+ IS=I,NSYMPL) READ (IREAD) ((LDAFSP(ISP,IS),ISP=1,NCSYMP(IS)),
+ IS=1,NSYMPL) ENDIF
FREESTREAM BOUNDARY IF (NFRSTPL.NE.O) THEN
READ (IREAD) (NCFRST(IFS), IFS=1,NFRSTPL) READ (IREAD) ((UFRST(IFS,I),I=1,3),PFRST(IFS),IFS=1,NFRSTPL) READ (IREAD) ((IAFRST(ICFS,IFS),ICFS=1,NCFRST(IFS)),
+ IFS=1,NFRSTPL) READ (IREAD) ((IBFRST(ICFS,IFS),ICFS=1,NCFRST(IFS)),
+ IFS=1,NFRSTPL) READ (IREAD) ((LDFRST(ICFS,IFS),ICFS=1,NCFRST(IFS)),
+ IFS=1,NFRSTPL) READ (IREAD) ((FRFLUX(ICFS,IFS),ICFS=1,NCFRST(IFS)),
+ IFS=1,NFRSTPL) ENDIF
VELOCITY SOURCES IF (NVELS.NE.O) THEN
READ (IREAD) OSfVSC(IV),IV=l,NVELS) READ (IREAD) (((UVS(ICV,IV,I),I=1,3),ICV-1,NVSC(IV)),
+ EVELS(IV),PVELS(IV),TEVELS(IV), + EDVELS(IV),IV=1.NVELS)
64
READ (IREAD) ((IAVELS(ICVIV),ICV-1,NVSC(IV)),IV=1.NVELS) READ (IREAD) ((IBVELS(ICV,IV),ICV=1,NVSC(IV)),IV=LNVELS) READ (IREAD) ((LDATBV(ICV,IV),ICV=1,NVSC(IV)),IV-1,NVELS)
ENDIF
C VAIUABLE VALUES FOR THE DOMAIN, FOR A START FILE THE C OLD TIME VALUES ARE SET TO THE CURRENT ONES, c IREC-O
999 READ (IREAD) IRSTRT,TIME c IF (IRSTRTLT.O) GOTO 1010 c IREC=IREC+1
READ (IREAD) NVRTEX,((XC0RN(1V,I),IV=1,NVRTEX),I=1.3) READ (IREAD) ((U(IC,I),IC=1,NC),I=1,3) READ (IREAD) (P(IC),IC-1,NC) READ (IREAD) 0E(IC),IC-1,NC) READ (IREAD) (TE(IC).IC=1,NC) READ (IREAD) (ED(IC),IC-1,NC)
C CONVECTIVE FLUXES READ (IREAD) ((CNVFLX(IF,IC),IF=1,6),IC-1,NC) CLOSE(IREAD)
C######################################################################C C23456789012345678901234567890123456789012345678901234567890123456789012 C#######ff##ff###########################################################C
DO 229 1=1,NW DO 230 J=l,3
UWV(I,J)=0.00 230 CONTINUE 229 CONTINUE
D0 231I=1,NW IW=I CALLTEST(IW,UA.VA.WA,FACTOR,XDIST,YDIST,ZDIST,VEL,RAD,CONS) WRITE(1,*)UA,VA,WA UWV(1,1)=UA*C0NSTANT UWV(I,2)=VA*C0NSTANT UWV(I,3)=WA*CONSTANT
231 CONTINUE
DO 232 I=1,NW WR1TE(1,*)I WRITE(1,*)UWV(1.1),UWV(I,2),UWV(I,3)
232 CONTINUE
C################################################################^^ C23456789012345678901234567890123456789012345678901234567890123456789012 C######################################################^^
WRITE (IWRITE) OTFTLE WRITE (IWRITE) NTIMEJUNITS.(DELT(I),ENDT(I),I=1,NTIME) WRITE (IWRITE) IVAR,(NAME(I),PRANN0(I),I=1,IVAR)
65
WRITE (IWRITE) MAXCCP,EPSP WRITE (IWRITE) C1,C2,C3,CMU,CMU25,CMU75 WRITE (IWRITE) CVFL,V1SREF
