WheelModeling CFD MSC

DF
CFD investigation on wheel modelling and

car aerodynamics
Master’s Thesis in Applied Mechanics
Anandh Ramesh Babu
Department of Mechanics and Maritime Sciences

C HALMERS U NIVERSITY OF T ECHNOLOGY
Gothenburg, Sweden 2019
Master’s thesis 2019:58
CFD investigation on wheel modelling and car

aerodynamics
Anandh Ramesh Babu
DF

Division of Vehicle Engineering and Autonomous Systems
Chalmers University of Technology
CFD investigation on wheel modelling and car aerodynamics
Master’s Thesis Report
Anandh Ramesh Babu
© Anandh Ramesh Babu, 2019.
Supervisor: Dr. Teddy Hobeika, Aerodynamics Group, Volvo Cars

Examiner: Prof. Simone Sebben, Division of Vehicle Engineering and Autonomous
Systems, Chalmers University of Technology
Master’s Thesis 2019:58

Division of Vehicle Engineering and Autonomous System
SE-412 96 Gothenburg
Telephone +46 31 772 1000
Cover: Resampled volume used to capture regions of low instantaneous velocities

around the car.
Typeset in LATEX, template by David Frisk

Printed by Chalmers Reproservice
iv
CFD investigation on wheel modelling and car aerodynamics
Master’s Thesis
Anandh Ramesh Babu
Abstract
It has been estimated that approximately 25% of the drag of a passenger vehicle
is due to the wheels and wheel housings. So studying the flow patterns around
them have been of great importance for several years. Traditionally, wind tunnel
experiments have been used to study the aerodynamic performance of vehicles but
with growing computational resources, CFD investigations have proven to be vital,
especially in the initial stages of development. With growing regulations on vehicle
performances, it is of paramount importance to be able to accurately simulate the
flow around wheels. The work included two studies: simulations of a rotating cylin-
der to represent a simplified wheel geometry and simulations of a full scale car.
In the first study, the Rotating Wall(RW) and Sliding Mesh(SM) methods were in-
vestigated on a cylinder and it was found that the case was extremely mesh and
timestep dependent. To obtain comparable results, very fine mesh and timestep
had to be employed which were computationally expensive. A parametric study
was performed on the SM case to understand the mesh, geometry and timestep de-
pendency. Investigations were done to see if pseudo-parallelization of mesh updating
in SM method could speed up the simulations. About 35% reduction in total time
and 68% reduction in mesh updating time was noted.
In the second study, aerodynamic analysis was performed on the car and wheels.
Moving Reference Frame(MRF) and SM wheel modelling approaches were investi-
gated and their differences were analyzed. Investigations on how blanking of rims
affect the aerodynamic performance of a car was performed. It was noted that
blanking reduced the drag by about 29 Cd A counts and increased downforce by 21
Cl A counts. An investigation on whether performing simulations with a timestep of
2.5e-4s on the mesh was done by comparing the results to a finer timestep of 1e-4s. It
was found that the 2.5e-4s yields acceptable results. Finally, pseudo-parallelization
of the interface updating was tested on the car by splitting the wheel interface into
three interfaces. About 21% reduction in updating time and 5% reduction in total
time was observed using this method. It was inferred that the method can be used
for speeding up SM simulation and it can be further improved by creating more
interfaces and evenly distributing the number of cells on each interface.
Keywords: Car aerodynamics, CFD, wheel modelling, SM optimizing, wheel blank-

ing, pseudo-parallelization of SM.
v
Acknowledgements
Firstly, I would like to express my sincere gratitude to my supervisor at Volvo Cars,
Dr. Teddy Hobeika, for his constant support and motivation, guiding me in the
right direction during the course of this project. His insightful recommendations in
the project has proven to be extremely helpful to me. I would also like to thank him
for teaching me a great deal about aerodynamics of passenger vehicles and CFD
modelling.
I would like to thank my examiner, Prof. Simone Sebben, for her valuable advice
and for all the help when needed.
Another sincere thanks to everyone at Volvo Cars and the aerodynamics depart-
ment, for giving me the opportunity to work in such an encouraging environment
and your valuable lessons in table tennis.
And finally, a big thanks to my parents and all my friends in Gothenburg and back
in India, who have always believed and encouraged me all these years. I am sure
that all the support and unconditional love you have given me, is the reason I am
an engineer today.
Anandh Ramesh Babu, Gothenburg, June 2019
vii
Contents
List of Figures xi
List of Tables xiii
1 Introduction 1
1.1 Environmental impact of Vehicle Aerodynamics . . . . . . . . . . . . 1
1.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Project Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Theory 5
2.1 Fluid Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.1 Governing Equations . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Computational Fluid Dynamics . . . . . . . . . . . . . . . . . . . . . 7
2.2.1 Turbulence . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2.2 RANS models . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2.2.1 k − ω Turbulence Model . . . . . . . . . . . . . . . . 8
2.2.3 LES model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.4 DES models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.4.1 IDDES model . . . . . . . . . . . . . . . . . . . . . . 10
2.3 Aerodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.4 Rotation Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.4.1 Rotating Wall boundary condition . . . . . . . . . . . . . . . . 11
2.4.2 Multiple Reference Frame . . . . . . . . . . . . . . . . . . . . 11
2.4.3 Sliding Mesh method . . . . . . . . . . . . . . . . . . . . . . . 12
3 Methodology 13
3.1 Cylinder Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.2 Car Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
4 Results and Discussions 23

4.1 Cylinder simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.1.1 Analysis of flow field . . . . . . . . . . . . . . . . . . . . . . . 23
4.1.2 Comparison between RW and SM methods . . . . . . . . . . . 26
4.1.3 Parametric Study on SM method . . . . . . . . . . . . . . . . 28
4.1.4 Splitting interface - Pseudo-parallelization . . . . . . . . . . . 35
4.2 Car simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.2.1 Car aerodynamic analysis . . . . . . . . . . . . . . . . . . . . 39
ix
Contents
4.2.2 Wheel aerodynamic analysis . . . . . . . . . . . . . . . . . . . 43

4.2.3 Comparison between wheel modeling approaches-SM vs MRF 45
4.2.4 Effect of rims in the flow field and aerodynamics of the car . . 49
4.2.5 Time step dependency study . . . . . . . . . . . . . . . . . . . 54
4.2.6 Splitting interface - Pseudo-parallelization . . . . . . . . . . . 56
5 Conclusion 59
5.1 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
Bibliography 61
x
List of Figures
2.1 Aerodynamic forces and moments acting on the car . . . . . . . . . . 11
3.1 Geometry description of the cylinder simulations . . . . . . . . . . . . 13

3.2 Segregation of regions: Grey region represents the rotating region and
blue region represents the stationary air domain . . . . . . . . . . . . 14
3.3 line probes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.4 Mesh around the cylinder and interface . . . . . . . . . . . . . . . . . 15
3.5 Mesh around the cylinder and interface . . . . . . . . . . . . . . . . . 15
3.6 Geometries of cylinder split into 2, 3, 4 and 8 faces . . . . . . . . . . 17
3.7 Volvo XC60 geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.8 Representation of the domain and boundaries . . . . . . . . . . . . . 19
3.9 Mesh planes about x-axis and y-axis . . . . . . . . . . . . . . . . . . 19
3.10 Wheel setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.11 Configuration of wheels . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.12 Geometry of the wheel’s SM region used in the study . . . . . . . . . 22
4.1 Mean velocity field around the cylinder from RW method . . . . . . . 24

4.2 Mean velocity plot along the line probes from RW method . . . . . . 24
4.3 Forces acting on the cylinder . . . . . . . . . . . . . . . . . . . . . . . 25
4.4 Moment in the rotating region . . . . . . . . . . . . . . . . . . . . . . 25
4.5 Mean velocity along the line probes comparing RW and SM . . . . . 26
∆V
4.6 V∞
plot comparing RW and SM methods . . . . . . . . . . . . . . . . 27
4.7 Mean velocity around the cylinder comparing RW and SM methods . 27
4.8 Parametric study results from different parameters in comparison
with the base case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.9 Parametric study results from different mesh and geometry settings
in comparison to the base case . . . . . . . . . . . . . . . . . . . . . . 30
4.10 Parametric study results from coupled solver and wake refinement as
compared to the base case . . . . . . . . . . . . . . . . . . . . . . . . 32
4.11 Final mesh representation . . . . . . . . . . . . . . . . . . . . . . . . 33
4.12 Mean velocity profiles along the line probes comparing the base and
final configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
∆V
4.13 V∞
plot of SM solutions . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.14 Effect on avg. time per timestep . . . . . . . . . . . . . . . . . . . . . 35
4.15 Effect on avg. updating time per timestep . . . . . . . . . . . . . . . 36
4.16 Effect on avg. time per iteration . . . . . . . . . . . . . . . . . . . . . 36
xi
List of Figures
4.17 Comparison in the time taken for each step in a timestep between 1
interface and 8 interfaces . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.18 Mean velocity field around the car about the plane y=0 . . . . . . . . 39
4.19 Mean Cp on the surface of the car . . . . . . . . . . . . . . . . . . . . 40
4.20 Mean Cp on the rear end of the car . . . . . . . . . . . . . . . . . . . 40
4.21 Mean velocity vector field representing the wake behind the car . . . 41
4.22 Mean velocity field across wheels on the left side of the car . . . . . . 43
4.23 Mean Cptotal on the surface of the car . . . . . . . . . . . . . . . . . . 44
4.24 Mean velocity field behind the wheels to visualize the wake . . . . . . 45
4.25 ∆Cd Ax and ∆Cl Ax plots for SM and MRF approaches . . . . . . . . 46
4.26 Mean velocity field across the centre of the rear wheel of the car . . . 47
4.27 Mean Cp on the base of the car comparing SM and MRF methods . . 48
4.28 ∆Cd Ax and ∆Cl Ax plots for OR and CR . . . . . . . . . . . . . . . . 49
4.29 Iso-surface of mean Cptotal =0 coloured by mean vorticity comparing
CR and OR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.30 Mean velocity fields along a plane adjacent to the wheels . . . . . . . 51
4.31 Mean Cp on the back of the car comparing OR and CR . . . . . . . . 52
4.32 Mean velocity vector field on the back of the car comparing OR and
CR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.33 ∆Cd Ax and ∆Cl Ax plots timestep dependency study . . . . . . . . . 54
4.34 CFL number comparison between both the cases . . . . . . . . . . . . 55
4.35 Comparison of the number of intersecting cells across the three inter-
faces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
xii
List of Tables
3.1 Boundary conditions for cylinder simulations . . . . . . . . . . . . . . 14

