GDP Project 2013 - Final Version

1

Abstract

An investigation into the aerodynamics of an open-wheel racing car has been conducted using

computational fluid dynamics (CFD) to visualize the complex flowfield generated by this type of

vehicle. The baseline model was a single-seater hill-climb car, which had been designed and wind

tunnel tested at the RJ Mitchell wind tunnel in Southampton University by the 2010 MEng GDP

project. In the present work, steady RANS formulations were employed to assess the performance of

the major components of the car with the intention of using basic aerodynamic and design principles

to improve the overall aerodynamic characteristics of the vehicle. First, an extensive CFD analysis of

the baseline car, including domain and mesh dependency studies was performed to obtain

component-wise numerical results for the lift and drag. This analysis revealed significant deficiencies

in the design of the sidepod upper surface and the car underbody. These deficits were addressed by

redesigning the car using a commercial CAD package in three separate optimisation cycles. A total of

42 full cars were simulated. The design was done in accordance with the flow physics observed via

pressure, velocity and vorticity contours, Q-criterion and coefficients of pressure. The main areas of

improvement included the front wing through the redesign of a complete new endplate, the

underbody of the car by creating two distinct channels that separated the sidepod underbody from

the diffuser, which has been redesigned to be a double expansion diffuser. As a result of a precise

design choice, the wings remained unchanged throughout the entire process. In addition to this, two

optimisation cycles were conducted using a Kriging algorithm with two variables in the front and rear

sections of the car. The optimisation in the front section employed the gap and overlap between the

wheel and the front wing while the optimisation in the rear section used the throat and the exit

angle of the diffuser. Both cycles yielded improved results with the final car being the outcome of the

second optimisation process. Final values for the car result in a downforce coefficient of 2.94, a drag

coefficient of 0.85, resulting in an efficiency of 3.46. These values show an increase in downforce of

30%, a reduction in drag of 2% and an efficiency increase of 33% with respect the baseline car. These

improvements show the key importance the interaction between the wheel and the front wing as

well as the diffuser performance play in race

2

Acknowledgments

The 2012-13 MSc in Race Car Aerodynamics Team wants to thank for the contribution of the

following people to the current work without whom the achievements of the current project

wouldn’t be so far reaching.

To Prof. Richard Sandberg, the project supervisor, for the guidance throughout the project

To CD-Adapco company in the person of Konstantinos Karatonis and Maxwell Star for the STAR-CCM+

training provided to the team members

To Prof. Neil W. Bressloff, the second supervisor, for the reamarks and orientation in the optimization

of the car.

To Mr. Manan Thakkar, as a member of the 2011-12 Class of MSc in Race Car Aerodynamics, for

helping us to get started in several areas and for all the day to day help and incentive.

3

Table of Contents

Abstract ....................................................................................................................................... 1

Acknowledgments ........................................................................................................................ 2

Table of Contents ......................................................................................................................... 3

Nomenclature .............................................................................................................................. 7

List of Figures ............................................................................................................................... 8

List of Tables .............................................................................................................................. 12

1. Introduction........................................................................................................................ 13

1.1. Objectives ................................................................................................................... 15

1.2. Assumptions................................................................................................................ 16

1.2.1. CAD related assumptions ...................................................................................... 16

1.2.2. CFD related assumptions....................................................................................... 17

1.2.3. Turbulence modelling ........................................................................................... 18

1.3. Management and Project Fundamentals ....................................................................... 20

1.3.1. Methodology........................................................................................................ 21

2. Bibliographical Review ......................................................................................................... 26

2.1. Previous Years Reports................................................................................................. 26

2.1.1. MSc in Race Car Aerodynamics GDP Report 2010-11 .............................................. 26

2.1.2. MSc in Race Car Aerodynamics GDP Report 2011-12 .............................................. 31

2.2. Race Car Aerodynamics Research ................................................................................. 39

2.2.1. Ground Effect Aerodynamics of Race Cars.............................................................. 39

2.2.2. Race Car Aerodynamics: Designing For Speed......................................................... 41

2.2.3. Aerodynamics of the complete vehicle................................................................... 44

2.2.4. Race Car Wings..................................................................................................... 47

2.3. Wing Research............................................................................................................. 50

2.3.1. Ali Wings .............................................................................................................. 51

2.3.2. High Lift Aerodynamics ......................................................................................... 52

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2.3.3. High-Lift Low Reynolds Number Airfoil Design ........................................................ 56

2.3.4. Design of High Lift Airfoils for Low Aspect Ratio Wings with Endplates ..................... 57

2.3.5. Design of Subsonic Airfoils for High Lift .................................................................. 60

2.3.6. Numerical Optimization of Airfoils in Low Reynolds Number Flows.......................... 63

2.4. Diffuser Research......................................................................................................... 64

2.4.1. Aerodynamic Interactions ..................................................................................... 67

3. First Semester Work ............................................................................................................ 71

3.1. Objectives ................................................................................................................... 71

3.2. Baseline Car Front Wing ............................................................................................... 71

3.2.1. Introduction ......................................................................................................... 71

3.2.2. Approach ............................................................................................................. 73

3.2.3. Results ................................................................................................................. 74

3.3. Baseline Car Wheel ...................................................................................................... 78

3.4. Baseline Car Simulations .............................................................................................. 84

3.4.1. Geometry and Domain.......................................................................................... 84

3.4.2. Wall y+ Approach .................................................................................................. 90

3.4.3. Boundary Conditions ............................................................................................ 91

3.4.4. Dependency Tests ................................................................................................ 93

3.4.5. Other Physics Conditions....................................................................................... 95

3.4.6. Numerical Results ................................................................................................. 96

3.4.7. Post Processing Baseline Car ................................................................................. 98

4. Second Semester Work.......................................................................................................112

4.1. Airfoil Study................................................................................................................112

4.2. Wing Study .................................................................................................................116

4.3. Meshing Settings ........................................................................................................123

4.4. First Design Cycle – Iteration A.....................................................................................129

4.4.1. A01 Car Introduction............................................................................................129

5

4.4.2. A01 Car Conclusion ..............................................................................................131


4.4.4. A02 Conclusion....................................................................................................136


4.4.6. Analysis and Discussion of Results of the A03 Car ..................................................138

4.4.7. Post-processing of Results....................................................................................141

4.4.8. A03 Car Conclusion ..............................................................................................146

4.5. Optimisation Methodology..........................................................................................147

4.5.1. Introduction ........................................................................................................147

4.5.2. Optimisation Procedure .......................................................................................148

4.5.3. Sampling Plans ....................................................................................................149

4.5.4. Surrogate Model .................................................................................................149

4.5.5. Kriging ................................................................................................................150

4.5.6. Infill Criteria ........................................................................................................151

4.6. Second Design Cycle – B Iteration ................................................................................151

4.6.1. Optimisation Variables and Initial Sampling...........................................................151

4.6.2. Results ................................................................................................................153

4.7. Third Design Cycle –C Iteration ....................................................................................157

4.7.1. Optimisation Variables and Initial Sample .............................................................157

4.7.2. Results ................................................................................................................159

4.7.3. Additional comments...........................................................................................163

4.8. FINAL CAR INTRODUCTION ..........................................................................................163

4.8.1. Analysis and Discussion of Results (C07-Final DESIGN) ...........................................165

4.8.2. Post-processing of Results....................................................................................168

4.9. B and C Interaction Conclusion ....................................................................................176

5. Summary and Conclusions ..................................................................................................178

6. Further Work .....................................................................................................................187

6

7. References .........................................................................................................................189

8. Appendix 1 - Regulations ....................................................................................................192

9. Appendix 2 - Gantt .............................................................................................................193

10. Appendix 3 – Grid Convergence Study for the Front Wing .................................................194

11. Appendix 4 – Sample Calculations for Boundary Layer Estimation of 2-D Profiles................195

12. Appendix 5 – Macros ......................................................................................................197

PreMeshPost macro ...............................................................................................................197

Geo macro.............................................................................................................................199

13. Appendix 6 – Sidepod and engine intake study .................................................................200

7

Nomenclature

Cl Airfoil lift coefficient

CL Wing lift coefficient

AR Aspect ratio of a wing

CFD Computational Fluid Dynamics

CAD Computer Aided Design

Cd Airfoil drag coefficient

CD Wing Drag Coefficient

y+ Non dimensional height

y1+ Non dimensional height of the first cell close to the wall

h Ride height

ρ Air density

Re Reynolds Number

RANS Reynolds-Averaged Navier-Stokes

k-ω k-omega turbulence model

k-ε k-epsilon turbulence model

c Wing chord

Q

V∞ Free-stream velocity

Γ Circulation

Sij

Ωij

8

List of Figures

Figure 1: Baseline car with coordinate system. ............................................................................. 17

Figure 2: Sketch of the workflow adopted in the project. .............................................................. 22

Figure 3: Drag coefficient by component for 1st and 2nd iterations. .............................................. 31

Figure 4: Lift coefficient by component for 1st and 2nd iteration. .................................................. 31

Figure 5: Split of drag (left) and downforce (right) (ignoring sources of lift). ................................... 34

Figure 6: Underbody downforce dependence on diffuser edge thickness. ...................................... 35

Figure 7: Iteration history of force coefficients, efficiency and aerodynamic balance. ..................... 38

Figure 8: The use of the Gurney flap on the rear wing and endplates of a race car. ......................... 44

Figure 9: The effect of the height of the side skirt on the body downforce generation. ................... 45

Figure 10: The use of a flat plate near the high pressure region to generate extra downforce (left)

and Channelling the flow from the front wing to the rear of the wheel can be used to reduce wheels

drag (right). ................................................................................................................................ 46

Figure 11: Different wing configurations tested in an open wheeled race car. ................................ 48

Figure 12: The effect of number of rear wing on lift and aerodynamic efficiency. ........................... 49

Figure 13: The loss on the downforce of the central part of the frontal wing due to the nose and

different nose arrangements. ...................................................................................................... 50

Figure 14: Canonical Pressure Distribution from A.M.O Smith. ...................................................... 54

Figure 15: Change of the incidence velocity vector angle due to downwash. .................................. 58

Figure 16: (Left) airfoil generated with the conventional methodology. (Right) airfoil generated with

the new methodology. ................................................................................................................ 58

Figure 17: Variation of the angle of the wing inside the regulations box and respective velocity

distribution and CL for each case. ................................................................................................ 59

Figure 18: Variation of the flap to main chord ratio, velocity distribution and CL for each case. ....... 59

Figure 19: Variation of the gap, velocity distribution and CL for each case. ..................................... 60

Figure 20: Optimum velocity distribution over an airfoil and modifications to make the airfoil

feasible. ..................................................................................................................................... 61

Figure 21: examples of single and multi-element airfoils and its Cp distribution plotted inside a

maximum possible Cp box. .......................................................................................................... 63

Figure 22: Pressure coefficient for diffuser mid-plane, experimental and LES results. From:

(Puglisevich S., Page G., Large eddy simulation of the flow around a diffuser-equipped bluff body in

ground effect, J. Automobile, Proceedings of the ASME 2011 International. .................................. 65

Figure 23: Influence of diffuser angle on lift coefficient, different ride heights. (From: Ruhrmann, A.

and Zhang, X. Influence of diffuser angle on a bluff body in ground effect. Trans. ASME, J. Fluids Eng,

2003, 125(2), 332–338). .............................................................................................................. 67

Figure 24: Lift coefficient for the front wing, in isolation (red) and with the wheel (grey). Hysteresis

effect shown. ............................................................................................................................. 69

Figure 25: Drag coefficient for the wheel, different overlap........................................................... 70

Figure 26: Geometry of the tested wing. ...................................................................................... 73

Figure 27: Approach for the front wing test. ................................................................................. 74

Figure 28: Domain size study. ...................................................................................................... 75

Figure 29: Wall y+ distribution for the front wing with no prism layer. ........................................... 76

Figure 30: Side view of the mesh for the front wing. ..................................................................... 76

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Figure 31: Results for the front wing with prism layer. .................................................................. 77

Figure 32: Comparison of results for meshes with and without prism layer. ................................... 78

Figure 33: Example of a trimmer mesh for the wheel. ................................................................... 81

Figure 34: Pressure countours around the wheel compared with Axon (above). ............................. 83

Figure 35: Tangential velocity vectors compared with Saddington’s theory (above). ....................... 84

Figure 36: The model after import into STAR-CCM+. ..................................................................... 85

Figure 37: The car after splitting it into different parts (Upper side). .............................................. 86

Figure 38: The car after splitting it into different parts (Lower side). .............................................. 86

Figure 39: The computational domain after Subtract operation. .................................................... 87

Figure 40: The Computational Domain showing some of the volumetric controls. .......................... 89

Figure 41: Mesh detail in the front wing. ...................................................................................... 89

Figure 42: Mesh at the near area of the car. ................................................................................. 90

Figure 43: The wall y+ distribution around the car. ....................................................................... 91

Figure 44: Variation of CL and CD with number of elements in the mesh........................................ 93

Figure 45: Residuals after 4000 Iterations .................................................................................... 96

Figure 46: Component Wise CL Split up for 2011 and 2012 baseline cars........................................ 97

Figure 47: Component wise split up for CD. .................................................................................. 98

Figure 48: Tri-dimensional views of the Baseline Car. .................................................................... 99

Figure 49: Comparison between Baseline car and the Benetton B190. ..........................................101

Figure 50: Downforce Breakdown for Each Component of Baseline Car. .......................................102

Figure 51: Drag breakdown for Baseline Car. ...............................................................................103

Figure 52: Mid-Plane Coefficient of Pressure for Baseline car (top), Middle section (top centre), Rear

section (bottom centre) Sidepod Coefficient of Pressure (bottom). ..............................................105

Figure 53: Sidepod Velocity for Baseline......................................................................................105

Figure 54: Streamlines for Baseline: from the top (top image) and from the bottom. .....................107

Figure 55: Streamlines for Baseline: Particular of the Venturi contraction zone. ............................107

Figure 56: Streamlines for Baseline: Particular of the helmet. .......................................................107

Figure 57: Vorticity and Velocity Vectors for the wake of the rear wheel (x=1.54). .........................108

Figure 58: Q-criterion Colored by Vorticity in Stream-wise Direction for Lower Surface of the Car

(top) and Isometric View (bottom) – Q = 10,000. .........................................................................110


(top) and Isometric View (bottom) – Q = 200,000. .......................................................................110

Figure 60: Maximum Coefficient of Lift versus camber. ................................................................114

Figure 61: Coefficient of Lift against Angle of Attack. ...................................................................115

Figure 62: Pressure Coefficient of Different Wings Tested in CFD. .................................................120

Figure 63: Wake Survey Velocity Profiles for the Wings. ...............................................................120

Figure 64: Contours of Velocity on Streamwise Direction for Baseline Wing (top), First wing (center)

and Second Wing (bottom).........................................................................................................122

Figure 65: Skin Friction Coefficient for the Wing Configurations....................................................123

Figure 66: Wing-endplate prism layers interaction. ......................................................................125

Figure 67: flow incidence angle (9 cm upstream of main element leading edge). ...........................126

Figure 68: Front Wing simulated boundary layers (from top to bottom: baseline, new setup with 10

points in gap, new setup with 5 points in gap). ............................................................................127

Figure 69: Rear Wing simulated boundary layers (from top to bottom: baseline, new setup with 10

points in gap, new setup with 5 points in gap). ............................................................................128

10

Figure 70: Flow incidence angle with 5 points in gap (left) and 10 points in gap (right). ..................128

Figure 71: Tri-dimensional views of the A01 Car. .........................................................................130

Figure 72: The nosecone of A01, with the ideal channel created by repositioning the struts...........131

Figure 73: Nosecone and diffuser for A01. Highlighted in red, the contraction-expansion zone

created in the central part of the underbody. ..............................................................................131

Figure 74: Middle section of the A01, coloured in blue. Highlighted in green, the windshield. The

splitter is circled in black. ...........................................................................................................131

Figure 75: Tri-dimensional views of the A02-1 car. .......................................................................133

Figure 76: Views of the endplate: on the left, the channel is highlighted in red. In the middle, a

section of the endplate showing the ramp is presented. On the right, the ramp is circled in blue, and

the particular shape of the endplate at the edges is circled in green .............................................134

Figure 77: Sidepods for A02 cars. Highlighted: in red the sideplate, in orange the sidepod inlet, in

blue the ramp. In the bottom figure, the aerofoil-like shape can be appreciated. ..........................135

Figure 78: Isometric view of the A02-3 car...................................................................................135

Figure 79: Middle section of the A02 cars, coloured in blue. Highlighted in green, the new

windshield. In the red oval, the prolonged engine cover and the new diffuser can be seen. ...........136

Figure 80: New rear wing endplates (A02), with louvres (blue) and cuts on the upper edge to reduce

drag (red). .................................................................................................................................136

Figure 81: Nosecone and diffuser for A03. Highlighted in red, the improved contraction-expansion

zone created in the underbody. ......................................................... Error! Bookmark not defined.

Figure 82: Bargeboards for A02-1 (left) and A02-3 (right). ............................................................136

Figure 83: Tri-dimensional views of the A03 Car. .........................................................................137

Figure 84: Particular of the windshield and the engine cover. .......................................................138

Figure 85: Downforce Breakdown for Each Component of A03 and Comparison with A02-3...........140

Figure 86: Drag Breakdown for A03. ...........................................................................................140

Figure 87: Mid-Plane Coefficient of Pressure for A03 Front section (top) and Rear section (centre).

Sidepod Coefficient of Pressure (bottom). ...................................................................................142

Figure 88: Streamlines for A03: from the top (top image) and from the bottom. ...........................143

Figure 89: Velocity vectors and contours at sidepod inlet. ............................................................143

Figure 90: Vorticity and Velocity Vectors for the wake of the front (top, x=0.48) and rear (bottom,

x=1.54) wheel. ...........................................................................................................................144

Figure 91: Skin Friction for A03. ..................................................................................................144



Figure 93: Turbulent Kinetic Energy for A03, x=1.24. ....................................................................146

Figure 94: Turbulent Kinetic Energy for A03, x=1.54. ....................................................................146

Figure 95: Optimisation process..................................................................................................148

Figure 96: Kriging prediction for the Branin function with 20 sample points (left) compared with the

true Branin function (right).........................................................................................................150

Figure 97: Gap and Overlap between the front wing and wheel....................................................152

Figure 98: Initial sample for iteration B. ......................................................................................153

Figure 99: Surrogate model prediction (20 samples). ...................................................................154

Figure 100: Surrogate model prediction (20 samples + 3 updates). ...............................................154


Figure 102: Width of throat and diffuser exit. ..............................................................................158

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Figure 103: Initial sample for iteration C......................................................................................159

Figure 104: Surrogate model prediction (11 samples). .................................................................160


Figure 106: surrogate model prediction for drag (Iteration B left, Iteration C right)........................163

Figure 107: Tri-dimensional views of the Final car. .......................................................................164

Figure 108: Downforce Breakdown for Each Component of C07 and Comparison with other

iterations. .................................................................................................................................166

Figure 109: Drag Breakdown for C07...........................................................................................168

Figure 110: Coefficient of Pressure for C07, from top to bottom: mid-plane, bottom, sidepod and

rear wheel, top. .........................................................................................................................170

Figure 111: Vorticity and Velocity Vectors for endplate (top, x=0.28), sidepod (middle, x=1.02), wake

of the rear wheel (bottom, x=1.54). ............................................................................................171

Figure 112: Vorticity for rear section of the car (top), Vorticity and Velocity Vectors for rear endplate

(bottom). ..................................................................................................................................172

Figure 113: Wall-shear stress, x-component, for C07. ..................................................................172



Figure 115: 2D Pressure Coefficient Plots for different components..............................................175

Figure 116: Design population plotted with lift on the abscissa and drag on the ordinates. ............176

Figure 117: Diagram of PreMeshPost.java. ..................................................................................198

Figure 118: A03 Car reversed flow faces in engine intake (left) and sidepod inlet (right). ...............201

Figure 119: Streamlines around intakes A03. ...............................................................................203

Figure 120: Streamlines around intakes A03-6. ............................................................................204

Figure 121: streamlines around engine cover to show pressure recovery in A03 (top) and A03-6

(bottom). ..................................................................................................................................206

Figure 122: pressure distribution around sidepod at z = 0.1m. ......................................................207

Figure 123: A03, A03-6 and A03-7 from top to bottom: streamlines released upstream from the

sidepod inlet and wall shear stress in x-direction. ........................................................................208

12

List of Tables

Table 1: Aerodynamic coefficients element-wise. ......................................................................... 27

Table 2: Mesh dependency study................................................................................................. 32

Table 3: Physical Models. ............................................................................................................ 33

Table 4: Relevant experimental data. ........................................................................................... 80

Table 5: Aerodynamic coefficients obtained in simulations............................................................ 81

Table 6: Final mesh parameters ................................................................................................... 90

Table 7: Boundary conditions and Settings used for the Simulations. ............................................. 92

Table 8: Mesh Dependency tests ................................................................................................. 94

Table 9: Domain Dependency Test. .............................................................................................. 95

Table 10: Rear wing CL showing the lift generated by the beam wing............................................. 97

Table 11: Comparison of CFD and Panel Method Results. .............................................................116

Table 12: Wing Configurations for CFD study. ..............................................................................117

Table 13: Iteration B data and results..........................................................................................157

Table 14: Optimisation Evolution. ...................................................... Error! Bookmark not defined.

Table 15: Iteration C data and results..........................................................................................161

Table 16: Airfoil Database with Maximum Camber and Thickness Values. .....................................196

Table 17: Summary of the engine intake and sidepods inlet study iterations .................................202

Table 18: Lift coefficient by part comparison between A03, A03-6 and A03-7................................205

13

1. Introduction

The well-known Merriam-Webster dictionary provides its readers with a definition of the

word engineering: “a field of study or activity concerned with modification or development in a

particular area”. This precise and concise statement could be further complemented by introducing

the Japanese word ‘Kaizen’, literally meaning “change for the better.” This word, which is often

translated as “continuous improvement” is perfect to put into words the concept behind engineering

and the purpose of the work presented in this report. As a matter of fact, other prominent branches

of science, like mathematics and physics, often evolve as a result of leaps and bounds; engineering,

instead, is an unstoppable process of adding little pieces of knowledge to the bulk of what has

already been discovered. It is now manifest how significant, for an engineer, is the capability of

building upon what is present in order to improve. This invol ves both the knowledge required to

understand previous results, and the practical sense and ability to put something new on the table.

Often underrated, it is this second characteristic that is the hardest to acquire as experience and

maturity are very important factors shaping the abilities of professionals within this field. It can be

now seen how important it is to work on this aspect, and in this light, the possibility of having a

design project integrated in a Master's degree is invaluable.

This Group Design Project (GDP) provides students with an opportunity to tackle a real

engineering problem using state-of-the-art computational tools. It is the only annual-based module

of the MSc in Race Car Aerodynamics. During the 2012-2013 academic year, six students composed

the aforementioned MSc program and formed a single team that was proposed to undertake a

design project in a six-month timeframe. The main purpose of the GDP was to apply the knowledge

of the students in aerodynamics and combine team work to face a real engineering problem:

specifically, to improve the aerodynamics of a hill climb race car through detailed aerodynamic

design, by means of Computational Fluid Dynamics (CFD) simulations only. The primary objective of

the project was to improve the aerodynamic performance of a given baseline car, which was

developed by the 2010 MEng GDP Team1, by carrying out a complete study of the relevant flowfield

using CFD, and subsequently by introducing new design to improve the flow characteristics of the

major components of the car following a custom methodology that was devised for the project at

hand. To broaden this perspective, however, a wider collection of detailed objectives is outlined in

the Objectives section of this introduction. To tackle this problem given its complexity, a number of

assumptions were made, and they are listed and explained in the assumptions section of this report.

It is now stressed that the group had freedom to choose the directions of the project, and in the

current 2012-2013 GDP work this led to a different methodology and project management with

respect to previous years groups. In the management section the pathway that was taken is

explained in more detail.

1 Howe, B., Leppan, W., Mulvaney, D., Owen, E., “Aerodynamic Development of a One Third Scale Open Wheel Racing Car

Model ”

14

Hill climb racing is a motorsport competition where drivers race against the chronometer in

narrow and short courses ranging from 800 m up to 2000 m in length. In the United Kingdom the

governing body of this motorsport branch is the Hillclimb and Sprint Association, and the regulations

are yearly released by the Motor Sports Association (MSA). There are different categories within this

championship, but the racing car that has been analysed pertains to the ‘Sports Libre Cars’ Category,

whose technical specifications can be found on page 325 of the MSA regulations 2. Section 15.1.1 of

this document stipulates the dimensions of the racing car. The regulations that have been used as

constraints for this project can be found in the appendix. A key aspect of this racing series, from a

design stand point, is that the designer has a lot of freedom to alter the car design in order to

optimise its performance as the regulations that govern this sport are not as stringent as they tend to

be in other racing series (e.g. Formula One, Indycar Series and others). This in turn, implies that

different approaches can be taken to maximise the performance of a given car. It is believed that

actual Hillclimb teams usually do not employ the computational resources that are presented and

used in this study to research aerodynamic designs, deriving in the freedom that the group had with

respect to the decision making. The racing car used as a baseline has previously undergone some

aerodynamic testing at the R.J. Mitchell wind tunnel at the University of Southampton. On the other

side, all the design was carried out in this project was purely conceptual, i.e. involving computational

simulations only; this stage was not followed by the usual validation with wind tunnel scale testing,

this was not in the goals of the investigation. The simulations aid the visualization of the main flow

field features that cannot otherwise be analysed in detail; it is this specific aspect which comprises

one of the main outcomes of this project: to understand the flow patterns involving a racing car

making use of CFD. A CAD model of the baseline car, the 2010 MEng GDP actual tested model, was

obtained and the flow was simulated using a commercial CFD package: STAR-CCM+.

The project was divided into two main stages: during the first stage of the work, the main

objective was to obtain suitable mesh settings that would generate grid independent results and to

solve the flow around the baseline car to assess its aerodynamic characteristics. After outlining the

possible improvements that could be introduced into the baseline car, the second stage consisted of

three different design cycles where the design of the car was modified progressively aiming to

improve its aerodynamics performance. One of these design cycles included the optimization of

specific components of the car with the intention to investigate the potential gains stemming from

single component optimization and the impact on the overall design of the car.

2 Motor Sport Association – United Kingdom – MSA, [online], available: http://www.msauk.org [accessed 01/11/2012]

15

1.1. Objectives

It has been reiterated that the paramount objective of this project was to increase the

performance of a racing car exclusively in terms of aerodynamics. In this section of the introduction,

a collection of the objectives is listed and explained.

Optimise the aerodynamic design of an open wheeled hill climb racing car.