WRITE (IWRITE) NC,(0^fEARCL(IF,IC),IF=l,6),IC=l,NC) WRITE (IWRITE) ((LDTHRF(IF,IC),IF=1,6),IC=1,NC) WRITE (IWRITE) ((ICORN(IC,IV),IC=l,NC),IV=l,8)
WRITE (IWRITE) NB,NW,NAXIS,NSYMPL,NFRSTPL,NVELS
IF (NW.NE.O) THEN WRITE (IWRITE) (IAWALL(IW),IW=1,NW) WRITE (IWRITE) (IBWALL(IW),IW=1,NW) WRITE (IWRITE) (LDATB(IW),IW=1,NW) WRITE (IWRITE) (IWV(IW),IW=1.NW) WRITE (IWRITE) (TWALL(IW)JW=1,NW) WRITE (IWRITE) (VELWAL(I), IW=1,3) WRITE (IWRITE) aJWV(IWJ). IW=1,NW) WRITE (IWRITE) (UWV(IW,2). IW=LNW) WRITE (IWRITE) (UWV(IW,3), IW=1,NW)
ENDIF
IF (NAXIS.NE.O) THEN WRITE (IWRITE) (NAXPOS(IX),IX=l,NAXIS) WRITE (IWRITE) ((NSURR(IXP,IX),IXP=1,NAXP0S(IX)),IX=1,NAXIS) WRITE (IWRITE) (((IASURX(ISN,DCP,IX:),ISN=1,NSURR(IXP,IX)),
IXP= 1 ,N AXPOS(IX)),IX= 1 ,N AXIS) WRITE (IWRITE) ((IBAXIS(IXP,IX),IXP=1,NAXP0S(IX)),IX=1,NAXIS)
ENDIF
IF (NSYMPL.NE.O) THEN WRITE (IWRITE) (NCSYMP(IS),IS=1,NSYMPL) WRITE (IWRITE) ((IASYMP(ISP,IS),ISP=1,NCSYMP(IS)).
+ IS=1,NSYMPL) WRITE (IWRITE) ((IBSYMP(ISP,IS),ISP=1,NCSYMP(IS)),
+ IS=1,NSYMPL) WRITE (IWRITE) ((LDAFSP(ISP,1S),ISP=1,NCSYMP(IS)).
+ IS=1,NSYMPL) ENDIF
FREESTREAM BOUNDARY IF(NFRSTPL.NE.O) THEN WRITE(IWRITE) (NCFRST(IFS), IFS=1,NFRSTPL) WRlTE(IWRITE)(aJFRST(IFS,I),I=l,3),PFRST(IFS),IFS=l,NFRSTPL) WRITE(IWRITE) ((IAFRST(ICFS,IFS),ICFS= 1 ,NCFRST(IFS)),
+ IFS=1,NFRSTPL) WRITE(IWRITE) ((IBFRST(ICFS,IFS),ICFS=1,NCFRST(IFS)).
+ IFS=1,NFRSTPL) WRITE(IWRITE) ((LDFRST(ICFS,IFS),ICFS=1,NCFRST(IFS)),
+ IFS=1,NFRSTPL) 66
WRITE(IWRITE)((FRFLUX(ICFS,IFS),1CFS=1,NCFRST(IFS)), IFS=1,NFRSTPL)
ENDIF
IF (NVELS.NE.O) THEN WRITE (IWRITE) (NVSC(IV),IV=1,NVELS) WRITE (IWRITE) (((UVS(ICV,IV,I),I=1,3),ICV=1,NVSC(IV)),
EVELS(IV),PVELS(IV), + TEVELS(IV),EDVELS(IV),IV=1,NVELS)
WRITE (IWRITE) ((IAVELS(ICV,IV),ICV=1,NVSC(IV)),IV=1,NVELS) WRITE (IWRITE) ((IBVELS(ICV,IV),ICV=1,NVSC(IV)),IV=1,NVELS) WRITE (IWRITE) ((LDATBV(ICV,IV),ICV=1,NVSC(IV)),IV=1,NVELS)
+
C====—-========END OF GEOMETRY/PARAMETER DATA-
ENDIF
WRITE (IWRITE) IRSTRT,TIME WRITE (IWRITE) NVRTEX,((XCORN(IV,I),IV=l,NVRTEX),I=l,3) WRITE (IWRITE) ((U(IC,I),IC=1,NC),I=1,3) WRITE (IWRITE) (P(IC),IC=1,NC) WRITE (IWRITE) (E(IC),IC=1,NC) WRITE (IWRITE) (TE(IC),IC=1,NC) WRITE (IWRITE) (ED(IC),IC=1,NC)
CONVECTIVE FLUXES WRITE (IWRITE) ((CNVFLX(IF,IC),IF=1,6),IC=1,NC)
CLOSE(IWRITE) STOP END
SUBROUTINE TEST(IW,UA,VA,WA,FACTOR,XDIST,YDIST,ZDIST,VEL,RAD,CONS) INCLUDE 'FLW3D.H'