3.2 Parametric study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.3 Boundary conditions on the domain . . . . . . . . . . . . . . . . . . . 18
4.1 Mean forces acting on the cylinder and moment acting in the domain 25
4.2 Means of forces and moment comparison between RW and SM ap-
proaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.3 Force, moment and time comparison for different cases . . . . . . . . 33
4.4 Summary of pseudo-parallelization study . . . . . . . . . . . . . . . . 37
4.5 ∆ of various aerodynamic parameters of Experimental data and CFD
data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.6 Delta of various aerodynamic parameters of the car obtained from
SM and MRF approaches . . . . . . . . . . . . . . . . . . . . . . . . 46
4.7 Delta of various aerodynamic parameters comparing OR and CR . . 49
4.8 Comparison of delta of mean values of aerodynamic variables for
timestep dependency study . . . . . . . . . . . . . . . . . . . . . . . . 54
4.9 Results from interface splitting . . . . . . . . . . . . . . . . . . . . . 56
4.10 Comparison of delta of aerodynamic variables for pseudo-parallelization
study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
xiii
List of Tables
xiv
1
Introduction
1.1 Environmental impact of Vehicle Aerodynam-

ics
Over the last few decades, concerns pertaining to climate change and global warm-
ing have increased. Climate scientists predict adverse impacts on the environment
over the next decade if industrialization continues at the current rate. This rise in
temperature could have devastating effects on the planet ranging from melting of
polar ice caps, rise in sea level, erratic rainfall and so on. The increase in CO2 levels
in the atmosphere is a key green house ingredient for this issue.
The transport industry is a major producer of CO2 gas. Combustion of various

types of fuels releases numerous harmful gases and even particulate matter in some
cases. Sometimes, it is difficult to convert them into less harmful substances using
filters and catalysts. So, authorities had to intervene and introduce regulations to
control the amount of emissions that vehicles produce. The European Union Council
aims to restrict the CO2 emissions to about 95g/km by 2020 [4]. Since then, energy
efficiency has been a priority. The forces making up for the driving resistance are
summarized in Eq. 1.1 which consists of aerodynamic drag, inertial force, rolling
and climbing resistance.
1 2
Fdrive = ρU∞ CD A + ma + mgfF cosα + mgsinα (1.1)
2
where ρ is the density of air, U∞ is the freestream velocity, CD is the coefficient of
drag, A is the reference area, m is the mass of the vehicle, a is the acceleration of
the vehicle, fF is the frictional coefficient, g is the acceleration due to gravity and α
is angle at which the vehicle moves relative the horizontal. Minimizing the forces is
key in reducing energy consumption. Out of the four terms, only aerodynamic drag
does not contain mass of the object and depends on size, shape and velocity. CD
depends on the shape, size of the object and is a function of the square of velocity.
Hence reducing this term can result in considerable change to the effective driving
resistance [2].
Standardizing driving cycles to compare the fuel consumption of different vehi-

cles on common basis forms the foundation for determining the official fuel con-
sumption. With the currently used New European Driving Cycle (NEDC) cycle,
the gap between cycle consumption and real world consumption has been increas-
1
1. Introduction
ing. So, Worldwide harmonized Light vehicles Test Procedures has been imple-
mented. WLTP has an average impact speed of 46km/h as compared to 34km/h on
NEDC[3][5]. With this new cycle, aerodynamics has been given more importance
given the drag is a function of the square of velocity.
1.2 Background
Trends in Computer Aided Engineering(CAE) increasingly impact a vehicle’s de-
velopment and plays an important role in today’s automotive sector. Traditionally,
wind tunnel experiments had been used to analyze flow patterns and improve car
aerodynamics. This proved to be expensive and time-consuming especially in the
early phases. With the development of modern CFD tools and turbulence models,
initial testing and analysis has become more feasible. Even complex modeling such
as wheel rotations is now more accurate and realistic with the modern tools.
Although modeling wheel rotation is relatively new, wheel aerodynamics has been
carried out for over 4 decades. Although the wheel is split into tyre and rim, the
aerodynamic effects of each cannot be separated easily and their effects interact
with each other continuously. Fackery and Harvey [7] were among the first ones to
investigate isolated, rotating wheel in contact with a moving ground experimentally.
It was shown that grooves reduced the pressure peak at the contact patch by equal-
izing the pressure in front of and behind it. Cogotti[8] and Merceker[9] described
vortex systems behind isolated wheels. Elofsson and Bannister[10] performed tests
on different vehicle shapes with wheel rotation and they concluded that local de-
crease in drag was noted from front wheel rotation but that did not necessarily
reduce the global drag. The largest effect arose from the rear wheel rotation and its
influence on the base wake. From a computational study performed by Landström
et al [11] on a saloon type car, a radial cover of 30mm showed a drag reduction of
10 Cd counts. Similarly, from a study by Qiu et al. [12] , several rim configurations
were tested and a fully blanked wheel gave a drag reduction of 17 Cd counts, while
a similar configuration from Landström showed 7 counts. Hobeika et al. [1][13][14]
investigated the different methods of modeling rotation of tyre and wheel geome-
tries computationally and the effects of wheel geometry on the flow stream. In this
study, it was noted that, rain grooves on tyres reduced the drag of a passenger car
as compared to slick tyres. Sofie et al. [15] investigated the effects of wheel blank-
ing of varied degrees and concluded that blanking decreases drag. The study also
compared the accuracy of CFD results with experimental data for difference sets of
rim geometry.
CFD simulations produce numerical solutions of real scenarios relying on assump-

tions and mathematical models. With proper corrections and relaxations on the
equations, CFD results can be correlated to experiments. Blacha et al. [16] de-
scribed an extensive study on using CFD for the aerodynamic development of Audi
Q5 and an account of how turbulence models work for aerodynamic simulations.
Bastian et al. [17] investigated Lattice Boltzmann approach to model rotation of an
2
1. Introduction
isolated wheel. They found that the contact patch separation was highly sensitive
to load variations while modeling tyre deformations. They also suggested coupled
FEA-CFD solvers to model tyre deformation in CFD simulations. Profir M. M [18]
investigated automated meshing and remeshing techniques to model motion in CFD
applications using java scripts. But the above mentioned methods to model contact
patches are computationally expensive.
Previous CFD investigations have been performed to model wheel rotation. The
available methods are Rotating Wall, Moving Reference Frame and Sliding Mesh
methods. It was found that using RW method on wheels resulted in inaccurate
prediction of rim velocities. MRF and SM methods are the most commonly used
methods to model wheels. SM method is computationally expensive but it accounts
for rotation of wheels by physically moving the mesh. MRF method accounts for ro-
tation by modifying the reference frame in the governing equations. It was observed
that MRF method produced unphysical flow field when applied on rotating cylin-
ders. Modeling tyre rotation due to contact patch deformation is difficult using SM.
Hence the common practice for modeling wheels is, to use RW for the tyres(valid
only for slick or rain grooves; lateral grooves on tyres produce unphysical velocity
field) and MRF or SM for the rims. Lateral grooves can be modelled using MRFg
which is a combination of MRF and RW. A detailed account on this can be found
in [1].
The SM method is computationally expensive in all CFD commercial tools. In

the CFD tool by Siemens, Star-CCM+, SM approach, which is called Rigid Body
Motion in the software, is no different. The mesh updating step is a serial operation
in this software. At the end of each timestep, the solver needs to stop after each
timestep, update the mesh and then restart the solver for the next timestep. It has
been found that, the speed of interface updating is highly dependent on the number
of intersecting faces between the stationary and rotating regions. So, by splitting
the interface into multiple boundary interfaces, the load on the CPU is effectively
reduced and this process of updating can be made more efficient while still being a
serial process. Thus, this approach can be termed as pseudo-parallelization.
1.3 Project Objectives

The objectives of this project are listed below:
• Study rotation modelling(RW and SM) on a rotating cylinder.
• Analyze flow field around a car and wheels.
• Analyze the differences between MRF and SM methods for wheel modelling.
• Study the effects of blanking a rim on the aerodynamic performance of a car.
• Investigate pseudo-parallelization on the cylinder and car cases.
3
1. Introduction
4
2
Theory
This chapter explains the theoretical background required to understand the differ-
ent concepts and methods used in the project. Firstly, the basics of fluid dynamics
starting from the concepts of continuum are explained, followed by CFD and its
various formulations and governing equations. Then concepts specific to a car aero-
dynamics are explained. Finally, the various methods used for rotational wheel
modeling of a car.
2.1 Fluid Dynamics

Fluid dynamics deals with the study of fluid flow. A fluid can be liquid, gas or a
combination of both in some cases. Matter is made up of discrete molecules and the
density with which they are packed defines its state. Fluid state has particles with
relatively low density as compared to solids. The particles in fluids are in a state of
random motion always colliding with each other. In general for engineering prob-
lems, matter is not studied in such microscopic scales whereas they are visualized
and studied in a more macroscopic level known as continuum.
In continuum, it is noted that the length and time scales of matter are larger than
the microscopic scales. The solutions to a fluid dynamics problem in continuum
scales typically represents the flow in terms of properties such as pressure, density,
flow velocity as functions of space and time. [22]
This framework of definition is given by the conservation laws- conservation of mass,

momentum and energy. The Navier-Stoke’s equations are obtained by formulating
the above mentioned principles to characterize fluid flow. These equations are ap-
plied in fluid dynamics problems, either in full or a simplified form and used in
various applications.
2.1.1 Governing Equations

The Navier-Stoke’s equation is a set of partial differential equations with basically
consists of the continuity equation and momentum conservation equation as stated
in Eq. 2.1 and Eq. 2.2.
The continuity equation or the mass conservation equation states that the rate of
increase of mass in the system is equal to the net rate of the mass flow into the
5
2. Theory
system.
∂ρ ∂ρvi
+ =0 (2.1)
∂t ∂xi
The first term in the Eq. 2.1 is the unsteady term which accounts for the change
in density of the fluid with time. The second term is the convection term which
accounts for the net change in mass flow rate across the boundaries. This equation
states that mass entering the system should be equation to the mass exiting.
The momentum conservation equation states that the rate of change of momentum
is equal to the net forces acting on the fluid.
dvi ∂P ∂τij
ρ =− + + ρfi (2.2)
dt ∂xi ∂xj
The first term in the Eq. 2.2 is a total differential term of velocity. This means that
terms is,
dvi ∂vi ∂vi vj
= +
dt ∂t ∂xj
The first term in the right hand side of Eq. 2.2 is the negative gradient of pressure
which acts the source term. The second term is the gradient of stresses(τij ) acting
on the fluid and the last term signifies the body forces on the fluid. The viscous
stress tensor is defined as,
τij = 2µSij − 2µSkk δij (2.3)

