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Report
On
Flow Analysis & Simulation of Formula SAE Vehicleusing CFD Techniques
Submitted in partial fulfilment of the requirements for the degree of
Bachelor of Technology
(Automotive Design Engineering)
From
University of Petroleum and Energy Studies
Dehradun
By
Prafull Chandra Moulekhi (R140207040)
Abhishek Dixit (R140207002)
Rohit Aggarwal (R140207044)
Under the Guidance of
Dr. Ugur Guven
Department of Aerospace Engineering
University of Petroleum & Energy Studies
Dehradun
May 07, 2011
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Flow Analysis & Simulation of Formula SAE Vehicle using CFD Techniques
A thesis submitted in partial fulfillment of the requirements for the Degree of
Bachelor of Technology
(Automotive Design Engineering)
By
Prafull Chandra Moulekhi
(R140207040)
Abhishek Dixit
(R140207002)
Rohit Aggarwal
(R140207044)
Under the Guidance of
Dr. Ugur Guven
Professor of Aerospace Engineering (PhD)
Nuclear Science and Technology Engineer (M.Sc)
Approved
Dean
College of Engineering
University of Petroleum & Energy Studies
Dehradun
May, 2011
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CERTIFICATE
This is to certify that the work contained in this thesis titled Flow Analysis & Simulation of
Formula SAE Vehicle using CFD Techniques has been carried out by Prafull Chandra
Moulekhi, Abhishek Dixit & Rohit Aggarwal under my supervision and has not been submitted
elsewhere for a degree.
Dr. UGUR GUVEN
Professor of Aerospace Engineering
(May 07, 2011)
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ACKNOWLEDGEMENT
Major Project in the final year is an indispensable part of any engineering curriculum. It provides
the students with an opportunity to gain experience on the practical application of their technical
knowledge and to study the various theoretical aspects as well.
We would like to thank our Project Guide Dr. UGUR GUVEN, Department of Aerospace
Engineering for giving us this opportunity to work under his guidance on this project. His
technical help and goal oriented approach has been unique and a stepping stone towards the
successful completion of the project.
May 2011 PRAFULL CHANDRA MOULEKHI
ABHISHEK DIXIT
ROHIT AGGARWAL
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i
TABLE OF CONTENTS
Page
TABLE OF CONTENTS i
LIST OF FIGURES v
LIST OF TABLES viii
SUMMARY x
1. INTRODUCTION.....1
1.1 Introduction.. ....1
1.2 Objective....2
1.2.1 SUPRA SAE Competition......2
1.2.2 Structural Analysis .....................................................................................2
1.2.3 Materials.2
1.2.4 Aerodynamics.2
2. LITERATURE REVIEW.....3
2.1 Structural Analysis....3
2.2 Aerodynamics3
2.2.1 Main Bodywork..3
2.2.2 Wings..4
2.2.3 Under body Diffuser...4
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2.2.4 Side Ducts...5
2.2.5 Spoilers...5
2.3 Aerodynamic Forces..6
2.3.1 Drag Force..6
2.3.2 Lift Forces7 2.4 Approaches to flow analysis8
2.4.1 Theoretical Approach .8
2.4.2 Experimental Approach..8
2.4.3 Computational Approach ...8
3. FEA ANALYSIS....9
3.1 Design Consideration for Roll cage..9
3.2 Material and Size optimization of Rollcage tubing..9
3.3 Structural Analysis...10
3.3.1 Front Impact..10
3.3.2 Side Impact...11
3.3.3 Rear Impact...11
3.3.4 Rollover Impact12
3.4 Rollcage Design Optimization .....13
3.4.1 Use of cross supports ....13
3.4.2 Use of Gussets ...15
4. FLUID DYNAMICS EQUATIONS...17
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4.1Euler's and Bernoulli's equations17 4.1.1 Eulers Equation for viscous flow174.1.2 Bernoulli's equation..18
4.2Navier- Stokes Equations for a viscous flow..194.3Eulers Equations for an inviscid flow214.4Navier stokes equation for a incompressible inviscid flow22
5. FLOW ANALYSIS..24
5.1 Modelling in Catia ..24
5.2 Creating Geometry in Gambit.25
5.2.1Creating Vertices.25
5.2.2 Creating Edges25
5.2.3 Creating Faces.26
5.3 Meshing..27
5.4 Parameters and initial boundary conditions...28
5.5 Flow Analysis in fluent...29
6. RESULT & ANALYSIS.....30
6.1 Flow Over Nose..30
6.2 Flow Over the body32
6.3 Flow Under body....33
6.4 Boundary Layer Separation35
6.5 Design Modification Based on result Obtained..39
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6.6 flow over Nose.40
6.7 Flow Over the Car Profile42
6.8 Flow Under Body.44
6.9 Boundary Layer Separation.46
6.10 Pressure Distribution Over and Below the Car..50
6.11 Drag Coefficient Plot.50
6.11 Lift Coefficient Plot...51
7. USE OF CFD RESULTS IN ENGINE PERFORMANCE CALCULATIONS52
7.1 Power Requirement ..52
7.1.1 Wheel Resistance..52
7.1.2 Air resistance ...52
7.1.3 Gradient Resistance ..53
7.1.4 Total Driving resistance....53
7.2 Drag Force Calculation at different speeds.54
8. CONCLUSION57
REFERENCES .. 58
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v
LIST OF FIGURES
Page
Figure 2.1: Areas Concerning Aerodynamics...........4
Figure 2.2: Spoiler........................5
Figure 3.1: Front Impact Stress Plot....10
Figure 3.2: Side Impact Stress Plot......11
Figure 3.3: Rear Impact Stress Plot.12
Figure 3.4: Rollover Impact Stress Plot.......................................................................................12
Figure 3.5: Optimized Front Impact Stress Plot..13
Figure 3.6: Optimized Side Impact Stress Plot....................................................................14
Figure 3.7: Optimized Rear Impact Stress Plot. ...............14
Figure 3.8: Optimized Rollover Impact Stress Plot.....................................................................15
Figure 3.9: Front members with gussets......................................................................................16
Figure 3.10: Analysis results after Gusseting..........................................................................16
Figure 4.1: Bernoullis Equation.....18
Figure 5.1: Shape Design in Catia...............................................................................................24