REAL FACTOR
COMMON /ADDRES/ NEARCL(6,NCMAX),LDTHRF(6,NCMAX)
COMMON /FIELDS/ U(-NBMAX:NCMAX,3),TE(-NBMAX:NCMAX), + P(-NBMAX:NCMAX),E(-NBMAX;NCMAX), + ED(-NBMAX:NCMAX)
COMMON /PROPS/ VIS(-NBMAX:NCMAX),DEN(-NBMAX:NCMAX), + DIVU(-NBMAX:NCMAX),TEMP(NCMAX)
COMMON /OLD/ DENVO(NCMAX),EDO(NCMAX),TEO(NCMAX)
COMMON /AXES/ NAXIS,NAXPOS(MAXAXS),NSURR(MAXXPS,MAXAXS). 67
+
+ +
IASURX(MAXSUR,MAXXPS,MAXAXS),IBAXIS(MAXXPS,MAXAXS)
COMMON /SYMPL/ NSYMPL,NCSYMP(MAXSMP), I AS YMP(MAXSMC,MAXSMP). IB S YMP(MAXSMC,MAXSMP), LDAFSP(MAXSMC,MAXSMP)
COMMON /MATRIX/ ACOEF(NCMAX,6),AZERO(NCMAX,3) MATRDC ELEMENTS FOR VELOCITY TRANSPORT COMMON /PCORR/ AU(NCMAX,3),SUU(NCMAX,3),PSU(NCMAX),SUPRES(NCMAX),
PSW(-NBMAX:NCMAX) EQUIVALENCE (PSW(1),GEN(1)) DIMENSION GEN(NCMAX)
COMMON /FLUX/ CNVFLX(6,NCMAX)
COMMON /GEOMl/ VOL(NCMAX) DIMENSION DELT(5),ENDT(5),NAME(5),PRANNO(5)
c COMMON /GE0M2/ XCORN(MAXVTX,3),ICORN(MAXVTX,8) C GRVELV=GRID CONVECTION VOLUMES
COMMON /WORK/ WORK1(0:NCMAX,9) C COMMON /WALL/ NW,LDATB(MAXWAL),IAWALL(MAXWAL),IBWALL(MAXWAL), C + WALLF(MAXWAL),WALLFE(MAXWAL),TWALL(MAXWAL), C + UWV(MAXIWV,3),IWV(MAXWAL),WGEN(NCMAX),IW,U,V,W C COMMON /GEOM2/ XCORN(MAXVTX,3),ICORN0VL/OCVTX,8)
DIMENSION X1(3),X2(3),X3(3),X4(3), + XD1(3),XD2(3),XD3(3)
REAL XX1,XX2,XX3,XX4,YY1,YY2,YY3,YY4,ZZ1, + ZZ2,ZZ3,ZZ4,VEL,RAD,OMEGA,X,Y,Z,XDIST,YDIST,ZDIST,CONS
DIMENSION NCORN(4,6),EPS(3,3,3)
OPEN(9,FlLE='ghe.dat',STATUS='NEW')
DATA (NCORN (1,1), I = 1,4 ) /5,1,4,8/ DATA ( NCORN (1,4), I = 1,4 ) /6,2,3,7/
DATA ( NCORN (1,2), I = 1,4 ) /2,1,5,6/ DATA ( NCORN (1,5), I = 1,4 ) /3,4.8,7/
DATA ( NCORN (1,3), I = 1,4 ) /4,1,2,3/ DATA ( NCORN (1,6). I = 1,4 ) /8,5.6,7/
DATA ((EPS(1,J,K),K=1,3),J=1,3) /0.,0.,0.,0.,0.,1.,0.,-1.,0./ DATA ((EPS(2,J,K),K=1,3),J=1,3) /0..0..-l.,0.,0.,0.,l.,0.,0./ DATA ((EPS(3,J,K),K=1,3),J=1.3) /0.,1.,0.,-1.,0.,0.,0.,0.,0./
68
FIND VERTEX COORDINATES OF WALL FACE:
DATA FACTOR/1000.0/
IF=LDATB(IW) NNC=IAWALL(IW) DO 5 1=1,3 IV=ICORN(NNC,NCORN(l,IF)) X1 (I)=XCORN(I V,I)/FACTOR IV=ICORN(NNC,NCORN(2,IF)) X2(I)=XCORN(IV,I)/FACTOR IV=ICORN(NNC,NCORN(3,IF)) X3 (I)=XCORN(IV,I)/F ACTOR IV=ICORN(NNC,NCORN(4,IF)) X4(I)=XCORN(IV,I)/F ACTOR CONTINUE
XX1=X1(1)-XDIST XX2=X2(1)-XDIST XX3=X3(1)-XDIST XX4=X4(1)-XDIST
YY1=X1(2)-YDIST YY2=X2(2)-YDIST YY3=X3(2)-YDIST YY4=X4(2)-YDIST