!
1 ∂vi ∂vj
Sij = + (2.4)
2 ∂xj ∂xi
The conservation of energy equation is derived from the first law of thermodynamics,
which states that the rate of change of energy of a fluid is equal to the sum of rate of
heat addition to the fluid and rate of work done. The energy conservation equation
is stated in Eq. 2.5.
!
∂ρE ∂vj E ∂ ∂T ∂vj p vi τij
+ = −ρq + k − + + ρfi vi (2.5)
∂t ∂xj ∂xj ∂xj ∂xj ∂xj
Where E is the total energy of a moving fluid element and E is defined as,
1
E = e + v2
2
2
where e is the internal energy per unit mass and v2 is the kinetic energy per unit
mass and p is the pressure which is given by the ideal gas law p = ρRT
Unless the flow is compressible or cases where heat transfer is involved, the energy
equation is not considered in the solution. So, for aerodynamics of automobiles,
where flow is incompressible and no heat transfer is involved, only the continuity
equation and momentum equation are considered.
6
2. Theory
2.2 Computational Fluid Dynamics
Solution of the Navier-Stokes equations are problem specific and analytic solution
to the problem is extremely difficult to perform. So, usually numerical methods are
applied. With growing computational power, CFD has gained significant impor-
tance over the past few decades.
Using numerical methods, the governing equations of fluid flow are discretized in
space and time based on different discretization schemes. By applying boundary
conditions to the discretized equations, the solutions are obtained based on the
given accepted level of accuracy. Since the continuum is split into discrete segments
in space and time for numerics, the accuracy is greatly dependant on their sizes.
For accuracy, it is recommended to have finely discretized mesh and time.
The fluctuations in flow parameters present in turbulent flows, occur locally in the
flow. These fluctuations define the flow energy and they need to be studied closely.
2.2.1 Turbulence
Almost all flows around us are turbulent in nature, from combustion in engines and
turbines to flow around automobiles and airplanes. Turbulence is governed by ed-
dies, which are swirling irregular scale of different sizes. They cause abrupt changes
in flow velocity locally.
The turbulent scales are important in understanding turbulence. The scales are dif-
ferentiated based on size into large scales, intermediate scales and dissipative scales.
The large scales of the order of the flow geometry and flow velocity. These scales
extract kinetic energy from the mean flow. Part of the kinetic energy is transferred
slightly smaller eddies by collision with other larger eddies. Through cascade pro-
cess, the energy is transferred to the smallest scales (Kolmogorov scales) where it is
dissipated.
The flow in turbulent regime is chaotic and irregular and yet the Navier-Stoke’s
equations govern it. The main advantage of this is that every detail of the turbulent
velocity field, from the largest to the smallest scales is described. Thus an extensive
amount of information is described by the Navier-Stoke’s equation and as a result,
the direct approach of solving them, Direct Numerical Solution (DNS), is available
but impractical. So, turbulence models are used which are statistical in nature which
depend on the mean velocity field to represent the turbulent flows.
The most common models are RANS : k − , k − ω, LES and DES models. A few
turbulent models are described below.[23]
7
2. Theory
2.2.2 RANS models

Reynolds Averaged Navier Stoke’s equation is a time averaged Navier-Stokes equa-
tion. A turbulent flow field can be decomposed into a mean and a fluctuating part.
ui = ūi + u0i (2.6)
Where ūi is the mean part and u0i is the fluctuating part. Each term in the continuity
and momentum equation can be decomposed in such fashion. The resulting equation
when Reynolds averaging these equation is called Reynolds Averaged Navier-Stokes
equation.
∂ ūi
=0 (2.7)
∂xi
!
∂ ūi u¯j ∂p ∂ ∂ ūi
ρ =− + µ − ρu0i¯u0j (2.8)
∂xj ∂xi ∂xj ∂xj
Where ρu0i u0j is the Reynolds stress tensor which is a unknown. This term is a con-
sequence of averaging. The RANS based models aim to model this term to close the
equation.
Unsteady RANS models have been developed which retains the same form as the
RANS equation stated in Eq. 2.8 along with an unsteady velocity term in the left
hand side which accounts for the rate of change of velocity.
In the problem at hand, k − ω turbulence model is used and so it is briefly explained

below.
2.2.2.1 k − ω Turbulence Model

The k − ω model is one of the most popular models used in CFD simulations. It
is a two equation eddy viscosity model that solves the RANS equations in addition
to two partial differential equations for k, the kinetic energy as in Eq. 2.9 and ω,
specific rate of dissipation as in Eq. 2.10.
! !
∂ρk ∂(ρuj k) ∂ ρk ∂k
+ = µt + σk + Pk − β ∗ ρωk (2.9)
∂t ∂xj ∂xj ω ∂xj
! !
∂ρω ∂(ρuj ω) ∂ ρk ∂ω γω
+ = µt + σw + Pk − β ∗ ρω 2 (2.10)
∂t ∂xj ∂xj ω ∂xj k
Where µt is eddy viscosity which is given by, µt = ρk/ω and β ∗ is a constant is
usually equal to 0.09.
∂ui
Pk = τij (2.11)
∂xj
!
2 ∂uk 2
τij = µt 2Sij − − ρkδij (2.12)
3 xk 3
!
1 ∂ui ∂uj
Sij = + (2.13)
2 ∂xj ∂xi
8
2. Theory
The Eq. 2.9 and Eq. 2.10 have the same structure. The first term is the unsteady
term which defines the rate of change of the quantity. The second term is the
convection of the quantity. The third term is turbulent diffusion of the the quantity.
The fourth term defines the production term and finally the rate of dissipation of
the quantity.
2.2.3 LES model

The basic principle of Large Eddy Simulation (LES) is to resolve the large grid
scales (GS) and model the small subgrid scales (SGS) of the turbulence. In LES,
the equations are volume averaged and since it is not averaged in time, the volume
averaged equations are functions of both space and time. Hence, the LES model
gives a transient solution in contrary to a RANS simulation. Since a part of the
turbulent scales are resolved and a transient solution is required, LES is much more
computationally expensive than a RANS simulation, but also more accurate since
less turbulence is modeled. The LES model requires a very fine mesh, especially in
the boundary layer, in order to give a good solution.
Due to the volume averaging, the turbulent eddies are filtered so that the small
scales are not solved for. The quantities are decomposed into a filtered part and a
subgrid part as
φ = φ̄ + φ0 (2.14)
The equations for the filtered variables have the same form as Navier-Stokes equa-
tions,
∂vi ∂ 1 ∂ p̄ ∂ 2 v̄i ∂τij
+ (v̄i v¯j ) = − +ν − (2.15)
∂t ∂xj ρ ∂xi ∂xj ∂j ∂xj
∂ v̄i
=0 (2.16)
∂xi
where v̄i is the filtered velocity, p̄ is the filtered pressure, ρ is the density, ν is
kinematic viscosity and τij is subgrid stress tensor which is given by, τij = vi¯vj − v̄i v¯j .
The subgrid stress tensor term needs to be modeled. Different LES models such as
Smagorinsky model, dynamic model and mixing length model aim in closing the
equation by modeling the subgrid stresses.
2.2.4 DES models

Detached Eddy Simulation (DES) is a combination of LES and URANS which is
commonly referred to as hybrid RANS-LES. URANS is used inside the boundary
layer, while LES is used to resolve the detached eddies outside of the boundary
layer. Thus DES uses the advantage of the accuracy of LES, while not requiring
an extremely fine mesh inside the boundary layer due to the usage of URANS. The
transition between the equations used for URANS and LES takes place through
reducing the turbulent viscosity. The length scale in DES model is dependant on
the grid size and so the creating an appropriate mesh is crucial for the switch between
URANS and LES models. In order to overcome this, DDES model was proposed
9
2. Theory
which protects the boundary layer from LES by preventing early switches from
RANS to LES. This was achieved by introducing blending and shielding functions.
The shielding functions are based on wall distance and eddy-viscosity. DES and
DDES are explained in detail in [22].
2.2.4.1 IDDES model
With suitable formulations in the shielding and blending functions, DDES can be
formulated in Wall Modelled LES (WMLES) mode. The length scale in this model
is a piece wise functions incorporating wall distance dependency and local cell size.
The modified sub-grid length scale accounts for anisotropic effects which results in
in significantly varying length scales that helps the flow destabilize. The DDES part
is designed to activate in flows without turbulent inflow and in cases where grid is
unlikely to resolve the dominant energy carrying eddies while the WMLES part is
activated when the unsteady turbulent inflow is provided and when the grid can
sufficiently resolve. A more detailed account on IDDES can be found in [21]. In this
work, the IDDES model has been used to simulate the cylinder and complete car
cases.
2.3 Aerodynamics
Aerodynamics is the study of how fluids interact with moving bodies. Aerodynamics
is primarily concerned with the forces and moments caused by air passing over and
around solid bodies. These forces, and moments greatly affect the performance and
handling of the vehicle, and are commonly decomposed into three rotational and
three translational terms. They are represented in Fig. 2.1. The two fundamental
forces act on a moving vehicle. The first one is drag, which acts along the direction
that resists the desired vehicle motion. Drag can be divided into pressure drag and
skin friction drag where the former is the most dominant one. The second force is
lift which acts in the direction perpendicular to the direction of vehicle motion. Lift
is generated in the vehicle due to the pressure difference between the roof and the
underbody of the car. Drag affects the vehicle’s performance characteristics while
lift affects the directional stability.
In general, lift and drag are non-dimensionalized so that these value represent drag
and lift for a particular shape and they can be used for performance comparisons
with other shapes. The formulae for computing the Cd and Cl are given below:
2Fd
Cd = (2.17)
ρU 2 Af
2Fl
Cl = (2.18)
ρU 2 Af
where Fd and Fl are drag and lift forces respectively, ρ is the density of air, U is the
velocity of the vehicle and Af represents the frontal area of the vehicle.
10
2. Theory
Figure 2.1: Aerodynamic forces and moments acting on the car
2.4 Rotation Modeling

The angular velocity of the wheels can be modelled in many ways with each having
certain advantages and disadvantages. And so the method to choose is problem
specific. There are three commonly used methods: Rotating Wall method, Mov-
ing Reference Frame method and Sliding Mesh method[14][24]. Traditionally MRF
method has been used for rim and spokes and RW condition on the tyre. But SM
method is also used instead of MRF in some cases. Hybrid methods such as MRFg
have been proposed for tyre modelling[1].
2.4.1 Rotating Wall boundary condition

The Rotating wall approach is possibly the simplest way of modelling rotation. In
this method, the rotational option allows the user to specify a rotational velocity
about a specified axis on a wall boundary. The velocity is applied tangentially to
each cell on the boundary. Hence, if the velocity vector is not on the same plane
as the cell surface, it is projected thereby losing its normal component. Hence, RW
method is not feasible when the velocity vector is normal to the cell surface like in
the case of rim spokes and lateral grooves.
2.4.2 Multiple Reference Frame

The MRF approach is implemented by prescribing the fluid cells to a moving frame
of reference, in this case, rotation. This allows it to apply a surface velocity normal
to the surface and hence produce a desired surface velocity in the region. The
user determines a number of regions with defined interfaces between them and in
each region, different rotational speeds can be defined. For the absolute velocity
formulation, the governing equations of fluid flow for a moving frame is written in
Star-CCM+ user guide[19] as follows,
11
2. Theory
∇ · (u~p × u~0 ) + ω~p × u~0 = −∇(p/ρ) + ν∇ · ∇u~0 (2.19)

∇ · u~0 = 0 (2.20)
where, up is the velocity relative to the moving reference frame, u0 is the absolute
velocity, wp is the angular velocity of the rotating frame, p is the fluid pressure and ρ
is density of the fluid. It also generates centrifugal accelerations and Coriolis effects
in the fluid.
If the flow field in an empty MRF region is uniform, then ∇.u~0 = 0. Then Eq. 2.19
reduces to
∇p = −ρ(ω~p × u~0 ) (2.21)
Hence, whenever ω~p × u~0 6= 0, a pressure gradient is introduced. The pressure gra-
dient becomes zero when the flow is along the axis of rotation. However for wheels,
the flow is more complex and the axis of rotation is orthogonal to the flow.
The MRF approach has a number of limitations. The interfaces defined by the
user affects the outcome. Additionally for a geometry that is not axisymmetric,
the positioning the model during the simulation can have significant effects on the
results. This means, two simulations of same CAD geometries can give different
results if the position of the spokes is different.
2.4.3 Sliding Mesh method