Figure 5.2: Creating Vertices...........................................................25
Figure 5.3: Creating Edges..................................................................................................26
Figure 5.4: Creating Faces...............................26
Figure 5.4: Edge Mesh .27
Figure 5.5: Face Mesh.28
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Figure 5.6: Specifying Boundaries.28
Figure 6.1.1: Velocity Contours at nose.........................................30
Figure 6.1.2: Static Pressure Contour at nose....................................................30
Figure 6.1.3: Contours of Turbulent Kinetic Energy.........................................31
Figure 6.1.4: Velocity Vectors at Nose.....................................................................................31
Figure 6.2.1: Velocity Contour over the car body.................................32
Figure 6.2.2: Contours of Turbulent Kinetic Energy over the car body....................................32
Figure 6.2.3: Velocity Vectors over the car body.............. ...................................33
Figure 6.3.1: Velocity Contour Under body..............................33
Figure 6.3.2: Static Pressure Contour Under body........................................34
Figure 6.3.3: Contours of Turbulent Kinetic Energy Under body.........................................34
Figure 6.3.4: Velocity Vectors Under body.......................35
Figure 6.4.1: Velocity Contour at front hoop.35
Figure 6.4.2: Velocity Contour at rear hoop..............................................36
Figure 6.4.3: Static Pressure Contour at front hoop..................................................................36
Figure 6.4.4: Static Pressure Contour rear hoop...................37
Figure 6.4.5: Contours of Turbulent Kinetic Energy at front hoop..........................................37
Figure 6.4.6: Contours of Turbulent Kinetic Energy...............................................................38
Figure 6.4.7: Velocity Vectors at front hoop...........................................................................38
Figure 6.4.8: Velocity Vectors at Rear ...................................................................................39
Figure 6.5: New Model in Catia .............................................................................................39
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Figure 6.6.1: Velocity Contours at nose..................................................................................40
Figure 6.6.2: Static Pressure Contour at nose..........................................................................41
Figure 6.6.3: Contours of Turbulent Kinetic Energy...............................................................41
Figure 6.6.4: Velocity Vectors at Nose...................................................................................42
Figure 6.7.1: Velocity Contour over the car body...................................................................42
Figure 6.7.2: Contours of Turbulent Kinetic Energy over the car body..................................43
Figure 6.7.3: Velocity Vectors over the car body....................................................................43
Figure 6.8.1: Velocity Contour Under body............................................................................44
Figure 6.8.2: Static Pressure Contour Under body..................................................................44
Figure 6.8.3: Contours of Turbulent Kinetic Energy Under body...........................................45
Figure 6.8.4: Velocity Vectors Under body.............................................................................45
Figure 6.9.1: Velocity Contour at front hoop..........................................................................46
Figure 6.9.2: Velocity Contour at rear hoop.............................................................................46
Figure 6.9.3: Static Pressure Contour at front hoop..................................................................47
Figure 6.9.4: Static Pressure Contour rear hoop.......................................................................47
Figure 6.9.5: Contours of Turbulent Kinetic Energy at front hoop..........................................48
Figure 6.9.6: Contours of Turbulent Kinetic Energy...............................................................48
Figure 6.9.7: Velocity Vectors at front hoop...........................................................................49
Figure 6.9.8: Velocity Vectors................................................................................................49
Figure 6.10: Static Pressure XY Plot.......................................................................................50
Figure 6.11: Drag Coefficient Plot..........................................................................................50
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Figure 6.12: Lift Coefficient Plot...........................................................................................51
Figure 7.1: Aerodynamic force Vs. Vehicle Speed...............................................................52
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LIST OF TABLE
Page
Table 3.1:Material Selection10
Table 7.1: Change in total resistance with velocity..55
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x
Summary
This project is about determination of Engine performance at high speed, while calculating
various resistances encountered by vehicle. Aerodynamic forces form major part of total
resistances. To calculate these aerodynamic forces (coefficient of lift and drag) Flow simulation
of different surface profiles has been performed using CFD techniques. We have analysed the
structural integrity by using FEA analyses.