Understand and have a better appreciation for the complexity of the aerodynamic

flow field generated by the racing car.

Learn how to work effectively with a commercial CFD package and develop good CFD

practice skills.

Learn the challenges and benefits of working as a team.

Develop good communication skills.

Gain familiarisation with decision and definition of the managerial aspects of a

project.

Learn how to implement an actual optimisation methodology in the design process

to improve the performance of the car.

Bring the theoretical disciplines learned throughout the MSc programme into

practice to solve a challenging engineering problem.

Develop an awareness of the fundamentals of a design process.

Bearing in mind the objectives and purpose of the project the group had to find a way to

obtain the best results possible whilst handling at the same time the rest of the course tasks, duties

and responsibilities. In addition, since none of the team members had any previous experience on

car design, it was important to acquire a set of initial skills being these, a general understanding of

the main flow features that characterise the flow over a competition car and the inherent challenges

associated with this type of problem. Then it was deemed important to acquire familiarisation with

general understanding of the software employed in the project and at least learning how to

efficiently operate the computational resources available. Having this set of skills would then provide

the ability to propose different means for improving specific areas of the car, always basing the

modifications on the physical insights and good engineering practice. Furthermore, it was considered

very important that the vast majority of the work was done as a team instead of a summation of

individual works. This also fulfilled the objective of understanding the importance that good

communications skills and information sharing play on a large team-based project, where to

accomplish the defined goals a fluent and clear communication strategy is paramount. Regarding the

computational approach, since the problem was to be solved by using state -of-the-art computer

software, it was deemed important to learn the good practices of CFD so as to work effectively and

with a methodology similar to that used in industry.

16

The foundation of the 2012-2013 project was based upon working as a team on the entire

car, instead of splitting the car in parts: the workload was divided in an attempt to give all the team

members the opportunity to work in every aspect of the project as opposed to specialising on a very

particular area of the problem. The initial aim was to improve the car progressively rather than

implementing large changes between iterations, in order to differentiate where the gains or losses

came from and surely enhance the performance of a complex system such as an open wheeled car.

Ideally, a curve tending asymptotically to a theoretical maximum value was sought for. In addition, a

very important consideration for this project was the ability to implement the knowledge acquired

on the individual classes in the project. This lead to the inclusion of an optimisation cycle onto the

design process to explore some of the learning outcomes from the design course during the first

semester of the MSc programme.

1.2. Assumptions

In order to tackle such a challenging project a number of assumptions ought to be taken into

consideration. Just like in any engineering problem, once the problem has been identified, a number

of assumptions that do not compromise the validity of the decided approach but that somehow

simplifies it, or makes the process of finding a suitable solution less complex are given. This is a

common practice both, in the academic and industry environments. It is also important that these

assumptions somewhat adhere to the prescribed objectives of the project. Because these

assumptions affect different parts of the project entity, they have been classified in different groups

to clarify the original intention of the simplifications and clearly identify the part of the project

where these assumptions have relevance.

1.2.1. CAD related assumptions

• For the entirety of the project, the x-coordinate is the streamwise direction (positive going

from the nose of the car to the rear wing). The z-coordinate is the spanwise direction, as shown in

Figure 1. The positive z-coordinates are in the direction from the centre plane of the car towards the

wheels. Finally the y-coordinate is the vertical direction being positive from the ground up. This incur

in the downforce being reported as positive in the downward direction ( -y direction). It is to be noted

that this reference system is completely opposite to what is described in the SAE J670 recommended

practice. However, the choice made in said paper clearly did not take into account any aerodynamics,

therefore it was decided to change the coordinate system to something more appropriate for this

case.

• The car is simulated without the suspension wishbones so that in the virtual model the

wheels are not connected to the car. It is obvious that the suspension would disturb the flow and

would change the flow conditions, but this simplification is made to ease the grid generation

process, also helping to just focus the flow analysis to the major aerodynamic components of the car.

17

• The simulated car is assumed to include the driver weight and the geometrical changes

implemented are supposed to not affect or vary the weight of the vehicle. This allows to model the

car at the limit of the ride height prescribed in the regulations.

Figure 1: Baseline car with coordinate system.

• Interior cavity of the cockpit is not simulated. The helmet and upper chest of the driver are

included as exterior surfaces, being on top of a flat plate located at a small depth into the cockpit. It

was considered that modelling the interior part of the cockpit and the driver inside would not be

efficient from CAD generation point of view, since any changes in the nose shape would infer in

readjusting the driver legs position and modelling too many elements that would not affect crucially

the aerodynamics of the car.

• Materials or roughness are ignored on the problem. Although geometrical volume of

mechanisms such as engine, gearbox and radiators was qualitatively respected, structural design was

not taken into account. The surfaces were assumed to be smooth and materials were not considered

as it is beyond the scope of the project.

• Interactions in downstream direction are stronger than upstream. It was assumed that

elements placed downstream would not have such strong influence in upstream components, whilst

very strong effects were observed vice versa. This assumption allows to study the car from the front

to the rear.

1.2.2. CFD related assumptions

• Aeroelasticity is not being considered in the design process, even though fluid -structure

interactions might be relevant. In a real case, aerodynamic forces can cause deflection in structures

causing geometrical variations, so the aerodynamic forces would change; however only rigid models

of the car were simulated, not taking into account the structural effects.

18

• The car is simulated facing directly the flow. Crosswinds, turning or yaw angles are not

considered. Hence the numerical domain simulates the car at 30 m/s in straight line with air in

complete rest in the surroundings.

• Compressibility effects are not considered. As a general rule in aerodynamics, compressible

effects can be neglected without any loss of accuracy when the Mach number is below 0.3.3 In the

current project the free stream Mach number in all simulations was approximately below 0.1,

therefore constant density in the simulations is assumed.

• The flow is assumed to be symmetric with respect to the plane that crosses the car in the

middle from the nose to the rear wing, therefore only half of the car is simulated reducing the

numerical cost to generate the mesh and solve the flow field over an entire car. It was assumed that

by prescribing a symmetry boundary condition at the mid-plane, the car could be mirrored with no

detrimental effects to the solved flow field.

• The contact patch of the wheels was approximated by a block of 1 mm height in contact

with the ground overlapping the wheel geometry. Other approaches are available to model the

wheel-road contact in CFD, however this approach was chosen based on the ease in grid generation

whilst still delivering accurate physical behaviour.

• Inner flows within the overhead intake ducts or the sidepods are not simulated. This

assumption simplifies in great deal the analysis, as the internal flow in these components is not

simulated and less effort is required also in CAD work, meshing and solving different regions in the

numerical domain. They were modelled as “outlets”, a boundary condition that considers that when

the air reaches these locations it exits the domain.

• The exhaust gases and temperature variations within the domain are not taken into

account. Exhaust gases from the engine could be used to enhance the aerodynamic performance of

the car, and the heated air expelled from the radiators might change the flow field. These aspects

were considered to fall out of the scope of this project. Discarding energy balance equations to be

solved in the simulations would speed up the process.

• Finally, the aerodynamic balance is computed as the ratio of the front wing downforce to

the total downforce, instead than employing the ratio of front axle downforce to total. The difference

between the two methods was calculated to be within 5% of the initial value, and therefore the

former method was adopted as a consequence of its intrinsic rapidity.

1.2.3. Turbulence modelling

The simulations were run in steady state. Even though the problem being solved presents

very unsteady features, to simplify the problem the flow field was assumed to be steady. Being

aware of the nature of the physics involved, with separation and vortex shedding as a common flow

3 Anderson Jr., J. D., “Fundamentals of Aerodynamics”, 2nd Edition, Mc Graw Hill, Inc.

19

pattern, unsteady simulations were not used since they are more compli cated to solve in terms of

computational effort, adding convergence uncertainties with respect to the simpler steady

simulations. Ultimately this would reduce greatly the times to solve the simulations and help to

accomplish the tasks within deadlines.

Reynolds-Averaged Navier-Stokes (RANS) are used for the simulations. The set of momentum

equations in 3D plus continuity equation that comprise RANS are implemented in steady state

(SRANS) to resolve the simulations. SRANS solves an averaged flow field in space which has been

assumed to be steady in time. Accordingly to the requirements of the project and the intended

quality computational grids to be obtained, SRANS was assumed to give the main characteristics of

large structures of the flow that can be used in the conceptual design stage to improve the

aerodynamic design. Furthermore, RANS is chosen because the details of the small scale turbulence

are in a sense not practical for the conceptual design stage where the focus is generally in the

approximate drag and downforce generated by the car.

High wall y+ was the selected approach to treat the boundary layer in the current project.

Field functions were used to approximate the boundary layer profile described by the logarithmic

law and it was considered to give trustful results (as it will be shown in section XX). Even if the

approach of a more refined y+ could be more precise, the size of the meshed files (approximately 40

million cells for a half car) when using y1+ <1, and difficulties using a hybrid y1+<1 and y1+>30 mesh

(further explained in the Section 4.3) prevented its use.

Unless stated otherwise, the turbulence model used on the simulations was the κ-ε 2-

equation model (one for transport and rate of dissipation and one for turbulent kinetic energy).

Being a RANS model, it models the entire energy spectrum of the turbulent flow. The solutions

obtained are a representation of the average flow field in steady state and it is important to notice

that spatial small scales cannot be handled properly by the simulations and that structures such as

vortex generators, serrated trailing edges, small scale vortices, flapping wakes or vortices shedding

cannot be precisely represented. It was assumed that the κ-ε turbulence model would give reliable

enough solutions. More complex simulations like URANS, DES or LES (in order of complexity) could

give better snapshots of the flowfield, however this was not attempted because stil l with SRANS a

deep understanding of the flow around a racing car can be met and numerous design solutions

found.

Finally, it is stressed that the race car that has been analysed is a hill climb car, the most

important goal is to improve the aerodynamic performance of the vehicle. It is understood that one

of the most important variables that make a successful hill climb car is acceleration and cornering

manoeuvrability. One key assumption is that the car will likely have a predefined engine that would

not change from the baseline car to the modified car. As mentioned before the racing tracks are not

longer than 2000m, top speeds rarely reach 120mph. Therefore drag force is not the main concern of

the project, although it is taken into account. On sight of these assumptions the objective is to

increase as much as possible the downforce generation, however it will also be optimised in terms of

20

aerodynamic efficiency (L/D), so drag is also considered. Based on the previous assumptions, it can

be stated that the solutions were intended to be as close as possible to reality according to the tools

available and the timeframe given to develop the project. Having largely simplified the problem, the

trends give the most relevant information; if all runs are simulated with the same aforementioned

assumptions, when an input modification presents better performance than previous designs, it is

likely that it would also present an improvement in real life behaviour.

1.3. Management and Project Fundamentals

The team management was found to be a critical and fundamental aspect to ensure the

goals the team set at the initial stages of the project were accomplished. A clear management

strategy that stipulated a “work-like-a-company” methodology was established at the very beginning

of the project, and shared by all the team. This strategy aimed to maximise the amount of work that

could be completed in the time frame that was given and also to ensure that the team members ’

capabilities and learning process were maximised.

The group that undertook this project was composed of six MSc students, each with diverse

backgrounds in engineering. Three of the team members had aeronautical backgrounds, while two

of the students were mechanical engineers and one member had previously completed an

automotive engineering degree. The execution of a design project of this kind demands a

considerable amount of work using design tools, thus a good knowledge of CAD and CFD principles is

very important and the fact that some of the team members had previous experience using them,

proved to be very valuable.

The team received a hard disk with the CAD files of previous years Group Design Projects

(GDP). This car is referred as the baseline car, which was tested in the R.J. Mitchell wind tunnel and

for which experimental data exists. The CAD files were used in conjunction with STAR-CCM+ to create

a suitable mesh and to simulate the flow around the car. The CAD software used for this project was

Solid Works, mainly because the baseline geometry had already been created with this software.

STAR-CCM+ was selected as the CFD software because of its user-friendly structure that merges the

geometry manipulation, meshing and solver environments into one unique software. In addition to

this, the automated mesher and the powerful post-processing tools that it includes were the main

reasons for selecting it over other commercial packages. More precisely, race cars present complex

geometries and an unstructured mesh seemed more adequate to deal with this type of problem

efficiently. STAR-CCM+ offers a robust meshing algorithm to generate unstructured meshes, which

with a choice of user defined settings, eases the mesh tuning process for a specific problem. For

instance, the prism layer generator is an important feature for solving the flow in the regions close to

the solid surfaces and STAR-CCM+ generates it automatically, if the mesher model is selected.

Furthermore, the ability of STAR-CCM+ to repair CAD-imported surfaces and to optimally prepare the

geometry for the CFD analysis was essential for obtaining high quality results. It is important to

mention that the team members received a one-week course of the fundamentals of STAR-CCM+,

courtesy of CD-Adapco. The course provided a first contact with the software and allowed the team

21

to address some of the initial problems encountered in the execution of the project direct ly with

people from CD-Adapco. Another important factor that was critical in the gradual understanding of

the CFD package and the fundamental principles of CFD was obtained by attending the Applications

of CFD (SESS 6021) module, which took place from October 2012 until January 2013 at the University

of Southampton.

The available computational tools to perform the flow calculations of the car are also an

aspect of the work that was defined early in the project. The team used the Lyceum Linux Teaching

Cluster Service throughout the project. The use of Lyceum allowed the team to obtain results for

computationally demanding grids in a shorter amount of time than it would have otherwise been

possible in a local workstation. During the first semester of work (October to December), the team

worked on Lyceum 1, which was equipped with 21 compute nodes (16 nodes with 2.3 GHz AMD

quad core processors and 5 nodes with 3 GHz Intel processors) with a peak performance of 2

Teraflops. Lyceum 1 was decommissioned in December so Lyceum 2 was used from January to the

completion of the project. Lyceum 2 supposed a high improvement in the computational resources

available since it increased the number of compute nodes to 32, with 16 processor cores and 32GM

of memory (8 of the compute nodes have 64GB of memory). In addition, the theoretical peak

performance of Lyceum 2 is 9 Teraflops. It is noted that a significant amount of time was spent into

learning the basics of the Unix operational system and the required procedures to perf orm the bulk

of the computational work with this supercomputer.

1.3.1. Methodology

The Start of the project was the first meeting with Professor Sandberg on October 2nd in

2012. Weekly meetings were held throughout the duration of the project to present the progress

that had been achieved within a defined period of time. In addition, the group had internal meetings

in order to define weekly objectives and to assess the progress made during the previous week.

Based on the initial team meeting, it was decided that good communication between the team

members was a priority. Several tools were used to fulfil this objective. Initially a common Internet

file management site was used to share files, subsequently common file storage within the University

of Southampton computer servers was obtained from iSolutions. Furthermore, electronic mails were

used extensively and the considerable amount of classes that all the group members attended

together also contributed to a good group communication.

The most important tool used, however, was the “work-like-a-company” methodology, which

consisted in compulsory weekly working hours in which all members of the group worked together in

the computers at the Tizard Building Design Studio. During the first semester an average of 16 hours

per week were achieved whereas during the second semester the average working hours per week

increased to 25 in order to complete the project objectives. This methodology allowed the team to

exploit the individual expertise of each of the members, to have frequent brainstorming sessions to

devise a plan of action for specific problems that needed to be solved or to bolster the

communication skills between team members.

22

The chart in Figure 2, presents the workflow adopted to develop the project. The group was

divided in three main departments (Design/CAD, Grid Generation/Meshing and CFD/Postprocessing),

similar to divisions in a company Engineering department. Since none of the team members had

previous experience in motor racing design, the inputs to the project came from a consensus from all

of the team members emulating the input from the Head of the Engineering Department in a

company). These inputs came in after the group post-processing sessions, which occurred after

finishing the numerical simulation of each new design. The inputs were listed by the group with

specific tasks determining which parts of the design had to be altered. Modifications on the CAD

models were executed by the Design/CAD division; once the drawings were approved by the project

manager, the Grid Generation/Mesh division proceeded with the mesh generation for the car. Once

the mesh was approved, the CFD division started the computation and presented a post processed

file to be analysed by the entire team. Upon the analysis of results, new inputs were generated and a

new cycle started. Finally, Version and document control was carried on to ensure that the correct

design was being submitted to Mesh and CFD. The files and directories generated by each one of the

divisions had a specific format to maintain the files organised and deal with the amount of designs

generated.

Figure 2: Sketch of the workflow adopted in the project.

Another tool that has been used extensively is a Gantt chart that details the major tasks that

were performed during the project. The Gantt chart of the first semester is presented in the

Appendix 2 - Gantt. As it can be seen, the first part of the project had a short duration, approximately

of two months from the date of the initial meeting (October 4th and the day of the first presentation

4th of December). Most of the first month was dedicated to bibliographical review; training and CAD

23

work. A great part of the bibliographical review consisted in reading the reports from previous years

and to research possible resources that could aid with the design of the car (e.g. books and journals).

The training period consisted in completing some fundamental Solid Works and STAR-CCM+ tutorials

in the Tizard Design Studio computers and it also included the STAR-CCM+ course attendance. Half of

the group attended an online course at the end of October while the other half travelled to the CD-

Adapco Headquarters in London to complete the training. A great effort was made in the CAD files

that were facilitated as some of the car surfaces presented numerous imperfections, such as screw

holes and rivets and therefore a considerable amount of time was implemented in cleaning the

geometry to make it ready for CFD.

The month of November was exclusively employed to complete the meshing and the

simulations of the baseline car. The meshing process proved to be more time consuming than

anticipated, since none of the group members had previous experience with Star-CCM+, and it took

some time to get acquainted with the way that the software worked. It was also necessary to get

familiarised with the geometrical parameters of the model the team was analysing. Different domain

sizes, cell types, grid refinement and turbulence models were tested. The inclusion of volumetric

regions for grid refinement was also tested. Separate work on the front wing of the car and the

wheels in isolation was undertaken while the meshing of the car was being attempted. Some of the

results that were obtained for the components in isolation were used in the baseline meshing and

simulation procedures. After the presentation in December there was approximately a one -month

and a half hiatus during the Christmas vacation and the examination period. The work for the second

semester resumed on the 28th of January of 2013.

The work on the second semester consisted in: performing a group of preliminary studies,

executing an extensive revision and post-processing of the results obtained in the baseline car

simulation; implementing the design methodology into three optimisation cycles and writing the

report. The Gantt for the second semester is also presented on Appendix 2 - Gantt.

The preliminary studies were made to answer practical questions proposed by the group

during the development of the project. To ensure that the selection of airfoils made for the wings of

the baseline car was a good for the application, a study on current and potential airfoils and wings

that could be implemented in the car was performed. To verify if the meshing setup used on the

baseline car could be improved a study on meshing settings testing different values of y+ was

performed. And finally, to verify if the boundary conditions adopted on the sidepods and engine

intakes was correct a study on these parts was performed.

Since one of the objectives of the current project was to optimise the aerodynamic design of

the baseline car, the revision and post-processing of the baseline car was intended to give an

understanding of the flow over that car so that modifications to improve the design could be

proposed. The other objective of the task was to get used to the post processing tools of the Star

CCM+ software; a set of commonly used views and geometrical entities to visualise flow patterns

24

were saved and then copied into the solution files of subsequent designs. The task was executed in

group, since the design modifications were proposed in consensus by the group members.

The design methodology presented previously was intended to be used into three

optimisation cycles. Based on the time for calculating the solution of the full car simulations on the

baseline car in the Lyceum 2 Cluster (approximately 16 hours) the group proposed that a new

approach for the design of the car should be attempted: instead of testing modifications and

optimising individual components of the car as it was implemented in previous years, the

modifications on the car parts would be tested in the full car simulations to see their impact in the

whole flow field. The group members also realised that the GDP could be used to implement some of

the knowledge obtained in the modules attended in the previous semester, such as the concepts

learned in the Race Car Aerodynamics (SESA6039), Turbulence (SESA6028) and Design and Search

Optimisation (SESG6018) modules.

1.3.1.1. First Design Cycle – “A” Iteration

In the First Design Cycle, changes in the design were proposed based on the group

knowledge. A total of 5 cars were simulated in the cycle, and the process took approximately four

weeks time. The first input for modifications was the results obtained in the postprocessing of the

baseline. The car was analysed based on what was learned in Race Car Aerodynamics (SESA6039)

module and from the bibliographical review. The main idea was to identify geometrical aspects and

flow patterns that could prevent the car from performing at its maximum, and propose changes to

improve the flow in the region. Suggestions were proposed, and the work was executed in the form

of the cycle from Figure 2 started by modelling, meshing and simulating. The results obtained were

once again post-processed in group and new inputs were suggested, restarting the cycl e. All the cars

created in the First Design Cycle, also called “A” Iteration, were named with the letter A followed by

number characters. It is to be noted how, from this moment on, all the new parts that were

produced by the CAD department were given a precise and univocal file name, so that the evolution

of a single part, or assembly, could be traced back at every point in time.

The methodology of the first iteration proved to be efficient and allowed a good version

control based on the generated documentation. As new designs were being tested the tasks were

being learned by the group members and an acceleration of the process was obtained. The group

also invested some time in learning how to take advantage of automating tasks with macros in STAR-

CCM+; this work that started as an unpretentious search became a very useful tool to meshing,

solving and post-processing. As the number of designs increased, the macros ensured that the same

meshing parameters and solution setups were maintained whilst boosting the throughput. The use

of Java macros was a pillar to implementing the optimisation methodology of the second and third

iterations. The time to implement modifications and test a new car took approximately one week,

but it was a consensus that with the development of the automated macros process, this time could

be reduced further.

25

It was noticed that the ad-hoc approach used on the first cycle led to inputs on the design

that sometimes generated a better performance and sometimes an inferior performance, however it

will be shown in the following sections that the final design from “A” iteration, presented a solid

improvement from the baseline car. This cycle demonstrated that previous knowledge and

experience in race car design are beneficial on this type of approach; an experienced engineering

manager could point the right direction to be followed, saving a lot of time by avoiding the

implementation of poor design solutions.

1.3.1.2. Second and Third Design Cycles – “B” and “C” Iterations.

The idea behind the Second and Third Design Cycles was to implement a more systematic

and scientific approach to the optimisation problem, therefore a procedure based on a surrogate

model was adopted. The learning process of the first cycle combined with the automation tool above

mentioned, gave the group the confidence to attempt this approach. A considerable number of cars

would have to be simulated and the group knew that time could be a real constraint. Two critical

parts of the car were investigated, based upon the idea of moving from upstream to downstream

areas of the car, since the frontal parts of the vehicle tens to have a stronger influence in

downstream components. In the second cycle the relative position between the wheels and the front

wings (gap and overlap) was varied. In the second optimisation cycle, geometrical parameters of the

diffuser were investigated. All the cars created in the Second Design Cycle, also called “B” Iteration

were named with the letter B followed by number characters; in the Third Design Cycle, also called

“C” Iteration were named with the letter C followed by number characters.

Starting from the best design of the first optimisation cycle, the variables for the second

optimisation cycle were defined and a population of 19 CAD designs were generated, meshed and

simulated. A response surface was generated with the results suggesting the region where the best

combination of variables should be; a new generation of designs in the optimal region was designed,

meshed and simulated. On the other hand, the best design from the second Optimisation Cycle was

the starting point for the Third Optimisation Cycle, and the same procedure described for the Second

Cycle was adopted. The process will be described in detail in further sections.

26

2. Bibliographical Review

2.1. Previous Years Reports

This part of the bibliographical review is intended to give a brief overview of the main results

and design approaches attempted by the 2010/2011 and 2011/2012 GDP groups. The main goal is to

summarise the major items investigated by these two teams and the most important conclusions of

each study. The aim is to use this information to understand the challenges associated with the

problem being investigated and also to gain useful knowledge of the potential areas of the car that

can be exploited to gain aerodynamic performance, and to avoid those areas that have been found

problematic.

2.1.1. MSc in Race Car Aerodynamics GDP Report 2010-11

2.1.1.1. Methodology

The 2010/2011 GDP project was formed by 6 individuals. The approach was to split the car

into seven different elements so that each member of the team could investigate the aerodynamic

performance of one major part of the full car in isolation. The car was split into the following

components: (1) Sidepod, (2) Front Wing, (3) Rear Wing, (4) Engine Cover, (5) Helmet, (6) Nosecone

and finally (7) Diffuser. In addition, the wheels were studied in isolation to gain a better

understanding of the flow behaviour around them. Furthermore, the most fundamental flow

features of the baseline car were not analysed in great detail because this team decided to analyse

extensively the individual components of the baseline car in isolation. Hence, the methodology used

was to optimise every component by itself prior to combining all the different parts to study the

effect of the flow interactions between all the components in the full car. Two iterations were

performed. Furthermore, the frontal area of the full car was used to calculate the aerodynamic

coefficient of the components in isolation in an attempt to keep consistency when comparing the

parts in isolation and mounted on the car.

2.1.1.2. Baseline Car Analysis

The Baseline CAD model used was taken from the 2009/2010 MEng GDP project and meshed

in STAR-CCM+ using a polyhedral mesh with a prism layer surrounding the car. This prism layer had a

y+ value that was below 5 on both the front and rear wings whereas the rest of the car had a prism

layer with a y+ value above 30. Because two different wall treatment approaches were taken, the “All

y+ treatment” model was selected for the walls. In order to achieve these y+ values, a local estimation

of the first wall distance was done using the flat plate approach with the characteristic length of each

part of the car (e.g. Wing element chord, Nosecone length, etc.)

Once the near wall treatment was fixed, two different dependency tests were carried out.

The mesh dependency test consisted on running two different meshes of 7 and 14 million cells. The

results indicated a 1% difference in lift and drag coefficients between the two meshes. In addition, a

domain size study was carried out by changing the length of the domain in the stream -wise direction.

Results of this test yielded a 1% difference in lift and drag coefficient between the longest domain

27

(inlet located 3.5 car lengths in front of the car and outlet located 6 car lengths behind it) and the

shortest domain (inlet positioned at 2 car lengths in front and outlet at 4 car lengths behind it). The

longest domain was chosen for the simulations. Finally, a mesh of 8.5 million cells over a chosen

domain was used for the baseline flow analysis and subsequent iterations. In addition, the k -ε

turbulence model was the selected as the turbulence model throughout the project because of its

robustness. More specifically the Realizable k-ε Two-Layer turbulence model with all y+ treatment

was used. The team also tested the k-ω turbulence model but it was found to be too sensitive to the

initial and boundary conditions and it was discarded. A segregated solver was used. With these

settings Table 1 shows the results:

Table 1: Aerodynamic coefficients element-wise.