The Sliding Mesh approach is implemented by physically moving the mesh each time
step. This means the simulation is inherently unsteady. The connection between
the sliding and stationary region, the interface, needs to be updated every time step.
This motion, allows SM to take into account the different positions of the rotating/-
moving object. This would be the most realistic way of modelling rotating rigid
geometry. However, it would typically result in significant increase in simulation
time to update the mesh after each timestep.
The generic transport equation for dynamics meshes is given as,

d Z Z
~
Z
~
Z
ρφdV + ρφ(~u − u~g ) · dA = Γ∇φ · dA + Sφ dV (2.22)
dt V ∂V ∂V V
Where,
rho is the fluid density,
~u is the flow velocity,
u~g is the mesh velocity of the moving mesh,
Γ is the diffusion coefficient,
Sphi is the source term of φ,
∂V is used to represent the boundary of the control volume V.
12
3
Methodology
In this chapter, the different cases and their setup in Star-CCM+ are explained. The
project was split into two studies, where the first study comprises of a simple model
involving a cylinder is used to verify RW and SM methods. Then a parametric study
on the mesh and time step for the sliding mesh was performed. Finally, by splitting
the interface between the stationary and moving region of the SM simulation, poten-
tial speedup in the mesh updating step was investigated, thereby reducing the time
taken per time step. The second part of the project comprised of testing different
wheel modelling approaches on a car - Volvo XC60. Additionally open and closed
rims were evaluated, time step dependency on the whole car was examined and fi-
nally it was investigated if splitting the interface resulted in a speed up of updating
time for a car.
3.1 Cylinder Simulations

The objective of the cylinder simulations was that the cylinder represents a simplified
model of a wheel without rims and tyre profiles. The objective of the study was to
comprehend how rotation modelling techniques worked.
Fig. 3.1 represents the setup used in this section. The domain is a box of dimensions
25m × 16m × 0.1m. A cylinder of radius 0.3m is placed at 10 m from the inlet.
Figure 3.1: Geometry description of the cylinder simulations
The boundary conditions used in the simulations are stated in Table 3.1.
13
3. Methodology
Boundary Setting
Inlet Velocity Inlet: 38.89m/s
Outlet Pressure outlet: 0Pa
Front, Back, top and bottom Symmetry
Wall wall (RW includes a tangential velocity specification)
Table 3.1: Boundary conditions for cylinder simulations
The sliding mesh simulation needs a separate region where the mesh physically
moves each time step. As seen Fig. 3.2, the grey region represents the rotating
region and the blue region represents the stationary air domain. The interface is
located at a radius 0.315m from the centre. To maintain consistency in the mesh
while comparing RW and SM methods, the same mesh was used.
Figure 3.2: Segregation of regions: Grey region represents the rotating region and
blue region represents the stationary air domain
Figure 3.3: line probes
14
3. Methodology
Various reports and monitors of drag, lift and moment in the rotating domain and
reports for their time averaged value were set up. The mean of velocity is also
calculated and plotted along line probes which are shown in Fig. 3.3.
The line probes are of length 4D placed symmetrically about the X-axis and at
distances 0.25D, 0.5D, 0.75D, 1D, 1.5D and 2D from the surface of the cylinder,
where D is the diameter of the cylinder.
In the first study, the RW and SM methods were verified for this case. Physically,
both the methods are the same. In the RW method, a tangential velocity is pre-
scribed at the cylinder wall by giving a rotational rate and axis of rotation while
in SM method, the entire region rotates about the specified axis of rotation at the
specified rotational rate.
By taking into account the CFL criterion and the frequency of vortex shedding, the
mesh was refined in stages. Finally, a reasonably refined mesh was obtained and it
is shown in Fig. 3.4 and Fig.3.5.
Figure 3.4: Mesh around the cylinder and interface
Figure 3.5: Mesh around the cylinder and interface
15
3. Methodology
The cell size was set to 2mm at the cylinder wall and interface. A volume cell
refinement was set around the cylinder with a cell size 4mm as shown in Fig. 3.4.
The first cell height from the wall was set at 1e-5m to obtain a y+<1 at the wall.
Fourteen prism layer were built with a growth ratio of approximately 1.5 which
resulted in a total height of 6mm.
The simulation was performed in two stages: first, a steady state SST k − ω model
was used with wall rotation boundary condition on the cylinder wall with a rotational
rate of 129.6 rad/s for 1500 iterations. Second, the unsteady IDDES solver was run
on RW or SM methods with a time step of 1e-5s and 6 inner iterations for a total
physical time of 4s.
The results from the study comparing the two methods are presented in section
(4.1.2).
Next, a parametric mesh and time step study was performed on the SM case. The
objective of this study was to see how dependent the case was to mesh and time
step changes. The parameters tested are given in Table 3.2.
Parameters Settings used

Time average study 4s, 5s
Time step dependency 2.5e-4s, 1e-4s, 1e-5s
Cell size dependency at the wall 2mm, 4mm
Size of the sliding domain 0.315m, 0.36m
Solver Segregated, Coupled
y+ dependency (first cell height) 1e-4m, 1e-5m
Table 3.2: Parametric study
The simulation performed in the first case, was considered as the ideal or the base
case and the solution (forces, moment and mean velocity on the line probes) obtained
by varying each of parameter was compared to the solution of the base case.
Finally, the pseudo-parallelization of interface updating was tested where the in-
terface between the rotating region and the domain was split into two, three, four
and eight faces. The geometries were modelled using ANSA as shown in Fig. 3.6.
The boundaries were interfaced using boundary mode. So, the interfaces branch in
simulation tree of Star-CCM+ has a number of interfaces. Reports of elapsed time
per time step and elapsed time per iteration and their means were used to analyze
if this method could speed up the simulation.
16
3. Methodology
(a) Two interfaces (b) Three interfaces
(c) Four interfaces (d) Eight interfaces
Figure 3.6: Geometries of cylinder split into 2, 3, 4 and 8 faces
17
3. Methodology
3.2 Car Simulations
The second part of the project was to perform CFD investigation on the car and
wheels. The car used in this case was a Volvo XC60. The domain used in this case
is a 70m × 40m × 30m. The existing CAD models of the car with the complete
setup was provided by Volvo. The preparations for this study was done in ANSA
v.18. The changes were predominantly in the wheel geometry, modeling approach
and the sliding mesh region. The complete car geometry is shown in Fig. 3.7.
Figure 3.7: Volvo XC60 geometry
The Fig. 3.8 shows the domain with the boundaries, inlet, outlet and ground which
are modelled as velocity inlet, pressure outlet and moving wall boundary conditions
respectively. By modeling the wall with moving wall boundary condition, develop-
ment of boundary layer on the wall is prevented. The other surfaces that enclose
the domain are modelled as symmetry boundary condition. The surfaces of the car
are also modelled as wall. The boundary conditions are given in table 3.3.
Boundary Setting Value

Inlet Velocity Inlet 140 kmph
Outlet Pressure Outlet 0 Pa
Ground Moving wall 140 kmph
Side and top faces of the domain Symmetry -
Car surface Wall -
Table 3.3: Boundary conditions on the domain
18
3. Methodology
Figure 3.8: Representation of the domain and boundaries
The aerodynamics group at VCC have developed the aero_vcacp scripts which au-
tomates the entire CFD simulation and post-processing. The scripts are split into
4 sections, namely: prep, mesh, run and post. The prep script imports geometry,
creates domain, performs surface wrapping, surface meshing and sets various other
settings such as coordinate systems, auto mesh settings, boundary settings and so
on. The mesh script performs volume meshing in the domain. The run script is
used to create various reports, monitors and plots and runs the simulation based on
the settings prescribed. And finally the post script does post-processing based on
user input and is capable of representing scalars, vectors, surfaces and iso-surfaces.
The result of the prep and mesh scripts contains the volume mesh of the fluid
domain. The domain has about 253 million cells. The mesh is refined close to the
body of the car and in the region of the wake behind the car. The mesh is also
refined close to the wheels to capture the turbulent air streams entering and exiting
the wheel. The Fig. 3.9 represents the mesh along the x-z plane and y-z plane.
(a) Mesh plane about the y axis (b) Mesh plane about the x axis near the
front wheel
Figure 3.9: Mesh planes about x-axis and y-axis
19
3. Methodology
The wheel setup consists of an 18-inch wheel with slick tyres as shown in Fig. 3.10.
A subtract is created in Star-CCM+ between the rims and the sliding mesh region.
The region represented by the transparent blue color in the figure is the sliding
region. The region is rotated about the corresponding wheel axis. The wheel setup
is modelled by using sliding mesh approach to the rims spokes and rotating wall to
the tyres. Since the tyre geometry is slicks, rotating with rotating wall method is
valid and easy to setup.
Figure 3.10: Wheel setup
The simulation was performed in steps where a steady state case was run initially
to achieve faster convergence in transient simulations. Then the time step was
slowly ramped to finer values in steps and the number of iterations per timestep was
decreased slowly.
• Steady state simulation for 1500 iteration. Then the physics was changed to
unsteady.
• ∆t=5e-3s for 0.1s with 20 iterations per timestep with velocity URF=0.7 and
pressure URF=0.25.
• ∆t= 5e-3s till 2s with 10 iterations per timestep with velocity URF=0.8 and
pressure URF=0.4 (URFs were unchanged henceforth).
• ∆t=1e-3s till 2.4s with 8 iterations per timestep.
• ∆t=2.5e-4s till 2.5s with 8 iterations per timestep.
• ∆t=2.5e-4s till 4s with 6 iterations per timestep.
With this ramping of timestep and iterations, the flow reached a fully developed
condition faster. Various reports were setup such as Cd , Cd A, Cl r, Cl f , time per
iteration and time per timestep to evaluate the performance of the car and the
simulations. Averaging was performed between 2.6s and 4s.
The setup described above was considered as the baseline configuration. Four studies
were made in comparison to this.
20
3. Methodology
• Comparison between SM and MRF methods to model wheel rotation.