2-D analyses of surface profile of car has been done using GAMBIT and FLUENT. The results
obtained from FLUENT has been useful in modifying the shape and carefully dealing with
critical points like nose, driver compartment, extended body work at rear end, and wings.
Results obtained from FLUENT were then used to calculate engine performance at varying
speeds.
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Chapter 1
Introduction
1.1IntroductionAerodynamic forces and moments, as well as tyre road forces, affect vehicle stability and
control. Unlike the tyre forces which are primarily independent of speed, aerodynamic forces
increase rapidly with speed. For example, aerodynamic drag determines the vehicles
performance characteristics at high speed including maximum speed, forward acceleration at the
higher speed and the braking acceleration. In addition to direct effects of aerodynamic forces the
interaction of aerodynamic and the tyre forces can have a large effect on lateral acceleration
performance. For example, aerodynamic down force (negative) increases the tyre loads and in
turn increases the lateral force capability of tyres.
One of the most important high tech tools for measuring aerodynamic performance in
today's racing is Computational Fluid Dynamics (CFD).
CFD is a computer-based technology that studies the dynamics of all things that flow.
In Formula 1 racing, CFD involves developing a computer-simulated model of a race car
and then applying the laws of physics to the virtual prototype to predict what the
downforce or drag may be on various components of the car or how the car will
respond in various wind conditions (head wind, cross wind or tail wind conditions), changing
environmental conditions or on different road surfaces.
We can use CFD to better visualize and improve their understanding of
how various designs will perform. It also allows them to experiment with more design
variables with high resolution in space in a shorter amount of time.
CFD allows engineers to use computer software like GAMBIT to divide components of a race
car into specific cells or grids. For each of those cells, supercomputers which use CFD softwares
like FLUENT, STAR-CD, FEMLAB and ANSYS CFX etc. to calculate mathematical equations
that compute the velocity and air pressure of the wind as it passes over, under and around the
specified components of the race car.
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1.2 Objective
This project is about modelling formula SAE vehicle while performing flow over analysis &
simulation as well as structural analysis. The project is concerned with the simulation of the
aerodynamic flow around the front section & over the surface of a Formula one racing car. This
will help us in developing the curved surfaces that are least resistive to airflow and are viable for
FSAE event.
1.2.1 SUPRA SAECompetition
The SUPRA SAE competition is for university students to design, build and race a small formula
style racing car. The competition is broken down in to different categories in which each team
earns points. The body work and the aerodynamics of the vehicle cover the maximum points
both in design and dynamic event.
This is the primary objective of the project with the following questions required to be answered.
1.2.2 Structural Analysis:
a) Rollcage Design Optimization.
1.2.3 Materials:
a) What are the material requirements for body & frame?1.2.4 Aerodynamics:
a) What SUPRA SAE rules apply to the bodywork?b) What generic shapes are most aerodynamically efficient?c) Would a forward wing be an effective way of avoiding under steer at speed?d) How far rearward should the bodywork extend?e) How can CFD be used to refine the bodywork design?f) How aerodynamic forces are affecting vehicle performance?
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Chapter 2
Literature Review
2.1 Structural Analysis
The most important aspect of the vehicle design is the frame. The frame contains the operator,
engine, brake system, fuel system, and steering mechanism, and must be of adequate strength to
protect the operator in the event of a rollover or impact. The roll cage must be constructed of
steel tubing, with minimum dimensional and strength requirements dictated by SAE.
The impact loading is simulated by restricting displacements at certain locations, and applying
discrete forces at various points on the frame where the weight is concentrated. The applied
forces are obtained by multiplying the deceleration value by the overall weight of the vehicle and
driver
2.2 Aerodynamics
When developing a bodywork package for any vehicle the aerodynamics of the bodywork should
be considered. This is most beneficial in racing where aerodynamics can be tailored to give
better vehicle economy, handling, and overall performance. While reviewing race car
aerodynamics pertinent to Formula SAE there are three main areas to be reviewed: use of wings,
use of an underbody diffuser and the general geometry of the main body work.
2.2.1 Main BodyworkIts most logical to focus on the main bodywork of the vehicle, with downforce production being
a secondary objective. The bodywork is classically shaped around the occupants, and the various
other sub-systems comprising of the vehicle; using this as the very basis of our design principals
we move on to recognise the possible causes of drag in the vehicle. Since our vehicle engine is
mounted at the rear and to provide sufficient cooling we have to provide a natural air flow over
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the engine compartment. For the positioning of the radiator in the side we must also consider the
effect of sidepods, the sidepod geometry can be used to generate downforce as well as influence
the flow speed over the radiator.