Component CD CL

Front Wing 0.08 0.9

Nosecone 0.02 -0.11

Front Wheel 0.15 -0.08

Splitter 0.05 -0.05

Cockpit & Driver 0.01 -0.02

Engine Cover 0.06 -0.09

Sidepod 0.13 0.49

Rear Wheel 0.17 -0.13

Diffuser 0.03 0.48

Rear Wing 0.30 1.13

Whole Car 1.02 2.52

It can be seen that the overall coefficient of lift was calculated to be 2.52 while the overall

drag coefficient was 1.02. The biggest contributors to lift were the rear wing, the front wing, the

sidepod and the diffuser. It can clearly be seen that the other components generated negative

downforce (lift). On the other hand, the components that generated the most downforce also

generated the highest levels of overall drag. It is noted that the front and rear wheels are also large

contributors to the drag of the car.

2.1.1.3. Iteration summary

As mentioned before, two optimisation iterations were completed. During the first iteration,

the team members struggled to improve the downforce of the individual parts and only the Sidepod

and the Diffuser presented some improvement. The second iteration was more fruitful and the team

managed to improve the overall performance of the car.

28

2.1.1.3.1. First Iteration

2.1.1.3.1.1. Front Wing

During the first iteration the front wing was modified quite extensively. First, the wing

profiles were changed from the LS413 of the baseline to the thicker NACA 9618 profiles.

Furthermore, a bridge wing was used with a Selig 1223 airfoil shape. The gap and overlap of the wing

elements were also changed according to Zhang and Zerihan4 in an attempt to maximise the

downforce, since it was noticed that the baseline gap and overlap distribution was aimed at a higher

efficiency rather than downforce. The endplate was also redesigned. It included a tyre ramp to

reduce the lift over the wheel, and some curvature was added to guide more air towards the sidepod

inlets. The results attained in this iteration were worse than those obtained for the baseline car with

a 57% drop in efficiency. In addition, the tyre ramp directed the edge vortex towards the upper side

of the front wheel causing a large increase in the lift of the front wheel.

2.1.1.3.1.2. Sidepods

The approach used to generate higher downforce was to shape the bottom of the sidepod

with an aerodynamic profile. Three airfoils were taken into consideration: a LS413, an Eppler E423

and a MH32. The LS413 profile was selected because it exhibited the best performance in ground

effect. The sidepods length was also increased, now extending beyond the rear whe el to avoid the

large effect the wheel had on the baseline sidepod exit. The last modification introduced in this

iteration stage was the flat plate on the side of the sidepods. The flat plate had two purposes: First, it

was aimed at creating high pressure on the upper surface near the rear wheel whilst low pressure

underneath the plate would increase the downforce. Secondly, the flat plate was postulated to seal

the channel that is formed under the diffuser targeting less flow spillage from the sidepod

underbody. With all these modifications, the sidepod attained a 79% increase in downforce and the

overall efficiency of the sidepod was doubled.

2.1.1.3.1.3. Diffuser

The same airfoil as the one used in the sidepod was implemented in the diffuser in order to

avoid flow spillage from the diffuser to the sidepod and vice versa. Furthermore, the sidepod and the

diffuser were merged into a single part so only one channel was seen under the car. The major effect

of this modification was to enlarge the edge vortex so that it covered up to ¾ of the diffuser span at

the expansion section, which reduced some of the pressure recovery. Although the modifications

brought some issues, the overall performance of the undertray was increased.

2.1.1.3.1.4. Engine cover

The engine cover was rebuilt from scratch. The engine intakes were placed on the sides as

opposed to the baseline configuration. This allowed the engine cover to be lowered so that the

frontal area of the car was reduced. The modifications applied had a positive effect since the drag

4 Zhang, X., Zerihan, J., Aerodynamics of a Double-element Wing in Ground Effect. AIAA Journal, Vol. 41, 2003 pp. 1007-

1015.

29

and lift coefficients were reduced. However, the flow over the sidepods and near the engine cover

turned out to be more turbulent, which could have led to worse flow conditions arriving to the rear

wing. Additionally a roll-bar was added due to security restrictions.

2.1.1.3.1.5. Rear Wing

The rear wing was completely changed from the baseline. The new rear wing had only two

elements with longer chords. The airfoil selected for both elements was a Church Hollinger CH 10-48-

13, a high lift low Reynolds number airfoil. The airfoils were simply extruded up to an endplate

provided with an inner foot. An important observation is that the rear wing was not attached to the

car because the design was lacking the rear wing struts. Furthermore, the wing was perhaps placed

too low, because from the frontal view, the main element of the rear wing was not visible.

2.1.1.3.2. Second Iteration

2.1.1.3.2.1. Front Wing

In the second iteration stage, the team decided to come back to the initial airfoil design used

by the MEng GDP, the LS413, for first and second element. However the airfoil was slightly modified

on the second element. An extension was added to the trailing edge of the second element based on

previous experience of the team members in other race car competitions such as “Formula 3”.

Moreover the endplate was redesigned again using a straight shape at the bottom part having a

constant width, whilst the upper side was kept curved inwards. Further modifications were made

over the upper side of the endplate, to breakdown the vortex generated by the upper ed ge. In

addition, the edge plate of the endplate was modified, defining a semi -circular profile that enhanced

the edge vortex production. Finally, a turning vane was added in the proximities of the endplate with

the intention of enhancing the strength of the edge vortex.

The results for this second iteration were better than those obtained in the first iteration,

nevertheless the team members agreed to maintain the bridge wing because of two main reasons.

First, the downforce increased with the bridge wing and secondly the addition of this third element

supposedly made the wing stiffer allowing the use of only a single strut for structural purposes. Even

though the bridge wing produced more downforce on the front wing, it worked in a sense as a poorly

designed tyre ramp since it lead to a significant increase on the front wheel lift. Figure 3 and Figure 4,

show the drag and lift breakdown by component.

2.1.1.3.2.2. Sidepods

For the second iteration, the sidepod designers decided first to try to increase the inlet area

in order to increase the mass flow rate incoming into the channel, this being a trend in recent GDPs,

with the difference that turning vanes were added to canalise and straighten the flow. However, the

results were observed to be worse than expected as the downforce dropped 50%. The design was

revised and the inlet went back to its original dimension with the addition of the turning vanes. The

channel under the diffuser was a straight channel in which the only variable affecting the cross area

30

was the ride height. The LS413 airfoil was still used as the aerodynamic profile for the lowe r surface

of the sidepod.

The sidepod performance after these modifications resulted in an increase of nearly 4% in

downforce and a decrease of 3.6% in drag so that the efficiency ended up to be almost 8% better

than in the previous iteration. Unfortunately the turning vanes encouraged flow spillage into the

central diffuser reducing the effectiveness of the sidepods in benefit of the former.

2.1.1.3.2.3. Bargeboard

A brand new element was designed for this second iteration since it was realised that the air

was entering the sidepod through the sides due to the pressure differential between the outer flow

and the sidepod channel. A bargeboard was then created with two main purposes: Firstly to direct

the flow towards the sidepods inlets and secondly to generate a vortex aimed to increase the sealing

effect of the sidepod skirts, acting as the rubber skirts used in F1 in the late 70’s.

2.1.1.3.2.4. Diffuser

For this second iteration the idea of merging the diffuser and the sidepod into a single large

channel was abandoned. Skirts were placed on the sides of the diffuser so two different tunnels were

used, one for the sidepod and another for the diffuser. Using the information from the first iteration

it was discovered that the diffuser was operating too close to the ground so the mini mum pressure

point was raised. Again, as it happened in the first iteration the modifications done in the undertray

slightly raised the value of the downforce generated by this element.


The analysis of the first design results lead to the conclusion that the flow features produced

by the engine cover were too turbulent and detrimental to the rear wing performance. A completely

new philosophy was then employed for the second engine cover model. The engine intake was

redesigned to a more usual configuration with a single intake placed above the driver helmet. This

second design managed to direct the flow to the rear wing in a proper way with the subsequent

reduction in drag production. Moreover this design did not include the rolling bar.

2.1.1.3.2.6. Rear Wing

A gap and overlap study was made for the rear wing elements and finally the best

combination was used for the second iteration. The design was almost the same as for the first

attempt with the difference that the wing was moved allowing it to be in a more “free-stream”

condition and two struts were added as mounting elements. Although the performance of the first

design was significantly improved by the second design, it was still worse than the MEng results,

almost 25% worse. The drag was, however, 15% less than the MEng design.

31

Figure 3: Drag coefficient by component for 1st and 2nd iterations.

Figure 4: Lift coefficient by component for 1st and 2nd iteration.

2.1.2. MSc in Race Car Aerodynamics GDP Report 2011-12

2.1.2.1. Methodology

The 2011-12 GDP team design approach was to split the car in four main sections (front

wing, diffuser, sidepods and rear wing) that were distributed amongst the four-team members that

composed the group. The intention was to improve each section’s performance by studying them in

isolation using CAD and CFD. Constraints were set for each individual part so as to account for the

interactions between the different components. Each of the individual component studies was given

a predetermined timeframe after which the full car was assembled and simulations of the entire

geometry were attempted. Once the full car simulations were completed, the general procedure the

team followed was to compare these results to what it could be expected from the isolation studies.

32

The working pace was gradually accelerated as the academic year evolved as the team

members gained experience with the software used (Solidworks and STAR-CCM+) and were able to

build up a robust CFD practice (for which they employed guidelines to follow after the CD-Adapco

training courses). This permitted, by the final stages of the project, to run more simulations and the

team members were able to test permutations of the different designs looking for the best choices.

2.1.2.2. Baseline Car Analysis

The first part of the project involved analysing a baseline car, which they obtained from the

2010 MEng GDP car. The initial stage of the CFD process was to set a proper meshing strategy, carried

out in STAR-CCM+. Some attempts with polyhedral cells were run at an initial stage following the

conclusions from the 2010-2011 MSc Group Design Project, but because the cells in this particular

meshing configuration have an average of twelve to fourteen faces, a high number of calculations per

iteration and heavy file storage are required. For the complex geometries dealt within this project it

was considered that a more efficient choice was to use a trimmer mesh, whose cells have only six

faces and are not as computationally demanding in terms of memory or time.

The workflow employed for the meshing approach was to import a parasolid file from

SolidWorks into STAR-CCM+, to then use a surface wrapper, surface remesher and finally generate

the mesh. The decision to use the surface wrapper stemmed from the poor CAD model that was

given and that required a significant amount of corrections prior to the meshing stage. The surface

wrapper virtually eliminates the need to repair manually the surfaces imported into STAR -CCM+

therefore making the problem less time consuming. However it is not mentioned that this may incur

in slight modifications of the geometry which would not give correct solutions. Once the surface

issues are solved by the wrapper the procedure is straightforward with the remesher and volume

mesh generation. The choice of y+ was justified in terms of computational cost affordability mainly,

stating that resolving the viscous sublayer (hence aiming to y + < 5) was not feasible in terms of

computing time.

It was justified a selection of a base size of 5 mm after the mesh dependency study. The

results are seen in Table 2. From the results it was concluded that aiming for a mesh coarser than 11

million cells was enough to obtain accurate results for the baseline car. It was assumed that the

design variations would not strongly affect the convergence of the simulations of the full car. Hence

these settings were employed consistently and no more mesh dependency studies were run for the

full car.

Table 2: Mesh dependency study.

Mesh base size [mm] Cell count CL

7 6,097,294 2.31

5 10,831,246 2.36

4.5 13,595,895 2.36

4 15,688,673 2.35

33

The boundary conditions defined in the Physics continua for the surfaces of the domain

were: no slip wall for the car surfaces, moving wall for the ground, rotating tires, velocity domain

inlet, pressure outlet for the engine and sidepods intakes, pressure domain outlet and symmetry

planes on top, side and middle planes. The resolution of the problem is highly influenced by the

initial and boundary conditions, but the selected conditions were assumed to be appropriate for the

simulations carried out. It was stated that the air intakes of the engine and sidepod, being modelled

as pressure outlets, force the flow to exit the domain; in a real scenario the air would re -enter the

domain through the exhausts, however this was not included in the modelling mainly to not

complicate the problem with the addition of other phenomena such as heat transfer or Coanda

effect. Some of the main settings are shown in the Table 3 below.

Table 3: Physical Models.

Physical Model Description/Value

Spatial Model 3D

Material Gas – Air

Pressure-Velocity coupling Segregated

Equation of state Constant density

Time modelling Steady

Viscous Regime Turbulent

RANS Model Realizable k-ε Two-Layer All y+ treatment

Despite not presenting the results, after the domain study that was carried out, the settings

selected for the domain were 3 and 5 car lengths in front and behind the car, respectively. With the

outlined settings the baseline analysis gave a CL of 2.363. No specific figures were explicitly listed for

drag, however pie charts were shown for both the lift and the drag as shown in Figure 5. In the final

stages of the project a comparison of these charts is commented to analyse variations in the balance

from the baseline to the new designs. The wheels and the body generated lift with C L of-0.184 and -

0.167 respectively.

From the results that were obtained it is clear that the main contributors to downforce are

the rear wing, the front wing and the diffuser. The wheels generate a significant positive lift and the

sidepod does not appear to be efficient. Moreover, the wheels are the components that generate the

highest drag followed by the rear wing and the body. Lastly, the flow over the car was analysed by

flow visualisation with Q-criterion iso-surfaces coloured by vorticity in x-direction and TKE contour

plots on streamwise planes at different distances from the symmetry plane. From the flow

visualisation design strategy for subsequent designs was drafted. Moreover, from the baseline

simulation they also compared and analysed the results obtained from the full car with each of the

simulations performed for the isolated parts. The differences were critically analysed to justify the

isolation studies and to extract extrapolations that might be taken into account.

34

Figure 5: Split of drag (left) and downforce (right) (ignoring sources of lift).

2.1.2.3. Iteration summary

A total of three iterations were successfully completed. The clear objective was to improve

the car with the new designs in each iteration. However they did not improve the baseline figures

until the last design iteration.

2.1.2.3.1. First Iteration

2.1.2.3.1.1. Front wing and nose

Two designs were created for the first iteration. The first design only implemented changes

in the endplates, adding curvatures both inwards and outwards of the wheel and also enveloping

part of the wheel to try to deflect the upper edge vortex over the ti re. The second design used a

wider front wing, with extended endplates that tried to direct the flow into the underbody of the car

passing into the wheels. As well as this, a new sharper nose was implemented whilst the wing

configuration was conserved from the baseline car. The first design resulted in an overall large

increase in drag (4200% for the endplate) whilst reducing the wheel drag by 85%. This design was not

used on the full car. The second design gave 20% increase in drag and 2% decrease in downf orce in

the full car simulation, resulting in approximately 20% drop of efficiency.

2.1.2.3.1.2. Diffuser

Given the reciprocal influence between the sidepod and diffuser the sidepod performance

was also included in this part. Two objectives were pursued in the first i teration: to increase

downforce by increasing the surface area of the diffuser and optimise the strength of the vortex by

varying the side-edge thickness. For increasing the surface area channel extensions were added from

the exit of the sidepod downstream, called outboard diffuser tunnel. A total of three different

designs of outboard diffuser tunnel were tested. The best outboard diffuser tunnel was the third

one, with a gain in diffuser downforce (11.9%) but decrease in sidepod under channel (16%). These

comparisons were made between the isolated elements analysis for the first iterations with respect

to their performance in the baseline full car. A simple graph shown in Figure 6 summarises the

conclusions from the side-edge thickness study, showing that the thinner the plate separating the

diffuser and sidepod the higher downforce generated by both elements.

35

Figure 6: Underbody downforce dependence on diffuser edge thickness.

The first design of the sidepods was based on actual F1 sidepod shapes and it also included

fins, vortex generators and a serrated side edge of the flat plate. A total of eight designs varying the

shapes of the serrated side edge, sizes of vertical fin placed at the front outer corner of the flat plate

were produced. The results from this study shows that the downforce was decreased after each new

design, going from CL = 0.92 from the baseline car to -0.125, even generating lift, for the last design

of the first iteration. However the drag coefficient was effectively reduced from 0.4584 to 0.09 in the

last two designs of this part.

2.1.2.3.1.3. Rear wing

A total of four design versions were run in the first iteration of the rear wing study. The first

step was to set the endplates size and shape. Louvers were added, leading edge rounded to

accommodate the wheel and top trailing edge was square -cut to aid the louvers’ performance. After

this, the aerofoils were changed from the baseline profiles to S1223, although the baseline chords,

gaps and overlaps settings were kept intact. Then the mounting struts were also considered in the

isolation study and lastly a gurney flap was introduced in the third element of the upper wing. It was

commented that the lift and drag estimations drop by 33% and 24%, respectively, between the

isolation study and the full car simulation with the new design.


For the engine cover isolated study, the cockpit and nose were also included. Only one

design of the engine cover was worked out in the first iteration. Longer and smoother slope towards

the rear part was shaped to try to reduce drag. A successful decrease in drag of 11% was achieved,

however increasing lift by 54% in comparison to the baseline car.

2.1.2.3.2. Second Iteration


The second iteration of the front wing and nose studied several aspects: 2D studies

of different aerofoils in multi-element and ground effect configuration, multi-deck wing designs and

a new nose shape. The aim of the 2D studies was to guide the design decisions about the front wing

setup. The aerofoil performance was judged using JavaFoil by monitoring the C L against angle of

36

attack and CL against CD plots. Once the profiles were selected (NACA 9618 for the main e lement and

Eppler E423 for the flaps) three variables were studied in STAR-CCM+ with 2-D simulations step by

step: Angle of attack of the mainplane, gap and overlap of the two flaps and finally the angle of

attack of the second flap. The chord of each element was kept as in the baseline car. The first flap

element angle of attack was chosen visually setting it as a tangent continuation of the mainplane. For

simplicity the gap and overlap between the main element and first flap and between the two flaps

were set to be the same at 5 mm, hence reducing the number of variables to analyse from four to

two.

A second deck with a wing composed of two elements was added, with dimensions,

vertical separation to the main wing and angles of attack selected based on vi sual judgement. They

were later optimised in iteration 3. In addition to this, a gurney flap was included at the trailing edge

of the flap element. This upper deck however was implemented only close to the endplate to leave

the middle section as clean as possible to lead more air into the diffuser inlet. Apart from this, two

other designs were experimented using single elements with long and short chords to test and

compare their performance. A new endplate was shaped pretending to deflect the top edge vortex

over the top of the front wheel to diminish the drag produced. The nose and the splitter were

redesigned as well, with a sharper nose in arrow point but with rounded edges and a splitter

following the nose shape in top view.

The first of the three designs was the design that yielded better results in the full car

simulations, increasing by 45% both the lift and drag with respect to the baseline analysis. A

thorough flow visualisation post-processing followed this section, showing separation in the upper

deck and how the top edge vortex went around the tire not over it. Still the modified wake of the

front wheel derived in a decrease of the wheel drag.

2.1.2.3.2.2. Diffuser

The second iteration of the diffuser was composed of geometrical variations, lengthening the

diffuser downstream and widening its outlet to increase expansion and enhance downforce further.

Ten different designs were tested, and with the maximum lateral expansion configuration a 65%

increase in downforce for the diffuser and 16% for the sidepod were obtained. These figures

however were for the isolation study. Larger and stronger vortices are visualised in the post -

processing section and 2D plots of pressure distribution were included to show the suction increase

with respect to the baseline geometry.

2.1.2.3.2.3. Sidepod

Downforce generation was the main focus of the second iteration study on the sidepods. For

the lower side of the sidepod, the NACA63(2)615 and Eppler 423 profiles were compared, concluding

that the second profile was more desirable because of higher CL. Two more designs with the Eppler

423 lower side were run adding vanes at the inlet of the lower channel. A smaller air intake for the

radiator and winglets at the rear part of the sidepod were also added. The last resulted to be the

best design from the second iteration, which whilst increasing by 4% the baseline car drag

37

coefficient, generated 43.65% more downforce. This meant an improvement of aerodynamic

efficiency from 2 to 2.77.

2.1.2.3.2.4. Rear wing

This section attempted to increase the size of the rear wing elements as much as the

regulations permitted. The rotating wheel was also included as part of the isolation study in order to

simulate the rear wing in more realistic conditions. Four designs were tested varying the wing

elements configuration, comparing elements chords, angles of attack and two versus three element

upper wing. A large three element wing plus a beam wing whose chord was also extended was the

configuration simulated in the full car, but results were not included in the report.


The new noses designed in the front wing study were the cause for simulating twice each of

the two new engine cover designs. With the intention of reducing surface area, the first design

included a roll bar and downstream displaced protruded side air intakes. The second design further

improved the first iteration design, concentrating in making the taper gentler; this was the design

chosen for the full car second simulation after the flow visualisation judgement via TKE plots. As a

result of the changes but probably also due to the other part designs, an increase in drag of 23% and

lift in 4% was produced.

2.1.2.3.3. Third Iteration


The third iteration main objectives were to optimise the upper deck of the front wing

settings, the endplate shape and the nose underside curvature to improve flow quality towards the

diffuser. For the upper deck same gap and overlap of 5 mm was kept from the lower deck analysis.

The first element of the upper deck Angle of attack was set to maximise downforce and the overall

Angle of attack of the double element upper deck was set to 15º, same as for the lower deck. The

endplate top edge was reshaped to point even more above the front wheel and the rear edge was

rounded to accommodate the wheel. The nose was squared and the leading edge was kept very high

and thin, to increase the frontal area beneath it and to increase the mass flow of the diffuser. After

the simulation of the third design in the full car, a 25% increase in lift was obtained but an 80%

increase in drag was observed. The visualisation showed that separation of the upper deck was

successfully avoided and that the top edge vortex was half deflected above the wheel and half

around the outer rim.

2.1.2.3.3.2. Sidepod

Four eccentric designs were run in the third iteration. The air intake for the radiators

was moved to the rear part close to the engine cover and the whole sidepod was shaped as an

inverted wing. Various double decker winglet at the outer part of the intake were tested and

ultimately the last design obtained a lift coefficient of -2.21 in comparison to the baseline -0.92, a

140% increase, whilst only increasing by 25% the drag with respect to the baseline configuration.

38

2.1.2.3.3.3. Rear wing

For the last iteration the same four configurations that were attempted during the

second iteration were run, but in all of them the mounting system was changed. The original two -

pylon structure from the body to the suction side of the upper wing was substituted by a small

device locking the whole rear wing through the beam wing. Reducing the influence of the struts

delayed separation at the trailing edge of the third element of the wing and results improved

notably. Final coefficients of 0.32 in drag and 1.071 in lift were obtained, meaning a worsening by

54% and 18%, respectively, with respect to the baseline car.


Again only one extra design for the engine cover was tried in the last iteration. Going

back to the roll bar design, NACA ducts were introduced as engine intakes. With respect to the

baseline car, whilst increasing CL by 20%, the drag was effectively reduced by 10% in the full car

simulation.

2.1.2.3.4. Final Design Analysis

After the third iteration, five full car simulations were run. Using the best front wing

design from the second iteration and the last designs of the rear wing, engine cover and diffuser

were used in all the simulations attempted. The first three consisted of slight variations in the rear

wing angles of attack and a comparison of the effect the guide vanes in the lower side of the

sidepods had on the overall car performance. The last design of the sidepod was replaced by the

baseline sidepods in the fourth simulation, improving figures from the third iteration. One last

simulation using a design of the sidepods from the second iteration was run but results worsened.

The definitive design gave a lift coefficient of 2.495, increasing by 6% the baseline downforce

generation. Figure 7 below shows the evolution of the full cars simulated in each iteration.

Figure 7: Iteration history of force coefficients, efficiency and aerodynamic balance.

39

2.1.2.4. Conclusions

From the 2010/2011 GDP project it can be extracted that in most cases, except for the front

wing, the interaction between elements and the actual geometry definition of the elements plays a

key role on the aerodynamic performance. From the results it appears that it is not worthwhile to

optimize the single components in isolation because their performance when mounted on the car is

very different. Furthermore, from an aerodynamic point of view the modifications made in the

sidepod inlet are very useful because in contrast of what is usually thought, the increase in the inlet

area does not produce the expected increase in downforce. Other major improvements such as the

extension on the second element of the front wing and the flat plate close to the rear wheel appear

to be the most interesting features to be further investigated. On the other hand, the 2011/2012

GDP project shows that for the final design, the improvement came from the front wing and diffuser

only, whilst the rear wing performance significantly dropped. Improvements in the rear wing and

engine cover in isolation studies were not effective in the full car assembly, and the final best design

was with the baseline sidepods. The incongruence occurs because the optimisation was split in parts,

and the aerodynamics of all the parts are enormously affected by the interactions. As a result, the

downforce improvement was only of 6%.

2.2. Race Car Aerodynamics Research

In the earlier days of F1, the design of a car was left to the genius and intuition of people

that became legendary as years went on: great individuals like Colin Chapman, Bruce McLaren and

Mauro Forghieri, just to name a few. As time progressed, and technology with it, the importance of a

systematical, organic approach to the design of a racing car grew dramatically. Nowadays, teams

need engineers with a very strong technical background, and with increasing theoretical capabilities.

It is consequentially obvious that, in order to build a competitive racing car in such a short time,

inspiration and information are to be searched in literature, from both the academic and industry

side. The relevance of the knowledge that can be acquired from people with outstanding experience

in the field can only be underestimated.

In this section, an overview of the various literature covering general race car aerodynamics

will be given. It is to be always remembered that various physical phenomena concur to the

performance of a race car: special attention is therefore paid to the most significant parts of the car,

i.e. the wings and the diffuser, which are covered in separate paragraphs. The literature review for

the wheel is presented in the corresponding chapter, for the sake of clarity.

2.2.1. Ground Effect Aerodynamics of Race Cars

A comprehensive overview on recent development in race car aerodynamics is found in

Zerihan et al5. Special attention is dedicated to the influence of ground effect on the overall

performance of racing vehicles: a racing car can be approximated as a bluff body with a very low

5 Zerihan, J., Zhang, X., Toet, W., Ground Effect Aerodynamics of Race Cars, Annual Review of Fluid Mechanics, Vol. 59, No.

1, 2006, pp. 33-49.

40

aspect ratio, and close to the ground. In particular, two elements operate in direct ground effect,

namely the front wing and the diffuser, with all the other parts being relevantly affected. Wheels can

also be seen as cylinders operating in ground effect, with a null gap-to-chord ratio. This paper gives a

full analysis of the force generation mechanisms for the main elements of the car.

First, the front wing is said to produce around 25 to 30% of the total downforce of the car.

The amount of force produced by this part is of critical importance, due to its large impact on the

balance of the whole car. In addition to figures, the front wing should be evaluated on the grounds of

the wake it produces, which greatly affects the rest of the car: factors like separation or vorticity of

the flow should be carefully controlled. Furthermore, it is reported that ground clearance is the main

mean to control front wing performance. Maximum for downforce was found to be at a height of

approximately 0.08c (8% of the chord) (Razenbach and Barlow6), which was confirmed by Zerihan

and Zhang, as long as free transition is considered. Below this value, two force reduction

mechanisms have been postulated: the first is the fusion between ground and aerofoil boundary

layers, the second is the stall of the wing because of an adverse pressure gradient, coupled with the

existence of a wall jet on the ground.