• Flow field comparison when using open rims and closed rims.
• Time step dependency study.
• Interface splitting across the sliding interface.
In the first study, wheel modelling approaches were investigated. The same CAD
geometry was used in evaluating both the SM and MRF approaches. In the SM ap-
proach, the region was modelled using rigid body motion where the mesh physically
moves and in the MRF approach, it was modelled in reference frames so, it accounts
for the motion numerically.
In the second study, the difference between open and closed rims were investigated.
In the same wheel setup as the baseline, a rim cover was modelled in ANSA and
surface meshed. In this study only SM approach was used. The two rims, open and
closed rims are shown in Fig. 3.11.
(a) Open rim (b) Closed rim
Figure 3.11: Configuration of wheels
Next, the time step dependency was checked. Two time steps were used for this
study. First was the default value of 2.5e-4s which was setup the same was the first
study and the second case used a finer ∆t of 1e-4s. 2.5e-4s was used for the reference
simulation because it was the only affordable timestep. The same ramping settings
was used for the case with 1e-4s for simplicity. But the settings were slightly altered
towards the end to ease the simulation into 1e-4s. The timestep of 2.5e-4s with 6
inner iterations was run till 2.55s and then changed to 1e-4s till 4.1s. The time
averaging of the reports and fields happened between 2.7s and 4.1s. This additional
0.15s in the beginning (from 2.55s to 2.7s) is to allow the solution to stabilize in
the new timestep of 1e-4s. The forces and Courant number in the domain were
compared between the two cases.
Finally, like in the previous section with the cylinder, the sliding region’s interface
was split into three faces in ANSA v.18 to see if speed up occurs. Fig. 3.12 shows
21
3. Methodology
the front left wheel in the baseline configuration and when split into different PIDs.
Using Java scripts, these different PIDs were created as separate boundaries in
Star-CCM+ and interfaced in boundary mode. This was done to all the SM regions
corresponding to the 4 four wheels of the car.
(a) 1 interface on the sliding mesh region(b) 3 interfaces on the sliding mesh region
of the wheel of the wheel
Figure 3.12: Geometry of the wheel’s SM region used in the study
22
4
Results and Discussions
In this chapter, the results are presented in the following way: the solution for the
cylinder simulations are presented first which includes analysis of the flow field, ver-
ification of results from the RW and SM simulations, parametric mesh and timestep
study and finally the results from splitting the interface. In the second part, the
flow field around the car is analyzed. Then the results from different approaches
of wheel modelling are evaluated, followed by the open and closed rims’ effects on
the flow field. The time step dependency study conducted on the car is presented.
Finally the results from the interface splitting and its influence on the time of the
simulation time is discussed.
4.1 Cylinder simulations

4.1.1 Analysis of flow field
The flow around the rotating cylinder is analyzed in this section, the setup was
explained in section [3.1]. The results shown in this section are based on RW method.
The Fig. 4.1 represents the mean of velocity field. The velocity decreases gradually
as the flow reaches the cylinder as it resists the flow. The flow accelerates as it passes
over it. The downstream side of the cylinder is dominated by a wake which results
in vortex shedding(vortex shedding is not seen in Fig. 4.1 because it represents time
averaged velocity field). Vortex shedding is characterized by flow detaching from a
bluff body in an oscillating fashion. This causes the body to experience alternating
forces.
The wake is the result of the development of flow separation behind the bluff body,
cylinder in this case. A wake region is characterized by reduced velocity and reversed
flow and vortices as seen in the figure. Flow separation is marked by a separation
point. There are two such points, one on the top and bottom of the cylinder.
Separation occurs depending on pressure recovery and boundary layer development.
It is noted that the flow accelerates more on the lower side of the cylinder because
of rotation. The oncoming flow is opposite in direction to the tangential velocity of
the cylinder on the upper side of the cylinder. So, the resulting velocity is very low
in magnitude whereas on the lower side, it is almost double the freestream as the
velocity vectors are parallel. Additionally, the cylinder rotation causes the vortex
shedding to occur slightly inclined to balance the flow. The separation point on the
top of the cylinder is more upstream than the bottom which is also due to rotation.
23
4. Results and Discussions
Figure 4.1: Mean velocity field around the cylinder from RW method
Fig. 4.2 gives the mean velocity along the line probes defined in the domain as
shown in Fig. 3.3. As the downstream side of the cylinder is dominated by the
wake, the velocity close to the cylinder is low (the red line in Fig. 4.2) but gradually
recovers as the flow moves further away from the cylinder wall. The shift in the
velocity profiles towards the right side is due to the rotation of the cylinder.
Figure 4.2: Mean velocity plot along the line probes from RW method
Fig. 4.3a and Fig. 4.3b represent the forces, drag and lift, acting on the cylinder and
Fig. 4.4, the moment. The simulation being transient and since a DES model was
used to resolve the turbulence, the forces and moment are fluctuating continuously
in time. So time averaging was performed for all the quantities which is marked by
24
the green line in the plots. The mean values of each of the quantities are shown in
table. 4.1.
(a) Drag force acting on the cylinder sur-(b) Lift force acting on the cylinder surface
face
Figure 4.3: Forces acting on the cylinder
Figure 4.4: Moment in the rotating region
Quantity Mean value

Drag (N) 19.9
Lift (N) -110
Moment (Nm) -0.142
Table 4.1: Mean forces acting on the cylinder and moment acting in the domain
25
Remark
From Fig. 4.2, it can be seen that the gradients of velocity are very high in the wake
and high spatial discretization is required to achieve good results. But high spa-
tial discretization imposes a restriction on the temporal discretization also. Hence,
the CFL condition had to taken into account and as a condition, it is restricted
to a low value(<5). With vortex shedding involved, it was essential to take into
account the shedding frequency and it was found to be 28.5Hz based on Delany and
Sorensen’s relationship between Re and Strouhal number[24]. By taking all that
into consideration, a timestep with ∆t=1e-5s was required for the simulation.
4.1.2 Comparison between RW and SM methods

With the setup given in section 3.1 and a timestep of 1e-5s, both RW and SM
methods were tested on a rotating cylinder. Fig. 4.5 shows the means of velocity
along the line probes. It can be seen from this figure that both velocity profiles look
similar. The velocity profiles closer to the cylinder appear slightly different but as
the flow moves downstream, the errors evened out.
(a) Rotating wall method (b) Sliding mesh method
Figure 4.5: Mean velocity along the line probes comparing RW and SM
A ∆V
Vin
plot was created where ∆V = VRW − VSM as seen in Fig. 4.6. We can observe
a small shift in the velocity profile across the domain along the line probes 0.25D
and 0.5D but beyond that, the errors are very small. This is clearly marked in the
plot by two peaks on those two corresponding velocity profiles. A possible reason
for this shift in velocity profiles is due to insufficient temporal discretization and
more about it is explained in section 4.1.3.
26
∆V
Figure 4.6: V∞
plot comparing RW and SM methods
(a) Rotating Wall (b) Sliding Mesh
Figure 4.7: Mean velocity around the cylinder comparing RW and SM methods
Fig. 4.7 represents the scalar scene of RW method and SM method. It can be seen
that both the scalars look very similar. In the region where the mesh moves in SM
method, the velocity value is averaged due to mesh motion and it cannot be read
accurately with the current setup.
The forces acting on the surface of the cylinder and the moment in the domain were
monitored and their mean values were calculated for both the methods. Table 4.2
shows that the mean values of these quantities are very close to each other.
27
Quantity RW SM
Drag (N) 19.9 19.8
Lift (N) -110 -113
Moment (Nm) -0.142 -0.146
Table 4.2: Means of forces and moment comparison between RW and SM ap-
proaches
Remark
The RW method took 90 hours and SM method took 206 hours on 1000 cores for
the simulation to complete. This increase in time for the latter method is due to the
physical motion of the mesh for each time step. This proved to be extremely costly
and impractical. So a parametric study was carried out to see how much the mesh,
timestep and the geometry of the rotating region of SM affect the final solution.
4.1.3 Parametric Study on SM method
Different settings were tested and a suitable setup has been finally suggested which
is computationally cheaper and has comparable results to the base case. Based on
the settings as given in Table. 3.2, each parameter was modified from the base
case and the results were compared. All simulations (including ¨Base case¨ in the
figures) were performed with 1e-4s timestep unless stated otherwise (for practical
reasons).
Fig. 4.8 presents the results for the time averaging study and time step dependency
study. It can be seen that averaging the solution to 4s and 5s, both yielded the
same results. Hence it can be inferred that, averaging the solution to 4s is sufficient.
The mean of the forces and moment did not stabilize until around 3.5 and so it
is essential to run the simulation for a physical time of atleast 4s. From the same
figure, it can be seen that the mean velocity profile shifts towards the right side with
coarsening the time step. This was initially construed to be because of mesh motion
interpolation and/or courant number effects. But, in the case with cell size 4mm
and a time step of 2e-4s, the courant number is relatively preserved as compared to
2mm cells with 1e-4s timestep. This was able to produce results with minimal shift.
Thus it can be stated that, the shift in the profiles is due to courant number. Hence
it is essential to maintain a good value of CFL number in the cells. The results
produced by the the simulation with 4mm cells was erroneous as the cell size was
too coarse to resolve the flow. In Fig. 4.6, it was observed that there was a similar
shift in velocity profiles for SM as compared to RW simulations. It is possible that
the timestep must be further refined for SM to achieve the same solution as RW.
But considering how expensive the SM method is, it was decided not to do so.
28
(a) Profiles at 0.25D (b) Profiles at 0.5D
(c) Profiles at 0.75D (d) Profiles at 1D
(e) Profiles at 1.5D (f) Profiles at 2D
Figure 4.8: Parametric study results from different parameters in comparison with
the base case
29
Figure 4.9: Parametric study results from different mesh and geometry settings in
comparison to the base case
30
The Fig. 4.9 shows the dependency of cell size at the wall, y+ values and the size
of the rotating domain in this case. It can be seen that the profiles were slightly
offset from each other. Coarsening the cell size to 4mm at the wall and having a
high y+ value at the wall produced poor results because the gradients near the wall
and in the wake region were very high and these coarser settings was not capable
of predicting them properly. This resulted in poor accuracy on the forces and mo-
ments. Enlargening the domain size yielded very similar velocity profiles and forces
that were close to the solution from the finest settings (with ∆t = 1e − 5s).
Finally, Fig. 4.10 represents mean velocity field obtained from a coupled solver and
wake refined mesh running segregated solver in comparison to the base case. It can
be seen that all the cases yielded similar results close to the wall. But away from
the wall, wake refinement under-predicted the velocity means. Solving with coupled
solver proved to be challenging due to certain instabilities in forces. Hence the
segregated solver proved to be the more reliable choice. Wake refinement produced
similar results as compared volume refinement around the cylinder. This proved to
very useful because the wake refinement reduced the number of cells in the domain
by around 35% as compared to using volume refinement.
31
Figure 4.10: Parametric study results from coupled solver and wake refinement as
compared to the base case
32
With these results, the best configuration to run the case using SM method was be
with the following setup:
• Time step - 1e-4s
• Total physical time - 4s
• cell size at the wall - 2mm
• 14 prism layers with first cell height of 1e-5m, growth ratio of 1.5 and height
6mm.
• Rotating domain radius - 0.36m
• 4mm cell size wake refinement for 2.4m with 8 degrees inclination and spread
angle of 10 degrees.
The resulting mesh is represented in Fig. 4.11. The solution from the mesh is shown
in Fig. 4.12 which is compared to the solution with the finest settings. Fig. 4.13
represents the ∆V
Vin
for the solution in Fig. 4.12. Table 4.3 compares the forces,
moment in the domain and time taken for simulation between RW method, the SM
method with the base setup and the newly suggested setup.
(a) Wake refinement downstream of the(b) Enlarged view of the rotating region
cylinder
Figure 4.11: Final mesh representation
Quantity RWbase SMbase SMf inal