2.2.2 WingsInverted wings have been extensively studied for use on a Formula SAE. The study undertaken
investigated the benefits of a wing package, as well as an initial performance prediction. The
results drawn from this investigation were a similar or slower time in the acceleration event, a
similar or faster time in the skid pan event, slower acceleration, higher cornering potential,
higher slalom speeds, higher braking potential, and an increase in fuel usage. The conclusion
drawn from this investigation was that a wing package would significantly benefit the vehicles
performance in dynamic events.
Figure 2.1: Areas Concerning Aerodynamics
2.2.3 Under body DiffuserA secondary method of producing down force is an under body diffuser. A diffuser works on the
principle that even a non-lifting body in the vicinity of ground effect can produce down force.
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Since FSAE rules prohibit skirts to seal the under body of the car to the ground, the research
regarding under body height to length ratio versus CL and CD must be considered.
2.2.4 Side DuctsSide ducts are mainly used in race cars for break and engine cooling of the vehicle. Conventional
fender design trap much of the turbulent air coming of top and back of the tyre generated by
rotation of tyres and wheels, combined with hot air moving through engine compartment and
brakes, this generates losses. Side ducts provides a smooth outlet for these hot and turbulent
gasses and turns the flow to exit smoothly along the side of the car instead of directly outward.
2.2.5 Spoilers
The spoilers and air foils on the rear check may serve several purposes. The rear spoilers, which
is attached either to the rear of the roof or the upper edge of the rear wings, has the effect of
increasing the pressure acting on the rear deck area. This increase in pressure acting on the rear
deck creates a down force at the most advantageous point as shown in the figure.
Figure 2.2: Spoiler
The spoilers may also serve to stabilize the vortices in the separation flow, thus reducing the
aerodynamic buffeting.
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2.3 Aerodynamic Forces
2.3.1 Drag Force
The air flow over a vehicle is complex and the aerodynamic drag is expressed by the semi -
empirical equation to represent the aerodynamic effect.
Drag Force is calculated as:
FD = V2
A Cd
Where;
FD = Aerodynamic Drag Force, N
= air density, Kg/m3
V = velocity, m/sec
A = Frontal Area, m2
Cd = Drag Coefficient
The total aerodynamic drag of a vehicle includes many factors which offer overall air resistance
to the motion of vehicle. The types of aerodynamic drag components and their approximate
relative contributions are;
Profile or Form Drag ~55 - 60 %
Induced or Lift Drag ~ 8 %
Surface or Friction Drag ~ 10 %
Interference ~ 15 %
Cooling & Ventilation System Drag ~ 10 %
Rotating Wheel & other ~1 %
a) Profile Drag
The profile drag depends upon the longitudinal section of the vehicle body, and plays the most
important part as its contribution is the maximum. A careful choice of body profile, essential for
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low drag, requires streamlines to be continuous and separation of boundary layers with its
attendant vortices to be avoided. A vehicle body produces accelerated air flow and the induced
drag is caused by the vortices formed at the sides of the vehicle travelling downwards.
b) Surface Drag
The surface or friction drag contributes substantially. It is due to the friction of the layers of air
passing over the outside surface of the vehicle body. The friction loss on the boundary layer and
the surface roughness has considerable effect on surface drag. If this surface is kept smooth, a
laminar boundary layer will be maintained further along the vehicle than with the rough surface
2.3.2 Lift Force
The pressure differential from the top to the bottom of the vehicle causes a lift drag. This lift
force depends on the upper surfaces especially in areas of the leading edge of the hood, wind
shield corners, leading edges of the cowl and underbody such as suspension, exhaust system
&other components protruding, and the ground clearance. Lift is not a serious problem at normal
speeds but at very high speeds it can affect stability and braking performance of the vehicle. The
lift tends to reduce pressure between ground and wheels. This causes loss of steering control on
the front axle and loss of traction on the rear axle.
Lift Force is calculated as:
FL = V2
A CL
Where;
FL = Aerodynamic Lift Force, N
= air density, Kg/m3
V = velocity, m/sec
A = Frontal Area, m2
CL = Lift Coefficient
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2.4Approaches to flow analysisThere are three approaches to fluid dynamics:
a) Theoretical Approach
b) Experimental Approach
c) Computational Approach
2.4.1 Theoretical Approach
This approach uses the energy mass momentum equation to solve the flow problems.
2.4.2 Experimental Approach
It uses experimental data measured from wind tunnel testing for determining fluid behaviour
2.4.3 Computational Approach
This approach uses Numerical methods, computer programming and computer simulation
softwares for fluid dynamics.
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Chapter 3
FEA Analysis
3.1 Design Consideration for Rollcage
Roll cage or the chassis frame is to provide the vehicle strength and structural integrity. The
function of the space frame is to protect the driver (in case of serious impacts and rollover) and
support front and rear suspension systems, engine, drive train, steering system and other systems
in the vehicle, and must be of adequate strength to protect the operator in the event of a rollover
or impact.
The objective of the frame design is to satisfy these functions while meeting the SAE regulations
with special considerations given to safety of the occupants, ease of manufacturing, cost, quality,
weight, and aesthetics. Moreover care has been taken to ensure that there are minimum welds on
the frame pipes and maximum bends ensuring better strength and less cost of production of the
vehicle. The roll cage must be constructed of steel tubing, with minimum dimensional and
strength requirements dictated by SAE.