Another interesting physical feature of the front wing is the edge vortex that is formed when

the shear layer, which separated at the edge of the endplate, rolls up, giving raise to a vortex -induced

suction on both the inside of the end-plate and the lower surface of the wing. Downforce levels are

increased as clearance is reduced, with drag following a similar trend. The wake produced is of two

different types, depending on the ride heights: shedding vortices in the force enhancement region,

and flapping motion at lower values. From a design point of view, the ideal ground clearance appears

to be between the two ride heights accounting for maximum rate of change and maximum force: this

allows to have a relevant value for downforce while ride height sensitivity is minimised.

Another component that is discussed in detail is the diffuser, which operates to some extent,

in a way that is similar to the front wing: three main zones of behaviour, related to ride height, can be

recognised, these being force enhancement, maximum force, and force reduction. Furthermore,

diffuser performance depends strongly on various geometrical parameters, such as the area ratio,

the characteristic length and angle and the aspect ratio, which have an intricate effect on force

generation. In general, downforce is increased when dif fuser is moved towards the ground, and a

dramatic decrease is found when an asymmetric and recirculating flow is present in the diffuser, as a

result of decreased ride height or of an excessively steep ramp. Ideally, a pair of counter-rotating

vortices, symmetric with respect to the centre plane, should be produced at the edge of the diffuser

and found intact at the exit of the diffuser. It is worthwhile to point out that the diffuser needs a

significant mass flow to produce sensible levels of downforce, and that starving the inlet, for example

with high levels of turbulence in the incoming flow, can lead to increased drag and almost null

downforce.

6 Razenbach, R., and Barlow, J. B., 1996, “Cambered Airfoil in Ground Effect—an Experimental and Computational Study,”

SAE Publ ication 960909.

41

The last part analysed is the wheel, which represent an unavoidable source of drag and lift

for the car. Moreover, these elements are very complicated to study, both for experimental and

computational means. A separate bibliographical review for the wheel itself is presented later on.

2.2.2. Race Car Aerodynamics: Designing For Speed

Race Car Aerodynamics by Joseph Katz7 presents a comprehensive and extensive analysis of

the aerodynamic characteristics of race cars along with key concepts such as boundary layers,

aerodynamic forces, coefficients and fundamental equations. In addition, a thorough discussion of

the existing tools for assessing aerodynamic performance, being these road testing, wind tunnel and

CFD is included. Finally and of critical interest for this project, the author introduces a very complete

analysis of several aerodynamic components. The aim of this book is to shed light on the physical

interpretation of the aerodynamic behaviour caused by different components without explaining in

detail the complex mathematics that are needed to fully understand the problem at hand.

The book begins by presenting the evolution of vehicle aerodynamics over the last century

and the change in paradigm that has shifted the focus of race car design from minimising as much as

possible vehicle drag by streamlining to maximizing the downforce levels allowing higher cornering

speeds and shorter lap times. This in turn has had an impact on the aerodynamic of production cars

whose role is vital to the development of new concepts and designs.

The three ways to evaluate the effects of the aerodynamic forces in a vehicle are: road

testing, wind tunnel testing and CFD. While road testing seems to be the simplest form to analyse

the performance of a car, it has the obvious drawback of having to build a full size model, which in

turn gives steep constraints on the number of design modifi cations that can be attempted without

increasing the financial cost. In addition, this type of testing is known to be sensitive to a number of

effects such as climate conditions, mechanical adjustments and driver’s ability to influence the car

performance. On the other hand, wind tunnels present a controlled environment but they demand

considerable financial investment either to build one or to rent time slots in commercial wind

tunnels. The construction of the model also is an important financial constraint and the conditions

that are used must be carefully planned as these can have a big impact on the results obtained.

According to the book, computer simulations are becoming increasingly popular tools to

obtain aerodynamic results especially with the increase of the computational power over cost ratio

and the possibility to create a controlled environment without the construction of car parts or

models. The commercial software are becoming more user friendly and cheap, being accessible to

small teams in different race categories. Major teams currently use CFD techniques in conjunction

with wind tunnel and road testing, as the latter two can provide correlations of real results and the

computational technique can provide the possible trends that might justify a particular modification.

Some of the major benefits of using computational tools listed by the author are:

Quick response: The generation of a model is faster than the manufacturing process

7 Katz, J. Race Car Aerodynamics: Designing for Speed. Cambridge, Ma: Bentley Publishers, 2006.

42

Reduction in manufacturing costs: Bad designs can be avoided by performing a quick

CFD calculation.

It can be used as a diagnostic tool to improve existing vehicles

Storage: after calculating a numerical solution, it can be stored and reviewed later

analysing a different flow feature or variable not analysed previously

A major disadvantage of CFD is the grid generation process, which constitutes an important

part of any computational simulation. A poor or inappropriate resolution of the mesh in critical

conditions can generate incorrect results. Furthermore the grid generation process can be very time

consuming.

The author devotes an entire chapter to aerofoils and wings. Regarding airfoils, basic

concepts, such as thickness and camber, and physical aspects such as lift, boundary layers (turbulent

and laminar), attached and separated flows are covered. The methodology developed by Liebeck 8

(which will be discussed further in subsequent sections) for obtaining high lift airfoils is also

presented. The most important concepts concerning race car design and with relevance to the

current project are summarized below:

For race car design two basic approaches can be implemented, one is a low drag

configuration based in laminar boundary layer airfoils that can be used in high speed

tracks and a high lift configuration for road races with unbanked turns

High lift airfoils have a fast transition to a turbulent boundary layer by rapidly

accelerating the flow (generating a strong suction on the leading edge region)

maintaining that level of pressure as long as possible and recovering the pressure in

the smallest chord distance possible (steepest slope in Cp curve)

The lift of an airfoil can be modified by changing its camberline, lift can be obtained

without increasing the angle of attack, and this effect is greatly affected at the

trailing edge of the camber line, hence the use of flaps can greatly increase the lift of

an airfoil configuration

When designing an airfoil for a race car application a more predictable and reliable

behaviour should preferred, therefore a stalled condition should be avoided and

airfoils with gradual stall should be preferred instead of abrupt stalls which are

characteristic of thin airfoils.

Regarding wings, the author explains the tri-dimensional effects and the formation of wing

tip vortex with a consequent loss on lift and increase on drag, it is also shown how the geometrical

parameters of the wing such as aspect ratio, sweep, taper ratio, wing planform shape and dihedral

affect the lift distribution.

8 Liebeck, R. H., “Design of Subsonic Airfoils for High Li ft,” J. Ai rcraft, Vol. 15, No. 9, 1978, pp. 547-561

43

A brief section presents the effect of generating lift by edge vortex formed in slender wings.

This is an important concept because it is known that a wing in ground effect generates a significant

amount of lift by the rolling up of the shear layer formed by the separation of flow in the endplate of

the wing4. Instead of having an attached flow on the suction side, it is possible to generate lift by

separating the flow at a sharp leading edge, the difference of pressure between the upper and

bottom surfaces will induce a rotational movement of the flow trying to curl from the surface of

higher pressure to the lower pressure and the separated flow will generate two counter rotating

vortices that induce a high speed and low pressure core that will ge nerate lift on the surface. The

author emphasises that the drag generated by such wings is in general higher than that for a wing

with attached flow. The effect can be explored to enhance the force in lifting surfaces, for example,

vortex generators can be included in the frontal wing to increase its lift, it is also pointed out that

several race cars use dive plates in the nose section to generate a vortex and an additional

aerodynamic force on the frontal wing. Lift surfaces such as delta wings that generate lift by

separated flow over the suction surface also have an increase on lift when increasing the angle of

attack, up to a certain point in which a loss of lift happens by a “vortex burst” which is the break

down of the organized structure of the leading edge vortex, this effect is similar to the wing stall.

The effect of the use of slanted surfaces on the bottom of the vehicle can be enhanced by

channelling the flow, these devices are often called diffusers, underbody channels or Venturis. The

last term was coined due to the similarity of physical phenomenon of pressure reduction and

increase of velocity that occurs in the throat of Venturi tubes. Diffusers try to take advantage of the

pressure reduction caused by that channelled flow that exits the dif fuser, the reduction of pressure

on the channels also brings some fluid from outside and generates strong vortices. A rear-mounted

wing can also be used to increase the pumping from the diffuser.

The design of wings in race cars is, in general, directed to obtain the maximum possible

downforce. This effect can be obtained by: increasing the wing area, increasing the wing camber and

delaying flow separation. The wing area is normally limited by regulations, therefore the most

common solution is to use multi-element wings, that have the aerodynamic effect of an increased

camber and the separation is delayed by the synergetic iteration between the elements of the wing

that result in a gain in the combined lift. In a multi-element wing, the camber can be increased much

more than in a single airfoil. The author also presents a few forms of enhancing the performance of

the wings such as:

Vortex generators: that can be added to generate a swirl on the flow that will bring

higher momentum fluid from a higher region of the boundary layer causing

transition and delaying the separation, their size is of the order of magnitude of the

boundary layer.

Wavy trailing edges: it mixes the flow from the pressure and suction side at the

trailing edge, it can reduce the trailing edge separation and the wing can operate at a

higher lift. However this geometry is complex and is hard to manufacture

44

Riblets: grooves added to the surface of the wing that reduces the cross flow at the

lower regions of the boundary layer and consequently reduces the total skin friction

of a turbulent flow.

Gurney Flaps: a small plate fixed at a high incidence at the pressure side of the

trailing edge of a wing, that increases the its lift. It can also be used at the endplates

of the wings creating camber there and increasing the suction of the wing, Figure 8

shows the Gurney flaps mounted on the wing and on the endplates.

Endplates: the reduction of lift caused by the leakage of the flow on the wing tips

justifies the use of this device, normally, the enhancement on lift is proportional to

the size of the endplate which has the effect of increasing the aspect ratio of the

wing.

Figure 8: The use of the Gurney flap on the rear wing and endplates of a race car.

2.2.3. Aerodynamics of the complete vehicle

When analysing the aerodynamic configuration of an entire vehicle it is important to define its

purpose. The correct balance of the aerodynamic forces is vital to the success or failure of a

particular design, for instance, if a race car is designed to break speed records in long straights, it will

need a streamlined body that generates very low drag while the downforce should be kept to a

minimum, only to maintain the stability of the vehicle at high speeds. On the other hand, race cars

on circuits with medium to high speed turns, should have a high downforce configuration allowing

shorter lap times. An alternative to conventional design that includes front and rear wings is to shape

the vehicle so that the whole body becomes a lifting surface in ground eff ect. However because the

car would be in general significantly longer than the span of the vehicle, the low aspect ratio implies

that the downforce is highly penalized by tri-dimensional effects. Side skirts are an attempt to create

a two-dimensional flow field underneath the car. In practice, sometimes the pressures generated are

so low that the skirts has to be rigid with the possibility of moving up and down allowing suspension

movements due to track irregularities. The closest the side skirt gets to the floor more intense is the

45

downforce generated, Figure 9 shows the effect of the gap between the skirt and the floor, a

decrease from 40mm to 20mm can increase the coefficient by almost three times.9

Figure 9: The effect of the height of the side skirt on the body downforce generation.

The major aerodynamic features of the flow over the wheels is also discussed and the most

important are summarized bellow:

In a car, the wheels will generate lift;

It has a considerable large separation region behind that will contribute to the total

drag of the vehicle;

Ahead of the wheel near the frontal stagnation point a region of high pressure is

formed and it is possible to mount a plate that will take advantage of the high

pressure to generate downforce, as shown in Figure 10;

In the upper part of the rear wheel it is also possible to change the bodywork by

shielding the wheel (deflecting some flow), which can also generate some extra

downforce;

Drag on the wheels is an important component of the total rag of an open wheeled

vehicle;

The use of fenders or rim covers can substantially reduce drag;

The injection of high-speed flow over the wheel can reduce the size of the separated

region on the wheel, with consequent reduction on drag.

The use of bargeboards was introduced to try to reduce the drag of the wheel. The

bargeboard support can also be used to generate some downforce.

9 The regulations for the hill climb cars requires a minimum clearance of 40mm from the floor, from Figure 9 is

possible to see that most of the enhancement on downforce is lost.

46

Bargeboards evolved into trapezoidal forms with sharp tips that could generate

vortices and reduce the pressure under flat body cars.

Another possibility is to channel the high-speed flow from the wing to behind the

wheel in an attempt to reduce the separated region, as shown in Figure 10.

Figure 10: The use of a flat plate near the high pressure region to generate extra downforce (left) and Channelling the flow from the front wing to the rear of the wheel can be used to reduce wheels drag (right) .

The author also presents a few other examples of aerodynamic devices that have been used

to increase a car performance:

VG - Vortex Generators: these VG’s are different from the ones mentioned before,

they are not intended to delay separation on wings, but they use sharp edges to

generate vortices that can be mounted throughout the car surface to generate extra

downforce, the idea is to direct vortex cores which have low pressure into the car

underbody.

Flat Plates: they can be mounted to take advantage of stagnation points on the

surface of the vehicle. Normal applications of flat plate include the aforementioned

flat plate in front of the rear wheel and it can also be placed in the end of the curved

region of the nose (for cars with high nose).

Spoilers: are simple devices placed on the rear part of a vehicle (they are not as

elaborated as rear wings, and are normally used in sedan cars), they contribute to

change the flow on the rear part of the car they can reduce the drag by reducing the

region of separation behind the car, they can also increase the effectiveness of

diffusers.

Strakes: small flat plates mounted throughout the car, with some incidence to the

flow, to generate small increments of downforce

Louvers: are ventilation slots (also called gills), that allow some flow to pass from zones of

higher pressure to lower pressure. They can be used on fenders where the high pressure from the

47

wheels is thrown on the upper part of the fender and reduce the lift on the fender, by allowing the

pressure to be reduced close to the wheel an increase on the flow speed underneath the vehi cle can

also be observed.

2.2.4. Race Car Wings

After presenting the physical phenomena behind these common aerodynamic devices used

to increase a vehicle performance, an entire section is devoted to the design aspects of wings. Wings

are used mainly to generate downforce, but their presence can influence the flow over the entire

vehicle, and the induced downforce can be at the same order of magnitude of the lift generated by

the wing, therefore the interaction between the wing and the entire vehicle must be comprehended.

Differently from aircraft applications, wings used in racing cars normally operate in a single

condition of operation (fixed angle of attack) therefore, according to the author, their design is easier.

The wings also have a low aspect ratio and this can affect the pressure distribution over the wing

that can be completely different from a two dimensional case. The low aspect ratio can also cause a

delayed stall where the angle of attack can be increased without an abrupt loss on lift. In addition, it

is mentioned that the ground effect is a relevant aspect of the wing design in race cars, the

movement of the suspension can alter the performance of the wing and change the handling of the

car.

Next, the author introduces a study of seven different wing configurations (position and

airfoil shapes) that were tested in an open wheeled race car. Figure 11 shows the cases studied with

measured drag and downforce, some of the configurations were studied at full scale. A few

conclusions can be drafted from the figure:

Car number 4 shows that the increase in the number of wings can have a

detrimental effect on the downforce because the flow from an upstream wing

affects the flow downstream.

A wing positioned in the middle of the car has an unfavourable interaction with the

body of the car.

The delta wing concept of configurations 3 and 5 can work reasonable well, however

it reduces the effectiveness of the rear wing.

The best results seem to be the traditional configuration of frontal and rear wings

apart from each other.

48

Figure 11: Different wing configurations tested in an open wheeled race car.

After the defining the approximate position of the lifting surfaces on the car, a fine tuning

process must be performed to obtain the best possible combination that work well with the body of

the vehicle and possibly increase its performance. To illustrate the effect of the interaction between

the wing and the body, the author presents the flow over a generic ellipsoid, which is attached

throughout most of the surface and separates at the trailing edge. The placement of a wing on the

rear part of the ellipsoid changes the flow path accelerating it underneath the body due to the

reduction of pressure induced by the wing, which increases the downforce of the body. In general,

the Cp distribution on the bottom surface of a car with and without the rear wing, show that the car

generates higher downforce when the wing is on the car. It is also shown that the proximity between

the wing and the body can change the spanwise lift distribution over the wing resembling one of a

twisted wing with higher angles of attack near the tips.

In open wheeled race cars, the arrangement of the rear wing is normally defined by

regulation, when only one rear wing is allowed, they are usually placed in a low position to interact

with the flow coming from the bottom part of the car. When the number of wings is not fixed by

regulation a second wing is positioned as high as possible to reduce the unfavourable interaction

between the wings. Figure 12 shows the effect on the CL and on the aerodynamic efficiency of

configurations with one to four wings, the addition of extra wings increase the total downforce,

however the increase is smaller at each new wing added, on the other hand the increase on drag is

considerable, therefore the use of more than 2 wings is not recommended unless the drag increase is

not a concern on the design. It also worth mentioning that the flow on the rear wing is also

influenced by the wheels and that this influence is minimized by the use of endplates.

49

Figure 12: The effect of number of rear wing on lift and aerodynamic efficiency.

Continuing, the front wing in an open wheeled race car is positioned in the free stream flow.

Its functionality is influenced by the proximity of the ground and the presence of the wheels, which

also modify the flow that goes to the rear part of the car, therefore its design must be done very

carefully not to reduce de aerodynamic efficiency of other components. Regarding the ground

proximity it is noticed that the shape of pressure distribution over the suction surface of the airfoil

does not change much from a condition far from the ground, however its magnitude is much lower

generating increased downforce. The use of well-established airplane type airfoils in the front wing is

common. The author points out that if the tip vortex on the front wing hits the front wheel it

reduces the pressure on the rear face and ultimately increases the wheel overall drag, therefore the

use of narrower front wings with flaps is common. However the use of flaps must be made with care

since they deflect the flow that goes to the cooling inlets. A common approach is to cut out the flaps

near the wing root.

The effect of the front wing on the rest of the car can be illustrated by a study performed on

the effect of the span of the front wing of Indycars, where a baseline wing had its span increased by

10 cm. The results obtained show that the wing attained a higher downforce on the front but it

caused a significant downforce loss on the rear wing reducing the total downforce. A similar study

was performed in the present work on the Second Design Cycle . Moreover, In the front wing, the

existence of the nose causes a reduction on the downforce on the central portion as shown in Figure

13: picture A shows the wing without the nose and it is represented by the dashed curve on the

graph, picture B is the wing with the nose and it is represented by the f illed line on the graph. Since

the flow on the bottom of the car is important two possible solutions can be adopted, shown on

pictures C and D, the author comments that by adding anhedral on the wing, the solution D is not as

aerodynamic efficient as C.

Another important issue on the frontal wing is the management of the wing tip vortex, as it

was mentioned before, it can cause drag penalties and also disrupt the flow on inlets, it can be

deflected by surfaces, blowing, suction or by other vortices. Common solutions include the deflector

50

shown previously on Figure 10, the use of dive plates to create a stronger vortex to enhance the

downforce of the wing can also deflect the wing tip vortex. Another solution is to use sharp vortex

generator to create a vortex rotating in the opposite direction of the wing tip vortex. It is suggested

by the author to use intense use of CFD tools when designing these changes in the front wi ng, since

they can affect several parts of the car such as inlets and rear wings.

Figure 13: The loss on the downforce of the central part of the frontal wing due to the nose and different nose arrangements.

2.3. Wing Research

Historically, the first elements to be put on a racing car to generate downforce were wings:

simple profile used in airplanes, inverted and positioned somewhere on the car, generally on the top

or slightly backwards, often resulting in bizarre shapes. This was the first and most rudimental

concept: nonetheless, engineers grasped the great potential of this configuration and gradually

refined it. Nowadays, a layout with a front and a rear wing is generally accepted to be the best, both

performance-wise and from a practical point of view. Much research has been done, and still is being

carried on, on the optimisation of the aerofoil shapes for low -Re condition. An account of the

progress in this field is hereby presented.

51

2.3.1. Ali Wings

Ali Wings by Enrico Benzing10, presents a general overview of the design of wings and their

application to racing cars. Particular emphasis is placed on the discussion of wing sections with

special distributions, flaps and their derivatives, investigation of slots and overlaps.

From the very beginning, it is clearly identified that a single wing profile may not be

sufficient to cope with high downforce requirements so that wings complemented with other devices

such as flaps and slats may be required. This being the case, the mainplane or the principal section

has different design requirements when compared to the flaps because they have different

aerodynamic goals. Along these lines, the author introduces a series of airfoil sections with especial

pressure distributions that were generated in a similar manner to NACA airfoil profiles. The Benzing

profiles are of the form Be 122-045 where the first two digits correspond to the maximum thickness

of the profile in percentage of chord, the third digit is the chord -wise position of the maximum

thickness (in tenths of chord). After the dash, the first and second digits give the maximum camber

of the airfoil in percentage of chord and finally the third digit gives the position of maximum camber

(in tenths of chord).

Flaps are another topic that is discussed in much detail. According to the author, “the prime

objective of flats has always been to increase the value of maximum Cp for the purpose of retarding

the stall phenomenon.” The use of flaps has to be wise enough so as to increase the downforce

without increasing significantly the drag levels of the car. As it is keenly pointed out, on aircraft, high

lift devices are in general deployed only on manoeuvres where high lift is required. In flight regimes

such as cruise they are not deployed and they do not contribute to the overall drag of the aircraft. On

racing cars however, the flaps cannot be moved so that they will always have a significant footprint

on the drag levels of the car. The application of a split flap in auto racing is highly discou raged

because it is not as efficient as a configuration with a normal flap. Moreover, the only split flaps that

are know to be highly effective in racing cars are the so called “Gurney Flaps” introduced earlier.

They are always placed perpendicular to the pressure surface of the airfoil.

The definition of a flap is given as “second wing, with high aspect ratio and thus highly

efficient, which is added to the basic section with various inclinations. The drag of such a wing

structure is significant, and its effect in terms of downforce is considerable.” The slots between the

flap and main wing are known to have a significant effect but the author explains that no

mathematical methods are available to compute their aerodynamic performance due to the

complexity of the aerodynamic phenomena that takes place within these gaps. The slot produces a

‘slot effect’ which essentially creates a passage through which air flows and increases its kinetic

energy passing to the lower surface of the flap where the flow is re -energized causing separation

delay.

10 Benzing, E. Al i Wings, Their Design and Application to Racing Cars. Giorgio NADA Editore, 2012.

52

Flaps are classified as:

Junkers-type Flap: where the flap is positioned above of the mainplane with the flap

rotational axis parallel to the trailing edge. This flap arrangement, which is used by

the baseline car is not recommended by the author for small flap deflection angles.

Fowler-type Flap: The mainplane section is shortened, the trailing edge rounded and

the flap is integrated into the mainplane. While the junkers-type extended the chord

significantly, this design alters the chord and it does not extend it as much. Overlap

between flap and main profile is almost nonexistent, but there is a gap that

separates them.

NACA double-slotted Flap: based on “retractable schemes” and similar to the

Fowler-type. The arrangement includes a flap in between the main element and the

third element with short chord that acts as a deflector, directing the flow to the

leading edge of the third element. As a consequence, this configuration generates

high negative Cp. It appears as though this configuration performs better with

thicker main elements.

Multiple venetian-blind Flaps: Three to four flaps are considered in this design. The

arrangement is disadvantageous in terms of the frontal area.

Some other guidelines for flap design are given. The most advantageous wing planforms are

straight wings as opposed to sweptback. Furthermore, the chord dimensions of the flaps appear to

have a profound effect on the downforce that can be generated. The increase in downforce ( -Cp) is

mentioned to be proportional to the increase in flap chord. The best results come with values of

25~30% of the chord. The best performance is achieved with gaps of 1% to 1.6% of the chord. Finally

some flaps profiles are suggested: Be 152-155, Be 122-125 and Be 152-105. Finally, the discussion

regarding the investigation of slots is centered at giving an example of the process followed to

optimize the performance of the wing-flap configuration by making use of the gaps that are formed

between the two components. Because the airflow is so complex here, the Benzing emphasizes that

the designer must proceed to optimize the configuration by trial and error. The example shown,

demonstrates that finding an optimal position between the wing and the flap is complex but that the

slot can have a significant impact on the downforce level of the chosen configuration.

2.3.2. High Lift Aerodynamics

A.M.O. Smith11 High Lift Aerodynamics presents a detailed introduction on the principles and

the understanding of the fundamental mechanisms of high lift design aerodynamics. This paper

covers a wide diversity of topics ranging from basic inviscid theory to power augmented lift (active

flow control). The latter is not discussed here because it is out of the scope of this project.

11 Smith, A. M. O.,"High-Lift Aerodynamics," AIAA Journal of Aircraft, Vol. 12, No. 6, June 1975, pp. 501-530.

53

Starting from an historical perspective, it is obvious that early aerodynamicists sought to

enhance the performance of wing profiles by modifying certain geometric parameters such as the

camber, the position of maximum camber or the thickness of the airfoils to name a few. How ever,

just by altering these parameters the lift augmentation would not be significant. Nevertheless, as the

author observes, the basic principles for lift augmentation were known from the early days of flight

but the early designers lacked some understanding of the phenomena that yielded the increase in

lift. This was certainly associated to the early designers limited capabilities to perform quantitative

analysis of their designs.

As with any aerodynamic flow that produces lift, much of the responsibility lies on the “load-

carrying capacity of the boundary layer”. Clearly for conventional airfoils one of the fundamental

mechanisms to generate lift involves accelerating the flow over the suction surface to generate low

pressure. If the flow is accelerated greatly this in turn means that it has to be decelerated towards

the trailing edge of the airfoil to values below freestream. If this recovery of pressure (or

deceleration of the flow) is too abrupt, the flow will tend to separate. Hence according to the author

there are two main components that must be examined to generate high lift: Boundary layer analysis

and inviscid flow analysis about a given profile aiming to find airfoils that “put least stress on the

boundary layer.” From these two components it becomes clear that separation prediction becomes

an important asset for airfoil performance analysis. The author discusses some of the fundamental

separation prediction methods that are available such as the Cebeci -Smith method, which at the

time the paper was published, appeared to be the most reliable and robust method for separation

prediction. This method predicts separation when the skin friction is zero, which nowadays is easily

monitored in CFD by looking at contour plots of the wall shear stress over the wetted surface of the

wing. It is observed that classical boundary layer variables such as momentum thickness become

unreliable near the point of separation.

Perhaps one of the biggest contributions of this paper is the canonical pressure distribution,

which in broad terms is a modified Cp that is constructed with respect to some point on the airfoil

(generally the point where maximum velocity or minimum pressure occurs) rather than the

freestream. It presents a better picture of how each of the elements that compose a multi-element

wing is performing. This Cp only has positive values and starts at zero (start of the pressure rise) and

the highest value is +1, which corresponds to the stagnation point.