Drag (N) 19.9 19.8 19.5
Lift (N) -110 -113 -115
Moment (Nm) -0.142 -0.146 -0.146
Time for simulation (hours) 90 205 22.5
Table 4.3: Force, moment and time comparison for different cases
33
(a)Mean velocity profiles from the final(b) Mean velocity profiles from the finest
mesh SM configuration
Figure 4.12: Mean velocity profiles along the line probes comparing the base and
final configuration
∆V
Figure 4.13: V∞
plot of SM solutions
It can be seen from this figure that the although there is a small shift in the solution
due to the coarser time step, the degree of error is low with an average error of +/-
4%.
34
4.1.4 Splitting interface - Pseudo-parallelization
In this section, the results from the simulation carried out by splitting the interface
of the cylinder into a number of boundaries are presented. The setup is as explained
in section 3.1 and as shown in Fig. 3.6.
The modification to the setup did not change the final solution. But it did bring
about a considerable change in the simulation time. Fig. 4.14 shows the change in
time per timestep as a function of the number of interfaces. Fig. 4.14a represents
the relation between avg. time per timestep and the number of interfaces while
Fig. 4.14b shows the percentage reduction in time per timestep with the number of
interfaces.
(a) Avg time per time step vs Number of(b) Percentage reduction in avg. time per
interfaces timestep vs Number of interfaces
Figure 4.14: Effect on avg. time per timestep
It can be seen that, the avg. time per timestep decreases with increase in the
number of interfaces. When using 8 interfaces, the time reduces from 2.02s (for
single interface) to 1.32s per timestep which is about 35% reduction in the overall
simulation time.
The time taken for updating the interfaces is the difference between the time per
timestep and sum of iterations per timestep. Fig. 4.15a represents the effect this
method had on the time for updating interfaces and Fig. 4.15b represents the
percentage reduction in the updating time. From the figures, it is seen that the
updating time of 1.15s for one interface decreased to 0.366s for 8 interfaces, which
is about 68% decrease.
35
(a)Avg mesh updating time per time step(b) Percentage reduction in avg. mesh up-
vs Number of interfaces dating time per timestep vs Number of in-
terfaces
Figure 4.15: Effect on avg. updating time per timestep
(a) Avg time per iteration vs Number of(b) Percentage increase in avg. time per
interfaces iteration vs Number of interfaces
Figure 4.16: Effect on avg. time per iteration
Additionally it was noted that, this method had an effect on the time per iteration.
Fig. 4.16a denotes the effect this method had on the time per iteration and Fig.
4.16b, the percentage change in the time per iteration. It is evident from the figures
that an increase in number of interfaces caused almost a linear increase in the time
36
per iteration. With 8 interfaces, around 9% increase was noted. A increase in

the number of boundaries increases the iteration time. Additionally the solution
updating at the beginning of each timestep across the interface takes more when
boundary mode interfaces are used instead than contact mode interfaces. So, the first
iteration takes slightly more time than the rest, thus increasing the mean iteration
time. This increase in time for the first iteration is proportional to the number of
interfaces.
Fig. 4.17 compares time taken for each step of SM operation in a timestep with the
configurations using 1 interface and 8 interfaces. Each timestep has a mesh updating
step followed by 6 iterations. It can be seen that while using 8 interfaces, the mesh
updating step is optimized by about 0.8s. The time per iteration increases slightly
with higher number of interfaces but it is negligible as compared to the time gained
from the updating step.
Figure 4.17: Comparison in the time taken for each step in a timestep between 1
interface and 8 interfaces
The results from the study are summarized in Table. 4.4. It is quite evident that
increasing the number of interfaces, reduced the time per timestep. But it is noted
that while the time per timestep decreases, time per iteration increases. So beyond
a point, even if the updating time was very low, time per timestep could increase.
From Table. 4.4, it is seen that the decrease in time between 4 interfaces and 8
interfaces is 0.04s, which is quite small. So, optimizing the number of interfaces is
important for the application.
Parameter 1 int. 2 int. 3 int. 4 int. 8 int.

Time per timestep (s) 2.02 1.50 1.41 1.36 1.32
Time per iteration (s) 0.146 0.147 0.150 0.153 0.160
Updating time (s) 1.15 0.622 0.508 0.447 0.367
Table 4.4: Summary of pseudo-parallelization study
Thus, pseudo-parallelization approach can be used for SM applications to speed up

the mesh updating step.
37
Summary of cylinder simulations

Simulations were performed to understand the behaviour of RW and SM methods to
model rotation. Since the case was very mesh and timestep dependent, a parametric
study was carried out and a configuration with coarser settings was suggested that
could yield acceptable results. Finally, pseudo-parallelization approach was tested
and it was found that this method can be used to speed up SM applications such
as, a complete car setup with rims modelled using SM method.
38
4.2 Car simulations
4.2.1 Car aerodynamic analysis

Fig. 4.18 represents the mean velocity field of the flow on the plane at y=0(centre
of the car). It can be seen that the flow at the front end of the car is decelerated due
to presence of the front shutters and the bumpers. This effect is carried upstream.
The flow along the upper body get accelerated slightly more than the under body
by continuity principle. The rear end of the car is dominated by the wake that is
characterized by the low velocity, re-circulation and vortex shedding.
Figure 4.18: Mean velocity field around the car about the plane y=0
For a car on the road, the flow enters the front shutters which is essential for cooling
flow and it tracks through the engine and the power train. This causes pressure build
up in the engine bay which is poor for the aerodynamics of the car but essential for
the functioning of the car. In this simulation, as seen in Fig. 4.18, the front shutters
are closed and so the flow does not enter the engine bay.
Fig. 4.19 represents the mean Cp on the surface of the car. Cp is the coefficient of
the pressure and it is used to characterize fluid motion. A higher Cp value indicates
that the flow decelerates towards the surface and it usually occurs when the flow
is perpendicular to a surface. A lower Cp value marks acceleration of the flow or
flow separation. From the figure, it can be seen that the front shutters, front part
of the side mirrors and the bottom of the windshield are marked as high pressure
regions as they are surfaces perpendicular to the flow and causes the flow to slow
down. Whereas the roof, A-pillar, the side bumpers and the front wheels are marked
by very low Cp values which means the flow accelerates and/or separates in these
regions.
39
Figure 4.19: Mean Cp on the surface of the car
Cp is an important parameter because it is represents where the forces act on the

body of the car. The drag force is calculated by integrating the Cp over area nor-
mal along x-axis, over the car. And similarly the lift/downforce is calculating by
integrating pressure over area normal along z-axis. Fig. 4.20 represents Cp on the
base of the car. This is important because, the difference between Fx on the front
end consisting of the front shutters, bumpers, windshield and the rear as shown in
fig. contribute to the drag. So higher the Cp at the base of the car, lower the drag.
Figure 4.20: Mean Cp on the rear end of the car
40
(a) Mean velocity vector about the plane y=0m
(b) Mean velocity vector about the plane z=1m
Figure 4.21: Mean velocity vector field representing the wake behind the car
The large wake behind the car is one of the most important features to be considered
while analyzing the aerodynamic performance of the car. Fig. 4.21a and Fig. 4.21b
represent the velocity vectors behind the car along the planes y=0 and z=1m. It
can be seen from these vectors that a strong reversed flow is experienced in this
region. A balanced wake is beneficial for the stability of the car. From Fig. 4.21a,
it can be seen that the base wake is imbalanced along the z-direction. This is the
effect of flow from the roof and the underbody profile of the car. The flow from
these surfaces greatly affect the shape, size and balance of the base wake. In this
case, it can be seen that flow experiences an upwash. From Fig. 4.21b, it can be
seen that the re-circulation near either sides of the car is balanced almost equally.
This means that the car does not have lateral flow instabilities.
The CFD simulations need to be bench-marked for accuracy with experimental re-
sults. The most important parameters that define a car’s aerodynamic performance
are Cd , Cl r, Cl f and Cd A. The table 4.5 represents the ∆=Exp-CFD for Cd and
Cd A. The other two variables for the lift are not considered from experimental data
because appropriate correction for road effects and contact patch had not been done.
But even with Cd and Cd A, it was helpful in establishing the accuracy of the results
presented in the project.
41
Quantity ∆ = Exp − CF D
Cd -0.001
Cd A -0.005
Table 4.5: ∆ of various aerodynamic parameters of Experimental data and CFD

data
It is to be noted that the experimental test was done on the same car with production
tyres while the CFD simulation considered slick tyres. It is known that, detailed
tyre profile affects the overall drag on the vehicle. There are always discrepancies
between experimental and numerical results due to leakages on surfaces, blockage
effects of the wind tunnel and so on. So, it can be established that the results are
within an acceptable level of accuracy.
42
4.2.2 Wheel aerodynamic analysis
(a) Mean velocity field across the centre of the front wheel
(b) Mean velocity field across the centre of the rear wheel
Figure 4.22: Mean velocity field across wheels on the left side of the car
As mentioned above, the flow in the wheel is extremely turbulent with the rotation
of the wheels along with air entering and exiting the region. Fig. 4.22 represents a
cross sectional plane about the front and the rear wheels on the left side of the car.
It can be seen from Fig. 4.22a that the flow velocity magnitude around the front
wheel is higher than the freestream velocity. This is because the flow accelerates
around the front side bumpers and the front wheels as seen from the mean Cp plot
in Fig. 4.19. The flow velocity reaches a higher value above the tyre bulge whereas
on the upper part of the wheel, the velocity is very low at the region of the bulge.
43
The high velocity is because of the resultant of wheel rotation and on-coming flow
while the low velocity is due to flow separation at the tyre bulge. In Fig. 4.22b, it
can be seen that the flow is much slower near the rear wheel. The flow is slowed
down by the combined effects of front wheel separation and skin friction drag on the
fluid close to the body.
Flow separation can be visualized from the isosurface of mean Cptotal =0 colored
by mean velocity field as seen in Fig. 4.23. It can seen from the figure that the
front wheel consists of a bubble covered predominantly by high velocity region. The
presence of this bubble indicates the separation of flow. The rear wheel, unlike the
front, does not have a bubble covering the wheel and has lower velocity. Thus we
can infer that the flow is relatively more attached.
Figure 4.23: Mean Cptotal on the surface of the car
The flow behind both the wheels is dominated by a wake after the flow passes around
and over the tyres. Fig. 4.24 is the mean velocity field on a plane behind the wheel
centres. It can be seen from Fig. 4.24a that the strength of the wake is stronger in
the front wheel that then rear. This is because the flow has higher energy at the
front wheels.
44
(a) Mean velocity field at 280mm behind the centre of the front wheel
(b) Mean velocity field at 320mm behind the centre of the rear wheel
Figure 4.24: Mean velocity field behind the wheels to visualize the wake
4.2.3 Comparison between wheel modeling approaches-SM