3.2 Material and Size optimization of Rollcage tubing
According to rule book provided by SAE the minimum size of the steel tube should not be less
than 1.0 inch (25.4mm) X 0.095 inch (2.4mm). We have chosen AISI 4130 steel tubes with
dimensions of 1.25 inch (31.75 mm) X 0.079 inch (2mm) but the problem with this material
was bending and weld ability. Since its a Medium Carbon, Chrome-Mo. Steel it requires
preheating before welding.
AISI 4130 AISI 1018
Type Medium Carbon Chrome-Mo. Steel Low Carbon Steel
Size 31.75 mm X 2mm 24.5 mm X2.5mm
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Yield strength 360 MPa 320 MPa
Benefits Strength and Weight Low Cost, Equal Strength,
Weld able , Easily Available
Problems Cost, Weld ability and Availability -
Table 3.1: Material Selection
Among many alternatives to this material we select AISI 1018 depending upon its availability,
low cost and equivalent strength to AISI 4130.
3.3 Structural Analysis
3.3.1 Front Impact
For the front impact case we have considered a sudden impact load with assumptions that two
vehicles running at speed of 130kmph collides, with an impact pulse of 0.8 sec. In this case the
impact force comes out to be 14000 N
Figure 3.1: Front Impact Stress Plot
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Analysis is done by restraining nodes at the rear roll hoop while applying static force on front
members. Analysis results shows that stresses are maximized at the front members with ------
Maximum Stress = 1.2e+08 N/m2
3.3.2 Side Impact
Figure 3.2: Side Impact Stress Plot
For side impact we have considered a side on collision condition with a force of 7000 N. We
restrained one of the side members with zero DOF and applying a force of 7000 N on the other
side members.
Analysis results shows that stresses are maximized at the front hoop with ------
Maximum Stress = 5.11e+07 N/m2
3.3.3 Rear Impact
For rear impact we have considered another car hitting from behind, with astatic equivalent force
of10000 N. For analysing it we restrained the front members with zero DOF and applying a
force on the Rear roll hoop.
Analysis results shows that stresses are maximized at the joint and cross support with Maximum
Stress = 8.07e+07 N/m2
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Figure 3.3: Rear Impact Stress Plot
3.3.4 Rollover Impact
In case of rollover condition the drivers head should not touch the ground and the cage must be
strong enough to resist the crushing, hence a force of 1000 N is applied at the two roll hoops
(together they forms a cage) front and rear while reducing the degree of freedom of lower frame
member to zero.
Analysis results shows that stresses are maximized at the rear roll hoopMaximum Stress = 8.07e+07 N/m2
Figure 3.4: Rollover Impact Stress Plot
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Hence we require a bracing support (as shoulder harness) to reduce the stress intensity, and
increase the factor of safety.
3.4 Rollcage Design Optimization
3.4.1 Use of cross supports
From the above results it is clear that the stress points are concentrated hence we provide the
additional cross members and supports. Optimized results after the application of supports and
gussets are as follows:
3.4.1.1 Front Impact
Figure 3.5: Optimized Front Impact Stress Plot
Maximum Stress = 3.2e+07 N/m2
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3.4.1.2 Side Impact
Figure 3.6: Optimized Side Impact Stress Plot
Maximum Stress = 4.65e+07 N/m2
3.4.1.3 Rear Impact
Figure 3.7: Optimized Rear Impact Stress Plot
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Maximum Stress = 5.03e+07 N/m2
3.4.1.4 Rollover Impact
Figure 3.8: Optimized Rollover Impact Stress Plot
Maximum Stress = 3.59e+07 N/m2
3.4.2 Use of Gussets
We applied Gussets to front members to prevent crushing of the cage in case of severe accidents.
Analysis done after gusseting yield better results with improved factor of safety.
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Figure 3.9: Front members with gussets
Figure 3.10: Analysis results after Gusseting
Maximum Stress = 2.85e+07 N/m2
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Chapter 4
Fluid Dynamics Equations
4.1 Euler's and Bernoulli's equations4.1.1 Eulers Equation for viscous flowEuler's equation derives from the equation of motion by substituting in it the simplest possible
constitutive equation for the stress tensor corresponding to an ideal fluid, expressed by
Consideration of the individual components of the volume force S, shows that
The associated Eulerian form is
Explicitly, the three Cartesian components of above equation are given by
These Euler equations do not give a full analysis of the flow, although by using them to
approximate flow values is a common engineering method. This way, some understanding of the
flow can be achieved, before a more final analysis can be done. In addition, the modelling of the
inviscid flow by the Euler equations help to set the initializations conditions for the full viscous
flow over the car body.
4.1
4.2
4.3
4.4
4.5
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4.1.2 Bernoulli's equation
Figure 4.1: Bernoullis Equation
The equation states that the static pressure Ps in the flow plus the dynamic pressure, one half of
the density r times the velocity V squared, are equal to a constant throughout the flow. We call
this constant the total pressure pt of the flow.