The canonical pressures become an important design tool because separation can be spotted

more easily than in conventional Cp plots. In general terms if there is separation there will not be as

much pressure recovery as shown in

Figure 14. Moreover, from these Cp distributions it is known that thinner boundary layers

are less likely to separate early (they can support higher adverse pressure gradients) and that

concave pressure distributions allow the greatest pressure recovery. The author states that Stratford

gave the best shape for the canonical Cp for late separation and greatest pressure recovery.

54

According to this, the boundary layer must be on the verge of separation in the recovery section of

the airfoil. This minimizes as well skin friction drag since the wall shear will be close to zero.

Figure 14: Canonical Pressure Distribution from A.M.O Smith.

Next, it is stated that “the problem of obtaining high lift is that of developing lift in the

presence of boundary layers: getting all the lift that is possible without causing separation. ” In this

sense the question becomes whether it is better to use a single-element airfoil or a multi-element

one. Several explanations are given. First, single element wings can improve lift by making changes to

the design aiming to obtain a specific pressure distribution (e.g. concave). This changes may include,

leading-edge radius, camber or trailing edge angle. The author states, “a cusped trailing edge

imposes less pressure rise at the trailing edge and increases the lift of the slope of the lift curve. ”

This effectively means that a higher lift can be achieved at lower angles of attack by effectively

lowering nose pressure peaks. However single element airfoils appeared to be limited to the amount

of lift that can be achieved. On the other hand, multi -element wings present a big array of

possibilities for increasing the lift. This is done making use of 5 well-known effects.

Slat Effect: A general misconception is that the slot formed between the main wing

and the slat induces some sort of boundary layer control by increasing the

momentum of the fluid in this region. According to Smith, this is incorrect because

by modelling the slat as a point vortex it is seen that the velocity of the fluid in the

slot is low. Essentially, the point vortex that represents the slat, induces a velocity

that runs in the opposite direction to the velocity in the leading edge of the main

airfoil. This effectively reduces the pressure peaks and therefore reduces the sharp

pressure gradient downstream of the airfoil. The author does not precisely give any

indication of the optimal position of the slat but rather it is described that it should

be placed where the pressure peak reduction is high. Furthermore, this effect is

observed to not have much effect on the recovery of the pressure of the airfoil, and

would not significantly increase the lift but its main effect is to delay stall angle of

attack.

55

Circulation Effect: This effect is once more explained by placing an airfoil and this

time a point vortex at the trailing edge of the airfoil. The point vortex induces a

velocity at the trailing edge of the airfoil where the velocity is in general low. The

point vortex increases the effective velocity so that it lowers the overall pressure

there. In effect this promotes a less steep pressure gradient. Hence the point vortex

causes the trailing edge of the upstream element to be at a higher velocity thereby

increasing the net circulation (lift) of the airfoil. A remark by the author clarifies that

“any method capable of introducing cross flow at the trailing edge will influence the

circulation. Any obstruction, properly placed, can be a powerful factor for controlling

circulation.” Other design suggestions by the author include: (a) cross flow strength

coupled with non-lifting stagnation point circulation, (b) nose placed at a slight

negative angle to avoid nose peaks so that circulation is introduced by mechanisms

other than pitching.

Dumping Effect: It has been mentioned that a forward element increases the

effective circulation because of the cross flow induced at the trailing edge by the aft

element. The interaction between these two elements also gives rise to an increase

velocity so that the forward element ‘dumps’ its flow at an increased velocity

therefore decreasing the adverse pressure gradient (pressure -recovery) on the aft

element. This is beneficial to the boundary layer as it is less likely to separate.

Off-the-Surface Pressure Recovery: Because the forward element dumps at

velocities much higher than the freestream, the final deceleration to the freestream

velocity is done off-surface in an efficient manner. Deceleration of the flow in the

wake is much more effective than in contact with a wall.

Fresh Boundary Layer Effect: Finally the simplest effect is that which states that for a

multi-element airfoil configuration, each of the elements starts with a thin newly

developed boundary layer which can sustain higher adverse pressure gradients

which in turn delays separation.

This paper provides a deeper understanding of the principles that can be used to augment

the lift of a given configuration. While the author does not dwell upon specific design guidelines to

optimize a particular multi-element wing design, the insights presented can be fully utilized to aid

the design process of some racing-car components such as the front and rear wings and also the

diffusers.

56

2.3.3. High-Lift Low Reynolds Number Airfoil Design

In this paper from 1997, Selig et al.12 argue that the design of high lift airfoils in the low

Reynolds number range of 2 to 5 x 105, is still a topic of interest since the development of such

airfoils in aeronautic industry can lead to aircrafts with increased payloads, short take -off and landing

distances and reduced noise. The authors compared a broad range of airfoils designed for low

Reynolds number and pointed that as a general pattern maximum lift decreases with decreased

Reynolds number.

The experimental study consisted in testing several one element airfoil profiles at low

Reynolds number and from the emerging trends design and test an airfoil for high lift. The research

was conducted at the University of Illinois open-return subsonic wind tunnel, with a cross section of

2.8 x 4 ft and test section 8 ft long. All the models had 12 in chord and 335/8 in span and were

isolated from the wind tunnel wall boundary layer by two horizontal spl itter plates, lift and moment

were measured by a servo-feedback-control force balance and drag was measured by momentum

method. Model accuracy was measured by a coordinate measuring machine with approximately 80

points taken around the airfoils. The validation of the experiment was made by comparing the results

obtained with the data from E387 airfoil taken in the NASA Langley Research Centre ’s Low

Turbulence Pressure Tunnel.

The authors listed the driving characteristics on the design of an airfoil, which are: the type

of pressure recovery, which can be convex or concave (Stratford-like)8, pitching moment; camber and

stall rate (a high stall rate refers to an abrupt trailing edge stall whereas a low stall rate refers to a

slow trailing edge stall). The main trends observed by the authors from the airfoils tested were:

More cambered airfoils have higher pitching moments

Convex pressure recovery airfoils tend to be more cambered

Stall rate is lower for concave pressure recovery

The maximum lift coefficient increases as the pitching moment increases and as the

pressure recovery approaches to Stratford distribution.

The airfoil FX 63-137 is presented as an example of a high Cl,max obtained through added

pitching moment, it has reached a Cl,max of 1.75 at Re of 2 x 105. The airfoil M06-13-128 is an example

of a Liebeck type airfoil. It has a high lift through the use of Stratford distribution to avoid sep aration,

since separation is avoided throughout the airfoil it has no aft loading and a low pitching moment. It

has reached a Cl,max of 1.52 at Re of 2 x 105.

12 Sel ig, M.S., Gugluiermo, J.J., “High-Lift low Reynolds Number Airfoil Design”

57

A new design philosophy was implemented by Worthmann13 by relaxing the constraint of no

aft loading on Stratford pressure recovery airfoils to increase airfoils pitching moment and hence

combine the increased lift due to pressure recovery and pitching moment. The airfoils obtained FX

74-CL5-140 was able to achieve a Cl of 2.4 at Reynolds number of 1 x 106. The authors argue that an

area of design to be explored is to obtain high lift characteristics by using the concave recovery and

the aft loading in the low Reynolds number region.

The design of such airfoil was made using low-speed airfoil codes such as: PROFOIL, Eppler

and ISES, an iterative design process was used and the profile generated was manufactured and

tested in the wind tunnel. The airfoil was called S1223 and its coordinates are presented on the

article. The frontal part of the suction side was designed to have a laminar boundary layer close to

separation up to the 0.20c point, at 0.20c a short bubble ramp14 is employed to reduce the laminar

bubble. The pressure recovery was obtained by specifying that the boundary layer would be

increasingly closer to separation on the trailing edge and an aft load was employed on the trailing

edge. This configuration reached a C l,max of 2.2. The use of a Gurney flap and vortex generators to

force transition on the leading edge were also tested with an increase of C l,max to 2.3.

2.3.4. Design of High Lift Airfoils for Low Aspect Ratio Wings with Endplates

The optimisation of two element rear wings in race car applications is extensively discussed

by Gopalarathnam and Selig15. Differently form aircraft applications, in order to maximize downforce,

race car wings are normally subjected to unusual constraints imposed by the governing bodies of the

sport. Following the constraints imposed in the 90’s which stated that the geometry of the two

element airfoil should be confined to a rectangular box parallel to the ground hence aligned with

respect to the free stream velocity and with dimensions of 20 x 5 in, the authors used an inverse

design code to generate candidate airfoils with the desired velocity distribution that were

subsequently tested in more computationally demanding viscous codes. They also used a graphical

tool that allowed to interactively change the geometry parameters such as flap position size and

angle of the airfoil.

The wingspan is also limited by regulations, resulting in a wing with aspect ratio of AR = 2.15,

the endplates do not generate lift but they contribute towards increasing the effective AR to 2.57.

Such a small AR wing has a considerable influence of the downwash component induced by the tip

vortex. This fact combined with the restriction that the box should be parallel to the ground, results

in an airfoil operating at a negative angle of attack as shown in Figure 15 therefore the problem can

be stated as maximizing lift at negative angles of attack.

13 Wortmann, F. X., ‘‘The Quest for High Lift,’’ Proceedings of the AIAA/MIT/SSA 2nd International Symposium of the

Technology and Science of Low-Speed and Motorless Flight, Soaring Society of America, Los Angeles, CA, 1974, pp. 97

101; a lso AIAA Paper 74-1018, Sept. 1974.

14 A bubble ramp is a gradual upper surface pressure recovery to gradually s low the flow down from its highest va lue. The

objective is to shorten the length of the bubble and reduce the bubble drag. It i s also called transition ramp on

Liebeck’s paper.

15 Gopalarathnam A. and Selig M. S., “Design of high-lift airfoils for low aspect ratio wings with endplates”. 15th AIAA

Appl ied Aerodynamics Conference, 1997.

58

Figure 15: Change of the incidence velocity vector angle due to downwash.

The conventional design methodology for high-lift airfoils is normally based in generating the

highest possible rooftop velocity on the frontal part of the airfoil followed by a Stratford pressure

recovery and with an aft load at the trailing edge. The authors state that this methodology does not

generate optimum airfoils for race cars subjected to the aforementioned regulations, since they

operate at negative angles of attack, an airfoil generated within this methodology can have a C l drop

from 4.5 to 1.59 when subjected to regulations. It is rather necessary to develop a new high-lift

design methodology which consists in having the strongest suction peak possible at the leading edge

and the strongest aft loading at the trailing edge. The flap is also used to load the trailing edge of the

main element. Figure 16 shows the difference of the airfoils, in the regulation box, generated using

the conventional and the new methodology with their respective velocity distribution and C l.

Figure 16: (Left) airfoil generated with the conventional methodology. (Right) airfoil generated with the new methodology.

After obtaining an airfoil that generated a high lift within the constraining box using the new

methodology, three parametric studies were performed: the first investigating the effect of the angle

of the airfoil in the box; the second investigating the flap to main chord ratio; and the third

investigating the effect of the gap between the main and the flap element.

When changing the angle of the airfoil in the box while maintaining its dimensions inside the

regulations, as shown in Figure 17, it can be observed that there is a change in its chord length. The

Cl has a small variation when the angle of the airfoil inside of the box is increased, the increase in the

lift due to increase in the operational angle of attack is off-set by the reduction on the chord length

of the airfoil; on the other hand a sharp decrease is observed when reducing the angle in th e box

caused by a negligible variation on the chord length but with a considerable reduction on lift caused

by reduction of the operational angle of attack. The velocity distribution for each case and the

inviscid and viscous CL obtained for the wing can also be seen on Figure 17.

59

Figure 17: Variation of the angle of the wing inside the regulations box and respective velocity distribution and CL for each case.

The second parametric study was the variation of the flap to main chord ratio (c f/cm), by

keeping the trailing edge of the flap fixed on the bottom right corner of the box and the same gap,

the flap chord was increased and a correspondent variation on its angle can be observed on Figure

18due to fixed gap. Inviscid calculations show a decrease on CL with increasing values of cf/cm, caused

by the reduction of the angle of flap. The same effect is not observed when viscous calculations are

performed, with a reduced cf/cm, the angle of the flap is too high and a separation of the flow occurs

reducing the wing CL. The velocity distribution for each case and the inviscid and viscous C L obtained

for the wing can also be seen on Figure 18.

Figure 18: Variation of the flap to main chord ratio, velocity distribution and CL for each case.

The final parametric study was the effect of the gap to total chord parameter. The trailing

edge of the flap was fixed on the bottom right corner of the box the c f/cm parameter was kept

constant and the flap angle was varied in order to modify the gap. The inviscid results shows a

constant increase in the CL with the reduction of the gap due to a higher velocity of the flow on the

gap that energizes the flow on the suction side of the flap, however when viscous effects are taken

into consideration if the gap becomes too small there is a reduction on lift due to the b lockage of the

flow on the gap caused by the formation of the boundary layer in the airfoil elements. The velocity

distribution for each case and the inviscid and viscous CL obtained for the wing can also be seen on

Figure 19.

60

Figure 19: Variation of the gap, velocity distribution and CL for each case.

2.3.5. Design of Subsonic Airfoils for High Lift

The paper “Design of Subsonic Airfoils for High Lift” is a result of 10 years of research on high

lift airfoils developed by Liebeck, R. H.8 at Douglas Aircraft Company. Several aspects of airfoil theory

are discussed, and just a few will be presented.

In an attempt to answer the question posed by A.M.O. Smith11: “What is the maximum lift

which can be obtained from an airfoil and what is the shape of that airfoil?” the author argues that

an optimization study must be employed by the definition of a few constraints: the use of a single

element airfoil, the flow remains attached and subsonic throughout the airfoil, powered lift would

not be considered and the profile must be geometrically feasible. The inverse approach is used to

design the airfoil shape based in the desired velocity or pressure distribution, hence the problem lies

on obtaining an optimized velocity distribution that maximizes lift. The design of the airfoil starts

from the trailing edge, which is defined as the origin. The variable s is defined as the arc length along

the airfoil surface. The lift coefficient can be expressed in terms of the circulation around the airfoil

and the velocity distribution on the airfoil surface

u(s)as follows:

Cl =L

12V¥

2c=

2G

V¥c= 2

u(s)

V¥

òds

c

(1)

The author explains that from the problem constraints

u(s) must have a stagnation point at

the leading edge and satisfy the Kutta condition at the trailing edge, it will also be affected on the

suction side by boundary layer separation considerations. On the pressure side cl will be maximized

by maintaining the

u(s) as close to the stagnation velocity as possible. On the suction side,

u(s)

should be maximized to maximize cl, this will be obtained by accelerating the flow from stagnation to

a peak velocity (rooftop velocity) that shall be maintained for some distance and then followed by a

deceleration or pressure recovery, which continuously avoids the separation of the boundary layer by

a constant margin (Strafford method) and it will be the maximum pressure recovery at a given

distance. Variation analysis can be applied to obtain a family of solutions with flat rooftop velocities

for a determined value of velocity at the trailing edge and free stream Reynolds number, from this

family it is possible to determine which rooftop length can provide the maximum C l to the airfoil.

61

Since the Stratford distribution avoids separation by a constant margin along its length, the

stalling behaviour of an airfoil that uses a Stratford pressure recovery is very abrupt as it separates

simultaneously everywhere when the margin is exceeded and the increase of angle of attack is a

reduction on the margin from separation. Another commonly used pressure recovery is the convex

pressure distribution, where separation is predicted at the trailing edge and with the increase of the

angle of attack the separation moves forward, in this case a more gentle separation will occur. In

general a highest lift can be obtained with the Stratford distribution.

The solid line in the curve presented on Figure 20 shows the theoretical solution with

maximum CL obtained by variation analysis, maintaining

u(s)= on the pressure surface. On the

suction surface a constant rooftop velocity is maintained followed by a Strafford distribution. This

solution meets the boundary layer separation constraint, but cannot provide a feasible airfoil shape,

therefore the velocity distribution was altered to the dashed line in Figure 20, taking into

consideration the leading edge radius and thickness, and the possibility to operate in angles of attack

above the design value. The suction surface also has a transition ramp at the end of the rooftop

region to force transition and also to “ease a turbulent boundary layer introduction to the severe

initial Stratford gradient”. The pressure surface is modified to maintain the velocity as low as possible

to obtain maximum lift and the flow is continuously accelerated to minimize drag. The velocity at the

trailing edge is also a very important parameter that can substantially change the value of c l, but it

depends on the trailing edge geometry. The author emphasises that the new velocity distribution can

no longer be called the optimal velocity distribution in the mathematical sense, nevertheless the

term kept being used by the lack of a better term.

Figure 20: Optimum velocity distribution over an airfoil and modifications to make the airfoil feasible.

Some airfoils generated with the methodology described above were manufactured for wind

tunnel testing: the airfoils L1003 and L1004 that were designed for a Reynolds number of 2 x 106, the

first for a laminar boundary layer on the rooftop region and the second for a turbulent boundary

layer all over the airfoil; the airfoils LA 2563, LA 2564 and LA2566 were designed for a Reynolds

number of 2.5 x105, because of the low Reynolds number LA2563 had a short rooftop length of

approximately 25% chord and a short transition ramp, LA2564 and LA2566 had the rooftop increased

to 35% chord they are identical except for the transition ramp which is longer in LA2566.

62

Previously, the airfoils were tested using a program for potential flow with boundary layer

calculation, the program predicted that the flow would remain attached for a significant angle of

attack range, a separation bubble with turbulent reattachment was predicted at the start of the

recovery region for airfoils LA2563, LA2564 and LA2566. In the development of airfoils at such low

Reynolds number the problem of where the transition will occur arises, and it can affect total drag

and cl of the airfoil, as can be observed by the wind tunnel tests performed by the author. LA1003

was designed for a laminar boundary layer on the rooftop, as predicted from the program, on the

wind tunnel tests it presented a reduction on c l,max from 2.2 to 1.0, when an early transition

happened, a few issues were reported when testing the airfoil at higher Reynolds number. LA1004

did not presented the same issues and behaved well in all Reynolds number range tested in the

tunnel. Both airfoils presented a sharp stall and no hysteresis effect on stall recovery.

The low Reynolds airfoils LA2563 and LA2564 did not performed well when the tunnel was

set to Re below 5x105, it seems that the wind tunnel used had a very low turbulence level and tests

on these airfoils were only possible using transition strips. The airfoil LA2566 performed well without

the use of transition strips, what is justified by the fact that its rooftop has a favourable gradient and

it is unlikely to premature transition at low Reynolds numbers. The presence of a transition bubble or

transition strips on the airfoil LA2566 did not appear to affect its stability of the flow on the recovery

region, which was pointed as a conservative margin on Stratford recovery and a reduction on this

margin could improve the airfoil performance. Based on these observations the author developed

the airfoil LA5055 to work at 2.5 x 105 Reynolds number, and tested it on a wing on a wind tunnel

comparing with a NACA 643-618 and obtaining better results for cl3/2/cd.

The author then discusses the modification of the airfoils developed usi ng his methodology

when designing with different constraints, for instance, the airfoil L1003 when at c l lower than 0.7

tends to have a formation of a laminar bubble at the pressure side, which increases its drag. A

modification at the leading edge making it less blunt increased the operational low drag range of the

airfoil. Thickness was also investigated, an airfoil with reduced thickness had its lift coefficient

increased however the author adverts that it might maintain the low drag with a broad range o f

angles of attack. The effect of the compressible flow is also investigated.

When considering the methodology for multi element airfoils the author states that when

the paper was published, optimized solutions for this type of airfoils were not well devel oped when

compared to single element airfoils by the lack of an operational inverse multi-element airfoil design

program. The design of such multi-element airfoils, for aircraft applications, normally involves

modifications on a previously designed cruise airfoil to provide higher lift for take-off and landing and

a few mechanical and structural constraints should also be considered. The specific problem of

finding an optimized multi-element airfoil to generate maximum lift on the other hand can be made

with relatively few constraints, for instance, when considering the classic multi element airfoil

design, the use of a slat is justified to suppress the pressure peak at the leading edge of a cruise

airfoil, when designing multi element airfoils for maximum l ift, the leading edge can be designed in a

way that a slat might not be necessary.

63

The problem of maximizing the lift of an multi-element airfoil is an attempt to design an

airfoil that Cp(x) distribution fills the maximum Cp versus x box which is bounded by Cp = 1 at the

lower boundary and Cp = Cpcrit (limited by the value of free stream Mach number) at the top

boundary, Figure 21 shows the Cp distribution for two airfoils and how they try to fill the maximum

Cp box. The two-element problem can be defined as one of determining the element chord lengths,

pressure distributions and orientation with respect to each other such that maximum c l is obtained.

The flow is required to be attached in all airfoil surfaces, the elements cannot touch each other and a

minimum gap width is define to account for boundary layer interactions.

Figure 21: examples of single and multi-element airfoils and its Cp distribution plotted inside a maximum possible Cp

box.

The author finds that the Stratford pressure recovery can also be used on the elements of a

multi-element airfoil, but the possibility of implementing the methodology and designing solutions is

limited by the lack of the inverse multi-element method. A few examples of applications for the

airfoils designed using the high lift methodology are presented by the author: high -altitude long-

endurance aircrafts, sailplanes, propellers, fans and wing of race cars. The use of these airfoils on

race cars must be made with caution since the airfoils were designed for maximum C l in a two

dimensional approach and the use of them in a low aspect ratio wing can lead to a very conservative

design in term of maximum rooftop velocity possible. The use of the Gurney flap is also described

showing the authors hypothesis on how it can increase lift and reduce drag when attached to a wing

trailing edge.

2.3.6. Numerical Optimization of Airfoils in Low Reynolds Number Flows

The problem of optimizing aerodynamic coefficients in airfoils is very important when

considering aircraft design, an airfoil with a higher aerodynamic efficiency can allow an aircraft to

have an increased range. The problem has become a more active research topic since the use of

unmanned aircraft vehicles (UAV’s) is becoming more common. Previous airfoil studies are normally

developed in a higher Reynolds number range common to light aircraft. Nelson, D.16 has developed a

16 Nelson, D., “Numerical Optimization of Airfoils in Low Reynolds Number Flows”, Journal of Aircraft, Vol. 46, No. 1,

January-February 2009.

64

study optimizing airfoils to the Reynolds number range of 1 x 105 to 5 x 105, he stated that most of

the progress on the development of airfoils in such a Reynolds number range was made by radio

controlled gliders, a few of these airfoils are taken as reference to compare with the results of the

optimization process, they have a maximum aerodynamic efficiency in the range of 70 to 86.

The optimization scheme adopted by the author is the direct gradient method and the

optimization function selected was drag. The airfoil geometry is defined by a 5th degree polynomial

equation with its coefficients being the design variables of the problem. The method finds the

gradient of the objective function at the point and takes a step on the direction that increases the

value of the function. According to the author the method is unconditionally stable, although

depending on the size of the step, a few problems can be encountered in the number of iterations to

reach the solution. He also points that a minimum thickness should also be defined as a constraint

otherwise the solutions will always tend to generate a very thin airfoil (reducing pressure drag). The

aerodynamic parameters are calculated by the XFOIL program.

In an initial optimization, optimizing for drag, the final solution had a thickness reduced from

13.7% to the constraint of 9%, it also had the camber increased to generate more lift at lower angles

of attack, the L/D ratio increased from 72 to 96. Since XFOIL is the program that calculates the

aerodynamic quantities, and its inputs are the lift coefficient and the Reynolds number, the author

varied both of the quantities, cl of 0.5, 0.8 and 1.0 and Re of 1, 2, 3.6 and 4.5 x 105. When changing

the cl, the best results obtained were from the highest lift coefficient (1.0), it had the highest L/D

ratio and minimum drag. When varying the Reynolds number the resulting optimum airfoils have

shown an increase in camber as Re increased, however the general shape was approximately the

same (thick rounded leading edge and thin highly cambered trailing edge).

When comparing the optimized airfoils with the reference ones from radio controlled gliders,

the new developed airfoils have shown a higher L/D and cd, the author justifies that high values of

drag obtained are due to a higher chord line and camber. The new airfoils also present the higher

values of L/D at smaller angles of attack when compared to the reference, this can be a desirable

characteristic, since an aircraft will be able to cruise at a smaller angle of attack. The drag polars al so

show that the optimized airfoils perform better in a region where they generate less lift. The author

also states that direct gradient method generate solutions that have a poor performance outside the

design coefficient and that the use of a polynomial to generate the airfoil imposes a limitations on

the optimization process.

2.4. Diffuser Research

In recent racing cars, the focus is partially being shifted from wings to another element,

which is proving itself to be a very delicate, but at the same pivotal , component: the diffuser.

Recently, in F1, the outcome of at least two seasons has been strongly influenced by technical

innovations on this component: the 2009 BrawnGP01 exploited the concept of a double diffuser, and

the 2011 RB8 sealed the championship with its blown diffuser. With many restrictions on the size of

the wings, and the ban of ground effect, the diffuser is now seen as a key part: it can produce

65

relevant amounts of downforce with a very little increase in drag, and this force is generally created

in the central part of the car, helping stability. It is therefore useful to examine in the depth the

physics behind this component.

Zhang17 18 19 has produced a series of papers regarding the effect of a diffuser, at different

ramp angles, on a bluff body. Experimental results were obtained in the wind tunnel at the University

of Southampton, which is equipped with a moving belt. Two different types of behaviour were

noticed, depending primarily on the diffuser angle, with the value of 10 degrees divid ing the two

zones: high ramp angles showed a drop in downforce at ride heights notably higher than what it can

be observed at low angles (see Figure 22). This massive reduction in downforce is coupled with the

appearance of extended separation bubbles at the inlet.

Figure 22: Pressure coefficient for diffuser mid-plane, experimental and LES results. From: (Puglisevich S., Page G., Large eddy simulation of the flow around a diffuser-equipped bluff body in ground effect, J. Automobile, Proceedings of the

ASME 2011 International.

Depending on both area ratio and diffuser angle, three main flow characteristics are present:

in case of low area ratios, a steady-symmetric flow is observed, regardless of diffuser angle, up to 25

degrees. At higher area ratios, the flow becomes unsteady, but still asymmetric; this kind of flow is

associated to maximum force. At area ratios higher than a certain value (6 for 25 degrees, linearly

increasing to 10 for 5 degrees), vortex breakdown is the main flow feature, leading to asymmetric

flow, separation, and ultimately to a significant loss in downforce.

Another outcome of this study is that the diffuser suffers from hysteresis at angles higher

than 15 degrees, which means that the forces and flow characteristics obtained when the body is

raised are different than when is lowered, at least in a transitional zone of ground clearance.

17 Ruhrmann, A. and Zhang, X. Influence of diffuser angle on a bluff body in ground effect. Trans. ASME, J. Fluids Engng,

2003, 125(2), 332–338.