vs MRF
The non-dimensional aerodynamic variables are the key parameters to look for in
a vehicle’s performance. Table 4.6 compares the deltas of Cd , Cl r, Cl f and Cd A
obtained from both the methods. Additionally, while comparing the two methods,
the time taken for the simulation is also important because the SM approach has
proved to be costly. It can be seen that the aerodynamic variables from both methods
have very comparable values but the SM method takes about 6.3 hours more than
MRF, which is about 25% more.
45
Quantity ∆ = MRF - SM
Cd 0.000
Cl r 0.004
Cl f -0.001
Cd A 0.001
Time taken for simulation(hr) -6.3
Table 4.6: Delta of various aerodynamic parameters of the car obtained from SM
and MRF approaches
Fig. 4.25 represents the ∆Cd Ax and ∆Cl Ax plots obtained both the methods. The
values are calculated by subtracting cumulative value at each local position of the
car along x-axis. The profile obtained is due to the difference the flow field caused by
the wheel modelling methodology. It can be seen that, the MRF method produces
slightly higher drag and lift around the front wheel of the car. Along the body of
the car, the difference in drag is almost constant whereas the MRF produces lower
lift around the centre of the car. Near the rear wheel, the MRF method produces
lower drag but higher lift as compared to SM method.
Figure 4.25: ∆Cd Ax and ∆Cl Ax plots for SM and MRF approaches
MRF is also called frozen rotor method as it accounts for rotation from a stationary
framework. The position of the rim spokes can affect the mean flow field of the final
solution as it remains stationary unlike SM where the mesh moves physically. The
mean flow field in SM is completely averaged in the region of rotation. This makes
46
it difficult to consider the solution in the rotating region. Outside the sliding mesh
region, the difference in wheel methodology causes a difference in the flow field.
Fig. 4.26 represents the scalar cross section of the mean velocity field across the rear
wheel from both the approaches. It can be seen that the flow over the rear brake
discs and the rims is faster in the solution from MRF than in SM. The flow outside
the wheel in MRF approach has a lower velocity along the rims as compared SM.
The flow on the inner side of the wheel also follows a similar trend as seen in the
figure.
(a) Mean velocity field from SM approach
(b) Mean velocity field from MRF approach
Figure 4.26: Mean velocity field across the centre of the rear wheel of the car
In Fig. 4.25, the slope of the Cd A line increased sharply at the base of the car. So,
the base pressure (Mean Cp ) was compared between the two approaches as shown in
47
Fig. 4.27. It can be seen that the mean Cp values from the MRF solution in slightly
lower than SM solution. This difference in the pressure could be the reason for steep
slope in the ∆Cd Ax at the base. It can also be seen that, the Cp is asymmetric for
the MRF solution as compared to SM solution. This is because of the underbody
profile of the car. The SM simulation, due to mesh motion, is able to generate large
disturbances in the flow near the wheels that reduces the asymmetric effect of the
underbody profile. This effect is carried over almost equally on either sides of the
base.
(a) Mean Cp from SM method
(b) Mean Cp from MRF method
Figure 4.27: Mean Cp on the base of the car comparing SM and MRF methods
48
4.2.4 Effect of rims in the flow field and aerodynamics of

the car
As mentioned in section 3.2, two rims as shown in Fig. 3.11 were tested with the
same conditions. Table 4.7 compares the deltas of aerodynamic variables from both
the simulations.
Quantity ∆ = CR - OR
Cd -0.011
Cl r -0.008
Cl f 0.000
Cd A -0.029
Table 4.7: Delta of various aerodynamic parameters comparing OR and CR
Fig. 4.28 represents the ∆Cd Ax and ∆Cl Ax of the car from either of the cases. The
∆ is calculated as CCR − COR . Blanking reduced 29 Cd A counts and 21 Cl A counts.
Figure 4.28: ∆Cd Ax and ∆Cl Ax plots for OR and CR
It is evident that closing the rim reduces the drag and increases the net downforce
of the car. From Fig. 4.28, a small peak is observed near the front shutters. This is
due to the difference in pressure caused between the two cases. CR has higher built
in pressure with the rims closed. The effect of the rims carries forward to the front
of the car resulting in lower drag. While the drag is reduced, the lift increases in the
front of the car when the rims are closed. Along the rear wheels and wheel housing,
49
a significant reduction in the drag and lift is encountered. This is mainly because
the flow is attached along the rims when they are closed and separation increases
the drag significantly. However at the base of the car, it can be seen from Fig. 4.28
that CR produces slightly higher drag as compared to OR. This is because, OR
produced higher base pressure as compared to CR. Higher base pressure results in
lower drag.
Figure 4.29: Iso-surface of mean Cptotal =0 coloured by mean vorticity comparing

CR and OR
Fig. 4.29 represents an iso-surface of mean Cptotal = 0 coloured by mean vorticity in

the flow comparing the solutions from OR and CR. Closing the rim prevents air flow
in and out of the rim. This reduces the chaotic nature of flow around the wheels
and tyres. Near the front wheel, blanking reduces the intensity of vorticity in the
separation bubble slightly. The flow separates near the wheel housing lip and till the
front door where it reattaches in either of the cases. But blanking the rim, reduces
the intensity of the vortices generated. This preserves the mean fluid energy and
helps in reducing the drag. The flow separation is not as prominent in the rear wheel
as the velocity of the fluid is reduced. But closing the rims stopped separation along
the rims. Though the flow still separated on the tyres, the flow was predominantly
attached over the rims. The base wake observed was slightly shorter and thinner
due to blanking.
50
(a) Mean velocity field from OR
(b) Mean velocity field from CR
Figure 4.30: Mean velocity fields along a plane adjacent to the wheels
Fig. 4.30 represents the mean velocity of the flow field along a plane adjacent to the
wheels. The influence of flow separation near wheels on the mean velocity field can
be clearly visualized in this figure. The strength of the flow separation is stronger in
OR. In the case of CR, the wakes are weaker and shorter. This allows higher energy
flow to mix with the base wake. So we would naturally expect higher base pressure
and upwash for CR. But we encountered lower base pressure for CR.
51
(a) Mean Cp field from OR
(b) Mean Cp field from CR
Figure 4.31: Mean Cp on the back of the car comparing OR and CR
Fig. 4.31 represents mean Cp on the rear end of the car. The pressure on the base
is slightly different in these cases. In the CR case, the flow over the rim is more
attached and faster as compared to OR as seen in Fig. 4.30. Though this allowed
higher energy fluid to mix with the base wake which promotes higher base pressure,
for this car, the mean Cp from the CR produced lower base pressure as seen in the
figure. In comparison, OR produced slightly higher base pressure. That is why the
drag increased at the base for CR in Fig. 4.28.
Fig. 4.32 represents mean velocity vector field at the base of the car. It can be seen
that the flow field in the wake region is very similar from the two cases along the x-z
plane. But the flow from CR produces slightly greater upwash and this is helped
in obtaining greater downforce. This could be a reason for the slightly lower base
52
pressure for CR. The flow could have shifted to an angle which promotes greater
upwash than base pressure.
(a) Mean velocity vector field from OR
(b) Mean velocity vector field from CR
Figure 4.32: Mean velocity vector field on the back of the car comparing OR and
CR
53
4.2.5 Time step dependency study

As stated in section 3.2, two time steps, 2.5e-4s and 1e-4s, were tested on the whole
car setup. For consistency, the same mesh and run script was used and both were
run on 2160 cores on the cluster. The table 4.8 consists of the ∆ from both the
simulations with the one with 2.5e-4 as the reference solution. The finer timestep of
1e-4s required much higher time. While the simulation with 2.5e-4s took 29 hours,
the one with 1e-4s completed in 70 hours.
Quantity ∆= C1e−4 -C2.5e−4

Cd 0.001
Cl r -0.002
Cl f -0.003
Cd A 0.004
Table 4.8: Comparison of delta of mean values of aerodynamic variables for

timestep dependency study
It can be seen that the simulation yielded only slightly different forces on the car.
But given the time taken to achieve this solution, it can be inferred that the solution
obtained with the timestep 2.5e-4s is acceptable. The Fig. 4.33 shows the ∆Cd Ax
and ∆Cl Ax of both cases.
Figure 4.33: ∆Cd Ax and ∆Cl Ax plots timestep dependency study
In terms of the stability of the solution, both the cases performed well. The residuals
and the aerodynamic variables converged to similar solutions and were quite stable.
54
Preserving the mesh and changing the timestep results in a different Courant number
in the domain. Fig. 4.34 compares solution for a CFL number greater than 1. It
can be seen that the solution with the coarser time step has a greater region with
CFL>1. But the majority of it still under a reasonably accepted level(<5). A
second order spatial discretization scheme is used in the two cases. Additionally,
the solution is obtained using a implicit solver, iterated many times per timestep.
Hence for a converged simulation, the final solution should not vary much and that
is evident from the table. 4.8. Hence, it is sufficient to run the simulation with
2.5e-4s.
(a) CFL number for time step 2.5e-4s
(b) CFL number for time step 1e-4s
Figure 4.34: CFL number comparison between both the cases
55
4.2.6 Splitting interface - Pseudo-parallelization

The results from the cylinder simulations were promising and the methodology was
adopted for modelling wheels as shown in Fig. 3.12. The method required the user
to split the interface in such as way that the number of faces from the rotating and
stationary regions, intersecting the interface are equal. But due to the complexity
of the rims intersecting the domain, this was difficult to achieve. The final setup
had a split ratio of 2:2:1 intersecting faces across the three interfaces. Table. 4.9
presents the time per timestep, time per iteration and the time taken for updating
the mesh per timestep.
Quantity 1 interface 3 interfaces

Time per timestep(s) 11.1 10.5
Time per iteration(s) 1.32 1.33
Time for updating(s) 3.18 2.52
Table 4.9: Results from interface splitting
The interface for each wheel consisted of 200,000 cells intersecting from both the
stationary and rotating regions. The Fig. 4.35 represents the split of intersecting
cells across the three interfaces. This uneven distribution resulted in unequal CPU
load and the approach does not run at optimal capacity.
Figure 4.35: Comparison of the number of intersecting cells across the three in-
terfaces
It can seen from the table that, this method decreased the time taken for updating
the mesh and interface each timestep. About 20.7% reduction in the time for updat-
ing, 5% reduction in time per timestep and 1% increase in time per iteration were
noted. The cylinder simulations recorded over 50% reduction in the updating time
and 30% reduction in time per timestep. The simulation on the car is extremely
big as compared to the cylinder and proportional results can not be expected. The
56
cylinder had about 96,000 intersection faces along the interface while each wheel
had 200,000 intersecting faces and the number of faces on the each of the interface
of the wheel were not split evenly. But by splitting the number of faces evenly on
all the three interfaces, the updating time could be further improved. Like in the
results from the cylinder, the simulation on the car also exhibited increase in time
per iteration with higher number of interfaces. While there was a 2% increase in
iteration time for the cylinder, there was 1% increase in the car. Like in the cylinder
case, this is because the solution updating at the beginning of each timestep across
the interface takes more time when boundary mode interfaces are created. So, the
first iteration takes slightly more time than the rest which increases the mean itera-
tion time. Additionally, increasing the number of boundaries increases the iteration
time.
Table 4.10 presents the ∆ of the aerodynamic variables from either of the solutions.
The change in setup did not alter the final solution by much. So boundary mode
interfacing does not change the solution.
Quantity ∆ = C3int - C1int