As discussed on the gas properties page, there are two ways to look at a fluid; from the large,
macro scale properties of the fluid that we can measure, and from the small, micro scale of the
molecular motion and interaction.
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4.2 Navier- Stokes Equations for a viscous flowThe Navier-Stokes equations are the basic governing equations for a viscous, heat conducting
fluid. It is a vector equation obtained by applying Newton's Law of Motion to a fluid element
and is also called the momentum equation. It is supplemented by the mass conservation equation,
also called continuity equation and the energy equation. Usually, the term Navier-Stokes
equations are used to refer to all of these equations.
The above equations are shown for a viscous flow. The speed of car is lower as compared to an
aircraft can be considered low; the density of the flow doesnt changes as there is no flow in the
altitude. The above equations are derived taken in consideration the change in density,
4.6
4.7
4.10
4.8
4.9
2.1
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temperature so the terms of stresses appear in the equations. A viscous flow is one where the
transport phenomena of friction, thermal conduction and/or mass diffusion are included.
These transport phenomena are dissipative viz. they always increase the entropy of the flow. The
equations that have been derived apply to a viscous flow, where mass diffusion is not included.
4.11
4.12
4.13
4.14
4.15
4.16
4.17
4.18
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Energy Equation
4.3 Eulers Equations for an inviscid flowInviscid flow by definition: flow where the phenomenon of viscosity, mass diffusion, and
thermal conductivity are neglected. The equations for an inviscid three dimensional flow are
given below
4.19
4.20
4.18
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Momentum Equations
4.21
4.22
4.4 Navier stokes equation for a incompressible inviscid flow
The Navier stokes equation for an incompressible in viscid flow are derived from the equations
given above. These equations can be obtained from the compressible form simply by setting
density as a constant. With equal to a constant, .V=0.
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In the Cartesian form the equations can be expressed as
4.23
For, full understanding of the flow over the vehicle, it is essential to analyze the full Navier
Stokes Equations for full analysis. Each term must be either calculated or approximated in order
to get accurate values. However, for such a problem, analytical solutions dont exist. Due to this,
Programming and Numerical Solutions need to be used in order to get the necessary approximate
results. In addition, CFD software such as Fluent has been used for full analysis.
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Chapter 5
Flow Analysis
5.1 Modelling in Catia
With the help of surfacing and wire frame tool, surface of the vehicle initially developed
according to the shape of the frame of the car. And the key Positions are noted to re-model it in
gambit.
Figure 5.1: Shape Design in Catia
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5.2 Creating Geometry in Gambit
By using the position parameters, taken from the Catia model, 2 D model of the body was made
in Gambit. Following are the steps used to form the 2D geometry of the car:
5.2.1 Creating Vertices
Figure 5.2: Creating Vertices
5.2.2 Creating Edges
By joining different vertex edges are formed to make a wire frame.
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Figure 5.3: Creating Edges
5.2.3 Creating Faces
Figure 5.4: Creating Faces
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5.3 Meshing
Meshing is the breaking of physical/solution domain that can be a 2-D or 3-D domain into
simpler sub domains/elements i.e. triangles, quadrilaterals for 2-D and tetrahedral, hexahedral for
3-D. Meshing make the solution easier and more accurate. The denser the meshing is more
accurate the result will be but at the same time it will be more complex to solve the problem.
Here we have used Quad/Tri mesh element & Pave type (creates unstructured grid of mesh
element) to have more accurate flow near the car surface.
To have more fine meshing first of all edges of the geometry are meshed. The edges of the car
geometry have more mesh counts.
Figure 5.4: Edge Mesh
After edge meshing face is meshed.
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Figure 5.5: Face Mesh
5.4 Parameters and initial boundary conditions
Figure 5.6: Specifying Boundaries
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The parameters according to the operating conditions are given as follows:
1. Inlet velocity is given to the vertex in front of the car.2. Pressure Outlet is given to the vertex rear of the car.3. Lower & upper vertices are given as wall.4. Car body is given as wall.
5.5 Flow Analysis in fluent
Now, the fluent condition to the car geometry is given as follows: -
1. 2 ddp version2. Density based solver3. Energy equation included.4. Viscous model- K epsilon5. Materials are air and aluminium for fluid flow and wall respectively.6. Operating Pressure = 07. Air velocity at inlet =36 m/s.8. Flow, turbulent kinetic energy & turbulent dissipation rate as Second Order Upwind.9. All other parameters are used as default.
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Chapter 6
Result & Analysis
6.1 Flow Over Nose
Figure 6.1.1: Velocity Contours at nose
As shown in above figure, when the nose of the car encounters the air, velocity of air at nose
becomes zero due to stagnation.
Figure 6.1.2: Static Pressure Contour at nose
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The figure shows that the pressure at the nose tip is about 2.34 KPa which is very high.
Figure 6.1.3: Contours of Turbulent Kinetic Energy
Figure 6.1.4: Velocity Vectors at Nose
Since the edge of the nose is very sharp the velocity vectors are diverging to above the car which
is not desirable.