18 Zhang, X., Senior, A., and Ruhrmann, A. Vortices behind a bluff body with an upswept aft section in ground effect. Int. J.

Heat Fluid Flow, 2004, 25(1).

19 Senior, A. and Zhang, X. The force and pressure of a diffuser-equipped bluff body in ground effect. Trans. ASME, J. Fluids

Engng, 2001, 123(1), 105–111.

66

Sampling also showed that the values were not constant, meaning that some unsteady phenomena

were taking place.

The first comprehensive study on automotive diffusers performed with modern experimental

techniques can be found in Cooper et al.20 in 1998. The main result was the definition of three main

aspects governing the behaviour of diffusers: ground effect, underbody upsweep and diffuser

pumping. The first effect is clearly related to the presence of a surface at some close distance from

the bottom of the diffuser, which induces an appreciable area ratio between inlet and outlet. The

viscosity of the fluid plays a decisive role on this feature, when the diffuser is positioned very close to

the ground. The upsweep refers to the ramp of the diffuser, which recalls the suction side of a

cambered aerofoil. Because of the direction of camber, the result of the flow climbing out of the

diffuser is primarily downforce. The last effect refers to the fact that the diffuser feeds air to a

constant-pressure environment around the car. The velocity drop that takes place as the area

increases has to be matched by an increase in pressure, which in turns reduces the pressure of the

diffuser inlet, effectively pumping down the underbody of the car.

An interesting insight into multi-channel diffusers is provided by Jowsey and Passermore21, in

2010. In this study, the behaviour of a diffuser at different ground heights is investigated in the

Loughborough University wind tunnel, which, remarkably, does not feature a moving ground;

however, the authors claim that the trends in forces can still be trusted, whereas actual values are of

little to no meaning, if resemblance to reality is sought for. The blockage ratio (5%) is also very close

to the limiting value for this kind of studies. A validation case is run without dividing the diffuser into

different channels. Features already reported in literature are generally found: maximum downforce

is at 13 degrees for all the ride heights that could possibly be included in a formula-type racing car.

Progressive reduction in downforce and corresponding increase in drag are found from 16 degrees

on. One interesting result lies in the apparent sensitiveness to diffuser length, at angles between 10

and 22 degrees.

The most relevant results for this paper are achieved when a multiple -channel diffuser is

employed. Although no big variation is measured when low angles (up to 9 degrees) are involved, at

midrange values (10 to 20 degrees), significant difference is obtained. As the ramp inclination

increases, the improvement sees a substantial increase, since separation is drastically reduced in the

lateral channels. Overall, a four-channel diffuser can lead up to a 4-5% growth in lift coefficient, with

little rise in drag. Regions in which the multi-channel diffuser works are different, depending on the

number of channels, the best trade-off being a three-channel diffuser at moderate angle of attack

(10-16 degrees) and low ride height.

20 Cooper, K. R. Bertenyi, T. Dutil, G. Syms, J. Sovran, G. The Aerodynamic Performance of Automotive Underbody Diffusers,

SAE 980030, 1998

21 Jowsey L., Passmore M., Experimental study of multiple-channel automotive underbody diffusers, Proc. IMechE Vol. 224

Part D: J. Automobile, 2010

67

A noteworthy computational study has been carried out by Puglisevich and Page22 in 2011,

when a diffuser-equipped bluff body was analysed with Large Eddy Simulation (LES) technique. The

compressible, density-based Hydra solver was employed, applied to spatially filtered, Favre Averaged

N-S equations. The sub-grid scale was resolved through a standard Smagorinsky SGS model. A model

with a fixed 13 degrees angle was utilised. Two main suction peaks were observed, with two

corresponding pressure recovery processes, one under the flat underbody, the other in the diffuser

as shown in Figure 23.

Figure 23: Influence of diffuser angle on lift coefficient, different ride heights. (From: Ruhrmann, A. and Zhang, X.

Influence of diffuser angle on a bluff body in ground effect. Trans. ASME, J. Fluids Eng, 2003, 125(2), 332–338).

Noticeably, transition to turbulence takes place in the diffuser only, whereas the upper

surface of the bluff body is laminar all the way to the outlet of the diffuser. Edge vortices are

observed from about half of the diffuser length onwards; the instantaneous position and direction

vary, but the time-averaged image is similar to what is generally found with a RANS solver. Two

counter-rotating vortices were observed in the wake, when the symmetry plane of the diffuser is

considered. The lower one is bigger than the upper one, and pushes it even more upwards; further in

the wake, the streamlines are more influenced by the lower vortex than the upper.

2.4.1. Aerodynamic Interactions

As already mentioned, just one misplaced element on a racing car can be highly detrimental

for the performance of all the other parts, and eventually result in a dramatic loss in

competitiveness. On that account, it is undoubtedly necessary to be aware of the mutual effect of

the various components; unquestionably, the two elements that affect the flow around the entire

vehicle are the front wing and wheel.

22 Pugl isevich S., Page G., Large eddy s imulation of the flow around a diffuser-equipped bluff body in ground effect, J.

Automobile, Proceedings of the ASME 2011 International Mechanical Engineering Congress, Denver, 2011.

68

2.4.1.1. Aerodynamic Interaction of an Inverted Wing with a Rotating Wheel

A study on the mutual effect of a front wing and a wheel was made by van den Berg23 (2007).

Even though some results are strictly confined to the specific experimental configuration, some

applicable trends, both in numerical results and flow characteristics, can be drawn from this

investigation.

The wing presence could help in reducing wheel lift and drag; this is remarkably

consequential since, as mentioned, the wheel accounts for a large portion of the latter. Compared to

the element in isolation, the introduction of the front wing can lead to very diverse results: a

reduction in drag of almost 15% for a very low ride height, or an increase of 23% for a h/c of 0.458. It

has to be pointed out that all these figures have been obtained with constant values of gap and

positive overlap (the wheel and the wing superimpose when viewed from the front). For the wheel,

the drag changes dramatically in a very small zone of varying ride heights, creating a step at a non -

dimensionalised ground clearance of approximately 0.35, oscillating to a certain extent only, outside

this condition. Reynolds number influence seems to be negligible.

This outcome is not straightforward to explain, and it is necessary to employ flow structures

in order to faultlessly do it. An effect that has been outlined is the “delayed separation”: the

separation point, which is right after the point of largest suction24, from the top of the wheel moves

downstream when the front wing is raised. This delay is due to two main mechanisms: for the first

the wing-induced circulation increases its effect as it is raised, inducing an opposite circulation on the

flow around the wheel; the second says that the upper vortex coming from the front wing, instead of

hitting the wheel or passing internally, is convected downstream, travels on the top on the wheel,

and postpones separation. This delayed separation moves, as said, the negative pressure peak

downstream, which means that both drag and lift are considerably larger.

The channel inflow effect is arguably the predominant one: as the flow is forced to

accelerate as it travels inside the wheels, the relative positions of vortices coming off the wing and

wheel are, again, of highest importance. Higher suction side velocities, and therefore downforce,

happen when the flap trailing edge sits in a particular position, just below the most forward point of

the wheel, allowing the vortices to be pushed inside of the wheel, reducing pressures and therefore

drag and negative lift. Additionally, it was noted that the flow never reaches stagnation conditions at

the centreline of the wheel when the wing is present. Its height varies too, and is highly dependent

on wing ground clearance. It can be stated that the main variable to consider is how the flow is

redirected around the wheel, and which part of it can be redirected between the wheels without

huge losses, to create a beneficial channel that reduces pressures on the inner side of the wheel

itself.

23 Van den Berg M.A., Aerodynamic Interaction of an Inverted Wing with a Rotating Wheel, PhD Thesis, University of

Southampton, 2007.

24 J. E. Fackrell, The Aerodynamics of an Isolated Wheel Rotating in Contact with the Ground, PhD thesis, University of

London, 1974.

69

For the wing, downforce levels exhibit a consistent trend: a clear improvement is observed

when the wing is lowered closer to the ground, very similarly to what would happen for the wing in

isolation as seen in Figure 24. From h/c=0.15 downwards, the downforce produced is even higher

than for the wing alone. Channeling effect tends to accelerate the flow on the suction surface

especially at low ride heights, and the wheel somewhat contributes to this acceleration through its

rotation. General physics are much alike what is known for the wing in isolation, with the presence

and influence of the main vortices of the wing almost unchanged. CFD showed the existence of a

third longitudinal vortex, crated by the flow field around the trailing edge of the last element, as a

result of the upwash from the wing and downwash from the wheel meeting.

Another interesting parametre is the actual distance between wheel and wing, quantified as

gap (streamwise direction) and overlap (cross-stream direction). The former apparently has a great

influence on the trajectory of the upper edge vortex, and consequently on both drag and lift, with

the manners seen before. Wing downforce is not significantly affected by this distance. Increasing

overlap slightly decreases wheel drag as shown in Figure 25, and at the same time has mixed effects

on wing downforce: positive overlap generally improves the pressure peak at low ride heights (below

0.15), but lowers downforce at h/c higher than 0.2; wing drag exhibits unclear behaviour at high

ground clearance, and is increased of values close to 50% at very low heights (below 0.1), regardless

of the actual amount of positive overlap.

To summarise on gap and overlap effect on the entire assembly, it can be stated that, as a

guideline, increasing overlap is advantageous for downforce, at cost of a large increase of drag. Gap

has a major effect on the efficiency of the channelling effect, and a precise calibration has to be put

into place depending on the geometry of the wing.

Figure 24: Lift coefficient for the front wing, in isolation (red) and with the wheel (grey). Hysteresis effect shown.

70

Figure 25: Drag coefficient for the wheel, different overlap.

71

3. First Semester Work

This section presents the work that was developed during the first semester from October 4th

to December 4th of 2012. The objectives set for this period of time; the division of tasks and how the

work was structured is also introduced.

3.1. Objectives

The main goal of the initial studies was to have a simulation of the baseline car that would

give the lift and drag values of the different components. This implied testing different approaches

and having a collection of different grid sizes and a grid dependency study that showed evidence of

grid independent results. This task was to be executed during a 2-month timeframe and it allowed

the team to understand the problem as a whole, define the tools required to solve the problem,

define a set of main constraints and draft a general strategy that could be used to proceed with the

design stage of the project in the second semester. Furthermore, given the limited knowledge of the

group members with Solid Works and STAR-CCM+ the task was divided into two subtasks, allowing

the group to tackle smaller problems before attempting to simulate the entire car. The first subtask

was to perform simulations on the front wing and the wheels in isolation. These two components

were selected as ‘case study’ components that could provide an insight primarily on different

meshing techniques and perhaps flow features that could be used on the full car. The second subtask

was to use the learning outcomes of the front wing and wheel simulation on the full car simulations.

3.2. Baseline Car Front Wing

3.2.1. Introduction

The front wing of the car, which is simply composed by the main plane wing, two flaps, the

endplate and the pylons that connect the front wing structure to the nose of the car was used to

investigate different types of meshing approaches and a general set-up that could be used for the

simulations of the full car. This was done primarily to save computational time, since small scale

testing is less time consuming that the full car simulation. In this sense, a full simulation of the front

wing with an average of 3 million cells would take an average of a quarter of the time a full car

simulation would take in Lyceum 1 with the same number of processors. This implies that different

types of meshing, prism layer configurations with different base sizes and even turbulence models

could be tested quicker. In general terms, this was the first step towards analysing the full car and it

represented a key part of the baseline analysis, since the information that was obtained from this

study was implemented into the full car analysis. Specific goals of this part were:

1. Estimate the boundary layer thickness of the front wing.

2. Evaluate the differences between the various meshing approaches in STAR-CCM+

3. Obtain acceptable y+ and boundary layer resolution.

4. Learn to overcome the issues that arise when using CFD.

72

The estimation of the boundary layer thickness coupled with an estimation of an acceptable

y+ and the number of layers within the prism layer were deemed the most important objectives of

the study. Correct description of the boundary layer is important for obtaining good results in

computational studies because the velocity gradient is largest near the wall and in order to capture

this, a large number of cells are needed25. Furthermore there are two possible approaches to resolve

the boundary layer. The first approach is to generate a prism layer with a large amount of small cells

near the surface that increase in size away from the wall to resolve the gradient and the viscous

sublayer. This approach however is computationally demanding. On the other hand, for high

Reynolds number flows when the computational cost of resolving the viscous sublayer becomes very

steep, a wall function can be introduced that reduces the computational requirements at the

expense of a small deterioration of the results. A decision on the appropriate modelling of the

boundary layer for the front wing of the car, and subsequently for the full car was made using the

outcomes of the front wing study. In addition, it was important to assess the difference between the

various volume meshing approaches available in Star-CCM+: trimmer, polyhedral and tetrahedral

mesh. The latter was not considered, because this type of meshing requires a good quality surface to

ensure a good quality volume mesh. The study was primarily focused on the differences between

polyhedral mesh, which typically has an average of 14 cell faces and a trimmer mesh which uses a

template mesh constructed from hexahedral cells from which it trims the core mesh based on the

starting surface26. According to Star-CCM+, polyhedral meshes are more accurate than trimmer

meshes but require significantly more memory. In all the simulations, the surface remesher was

selected as the preferred surface mesh generator. STAR-CCM+ includes a surface wrapper, which is

used for poor CAD geometries. The surface wrapper was not used because it could potentially alter

the geometry and as a result this could produce poor quality results. Finally, it was important to get

some experience with the software by tackling a small problem prior to simulating the full car. As

novel CFD users, it was critical to understand the challenges that arise in the grid generation process

and to devise solutions and a fundamental procedure that could be used for the entire car, which is

obviously a more complex problem. It is to be stressed that the goal of this study was not to discuss

the aerodynamic behaviour of the wing, but rather to discuss and analyse in detail the CFD

parameters that must be used to generate reliable results. Figure 26 shows the geometry of the wing

that was tested.

25 Bredberg, J., “On the Wall Boundary Condition for Turbulence Models.” Report 00/4, Department of Thermo and Fluid

Dynamics, Chalmers University of Technology, 2000.

26 STAR-CCM+ Tra ining manual Version 01/12, CD-Adapco.

73

Figure 26: Geometry of the tested wing.

3.2.2. Approach

The process that was followed to obtain a solution for the front wing was divided into four

different parts shown in Figure 27. The first stage of the process was a 2-D analysis of the wing to

obtain a first quick estimate of the boundary layer thickness. This was done in JavaFoil primarily

because the geometry of the wing with the 2 flaps could be used (as opposed to XFOIL where only

the main wing can be tested in isolation without the flaps) and because the wing can also be tested

under ground effect, which is known to alter significantly the state of the boundary layer5. From the

CAD geometry given, it is known that the baseline model uses the aerofoil profile NASA/LANGLEY

LS(1)-0413 in the main wing and the flaps of the front wing. This aerofoil profile along with the same

flap arrangement of the baseline car was introduced into JavaFoil to simulate the flow. The Reynolds

number was taken with respect to the chord of the wing (from leading edge of the main wing to the

trailing edge of the second flap) giving roughly a Reynolds number of 345,080. JavaFoil gave a first

estimate of the boundary layer to be approximately 1.5 mm.

During stage 2, a coarse grid (250,000 cells) was generated and the settings used were

modified accordingly to improve the mesh in key areas, such as the gaps between the wings, the

sharp edges of the geometry (where special care must be taken to place enough nodes to describe

the curvature of the surface) and the areas surrounding the front wing. In addition, at this stage,

refinement in key areas, such as trailing and leading edges and the region adjacent to the wing were

done by including control volumes that placed the bulk of the nodes near the wing. A grid

refinement study was pursued during the third stage of this process aiming to obtain grid

independent results. These results can be found in the appendix of this report. It was found that the

results were grid independent and that beyond 2 million cells the lift and drag values did not

significantly change (less than a 1% error). The results presented in this section were generated with

a grid size of 2 million cells because with coarser grids, a proper resolution of the surface of the

74

geometry could not be obtained so that fidelity in the results could not be guaranteed. Furthermore

as the grids were refined, the quality of these meshes was monitored to ensure the refinement

process did not alter any of the important grid qualities.

Stages two and three of this process were carefully treated by following an iterative process

that lead up to seventy simulations in total. In those simulations a wide variety of meshing

approaches was tested and its posterior analysis during stage 4 gave proper settings and parameters

that were used in the full car simulations aiming to save computational time. The impact that the

turbulence models may have on the results was not investigated in detail. Turbulence models s uch as

the Spalart-Allmaras, K-Epsilon and K-Omega were attempted. The results presented here make use

of the K-Epsilon turbulence model.

Figure 27: Approach for the front wing test.

3.2.3. Results

3.2.3.1. Domain Size Study

A domain size study was carried out to establish the appropriate length of the domain for

which the results are independent of the dimensions of the domain. The CFD simulations of the front

wing and the car are in some sense a simulation of the wind tunnel tests that were carried out in the

R.J. Mitchell wind tunnel at the University of Southampton and for which experimental data was

obtained. While the width and height dimensions of the wind tunnel were kept the same in the

computational domain, the length of the domain does not need to be the same as the wind tunnel

length. An appropriate length must be chosen in order to obtain sensible lift and drag results that are

not altered by the proximity of the inlet or outlet. Also, an inappropriate domain dimens ion can

cause problems with the convergence of the results. A rule of thumb indicates that for a car, a good

starting point is to leave 3 car lengths in front of the model and 5 car lengths behind to ensure

domain independency. However, the front wing is a different geometry and these same guidelines

may not apply. It is to be reminded that the simulations are carried out in the incompressible regime.

The Navier-stokes and the continuity equations are used to solve the flow field. This involves solving

a Poisson equation that enforces the conservation of mass. This equation is elliptic, which in turn

implies that disturbances are felt everywhere in the flow field. In this sense, the outlet and inlet need

to be far enough from the model so that if a quantity is measured in a plane at either end of the

tunnel, the value of the quantity is constant. For this study, the value monitored at the domain inlet

75

and outlet was the pressure. A total of two iterations were necessary to obtain domain independent

results. The first iteration used 0.8 and 1.6 car lengths in front and behind the front wing respectively

and this was still found to be small. For the second and final iteration, the domain length in front of

the front wing was approximately 3 cars and behind 5 cars in length. This was found to work as

shown in Figure 28, where the pressure is constant at either end of the tunnel. It is noted that the

pressure at the outlet is constant because the pressure outlet boundary condition enforces a

constant pressure there. Some variation is noticed at the inlet but this variation is below 1 Pa. In

addition, it could have been possible to perhaps reduce the length of the wind tunnel, as the second

iteration is perhaps an overestimation. However, the cell count did not increase significantly due to

the longer domain because most of the cells were concentrated near the wing.

Figure 28: Domain size study.

3.2.3.2. Meshing Results

The first approach tested was meshing without the prism layer mesher to check how results

behaved. A priori it is well known that a proper boundary layer resolution is needed in order to

obtain cogent drag and lift results, but it was decided to test whether comparable results to those

with prism layer could be achieved without having to generate the prism layer with all time

consuming calculations and operations that it entails in order to obtain a high quality mesh near the

surface of the body. Both polyhedral and trimmer meshes were tested, and after two simulations it

was concluded that this approach would not be valid due to the heterogeneous distribution of y + on

the wing surfaces that can be seen in Figure 29.

It is believed that this approach is not valid because Star-CCM+ meshes from the walls

outwards and without prism layer, which adapts to the curvature of the body, the two meshing

options attempted do not give a feasible grid near the surface. With the trimmer mesh the cells are

built using only vertical and horizontal faces so that the cells do not maintain a constant distance

between the surface of the body and the upper edge of the cell which results in a discontinuous

distribution of wall y+ where the curvature of the wing is more pronounced. Because the polyhedral

mesh has more faces and the grid is unstructured, it does not have this problem: all the cells grow in

size from the surface outwards. However their sizes are not homogeneous and distribution of y+ is

76

very scattered which is not desired. Hence, if the prism mesher is not employed the obtained results

are likely to be incorrect due to the poor quality cells that are obtained close to the surface and that

do not give a constant distribution of y+. To avoid this, a prism layer must be used for this project.

Figure 29: Wall y+ distribution for the front wing with no prism layer.

With the results indicating that a prism layer is necessary to obtain good results, a prism

layer was included as shown in Figure 30. The prism layer had 5 layers of 1 millimetre of thickness

each and the targeted wall y+ was 30 or above to be in the logarithmic region. While the 2-D analysis

indicated that the boundary layer thickness would be approximately 1.5 mm it was decided to

overestimate this quantity in the initial stages of this process to ensure that the boundary layer was

captured correctly. In this figure, it can also be seen the trailing edge and leading edge refinements

for each of the three elements composing the front wing. Moreover it is also noticed that the

transition from the prism layer to the outer region is done smoothly by setting a slow cell size growth

from the cells near the surface of the wings to the outer cells. This is done to avoid large cell aspect

ratio changes from regions where small cells are required to regions where large cells can be used.

Figure 30: Side view of the mesh for the front wing.

The first conclusion from this part is that the thick prism layer that was used in the front wing

caused some problems in the gaps of the wing where the grid generation software starts diminishing

the prism layer thickness. If the prism layers of the two wings are too thick, they will collide and the

77

software chops off the prism layer in the gap creating and unfeasible prism layer towards the trailing

edge of the wing. It was found that it was very delicate to get a good mesh in the tiny gaps that

separated the wings. In this regard, it may be a better option to generate the wings of the car (e.g.

front and rear wing) with a wall y+ of 5 or below so as to obtain a smaller prism layer that would not

cause problems on the small gaps that separate the wings.

Figure 31 shows the results for the front wing with prism layer. The two cases in the upper

part of the figure shows the case where y+ was less than 5 on the suction surface, which was found

to be the most challenging surface to meet the y+ requirements. It can be seen that most of the

suction surface of the wing is below y+ of 5. Only areas near the leading edge of the wing where the

boundary layer is starting to develop and the trailing edge are above y + of 5. It was found challenging

to obtain optimal y+ values at the trailing edge of the wing because STAR-CCM+ tends to start

reducing the prism layer thickness so that it becomes zero at the trailing edge. An attempt to solve

this was done by putting a very fine control volume in the trailing edge but it w as not found to

improve the y+ resolution. In any way, even if the y+ is below 5, to correctly resolve the viscous

sublayer it is necessary to obtain a wall y+ of 1 or less and most of the wing suction surface is above

this value. In this sense, the computational requirements would be more demanding, as more cells

would have to be placed within the prism layer. The bottom part of Figure 31 shows the pressure

surface for the wings at y+ above 30. As it can be seen, the leading and trailing edges appear to be

well in the buffer region while the rest of the surface is above y + of 30, in the logarithmic region. The

same happens in the pressure surface, where only a small portion of the leading and trailing edges

are in the buffer region. From this figure it can be seen that as the cell count increases, a larger

portion of the wings steps into the buffer region becoming very clear at 7 million cells where the

third element is mostly within y+ of 25 and 30.

Figure 31: Results for the front wing with prism layer.

These results suggest that a prism layer is necessary and that y+ of less than 5 is most likely

very expensive for the entire car as the cell count needs to increase significantly and it is complex to

generate a high quality prism layer with cells very close to the surface of the wings. Nonetheless, a

78

wall y+ of 5 or below is likely affordable for the front and rear wings since it has been discussed that

the mesh in the gaps of the multi-element wing is not properly described with a thick prism layer

required for a wall y+ of 30. In addition, it is important to not use an excessive number of cells in the

simulation because as shown above, some of the components of the car could be within the buffer

region, which cannot be resolved correctly with any of the turbulence models available in STAR-

CCM+. Furthermore, a comparison of the skin friction coefficient for the meshes without prism layer

(labelled as polyhedral and trimmer) and the mesh with y+ above 30 shown previously (shown in red)

can be seen in Figure 32. It is noted that the only mesh that gives a physical skin friction distribution

is the mesh that uses the prism layer. The other two meshes without the prism layer give in general

terms a similar behaviour of skin friction but it is discontinuous and scattered. The trimmer mesh

without prism layer gives better results than the polyhedral mesh. This along with what has been

explained earlier confirms that a prism layer must be used to get a correct physical solution.

Figure 32: Comparison of results for meshes with and without prism layer.

3.3. Baseline Car Wheel

In an open-wheel race car, the wheel accounts for a very high percentage (40% circa27) of the

total drag, making it worthwhile to investigate these devices in isolation to get a clear picture of the

fundamental mechanisms that govern the flow. Research has been carried out throughout the years

on wheel aerodynamics, but not in a systematic manner, especially when compared to other parts of

a race car. Two main reasons can explain this trend: first, the wheel is not a proper aerodynamic

device although, as it was mentioned before, large proportions of total drag can be related to it. In a

sense, the wheels are more of an unavoidable mechanical device with very little freedom in shape,

position with respect to the car and overall characteristics. The Second explanation lies in the fact

that both experiments and CFD analysis on the wheel are, in general, more complex than similar

studies on streamlined bodies such as a wing due to the intricate flow phenomena that develops on

the wake of a bluff body. Nonetheless, understanding the main flow features around the wheel in

isolation can be beneficial to the project in two ways:

27 Zhang X. et a l., Ground effect aerodynamics of race cars , Applied Mechanics Review , Transactions of the ASME, Vol . 59,

2006.

79

From a CFD point of view, the experience derived from the wheel (which is, in some

sense, the epitome of a bluff body) can be pertinent when the full car is investigated.

Analysing the wheel in isolation makes it possible to optimize the design of the parts

of the car most influenced by the wheel, i.e. the front wing and the sidepods.

Limited and scarcely coherent data are available from literature. As a matter of fact, the

relevant number of variables makes different studies challenging to compare: three main numerical

values decisively drive results, these being Reynolds number, the aspect ratio of the wheel (total

width over total height) and ground speed. A model of the influence of the first variable has been

introduced by Cogotti28, whereas trends for the other two variables are not known to the authors.

Another notable parameter is the shape of the wheel, especially the rim: the presence of a fairing, or

the different curvature of the upper part of the rim, can significantly affect the flow characteristics. In

order to validate the obtained results, various aspects were taken into consideration:

Relevant numerical values such as the lift and drag coefficients.

Flow characteristics: vortices, pressure contours and other relevant variables.

Occurrence of physical phenomena: front and rear jetting.

Convergence of pressure coefficient on the tread

In addition, a number of reference values were used to control the results that were

obtained. Moreover, from an experimental point of view, one of the very first investigations was

carried out by Fackrell24 by placing a F1 tyre in conjunction with a moving ground in the Imperial

College London wind tunnel. Later, Cogotti tried to address the problem of the Reynolds number

influence. In his study, it was found that a critical Reynolds number exists, above which the

coefficients stop to drop and their values become almost constant. One more recent enquiry was

done by Mears29, who analysed the wheel both in stationary and rotating condition. Furthermore,

Axon30, used one more validation based on a CFD code. Finally, before introducing the results of the

CFD simulations, it should be noted that, in literature, the only mention for a level of repeatability for

experimental values was found in Stapleford31, who mentioned a ±0.10 for drag coefficient, and

±0.15 for lift coefficient. These high values might be a consequence of the intrusive nature of the

measuring device, which could produce biased results. Relevant data used for comparison is shown

in Table 4.