ZZ1=X1(3)-ZDIST ZZ2=X2(3)-ZDIST ZZ3=X3(3)-ZDIST ZZ4=X4(3)-ZDIST
X=(XXl+XX2+XX3+XX4)/4.0 Y=(YYl+YY2+YY3+YY4)/4.0 Z=(ZZ 1+ZZ2+ZZ3+ZZ4)/4.0
C VEL=1.00 C RAD=0.20
OMEGA=CONS*VEL/RAD
STATIC WALL VELOCITIES
IF(IWV(IW).EQ.1)THEN
UA=0.0 VA=0.0 WA=0.0
69
ENDIF MOVING WALL VELOCITIES (TRANSLATION)
IF(IWV(IW).EQ.2.AND.TWALL(IW).EQ.0.0)THEN UA=1.00 VA=0.0 WA=0.0 ENDIF
MOVING WALL VELOCITIES (ROTATION)
IF(IWV(IW).EQ.2.A>JD.TWALL(IW).EQ.1.0)THEN
IF(XGT.O.O.AND.Y.GT.O.O)THEN THETA=ATAN(ABSC^)/ABS(X)) UA=-OMEGA*ABS((SQRT(X**2+Y**2)))*SIN(THETA) VA=OMEGA*ABS((SQRT(X**2+Y**2)))*COS(THETA) WA=0.0
ENDIF
IF(X.LT.O.O.AND.Y.GT.O.O)THEN THETA=ATAN(ABSO')/ABS(X)) UA=-OMEGA*ABS((S(5RT(X**2+Y**2)))*SIN(THETA) VA=-OMEGA*ABS((SQRT(X**2+Y**2)))*COS(THETA) WA=0.0
ENDIF
IF(X.LT.O.O.AND.Y.LT.O.O)THEN THETA=ATAN(ABS(Y)/ABS(X)) UA=OMEGA*ABS((SQRT(X**2+Y**2)))*SIN(THETA) VA=-OMEGA*ABS((SQRT(X**2+Y**2)))*COS(THETA) WA=0.0
ENDIF
IF(X.GT.0.0.AND.Y.LT.0.0)THEN THETA=ATAN(ABSO')/ABS(X)) UA=OMEGA*ABS((SQRT(X**2+Y**2)))*SIN(THETA) VA=OMEGA*ABS((SQRT(X**2+Y**2)))*COS(THETA) WA=0.0
ENDIF
IF(X.EQ.O.O.AND.Y.GT.O.O)THEN U A=-OMEGA* ABS(SQRT(X* *2+Y* *2)) VA=0.0 WA=0.0
ENDIF
IF(X.EQ.O.O.AND.Y.LT.O.O)THEN UA=OMEGA*ABS(SQRT(X**2+Y**2)) VA=0.0 WA=0.0
ENDIF
70
IF(X.GT.O.O.AND.Y.EQ.O.0)THEN UA=0.0 VA=OMEGA*ABS(SQRT(X**2+Y**2)) WA=0.0
ENDIF
IF(X.LT.O.O.AND.Y.EQ.O.O)THEN UA=0.0 VA=-OMEGA*ABS(SQRT(X**2+Y**2)) WA=0.0
ENDIF
ENDIF
WR1TE(9,*)IW WRITE(9,91 )UA, VA, W A WRITE(9,91)X,Y,Z
91 FORMAT(3(3X,F10.3)) DO 61 1=1,3 WRITE(9,89)X1(I),X2(I),X3(I),X4(I)
89 FORMAT(4(2X,F10.3)) 61 CONTINUE
RETURN END
71
PERMISSION TO COPY
In presenting this thesis in partial fulfillment of the requirements for a
master's degree at Texas Tech University or Texas Tech University Health Sciences
Center, I ag^ee that the Library and my major department shall make it freely
available for research purposes. Permission to copy this thesis for scholarly
purposes may be granted by the Director of the Library or my major professor.
It is understood that any copying or publication of this thesis for financial gain
shall not be allowed without my further written permission and that any user
may be liable for copyright infringement.
Agree (Permission is granted.)
\,xi-\c^^ or 11-^^ -T
y{r-ChM\^Cy Sttldeht's Signatu^ e Date
Disagree (Permission is not granted.)
Student's Signature Date