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6.2 Flow Over the body
Figure 6.2.1: Velocity Contour over the car body
Figure 6.2.2: Contours of Turbulent Kinetic Energy over the car body
Flow over the body profile shows that velocity and pressure change is very high at different
places and boundary layer separation occurring at two points, which is not good.
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Figure 6.2.3: Velocity Vectors over the car body
6.3 Flow Under body
Figure 6.3.1: Velocity Contour Under body
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For race cars flow under the body should be more then over the car, as to reduce lift force. The
pressure distribution under body shows that the pressure is slightly lesser to the ambient
pressure.
Figure 6.3.2: Static Pressure Contour Under body
Figure 6.3.3: Contours of Turbulent Kinetic Energy Under body
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Figure 6.3.4: Velocity Vectors Under body
6.4 Boundary Layer Separation
Figure 6.4.1: Velocity Contour at front hoop
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Since the edges at the front roll hoop and rear hoop are very sharp and the velocity vectors start
separating at this point.
Figure 6.4.2: Velocity Contour at rear hoop
Figure 6.4.3: Static Pressure Contour at front hoop
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A negative pressure gradient is observed at these points which should be minimised to have more
uniform flow. For this Sharp edged are to be minimised and made uniform.
Figure 6.4.4: Static Pressure Contour rear hoop
Figure 6.4.5: Contours of Turbulent Kinetic Energy at front hoop
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At these two point turbulence is maximum and which affecting the uniformity of the flow. The
maximum turbulence kinetic energy is observed at front main hoop but as a negative pressure
gradient is observed at the end of the vehicle the turbulent kinetic energy becomes lesser.
Figure 6.4.6: Contours of Turbulent Kinetic Energy
Figure 6.4.7: Velocity Vectors at front hoop
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The velocity vectors are showing that the velocity vectors are separating at the bottom portion of
the main hoop & car rear end and a reverse is observed at these points.
Figure 6.4.8: Velocity Vectors at Rear
6.5 Design Modification Based on result Obtained
Figure 6.5: New Model in Catia
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The design was modified based on the results obtained from the analysis of first shape. Above
model showing the new design in which the nose, profile, ground clearance, driver compartment,
and rear compartment is modified.
Results for new Design
6.6 flow over Nose
Figure 6.6.1: Velocity Contours at nose
Since in the new model the nose of the car is modified & sharp edges are modified the impact at
the nose is minimised. The distribution of pressure is well distributed over the nose and no very
high pressure is observed. The nose is so modified that the velocity vectors are allowed to pass
bellow the car body to have less pressure under body.
The turbulence kinetic energy is also less in this case as the flow is well diverged.
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The nose is also lifted at front to avoid striking of it to ground at the time of pitching i.e. braking;
also the flow becomes more to under body.
Figure 6.6.2: Static Pressure Contour at nose
Figure 6.6.3: Contours of Turbulent Kinetic Energy
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Figure 6.6.4: Velocity Vectors at Nose
6.7 Flow Over the Car Profile
Figure 6.7.1: Velocity Contour over the car body
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The velocity contours are well distributed over the profile of the car profile. The points where the
negative pressure was more is now minimised.
Figure 6.7.2: Contours of Turbulent Kinetic Energy over the car body
Figure 6.7.3: Velocity Vectors over the car body
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6.8 Flow Under Body
Figure 6.8.1: Velocity Contour Under body
Since the ground clearance is now reduced from 190 to 130 mm the velocity vectors are becomes
denser under body.
Figure 6.8.2: Static Pressure Contour Under body
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Figure 6.8.3: Contours of Turbulent Kinetic Energy Under body
Figure 6.8.4: Velocity Vectors Under body
More air velocity resulting less air pressure and hence the lift force is less in this case.
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6.9 Boundary Layer Separation
Figure 6.9.1: Velocity Contour at front hoop
Figure 6.9.2: Velocity Contour at rear hoop
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Figure 6.9.3: Static Pressure Contour at front hoop
Figure 6.9.4: Static Pressure Contour rear hoop
Since the shape at front hoop and rear hoop is modified and the edges are now filleted, the flow
is more uniform then the previous design.
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Figure 6.9.5: Contours of Turbulent Kinetic Energy at front hoop
Figure 6.9.6: Contours of Turbulent Kinetic Energy
The turbulence kinetic energy in this model is less in this case as boundary layer separation is
less in this case.
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Figure 6.9.7: Velocity Vectors at front hoop
Figure 6.9.8: Velocity Vectors
The velocity contours are more uniform then the previous design at the point of boundary layer
separation. Also the reverse flow of the air is minimised to some extent.
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6.10 Pressure Distribution Over and Below the Car
Figure 6.10: Static Pressure XY Plot
The XY plot is showing the pressure variation above and below the car. As in the figure the
pressure above the car surface is more than that of the lower part, a lift is generated. Since the
difference of these pressures is less, the lift will be lesser in this case.
6.11 Drag Coefficient Plot
Figure 6.11: Drag Coefficient Plot
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The drag coefficient graph shows that drag coefficient for our vehicle is about 0.21, which is low
and good for our vehicle. Hence energy used in resisting the aerodynamic force is also low and
can be utilized in moving the vehicle.