28 A. Cogotti , Aerodynamic characteristics of car wheels. Int. J. of Vehicle Design, pages 173-196, 1983. Special Publication

SP3.

29 Mears , Andrew Paul (2004) The aerodynamic characteristics of an exposed racing car wheel , PhD Thesis, Durham

University.

30 L. Axon, The Aerodynamic Characteristics of Automobile Wheels - CFD Prediction and Wind Tunnel Experiment. PhD

thes is, Cranfield University: Col lege of Aeronautics, 1999.

31 W. R. Stapleford and G. W. Carr, Aerodynamic characteristics of exposed rotating wheels Technical report 1970/2, MIRA,

1970.

80

Table 4: Relevant experimental data.

Author Type AR Configuration Re GS (m/s) CD CL Fackrell (1974) WT 0.41 Stationary 5.30E+05 X 0.76 0.77 0.41 Rotating (profile 1) 5.30E+05 17.3 0.4 0.63

0.41 Rotating (profile 2) 5.30E+05 17.3 0.44 0.58 Cogotti (1983) WT ? Stationary, standard 1.10E+06 X 0.593 0.272 ? Rotating, standard 1.10E+06 35.5 © 0.579 0.18

? Stationary, special rim 1.10E+06 X 0.544 0.296

? Rotating, special rim 1.10E+06 35.5 © 0.488 0.178 Axon (1999) CFD 0.6 Rotating, 250k cells 4.00E+05 UnK 0.501 0.635 (RNG k-ε) 0.6 Stationary, 250k cells 4.00E+05 X 0.62 0.728

0.6 Rotating, 400k cells 4.00E+05 UnK 0.466 0.592

0.6 Stationary, 400k cells 4.00E+05 X 0.633 0.713


0.6 Stationary, 540k cells 4.00E+05 X 0.632 0.707


0.6 Stationary, 700k cells 4.00E+05 X 0.647 0.704 Mears (2004) WT 0.53 Stationary (press. Distr.) 2.50E+05 X 0.73 0.60 Stationary (load cell) 2.50E+05 X 0.70 N/a

Rotating (press. Distr.) 2.50E+05 14.7 0.56 0.42

Rotating (load cell) 2.50E+05 14.7 0.63 N/a

CFD (k-ε) 0.53 Rotating 2.50E+05 14.7 0.61 0.29

Legend: WT: Wind Tunnel; CFD: Computational Fluid Dynamics

The first step in this study was to select a mesh type and RANS turbulence model. Four

different configurations were attempted: The Realizable k-ε and k-ω SST turbulence models were

tested on a polyhedral and a trimmer mesh. Right from the start, the polyhedral mesh showed

problems when interacting with the central section of the wheel, creating cumbersome cells. After

several attempts, it was decided that the polyhedral mesh was not reliable enough, and the trimmer

mesh was selected. Furthermore, trimmer mesh was selected in light of the conclusions drawn from

the front wing study, which suggested that trimmer mesh was the only feasible possibility for the full

car simulations. Figure 33 shows an example of a trimmer mesh used on the wheel. Regarding the

turbulence models, no appreciable difference (under 1.5%) was found in numerical results, only a

slight difference in residuals convergence (slightly better for k -ε); therefore the choice had to be

made on the base of practicality grounds, which steered preference towards the Realizable k -ε, in

order to match the mesh-model configuration used for the full car.

Much attention was used when dealing with the wall y+, with the mesh that was carefully

tuned to obtain a value higher than 30 on almost all the surface. Three different rectangular control

volumes were used to improve efficiency (the third being before and after the contact patch). It

should be here noted that the sunken ground approach was used, instead of the more common,

easier-to-mesh but less physically correct plinth5. It was decided to not employ a prism layer around

the tyre because no evidence of the implications its use could be found in literature. Then, four

different meshes were used for the stationary wheel, and three for the rotating configuration. The

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Reynolds number, was computed to be 4.40 x 105, based on a diameter of 214 mm and a free-stream

speed (equivalent to ground speed) of 30 m/s. Other relevant data can be found in Table 5. As

mentioned, the amount of variables that can influence the force coefficients, and their relevance,

makes almost impossible to put forward a direct validation. Nonetheless, some observations can still

be made.

Figure 33: Example of a trimmer mesh for the wheel.

Table 5: Aerodynamic coefficients obtained in simulations.

AR Configuration Re GS (m/s) CD CL 0.477 Stationary, 500k cells 4.40E+05 X 0.575 0.545 - Stationary, 1m cells 4.40E+05 X 0.541 0.532

- Stationary, 2.5m cells 4.40E+05 X 0.513 0.543

- Stationary, 3.7 cells 4.40E+05 X 0.538 0.547

- Rotating, 500k cells 4.40E+05 30 0.527 0.493

- Rotating, 1m cells 4.40E+05 30 0.506 0.478

- Rotating, 2m cells 4.40E+05 30 0.545 0.477

For the stationary case, the lift shows an almost negligible oscillation around a mean value of

0.542, which is lower than the values reported by Axon and Mears; it observed that, a negative trend

with a decreasing aspect ratio exists, which would be well in accordance to the fore mentioned

value. Residuals and mesh convergence showed that this number is well within the realms of

possibility. On the other hand, the drag coefficient is less well -behaved, with the mean value of,

curiously, 0.542 as well. Other experimental and CFD results in literature vary greatly, but in general

are higher. Again, this could be a consequence of the different aspect ratio and unusual shape that

the wheel features; this would be discussed more in deep when flow characteristics are analysed.

Finally, it is to be pointed out that the stationary wheel runs were used primarily as a mesh validation

cases for the rotating simulations since the latter is the one that actually carries any interest for the

full car simulation.

The first simulations with the rotating wheel showed that a RANS approach did not work, as

residuals did not converge and force coefficients were found to oscillate significantly. This behaviour

is explained by the existence of shedding vortices behind the body, as presented by Mears6. In order

to obtain some appreciable results, it was necessary to switch to an unsteady RANS (URANS)

analysis. The intrinsic computational requirements of the unsteady solver made possible to only run

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three different meshes, with a maximum number of cells of around 2 million. The results in this case

were grid independent with a lift coefficient tending to a value of 0.477. As mentioned earlier, it is

hard to assess the validity of this result because the experimental results in literature range from

0.18 to 0.63 while CFD analyses range from 0.29 to 0.635. The most recent wind tunnel investigation

by Mears, however, showed a value of 0.42, which presents a 10% discrepancy with the value

obtained in the CFD study presented here.

To obtain an acceptable validation, it is possible to try to compare the drag coefficient. The

values oscillate within a range that is around 7% of the maximum value, with the average at 0.529.

For the drag, results found in literature seem to be in better accordance with what has been found

here: the minimum value was observed by Fackrell (0.4), the maximum being obtained by Mears

when using the load cell (0.63). No appreciable trend can be observed when varying aspect ratio or

Reynolds number. In addition, considering recent investigations found in literature, the value is in

close agreement with what observed by Axon in the finest mesh (0.535), and not too far away from

what Mears presented in his CFD analysis (0.61). It should be noted that this last value was obtained

with standard k-ε turbulence model, which is known not to perform well in case of rapid strains 32.

An insight into the main features of the wake can help to understand more of the influence

of the wheel on the full car. The pressure contours where compared with what has been obtained by

Axon. As it can be seen in Figure 34, a decrease in pressure on the ground at midplane is present,

and is propagated downstream. In the case analysed here, the particular shape of the rim leads to

another change in pressure (probably, as it will be explained, connected to a vortex) in the upper

part of the wheel; the two zones meet downstream to create two different zones of hi gh and low

pressure in the wake.

Satisfactory results were obtained when an analogy was drawn between the vortices that

were obtained in both the near and far wake, and what has been proposed by Saddington in 200733.

A pair of counter-rotating vortices of dissimilar dimension is, in fact, present close to the wheel,

when seen from behind; eventually, the upper vortex dissipates and the lower ones is convected

downstream, as it can be observed in Figure 35. Streamlines were not thoroughly analysed in neither

of the works mentioned heretofore, and are therefore not presented here.

The third validation point relies on the presence of the physical phenomena of front and rear

jetting. The front rear jetting consists in an abrupt increase in pressure just in front of the contact

patch. The pressure coefficient was measured by Mears (1.9) and derived through CFD by Axon (1.1).

For the wheel in isolation, a value varying between 1.07 and 1.14 was obtained, depending on the

lateral position of the virtual probe. On the full car, the front wing changes considerably the pressure

32 Versteeg H.K., Malalasekera W., An Introduction to computational fluid dynamics, 1 st edition, Longman

Scientific & Technical

33 Saddington A.J., Knowles R.D., Knowles K., Laser Doppler anemometry measurements in the near-wake of an isolated

Formula One wheel, Exp Fluids (2007) 42:671–681.

83

distribution, and no significant front jetting was recorded. Rear jetting is described as the presence of

a flow that is parallel to free-stream, just behind the contact patch. Velocity vectors are acquired

either with optical methods (in wind tunnel) or plotted in CFD. The magnitude of the jetting is then

measured non-dimensionally as the ratio between the maximum velocity obtained and the free -

stream velocity. Mears, with his wheel model, obtained a value of almost 1, whereas Axon did not

register any relevant velocity. Velocity vectors coherent to free -stream were not observed in this case

either; it has to be noted, however, that the physical meaning of this phenomenon, and even its

actual existence, is still debated.

Figure 34: Pressure countours around the wheel compared with Axon (above).

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Figure 35: Tangential velocity vectors compared with Saddington’s theory (above).

In the end, it can be safely stated that the studies performed on the wheel in isolation

conform, for the vast majority, to literature results. This allows to confidently apply the findings to

the whole car, and expect the flow physics around this element to be correctly modeled.

3.4. Baseline Car Simulations

The first step in any design process is the analysis of the starting geometry. The procedure

implemented and the CFD methodology play a crucial role in establishing a consistent approach

towards producing reliable and trustworthy results. The following section provides an overview of

the steps undertaken in simulating the baseline car and the most important settings and decisions

that were made during this process.

3.4.1. Geometry and Domain

The baseline geometry used was the 2009/2010 MEng project model. The geometry

provided was saved as an Assembly in SolidWorks. It is essential to export thi s geometry as a single

part, so that the intersecting faces are eliminated; if it were exported as different parts, the surfaces

would need to be merged or imprinted in STAR-CCM+, which is both time-consuming and complex.

Some corners in the model were too sharp and had to be chamfered because during the meshing

stage, sharp corners are approximated as zero surfaces leading to generation of poor quality cells

around them. Moreover, there may be zero volume cells generated around these faces, which could

lead to a floating-point exception during computation. Another action performed on the CAD

geometry was to define an origin and a coordinate system. The general coordinate system, and the

reasons behind its choice, has already been discussed in the introduction.

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The following step was to save the current geometry as a parasolid (extension *.x_t) file.

Parasolid files save the geometry as a combination of free form surfaces in a text format. This

decreases errors while transferring (exporting or importing) between different software modules

whilst also reducing the overall size of the file. As it can be easily imagined, exporting the geometry

with the proprietary format (.sldasm) would have been more precise, since this format allows to

keep the generating curves, improving surface continuity. However, the license that enables the

direct transfer of the CAD geometry from a SolidWorks file into STAR-CCM+ was not available.

Next, the geometry was imported into STAR-CCM+ by using the ‘Import Surface Mesh’

option. STAR-CCM+ automatically tessellates all imported geometries and the quality/intensity of

tessellation can be set. Tessellation is the process of converting the surface of the geometry into

constituent planes that have no gap or overlap. Having imported the geometry into STAR-CCM+, as

shown in Figure 36 a Surface Diagnostics was performed to check for any flaws in the imported

geometry. This was done using the Repair Surface tool. The major problems rectified in this mode are

the free edges, non-manifold edges and free vertices, as these may interfere with the meshing

algorithm. The other surface errors such as Surface Proximity and poor Surface Quality are fixed by

selecting the Surface Remesher model in the mesh continuum. This will be discussed in the later

sections.

Figure 36: The model after import into STAR-CCM+.

Having performed the Surface Repair operation, the model was split into different parts, to

facilitate setting different boundary conditions, and to correctly perform the required component -

wise analysis on a later stage. This also allows customisation of mesh settings for each part. Figure 37

and Figure 38 shows the different parts into which the car was split.

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Figure 37: The car after splitting it into different parts (Upper side).

Figure 38: The car after splitting it into different parts (Lower side).

After all the part surfaces were split and named accordingly, the control volume (or

computational domain) was created. The domain is a rectangular block, with the half cross-section of

the RJ Mitchell Wind Tunnel at the University of Southampton. Furthermore, the computational

domain was split into different parts: Inlet, Outlet, Symmetry plane, Side, Top, and Ground. To save

computational cost, only half the car is simulated, assuming symmetry condition along the dividing

plane. If the CAD is cut exactly at the symmetry plane, merge and imprint operation have to be

performed in the subtract operation to ensure contact between the model and the domain surfaces.

To tackle this problem the car was cut at a plane 10 mm from the plane of true symmetry to ensure

that the subtract is carried out efficiently. Though the flow characteristics on both sides of the car

may not be the same, having a symmetry plane is justified since it is a steady RANS simulation.

Moreover, as mentioned in the assumptions part before, the car is simulated with an attitude that

corresponds to zero yaw angle (e.g. facing directly the flow) so that the flow should be symmetric.

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Since the flow around the car is modelled (and not the car itself), the volume of the fluid

region for the simulation has to be created. There are two approaches to get the fluid region in STAR -

CCM+. The first is by using the surface wrapper. The other is through the subtract operation. Surface

wrapper is usually used to provide a closed, manifold, non-intersecting surface when starting from

poor quality CAD and hence there may be a small, but significant, change to the actual geometry of

the model: this was the choice of every previous team. After discussing this solution with the

technical support at CD-adapco, it was decided that this is not fully satisfactory for the purpose of

this project. Therefore, the subtract operation was selected: this required a great amount of work to

be carried out on the initial CAD file, since this was defective in many of its parts. Anyway, this

allowed higher precision to be achieved for the final results, and is presumed to account f or the final,

although little, discrepancies that were detected. The Boolean Subtract operation removes one or

more intersecting closed volume surfaces from another closed volume surface to get the fluid region

where the flow is to be modelled. In this case, the volume of the car was subtracted from the volume

of the Block to get the fluid region.

After the subtract operation, the geometric extent of the fluid region was created by

invoking the ‘Assign Parts to Regions’ option. Here, ’One Boundary per Part Surface’ was selected, as

it is required to impose different boundary and physics conditions on different part surfaces. Figure

39 shows the domain after the subtract operation and the nomenclature followed for the different

parts of the domain were different boundary conditions are implemented.

Figure 39: The computational domain after Subtract operation.

3.4.1.1. Mesh Generation and Fundamental Settings

Meshing can be defined as the process of discretising the computational domain so that

numerical schemes can be applied to model the governing equations – in this case, steady RANS

equations. The STAR-CCM+ meshing algorithm is an unstructured meshing code and offers three

different types of meshing approaches: trimmer, polyhedral and tetrahedral. The meshing approach

adopted for this project is the trimmer mesh following the results from the preliminary studies for

the Front Wing and the Wheel in isolation. The trimmer mesh offers the best trade-off between

computational accuracy and the computational cost. Other advantages of the trimmer mesh type

include:

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Predominantly hexahedral mesh with minimal cell skewness

Curvature and proximity refinement based upon surface cell size

Surface quality independence

Optional alignment with a user specified coordinate system.

The trimmer mesh model utilises a template surface mesh made up of hexahedral cells

(based on the geometry) that contains refinement at areas of curvature and close surface proximity.

Mesh transition (from small elements to big elements) can be controlled by user defined growth

parameters. The user can also define the maximum and minimum cell size that can exist in the

domain. Another meshing model chosen was the surface remesher, which is used to re -triangulate

an existing surface in order to improve the overall quality of the surface and optimize it for the

volume mesh models. As well as improving the surface for the volume me shers it also aids the

subsurface generator when the prism mesher option is selected.

RANS Turbulence modelling in most instances needs a large concentration of cells to

correctly resolve the high gradient near the wall regions and these are assisted by the, the Prism

Layer Mesher selected in the meshing models. The prism layer mesh model is used (in conjunction

with a core volume mesh) to generate orthogonal prismatic cells next to wall boundaries. In typical

boundary layers, the flow is aligned with the wall, and the largest gradients tend to be normal to the

wall. The use of prism layers is an approach that enhances accuracy as a result of the intended

alignment of the flow with the mesh. Prism layers also allow high-aspect-ratio cells to be used in the

mesh, thus providing better cross-stream resolution without incurring in excessive stream-wise

resolution. Based on the Wheel Analysis, it was concluded that the prism layer around the wheels

was not needed therefore it was disabled. Another surface where the prism layer was not used is the

Ground, as theoretically, development of the boundary layer on a moving wall at the same speed as

the flow should be negligible. Further research into effects of changing prism layer settings is

elaborated in the Front Wing study and Prism Layer Study in this report. It is here recognised that the

presence of a Venturi on the underbody could lead to differences in velocity between the flow and

the ground; nonetheless, these discrepancies were deemed to be of little importance, since the

resolution in that zone was considered to be capable of well resolving the flow characteristics.

Ideally, a finer mesh gives more accuracy in the results, but having a really fine mesh can be

computationally costly. Hence, it is a better strategy to refine the mesh in areas of the flow where

important flow phenomena can be observed (such as the wake area, near region of the model or the

boundary layer). This can be done in STAR-CCM+ using the Volumetric Control option in Meshing. A

volumetric control expedites the increase of mesh density for a surface and/or volume mesh based

on a volume shape (block, cone, cylinder or sphere). The mesh size in each of these shapes is input

by the user. There are five volumetric controls used in the simulations. One is for the near area of the

car where the complex geometry of the car requires better mesh refinement and hence it has a

smaller base size. Another volumetric control was created around the existing one to aid smooth

transition into large size elements far away from the car. The rest are those used for refinement the

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wake of the car. Figure 40 shows the computational domain and the different mesh densities

achieved around the car with the use of different volumetric controls.

For better resolution, following the Front Wing study, the mesh was highly refined near the

front and rear wings, as they are the most important downforce generators in the car. Special

importance was given to resolve the gap between the different elements of the front and rear wings

as mesh generation in small gaps is challenging. Moreover, in these areas, there are two prism layers

that exist in close proximity and they occupy most of the gap. This causes chopping of both the prism

layers to accommodate the gap. To overcome such a problem, the number of points -in-gap was

reduced and the layer reduction percentage (prism layer settings) was increased. Other settings for

the front and rear wings were taken from the Front Wing Analysis. Figure 41 shows the mesh around

the frontal wing of the car and Table 6: Final mesh parameters gives the settings used. Furthermore,

some surfaces in the domain are very far from the car and do not contribute to the flow around the

car. Such surfaces are set as Symmetry Plane (with slip). These surfaces are assumed to be with slip

to minimize the effect they have on the analysis of flow around the car. Figure 42 shows the mesh

around the car and the different volumetric controls that were created.

Figure 40: The Computational Domain showing some of the volumetric controls.

Figure 41: Mesh detail in the front wing.

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Figure 42: Mesh at the near area of the car.

Table 6: Final mesh parameters

COMPONENT TYPE OTHER SETTINGS

Front Wing 1ST and 2ND Elements (FW 1 & FW2) Rear Wing 1ST and 2ND Elements (FW 1 & FW2) Beam Wing

Wall with Five prism Layers; 5.0 mm thickness

Surface Size: 0.5-4% of Base Size

Front Wing 3 (FW 1) Rear Wing 3 (RW3)


Surface Size: 0.35-3% of Base Size

Front and Rear Endplates Front and Rear Struts


Surface Size: 1-10% of Base Size

Front/Rear Wheels Wall with no prism layers Surface Size: 1-20% of Base Size

Sidepod Wall with Five prism Layers; 5.0 mm thickness

Surface Size: 1-12.5% of Base Size

Diffuser Wall with Five prism Layers; 5.0 mm thickness

Surface Size: 1-10% of Base Size

Engine and Sidepod inlets Domain Outlet

Pressure Outlets Continuum values

Rest of the Model Wall with Five prism Layers; 5.0 mm thickness

Surface Size - 1-12.5% of Base Size

3.4.2. Wall y+ Approach

The wall y+ is an important parameter in CFD. This gives the non-dimensional distance of the

first element of the prism layer from the wall. STAR-CCM+ allows the user to set the value of this

parameter implicitly (through Near Wall Prism Layer Thickness). The approach adopted for the

project was to maintain the y+ above 30, as this is consistent with what prescribed for the selected

turbulence model. The values from 5 to 30 represent the transition from near wall viscous sub -layer

to the logarithmic region of the boundary layer. The approach that aims at maintaining the y+ near

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unity was abandoned, as this translates to very a fine mesh with a large number of cells, which

ultimately is computationally expensive. Further research and justification into the prism layer

settings are discussed in forthcoming sections. Moreover, the increase in the near wall prism layer

thickness is also compensated by the presence of Volumetric Controls in key areas where the flo w

has to be resolved, independent of the presence of prism layers. Figure 43 shows the mesh in the

near area of the car.

Figure 43: The wall y+ distribution around the car.

3.4.3. Boundary Conditions

Prior to the simulation of the full car, the boundary conditions were prescribed in each of the

regions that were defined in STAR-CCM+. The most important parameters are shown in Table 7. As

shown, the inlet was defined as a velocity inlet with a velocity of 30 m/s. This velocity was selected

because the baseline model was tested at this speed in the wind tunnel. Furthermore, the

turbulence intensity was set as 0.2%, which also corresponds to the turbulence intensity of the wind.

Turbulence intensity is defined as the ratio of the root-mean-square of the turbulent velocity

fluctuations to the mean velocity. It is pointed out that the magnitude of this quantity corresponds to

a very low turbulence environment that is clearly not what the car would encounter in real

conditions. The Top, Side and Middle planes were defined as symmetry planes. Top and Side are not

exactly geometric symmetry planes but the flow is expected to be symmetric with respect to those

planes. In real operation, there will be large quantities of air entering the engine and sidepod inlets

and this cannot be ignored while simulating the model in a computational domain, as this

assumption may cause great disparity in the results obtained from CFD when compared to actual

results. Hence, to accommodate the air exiting the system from these inlets, both the engine and

sidepod inlets were set as Pressure Outlets. This approach was strongly supported by the

convergence of the residuals though the team accepted the presence of a small degree of

uncertainty. A further exploration on the implications of this choice will be presented in the

preliminary studies of the second phase of the project in the next chapter. In addition, the

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simulations are conducted with moving ground with a tangential velocity of the same magnitude and

direction as the Inlet (30 m/s). Again, this emulates a real life scenario where the car is moving with

respect to the ground and the air is stationary. Also the simulations included rotating wheels, with

the rotation rate calculated with respect to their individual radii. The front wing, rear wings and the

body of the car were set as walls where the no-slip boundary condition is enforced.

Table 7: Boundary conditions and Settings used for the Simulations.

PART SURFACE BOUNDARY TYPE SETTINGS

Inlet Velocity Inlet

Streamwise velocity of 30m/s.

Turbulence intensity of 0.2% (same

as the RJ Mitchell Wind Tunnel)

Top

Side

Symmetry

Symmetry Plane Slip condition

Engine Inlet

Sidepod Inlet

Domain Outlet

Pressure Outlet Set at 0.0 Pa gauge pressure to

mimic real life operation

Ground Moving wall with tangential

velocity of 30 m/s

No prism layer to save cell count,

compensated by presence of

volumetric controls

Front Wheel

Wall with local, tangentia rotation

rate

[Axis at wheel centre]

No prism layer (from Wheel

Analysis)

Rotation rate of 44.623 rps

Rear Wheel

Wall with local, tangential rotation

rate

[Axis at wheel centre]

No prism layer (from Wheel

Analysis)

Rotation rate of 42.246 rps

Front Wing

Rear Wing Wall

Settings obtained from Wing

Analysis

Rest of the Model Wall No slip Condition

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3.4.4. Dependency Tests

In CFD, the results are only as good as the mesh that is used in the simulations. The validity

and quality of a mesh can be assessed in multiple ways but in the present study this is evaluated by

performing a dependency test. This can be done by varying the major parameters like the size of the

cells within the computational domain to obtain converged results. Converged results in this case

refer to the case where as the cell size tends to progressively smaller sizes, the variable that is being

monitored (e.g. lift or drag) does not vary sensibly or reaches a stable value. In this sense it would be

easy to just generate a mesh that is as fine as the computational resources would allow, but it is an

objective of the project (and an engineering mantra) to be as efficient as possible, meaning to seek

for the coarsest mesh that yields converged results, or that shows results that can be trusted. On the

other hand it is important to also establish the appropriate length in the streamwise direction of the

computational domain and a dependency test can also be carried out by changing the length and

monitoring how the solution changes.

3.4.4.1. Mesh Dependency

In conjunction with the methodology followed by the previous teams, a mesh dependency

test was conducted on the baseline car to get the best compromise between mesh resolution and

computational accuracy. In short, as mentioned before a coarse mesh will tend to give inaccurate

results due to presence of discretisation errors and on the other hand, an ultra-fine mesh may prove

to be computationally costly. Hence, the purpose of this test was to get a mesh that was not too fine

(possibly a coarser mesh with lesser number of elements) that had reasonably accurate results. The

accuracy of these results was tested by simulating finer meshes, obtained by varying the Base Size

parameter in the mesh continuum. The mesh with 12.5 million cells was chosen owing to the fact

that the results behaved fairly independent of the mesh upon increasing the number of elements.

Figure 44 shows the lift and drag results of the mesh dependency study.

Figure 44: Variation of CL and CD with number of elements in the mesh.

Table 8 also show the numerical values and the percentage difference in lift and drag

coefficients always computed with respect to the finest mesh generated. As it can be observed the

2.00

2.10

2.20

2.30

2.40

2.50

0 2 4 6 8 10 12 14 16

Coeffi

cie

nt

of

Lift

Number of Cells [Million]

0.80

0.82

0.84

0.86

0.88

0.90

0.92

0.94

0 2 4 6 8 10 12 14 16

Coeffi

cie

nt

of

Dra

g

Number of Cells [Million]

94

coefficient of lift appears to converge as the mesh gets finer. The 12.5 million cells mesh obtains the

lowest discrepancy in both coefficient of lift and drag. The variations in coefficient of lift and drag

with mesh refinement after the baseline mesh can be attributed to many factors including but not

restricted to: y+ entering the buffer region, numerical dissipation and excessive wake refinement.