Cd 0.001
Cl r -0.005
Cl f 0.000
Cd A 0.004
Table 4.10: Comparison of delta of aerodynamic variables for pseudo-

parallelization study
It can be inferred that this method is viable for speeding up the simulation. Splitting
the surface into more than 3 PIDs is also an option to further improve the speedup.
But it essential to be cautious on the time spent in doing this. This process of
creating multiple PIDs is a manual process done on ANSA which is time consuming.
Additionally, with growing number of interfaces, the time per iteration also increases.
So it is necessary to be aware that the effective time spent on the simulation could
increase if too much time is spent on the setup creating many surfaces for the
wheel which results in spending more time per iteration. So, the method has to be
optimized for each application.
57
58
5
Conclusion
The thesis presents a number of CFD studies, investigating a simple rotating cylin-
der and then a car.
Analysis on rotation modelling was performed on a rotating cylinder comparing RW

and SM methods. A mesh, timestep and solver sensitivity study was performed on
SM method. Pseudo-parallelization approach for SM was tested and analyzed on
the cylinder.
After studying the flow field around the car, MRF and SM wheel modelling ap-
proaches were analyzed. The effects of blanking on the aerodynamic performance of
the car was studied. A timestep sensitivity study was performed. Finally, pseudo-
parallelization approach for SM was tested on the car.
The main outcomes from the work are presented below:

Cylinder simulations
• Both RW and SM methods produced very similar results when an adequate
mesh size and timestep were used.
• The SM method was more sensitive to mesh size and timestep selection than
RW. From the parametric study, a coarser configuration was suggested for SM
to obtain comparable results to RW at low simulation cost.
• Pseudo-parallelization approach yielded 68% reduction in mesh updating time
and 9% increase in iteration time when 8 interfaces was used. This resulted in
35% reduction in total time. It was inferred that this approach could be used
for speeding up SM simulations.
Car Simulations
• MRF and SM methods produced similar values for the aerodynamic variables.
But the flow field locally around the wheels and the base of the car was quite
different.
• Since SM method is more realistic in the modelling approach, it is recom-
mended for the modelling of rims.
• Blanking the rims reduced the drag by 29 Cd A counts and lift by 21 Cl A counts
for this car. This reduction in drag was due to lower flow separation for CR
around the wheels as compared to OR. This allowed high energy fluid to mix
with the base wake which increased the upwash, producing higher downforce.
• From the timestep dependency study, it was found that for the current mesh
settings, a timestep of 2.5e-4s is capable of producing acceptable results.
59
5. Conclusion
• Pseudo-parallelization approach on SM for the car produced about 21% reduc-

tion in mesh updating time when three interfaces were used. The number of
intersecting faces across the interface was not evenly split across them. So by
splitting the intersecting faces evenly across the interface and creating more
than three interfaces, this method can be further improved.
5.1 Future Work

A few suggestions for future work are listed below:
• Experimental investigations to validate the solution obtained from the sim-
ulations on the rotating cylinder could be useful to further investigate the
accuracy of rotation modelling techniques in CFD.
• Pseudo-parallelization method has a lot of potential for speeding up SM sim-
ulations and this can be investigated more.
• Investigate mesh resolution sensitivity with a especially attention to the inter-
faces.
• Modelling contact patch.
• FEM-CFD coupling to model the contact patch to obtain the exact solution
for wheel modelling.
60
Bibliography
[1] Hobeika, T., 2018. Wheel Modelling and Cooling Flow Effects on Car Aerody-
namics. Chalmers University of Technology.
[2] Landstrom, C., Josefsson, L., Walker, T. and Lofdahl, L., 2012. Aerodynamic
effects of different tire models on a sedan type passenger car. SAE International
Journal of Passenger Cars-Mechanical Systems, 5(2012-01-0169), pp.136-151.
[3] Wittmeier, F. and Kuthada, T., 2015. The influence of wheel and tire aerody-
namics in WLTP. In 6th International Munich Chassis Symposium 2015 (pp.
149-160). Springer Vieweg, Wiesbaden.
[4] Ten Brink, P., 2010. Mitigating CO2 emissions from cars in the EU (Regulation
(EC) No. 443/2009). The new climate policies of the European Union: Internal
legislation and climate diplomacy, 15, p.179.
[5] European Parliament and the Council of the European Union, 2014. Regulation
(EU) No 333/2014 of the European Parliament and of the Council of 11 March
2014 amending Regulation (EC) No 443/2009 to define the modalities for
reaching the 2020 target to reduce CO2 emissions from new passenger cars. Off
J Eur Union, 103(333), pp.15-21.
[6] Kandasamy, S., Duncan, B., Gau, H., Maroy, F., Belanger, A., Gruen, N. and
Schäufele, S., 2012. Aerodynamic performance assessment of BMW validation
models using computational fluid dynamics (No. 2012-01-0297). SAE Technical
Paper.
[7] Fackrell, J.E. and Harvey, J.K., 1972. The flow field and pressure distribution
of an isolated road wheel.
[8] Cogotti,A., "Aerodynamics Characteristics of Car Wheels", 1983, International

Journal of Vehicle Design, SP3.
[9] Mercker, E., Berneburg, H., 1992," On the simulation of Road Driving of a
Passenger Car in a Windtunnel Using a Moving Belt and Rotating Wheels",
Lecture at the Third International Conference Innovation and Reliability in
Automotive Design and Testing, Florence.
61
Bibliography
[10] Elofsson, P. and Bannister, M., 2002. Drag reduction mechanisms due to
moving ground and wheel rotation in passenger cars. SAE Transactions,
pp.591-604.
[11] Landström, C., Walker, T., Christoffersen, L. and Löfdahl, L., 2011. Influences
of different front and rear wheel designs on aerodynamic drag of a sedan type
passenger car (No. 2011-01-0165). SAE Technical Paper.
[12] Zhiling, Q., Landström, C., Löfdahl, L. and Josefsson, L., 2010. Wheel
Aerodynamic Developments on Passenger Cars by Module-based Prototype
Rims and Stationary Rim Shields. In FISITA 2010 Automotive World Congress.
[13] Hobeika, T., Sebben, S. and Landstrom, C., 2013. Investigation of the influence
of tyre geometry on the aerodynamics of passenger cars. SAE International
Journal of Passenger Cars-Mechanical Systems, 6(2013-01-0955), pp.316-325.
[14] Hobeika, T. and Sebben, S., 2018. CFD investigation on wheel rotation
modelling. Journal of Wind Engineering and Industrial Aerodynamics, 174,
pp.241-251.
[15] Koitrand, S., Gaylard, A. and Fiet, G.O., 2015. 18 An Investigation of Wheel
Aerodynamic Effects for a Saloon Car.
[16] Blacha, T. and Islam, M., 2017. The aerodynamic development of the new
Audi Q5. SAE International Journal of Passenger Cars-Mechanical Systems,
10(2017-01-1522), pp.638-648.
[17] Schnepf, B., Schütz, T. and Indinger, T., 2015. Further investigations on
the flow around a rotating, isolated wheel with detailed tread pattern. SAE
International Journal of Passenger Cars-Mechanical Systems, 8(2015-01-1554),
pp.261-274.
[18] Profir, M.M., 2012. Automated moving mesh techniques and re-meshing
strategies in CFD applications using morphing and rigid motions.
[19] SIEMENS, P. L. M. STAR-CCM+ Documentation. 2018, Siemens PLM Soft-

ware Inc, 13.
[20] Axon, L., Garry, K. and Howell, J., 1998. An evaluation of CFD for modelling
the flow around stationary and rotating isolated wheels. SAE transactions,
pp.205-215.
[21] Gritskevich, M.S., Garbaruk, A.V., Schütze, J. and Menter, F.R., 2012.
Development of DDES and IDDES formulations for the k- shear stress transport
model. Flow, turbulence and combustion, 88(3), pp.431-449.
62
Bibliography
[22] Davidson, Lars. 2018. Fluid mechanics, turbulent flow and turbu-
lence modeling. Göteborg: Division of fluid mechanics, Department of
Applied Mechanics, Chalmers University of Technology. URL: http:
//www.tfd.chalmers.se/~lada/postscript_files/solids-and-fluids_
turbulent-flow_turbulence-modelling.pdf
[23] Davidson, L., 2015. An introduction to turbulence models.
[24] Roshko, A. (1961). Experiments on the flow past a circular cylinder at very
high Reynolds number. Journal of Fluid Mechanics, 10(3), 345-356.
63
Bibliography
64

WheelModeling CFD MSC

Uploaded by

Document Informationclick to expand document information

Copyright:

Available Formats

WheelModeling CFD MSC

Uploaded by

Document Information

Original Title

Copyright

Available Formats

Share this document

Share or Embed Document

Sharing Options

Did you find this document useful?

Is this content inappropriate?

Copyright:

Available Formats

WheelModeling CFD MSC

Uploaded by

Copyright:

Available Formats

DF

CFD investigation on wheel modelling and

Anandh Ramesh Babu

Department of Mechanics and Maritime Sciences

CFD investigation on wheel modelling and car

Anandh Ramesh Babu

Department of Mechanics and Maritime Sciences

© Anandh Ramesh Babu, 2019.

Supervisor: Dr. Teddy Hobeika, Aerodynamics Group, Volvo Cars

Master’s Thesis 2019:58

Cover: Resampled volume used to capture regions of low instantaneous velocities

Typeset in LATEX, template by David Frisk

Keywords: Car aerodynamics, CFD, wheel modelling, SM optimizing, wheel blank-

Anandh Ramesh Babu, Gothenburg, June 2019

List of Tables xiii

4 Results and Discussions 23

4.2.2 Wheel aerodynamic analysis . . . . . . . . . . . . . . . . . . . 43

2.1 Aerodynamic forces and moments acting on the car . . . . . . . . . . 11

3.1 Geometry description of the cylinder simulations . . . . . . . . . . . . 13

4.1 Mean velocity field around the cylinder from RW method . . . . . . . 24

3.1 Boundary conditions for cylinder simulations . . . . . . . . . . . . . . 14

1.1 Environmental impact of Vehicle Aerodynam-

The transport industry is a major producer of CO2 gas. Combustion of various

Standardizing driving cycles to compare the fuel consumption of different vehi-

CFD simulations produce numerical solutions of real scenarios relying on assump-

The SM method is computationally expensive in all CFD commercial tools. In

1.3 Project Objectives

2.1 Fluid Dynamics

This framework of definition is given by the conservation laws- conservation of mass,

2.1.1 Governing Equations

τij = 2µSij − 2µSkk δij (2.3)

2.2 Computational Fluid Dynamics

2.2.2 RANS models

ui = ūi + u0i (2.6)

In the problem at hand, k − ω turbulence model is used and so it is briefly explained

2.2.2.1 k − ω Turbulence Model

2.2.3 LES model

2.2.4 DES models

2.2.4.1 IDDES model

Figure 2.1: Aerodynamic forces and moments acting on the car

2.4 Rotation Modeling

2.4.1 Rotating Wall boundary condition

2.4.2 Multiple Reference Frame

∇ · (u~p × u~0 ) + ω~p × u~0 = −∇(p/ρ) + ν∇ · ∇u~0 (2.19)

2.4.3 Sliding Mesh method

The generic transport equation for dynamics meshes is given as,

3.1 Cylinder Simulations

Figure 3.1: Geometry description of the cylinder simulations

Table 3.1: Boundary conditions for cylinder simulations

Figure 3.3: line probes

Figure 3.4: Mesh around the cylinder and interface

Figure 3.5: Mesh around the cylinder and interface

Parameters Settings used

Table 3.2: Parametric study

(a) Two interfaces (b) Three interfaces

(c) Four interfaces (d) Eight interfaces

Figure 3.6: Geometries of cylinder split into 2, 3, 4 and 8 faces

3.2 Car Simulations