6.11 Lift Coefficient Plot
Figure 6.12: Lift Coefficient Plot
The figure shows that drag coefficient is very low in this case, which is good for racing vehicles.
Further the lift coefficient can be reduced by using front & rear wing to have negative lift. But
since the vehicle is to run at low speed, use of wings may not be as beneficial as for vehicle with
higher speeds. So the idea for using wings was dropped.
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Chapter 5
Use of CFD Results in Engine Performance Calculations
7.1 Power Requirement
Wheel Resistance = FR
Air resistance = FL
Gradient resistance = Fg
Acceleration resistance = Fa
7.1.1 Wheel Resistance:
V dry wet
50 0.85 0.65
90 0.80 0.60
130 0.75 0.55
Rdyn - Dynamic Radius
m= mass of vehicle
F = R (on Straight Pavement)
FR = Rcos (on Gradients)
FR = (cos + sin )mg
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7.1.2 Air resistance
FL = *Cd*A*L*v2
CdDrag Coefficient
AFront Area
L1.199 kg/m3
7.1.3 Gradient Resistance
Fg = mgsin
Acceleration Resistance
Fa= ma
rotational inertia coefficient
7.1.4 Total Driving resistance
FT = FR + FL + Fg + Fa
FT = mg(cos + sin ) + *Cd*A*L*v2
+ ma
At steady state
a = 0 ; cos ~ 1; sin ~ 0
FT = mg() + *Cd*A*L*v2
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7.2 Drag Force Calculation at different speeds
Power required
P = FT*V
M = 400 kg at = 0;
FR = 4000 * 0.80 (for dry) = 3200 N
Rdyn = 0.267 m
Fz = mg(cos + sin ) + *Cd*A*L*v2
L = 1.199 kg/m2
The total aerodynamic drag of a vehicle includes many factors which offer overall air resistance
to the motion of vehicle. The types of aerodynamic drag components and their approximate
relative contributions are
Profile or Form Drag ~ 55 - 60 %
Induced or Lift Drag ~ 8 %
Surface or Friction Drag ~ 10 %
Interference ~ 15 %
Cooling & Ventilation System Drag ~ 10 %
Rotating Wheel & other ~ 1 %
Profile Drag Obtained from CFD Analysis = 0.19
Total Air drag ~ 0.28
Following are the values obtained for different velocities of FR, Fa, and Fz
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V FR Fa Fz
10 49.6 1.8 51.4
20 49.6 7.4 57
30 49.6 16.6 66.2
40 49.6 29.6 79.2
50 49.6 46.2 95.8
60 49.6 66.6 116.2
70 50 90.6 140.6
80 50.8 118.4 169.2
90 52 149.9 201.7
100 52.4 185.1 237.4
110 54 223 277.9
120 54.4 266 320.8
130 54.8 312.7 367.5
Table 7.1: Change in Total Resistance With velocity
Figure 7.1: Aerodynamic force Vs. Vehicle Speed
0
50
100
150
200
250
300
350
400
0 20 40 60 80 100 120 140
fr
fa
Fz
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From the above graph it is clear that the aerodynamic forces are increasing in parabolic manner,
with increase in speed. The aerodynamic forces are less significant at lower speeds but at higher
speed these forces account for major source of vehicle resistance.
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Chapter 8
Conclusion
After simulation of first model and the modified one, we conclude that the second model is
selected as the final choice which could be used for creating the surface of formula 1 car.
Following conclusions are made from the CFD analysis of both the models:
The pressure profiles and contours justify the decision as the pressure is more evenly
distributed.
The velocity vectors show that the flow is more uniform.
The area of negative pressure developed at the point near front hoop & rear end is
minimised by giving fillets at those points.
Pressure difference & turbulence at the points of boundary layer separation is highly
minimised in modified model.
The idea of lowering the ground clearance shows that the pressure under body is lowered
resulting negative lift, which is required for to have traction at higher speeds.
The rear body is extended in order to reduce the reverse flow in driver compartment.
The nose profile is able to diverge the air stream in both directions (above and below)
without any stagnation point.
Reducing the driver compartment resulted in having more uniform air flow over the car
body.
The profile drag coefficient is as low as 0.19.
From the total resistance data and graph it is clear that the aerodynamic forces are more
prominent at very high speed and they increase proportionally to the square of velocity.
And these forces in turn affect the engine performance at high speeds.
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REFERENCES
R. Peyret, February 1996: Handbook of Computational Fluid Mechanics.
Milliken & Milliken, 1995: Race Car Vehicle Dynamics.
Thomas D Gillespie, 1999: Fundamentals of Vehicle Dynamics.
Chan, L.Y, et al. Design/Build of a Formula SAE Vehicle. Paper, Adelaide: University of
Adelaide
Doddegowda, Punith, Aleksandr Bychkovsky and Albert George, Use of Computational
Fluid Dynamics for the design of Formula SAE Race Car Aerodynamics: SAE Technical Papers,
2006