Table 8: Mesh Dependency tests

Number of Elements

(Millons) Base Size (m) CL Δ(CL) (%) CD Δ(CD) (%)

2.4 0.150 2.206 -2.62 0.894 2.41

3.3 0.120 2.235 -1.32 0.880 0.80

4.5 0.100 2.277 0.52 0.880 0.80

6.0 0.075 2.290 1.10 0.890 1.95

9.0 0.060 2.275 0.44 0.890 1.95

12.5 0.050 2.257 -0.35 0.870 -0.34

13.8 0.048 2.265 0.00 0.873 0.00

3.4.4.2. Domain Dependency

The length of the computational domain is a very important factor affecting the reliability of

the CFD analysis. As mentioned before, the cross-section dimensions of the RJ Mitchell wind tunnel

were kept the same but the length of the domain had to be adjusted to the specific geometry being

investigated, as it is highly dependent on the geometry and also on the type of flow that it generates.

In this sense, the length of the domain does not need to be the same as the wind tunnel length. For

this project, the domain length is measured in car lengths (total length of the model). There were

three domains simulated in an attempt to get appropriate streamwise dimensions:

Two car lengths in front and four car lengths in the rear of the model;

Three car lengths in front and five car lengths in the rear of the model and;

Five car lengths in front and ten car lengths in the rear of the model.

Based on the results shown in Table 9, it is possible to see that the variation in coefficient of

lift with different domain lengths is not significant. Similar to the Front Wheel analysis a criterion that

established the validity of the domain length was to measure a constant pressure on both the outlet

and inlet of the domain. The first case tested did not yield a constant pressure on the inlet but the

second and third tests did as shown in Figure Y9 (MISSING). Since the second test gave a smaller

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domain and the change in lift between the second and third tests was under 1%, it was concluded

that the domain with three car lengths in the front and five car lengths in the rear was appropriate

for the simulations.

Figure Y9: Pressure at Inlet and Outlet MISSING: TO BE ADDED AFTER WE RETURN

Table 9: Domain Dependency Test.

Configuration CL Generated

Two car lengths in front and four car lengths in the

rear of the model 2.2615

Three car lengths in front and five car lengths in the

rear of the model 2.277

Five car lengths in front and ten car lengths in the

rear of the model. 2.275

3.4.5. Other Physics Conditions

In addition to a good mesh, the physics are equally critical to the simulation as they decide

the how the actual flow field behaves and how it is resolved. The simulations were conducted

assuming incompressible conditions (Constant Density, 1.225 kg/m3). Other important settings are

discussed in brief below.

3.4.5.1. Steady State Incompressible Flow

Although the flow around the model is inherently unsteady, the CFD simulation uses steady

state equations to simplify the numerical approach as running an unsteady simulation is

computationally intensive. The steady simulation provides a representative picture of the actual flow

phenomena.

3.4.5.2. Segregated Solver

Segregated solver was chosen as the pressure-velocity solver. In a segregated solver, the flow

equations (one for each velocity component and one for the pressure) are solved in an uncoupled

manner. There are many advantages of using the segregated model: e.g. the segregated model uses

less memory than the coupled solver model.

3.4.5.3. Selecting the Turbulence Model

An appropriate turbulence model is required for resolving the flow around the model. STAR-

CCM+ includes four of the major turbulence models – the Spalart-Allmaras, k-ε, k-ω, and the

Reynolds stress transport models. For the baseline and further simulations, the realizable k-epsilon

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turbulence model was adopted. The k-ε model is a two-equation model that provides a good

compromise between robustness, computational cost and accuracy. Moreover, in its “realizable”

declination, its reliability has been proved in a relevant number of industrial case, and in general it

can be considered the standard model for this kind of application32. It captures most of the mean

flow features and is not computationally intensive like the SST models, hence converges in lesser

number of iterations.

3.4.6. Numerical Results

The simulations were run for 4000 iterations (to achieve fair convergence). By setting up

reports (Lift and Drag coefficients), component wise CL and CD were obtained. Figure 45 shows a

typical convergence plot for any of the simulations that were performed during the proj ect.

Specifically this pertains to the baseline car simulation. As it can be seen convergence of results were

reached within approximately 2000 iterations with the correct settings (e.g. Engine and sidepod

intakes as pressure outlets). It is pointed out that the first simulations carried out considered these

as walls because some of the wind tunnel experiments that were carried out had the engine and

sidepod intakes covered. The team decided to model them as actual ducts because it represents a

more realistic scenario.

Figure 45: Residuals after 4000 Iterations

Figure 46 shows the coefficient of lift of the individual components of the car. The total C L for

the car is 2.277. As expected, the largest downforce contributors are the front and rear wings with

rear wing producing (53.8%) and front wing producing (35%). This is followed by the diffuser

generating 16.29% and the sidepod generating 10.5%. The Body and the wheels are generating lift,

hence reducing the total downforce generated by the car as a whole. The discrepancy in the results

of the 2011 and 2012 baseline cars can be attributed to the difference in the mesh configurations.

The 2011/2012 project made use of a surface wrapper which could have altered the configuration.

Moreover the comparison with the previous years’ baseline simulation may be flawed due to the fact

that the baseline model for the 2013 project had an additional beam wing at the rear that generated

Engine and Sidepod intakes as walls

Engine and Sidepod intakes as Pressure Outlets

97

lift. The difference in the downforce generated by the rear wings of the two cars is ex actly the same

as the lift generated by the beam wing in the 2013 baseline. This is shown in

Table 10 and discussed in detail in the upcoming chapters. In addition to generating lift

(negative downforce) it was seen that the beam wing did not aid the diffuser as it might have been

contemplated by the designers; nor did it reduce the overall drag generated.

Figure 46: Component Wise CL Split up for 2011 and 2012 baseline cars.

Table 10: Rear wing CL showing the lift generated by the beam wing.

Rear Wing Components 2012-13 2011-12

CL (Downforce)

First Element 0.838

Second Element 0.303

Third Element 0.133

Beam Wing -0.0531

Endplate negligible

Strut / Mounting plate 0.003

Total 1.223 1.276

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Error 0.053

The drag totals at 0.870, with an overall efficiency of 2.617. The largest drag generators are

the rear wing and the wheels, producing 41% and 25% of the total drag, respectively. Figure 47

shows the component wise split up of the drag for the baseline model. The remaining components of

the car generate the rest of the drag. Further discussion in this regard is presented in the upcoming

chapters.

Figure 47: Component wise split up for CD.

3.4.7. Post Processing Baseline Car

3.4.7.1. Baseline Car Introduction

Every design process needs to clarify, as a first and foremost requirement, two points: the

start and the end. This latter is established through the definition of clear objectives, while the

former requires deep knowledge of the foundations for the project. For this study, the foundations

are represented by the initial car, which required an attentive visual investigation to begin with.

Figure 48 shows tri-dimensional views of the Baseline Car. The first feature that can be

immediately observed is the very low and curved nose, inspired by some older F1 cars (see

Figure 49). The bottom surface is almost flat, whereas the upper surface starts flat (at the

driver’s cockpit) and bends quite dramatically upstream of the front wheels. Moreover, the part of

the nosecone that “breaks” the flow seems very bulky, and it is soon identified as a possible area of

improvement. Seen from the top, the nose is highly tapered. The front wing follows a clas sical

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Body

Sidepod

Rear Wing

Wheels

Front Wing

Diffuser

Total

Body Sidepod Rear Wing WheelsFront

WingDiffuser Total

Baseline 2012-2013 0.085 0.071 0.357 0.219 0.065 0.085 0.870

99

configuration, with three elements at moderate angle of attack, not to exaggeratedly disrupt the

flow. The first two elements appear with constant chord, while the third element sees its chord

reduced below half the initial value at middle span, possibly to improve the diffuser performance.

The struts supporting the front wing follow the shape of a non -cambered aerofoil, in order to

minimise drag creation. Curiously, a lump appears on the last element, in contact with the endplate.

No one of the team members was able to hypothesise a reason for this, and further study was left

for the CFD post-processing. The last part of the front wing that caught attention was the endplate,

which exhibits a sculpted shaped, probably to manage the flow around the front wheel. Measuring

the CAD showed that the front wing was almost 70 mm (scale measure) shy of its maximum allowed

spanwise size.

Figure 48: Tri-dimensional views of the Baseline Car.

From the side view, it is possible to observe that the front wheel is singularly distant from the

front wing. This could lead to relevant masses of flow being entrained in between the wheels,

potentially nullifying the channelling effect. In the middle section of the car, the first subassembly to

analyse is the underbody. Differently from what happens in a F1 nowadays, the bottom part for this

car is not flat, but it is divided in three parts: the central diffuser and the two sidepods, which

resemble the shape of a big aerofoil. This concept is unquestionably adopted from the Lotus 79,

which reached considerable amounts of downforce with this system. What is manifest, however, is

that no relevant ground effect is permitted in this series: this ban is enforce d via the imposition of a

minimum ground clearance of 40 mm for all elements of the car. As already stated before in this

report, this height limit for a vertical skirt highly reduces the efficiency of such a system, preventing

the car from producing high forces in the sidepods, at least with a similar configuration.

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Another issue for this car is that the sidepods and the diffuser are not separated, which

means that, at the lowest point of the sidepod, the two are eventually merged, which could lead to

flow moving fore and aft from the point of higher pressure to the area of lower pressure, inducing

high turbulence, possibly vortices, and a general instability and unsteadiness, which would, in all

likelihood, remarkably diminish the amount of downforce that the underbody could produce. It is

also to be noted that the exit of the sidepod is partially obstructed by the wheel, which possibly

reducesthe effective area ratio and therefore maximum expansion. The last remarks, for the sidepod,

regarded the absence of a sideplate and the presence of the exhaust on the top surface, disrupting

the flow.

Right from the start, the possibility of introducing a more modern configuration, with a T-

tray and a flat bottom, was discussed upon. Being this a radical modification, the decision was

postponed, in order to obtain better ground to base the resolution on. The inlet of the Venturi raised

questions on its efficiency, and in particular the very thick wall that obstrucst the flow path at the

contraction section. The two side walls, which shall be referred to as splitters for the remainder of

the report, can be seen in the bottom view. As a matter of fact, they present a combined thickness

almost equal to the diffuser inlet itself. Furthermore, the high curvature side wall that directs the

flow to the sidepod is arguably promoting separation. In general, the area of the Venturi inlet was

deemed to be in need for a complete redesign.

Regarding the top part of the car, it was noticed that the helmet was well outside the

cockpit, a situation almost never seen in similar vehicles. Measurements revealed that, in real life,

the scaled model would translate to a helmet 400 mm-high, which is indubitably an excessive size.

The engine cover did not show any particular feature worth of attention. Moving downstream to the

rear section, it was soon noted that the struts for the rear wing would pose some problems in actual

working conditions: in particular, they are definitely too small to carry the appreciable amount of

downforce that the rear wing generates; moreover, it is not clear where they would connect to the

chassis. Although being prominently an aerodynamic study, it is still necessary, in the team’s opinion,

to make some reality checks and try to employ engineering judgement in all design stages. Another

feature of the struts lies in the fact that, unlike the front pylons, they do not include an aerofoil

shape, but are simple rectangular extrusions with sharp edges that would generate a critical amount

of turbulence and drag. The rear wing is composed of four main elements: three at the top (main

and two flaps) and a beam wing close to the diffuser. The rear wing sits low, which means that an

effective angle of attack different from the geometric is possibly induced by the upwash. The struts

are linked to the suction side of the first element only. The endplate is very simple.

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Figure 49: Comparison between Baseline car and the Benetton B190.

Finally, maximum height was measured to be 1030 mm for the bodywork and 928 mm for

the top aerofoil of the rear wing (real car measures). Minimum ground clearance was found to be 25

mm, measured from the lowest part of the wheel 34. Overall, general consensus was that the car

lacked in overall proportions and in what could be defined as “aerodynamic elegance”. Many areas of

improvement were individuated just by this visual inspection.

3.4.7.2. Analysis and Discussion of Results

The downforce coefficient values for the baseline car, split by parts, are presented in Figure

50. Some considerations can be made just by looking at it: as much as six components produce lift,

some expectedly (wheels and body), some not (beam wing and sidepod top). In particular, the rear

wheel presents a lift coefficient that is three times the one for the front wheel, meaning that it is in a

position of particularly dirty flow. It is noteworthy to recall that these coefficient cannot be

compared to the ones obtained in isolation, since they have been rescaled with the car frontal area,

and not with the wheel itself. Throughout the postprocessing, discussions and the analysis of the

results of all upcoming cars, the coefficients presented are always rescaled to the frontal area of the

car. The body and the nose combined produce a lift of 0.20, probably as a result of the high curvature

present in these components; further explanation will surely come from Cp plots. As mentioned, the

sidepod top produces, somehow surprisingly, a huge amount of positive lift, the highest by a single

component. It is therefore speculated, just looking at these figures, that a significant region of

separation is present on the top of the sidepod. The beam wing produces lift as well: however, as it is

widely known, this part is placed on a racing car just to aid the diffuser to reduce the pressure

underneath the car, and it is not relevant in downforce generation per se. It is to be investigated if

this mechanism is true for this car. The rear wing accounts for half the total downforce of the car, a

result that shows how much the car was probably optimised around this component. For

comparison, the front wing produces a limited 35%, with the sidepod and especially the diffuser

lagging behind. Just from this breakdown, it is possible to observe the immense room for

improvement existing for these two components.

34 It is not clear how this car abided by minimum ground clearance regulations. Potentially, the ride height was measured starting from the bottom surface of the added contact patch, which is unquestionably wrong from a physical perspective.

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The drag breakdown in Figure 51 shows what could have been easily predicted, i.e. that the

rear wing is producing the highest amount of the drag, with the rear wheel interestingly close. The

front wheel follows with 17% of the total drag, bringing the aggregate of the two wheels to more

than 40%. The front wing is undeniably the best component, as far as efficiency is concerned, on this

car: despite producing more than one third of the total downforce, it accounts for only 8% of the

total amount. Comparatively, the 10% value for the body show that a redesign in this area, from a

drag standpoint, is required. Diffuser and sidepod produce relatively low amount of drag, and they

do not appear to be penalising the car in this sense.

For all the upcoming cars, the overall efficiency and the balance will be computed. First, the

overall efficiency, computed as total lift over total drag, is of 2.60, a more than decent value for this

type of car, if we take into consideration the fact that it is an open-wheeler. On the other hand,

aerodynamic balance is theoretically computed as the ratio of the force vertical component

transmitted to the ground through the front axle, to the total vertical force. Calculations for the first

and last car showed that this value, which is very time -consuming to compute, can be well

approximated by the ratio of the front wing downforce to the total downforce. The balance is then

straightforwardly computed as 35%, which is not of great interest per se, but noteworthy if

compared to following iterations.

Figure 50: Downforce Breakdown for Each Component of Baseline Car.

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Figure 51: Drag breakdown for Baseline Car.

3.4.7.3. Post-processing of Results

In order to explain the results obtained, it can be useful to observe some particular physical

quantities in the most influential zones. The post-processing tools present in Star-CCM+ allow the

investigation of an outstanding number of different features at the same time, leaving to the

knowledge and expertise of the user to choose only the ones that can help building the big picture of

what is happening around the car. A post-processing section will be inserted for every car in the

correspondent chapter, and, for the sake of consistency, some figures (e.g. the pressure coefficient

ad mid-plane or the q-criterion at 10,000) will be shown for each car. Where relevant, some other

plots or images will be added in order to focus more on the distinctive characteristics of a part icular

car. In order not to be exaggeratedly tedious, not all the figures that have actually been analysed by

the group are presented, but only the one that are relevant to grasp the reasoning behind the

modifications introduced in the design process.

It was decided to always start the post-processing procedure with the pressure coefficient at

mid-plane, since this can reveal the level of performance reached by most components, such as the

wings and the diffuser. In Figure 52, the pressure coefficient is shown for the whole car at mid-plane,

and for the sidepod at its mid-plane. No comparison is available at this stage, therefore the team

members can only speculate on the effective meaning of these figures, and try to find a way to

develop the design. First, the nose shows a massive stagnation region, as a consequence of its

bluntness; moreover, its steep curvature induces a region of low pressure on the top which, coupl ed

with the wing-induced high pressure on the bottom surface, clearly pushes the nose up, inducing the

lift that has been already observed in the downforce breakdown. Arguably, this pressure raise could

result to be slightly beneficial for the upper surface of the front wing elements; in any case, the

amount of drag that it is generating is doubtlessly detrimental for the performance of the whole car.

It is at this stage decided to raise the nose, in a fashion similar to modern F1, and to reduce its

thickness at the front end, to achieve three different goals at the same time: reduce the lift and the

drag caused by this body, and increase the mass flow in the Venturi. At the same time, this would

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imply an increase in the blockage caused by the pylons: as a result, it is also decided to increase the

distance between them.

It is also questioned why the suction peak for the main element is at mid-chord, which seems

to be a curious feature, even if the various effects of the ground and of the flap is taken into account.

The entry of the Venturi channel shows an increase in pressure coefficient which effectively pushes

air out of it. The middle section shows immediately that the helmet, as it could be easily guessed, is

producing elevated amounts of drag, with two big stagnation region that can be individuated, one on

the visor, the other in the body. The presence of the step is not beneficial either, since it is causing

recirculation, with the corresponding low pressure zone generating positive lift on the body. Gi ven

the zones of low pressure on the body, it is decided to redesign the engine cover to obtain a better

flow management. The teams came also to the conclusion that a windshield was highly needed, and

that the helmet and the body should be repositioned in a more realistic way.

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Figure 52: Mid-Plane Coefficient of Pressure for Baseline car (top), Middle section (top centre), Rear section (bottom centre) Sidepod Coefficient of Pressure (bottom).

The sidepod presents a few interesting features: it can be noticed how the upper stagnation

region is very small and inside the inlet, which means that a region of low pressure is created on the

top surface, giving raise to the lift that has been already observed. A velocity plot is presented in

Figure 53 to confirm this hypothesis: the zone of reverse flow, with high magnitude for the velocity in

x-component, clearly shows that recirculation is taking place over the sidepod. Another area of low

pressure is induced by the exhaust. As previously mentioned, significant improvements, both in drag

and downforce, could be obtained developing the sidepod. In Figure 52 and Figure 53t is also

possible to observe the behaviour of the rear beam wing, which is actually much influenced by the

presence of the three elements above, and by their induced pressure. There is no relevance, from

these pictures, that this component is aiding the downforce generation of either the diffuser or the

sidepod.

Figure 53: Sidepod Velocity for Baseline.

Another feature that can help interpreting the main characteristics of the flow are the

streamlines Figure 54. From the top, it is possible to see how the very good channelling effect that is

obtained, with the flow being accelerated while it is squeezed to pass between the wheels, is

somehow worthless for the performance of the car: the portion of flow that goes inside the

contraction zone (in between the splitters) is not affected by this phenomenon, whereas the flow

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going into the sidepod slows down again after the front wheels. From the top it is also noted that a

relevant amount of flow goes through the gap formed by the front and the rear wheel, whose effect

can be debated. In this case this phenomenon is believed to notably increase drag, since it is curving

the flow. The entrainment of high-velocity, low-pressure air from the outside creates a vortex on the

inboard side of the wheel, reducing the lift. Nonetheless, it was decided to move the wheel

upstream in the following iteration, closer to the wing, to seal this gap. It can be also seen how the

flow follows nicely the engine cover for some portion, and then some large -scale vortices are created

as a consequence of the observed the discontinuities on the surface. As a result, the next iteration is

decided to be implemented with some radical changes on this section of the car, which means

redesigning the whole engine cover, smoothen the transition from this to the rear wing supports,

and make the top surface of the sidepod coplanar with the lower construction plane of the engine

cover. Another remark is that the effective width of the car gets increasingly larger as the flow

progresses downstream, meaning the relevant masses are displaced, and as a result drag increases.

From the second picture, it can be observed how the flow accelerates under the front wing

to slow down again downstream. Apparently, not much flow goes into the diffuser and the sidepod,

and a large amount of air simply goes around the car. The splitter is clearly not working as it should,

since it is pushing air outside of the Venturi. A possible oblique vortex is observed in the sidepods. In

Figure 55 the source line for the streamlines is place close to the splitters: it is easy to see how the

flow tries to escape to zones of lower pressure outside of the splitters themselves. Moreover, the

velocity-coloured streamlines show that the acceleration of the flow can definitely be increased. The

streamlines on the helmet in Figure 56 confirm what was already postulated: a huge recirculation

bubble is created in the slot between the driver and the step, with a further zone of low pressure

behind the neck of the driver. The acceleration on the helmet top probably induces a significant

amount of positive lift.

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Figure 54: Streamlines for Baseline: from the top (top image) and from the bottom.

Figure 55: Streamlines for Baseline: Particular of the Venturi contraction zone.

Figure 56: Streamlines for Baseline: Particular of the helmet.

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Figure 57 shows vorticity and velocity vectors for the rear wheel wake. It is very

straightforward to observe that the very long endplate is greatly influencing the flow structures. As it

is known, two counterotating vortices are expected behind a rotating wheel on the floor, and other

two, smaller, approximately centered at a height corresponding to the top of the wheel. What is

possibly happening for this configuration is that the two upper vortices are disrupted by the

endplate, and are not present. The outboard ground vortex is strong enough not to dissipate, and is

divided in two by the endplate, with the lower edge vortex to keep them separate and eventually

increasing their strengths. The simultaneous presence of the wheel vortex and of the sidepod edge

vortex induces a massive region of positive vorticity that improves the formation of the diffuser edge

vortex.

A relatively newly-introduced parameter to distinguish vortices is the so called Q-criterion35,

defined as:

(2)

Figure 57: Vorticity and Velocity Vectors for the wake of the rear wheel (x=1.54).

As a matter of fact, iso-surface of Q-criterion makes possible to see where rotation is

predominant over strain, by a factor depending on the value set for it. Thanks to this technique ,

many vortices can be seen in Figure 58. Dominating the scene on the front is, as expected, the edge

vortex of the front wing, responsible for downforce enhancement. This vortex, as well as the

sidepod, prevents the development of the inboard ground vortex in the wake of the wheel (B), which

appears to be very small, whereas, on the outside, the B’ vortex develops and becomes D, a

detrimental zone of low pressure that attracts flow out of the sidepod. The splitter generates two

long and narrow vortices (C) that end up in the diffuser and sidepod respectively. The sidepod edge

35 Hunt, J. C. R., Wray, A. A. & Moin, P. 1988 Eddies, s tream, and convergence zones in turbulent flows. Center for

Turbulence Research Report CTR-S88, pp. 193–208.

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vortex (E) is remarkably big and meets the internal vortex F (starting at the point of lowest suction),

forming just one big structure that improves the performance of the sidepod expansion and also

creates a region of low pressure underneath the side plate. The wake of the rear wheel is partially

clarified here: the two vortices observed either side of the endplate lose strength as the lower edge

vortex (I) gains momentum and develops downstream. The upper edge vortex is identified with J,

and is, as expected, more rotational than I. The diffuser edge vortex is in contact with the wall and

occupies about half of the total width of the diffuser, which represents room for improvement. From

this picture it is possible to see also the pair of strong counterotating vortices formed by the rear

wing strut (H), which could be easily eliminated using a better profile.

The isometric view shows some more structures: the upper edge vortex of the front

endplate, which hits the front wheel when still highly rotational (L). The vortex labelled with M is the

one generated by separation on the wheel, which apparently takes place quite early, an effect that is

sought for if drag reduction is considered. Finally, the vortex that is created on the top of the sidepod

(N) is believed to be responsible for the region of low pressure and consequent drag that was

observed before, and effort should be made in order to avoid this, and improve the pressure

difference for the two surfaces of the sidepod itself. Figure 59 shows a value for Q-criterion

appreciably higher (200,000), with an increased span for vorticity as well. This means that the

regions of the flow where rotation is highly dominant are pictured, and then coloured according the

actual vorticity. This procedure is expected to highlight the strongest vortices. At this level of Q-

criterion, only five main coherent structures are observed, with some smaller-scale local vorticity

happening behind the wheels. The three aforementioned edge vortices can be seen (A, C, G), with

the front endplate one (A) showing a highly rotational core. The upper vortex for the rear wing

endplate is perhaps the biggest structure that can be seen, meaning that significant drag is being

created in this region.

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Figure 58: Q-criterion Colored by Vorticity in Stream-wise Direction for Lower Surface of the Car (top) and Isometric View (bottom) – Q = 10,000.


3.4.7.4. Baseline Car Conclusion

From the features analysed in the previous sections, it was possible to notice that the

baseline car had several parts that were not performing well from an aerodynamic point of view and

the design could be improved by changes in key areas. It is important however to trace back the

origin of the baseline car. It was built and developed as a wind tunnel model, and throughout the

years, GDP groups tested it and attempted to improve its characteristics. It is well-known that the

process of designing, manufacturing and testing a new part for a model takes a longer time than

designing and updating a CAD model for CFD analysis. The time for development and analysis added

to the flow visualisation tools in a wind tunnel which are not as easy to manage as their counterparts

in CFD, certainly had an impact on having a design which is not optimised. Another important aspect

that should be considered is that as a real model, the baseline car must have connections and parts

that might seem inexplicable for aerodynamic purposes, but are necessary for structural reasons, to

ensure that the model will support a wind tunnel test.

After a rigorous post processing on the baseline car, the team made a long list of changes

that could be implemented on the car. However the idea behind the subsequent design was to have

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an evolution of the baseline car, instead of a radical change, in a way that the impact of the changes

could be analysed individually. For this reason, some of the modifications were not implemented on

the following car.

The group focused on trying to improve the overall flow over the car. From the previous

sections it was observed that the flow underneath the car was not performing as expected. Some

changes on the nose and on the position of the wheels could be beneficial on that region, trying to

increase the mass flow incoming the diffuser and sidepods. Despite the limitation on minimum

ground clearance imposed by the regulation, that limits the ground effect, the concept of using

Venturis on the bottom of the car for downforce generation was maintained. Regarding the flow on

the upper side of the car, changes in the geometry of the cockpit, struts and engine cover were also

attempted trying to reduce some of the positive lift and reduce the drag. The expectation of the

group was to have a considerable improvement on the overall downforce generation by allowing

more flow through the diffuser and sidepods and a slight increase i n drag, since the introduced

changes would increase the wetted area of the car.

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4. Second Semester Work

4.1. Airfoil Study

The two-dimensional aerodynamic characteristics of different airfoils were investigated in

XFLR5 and XFOIL. The main objective of the study was to analyze the lifting properties of a database

of airfoil profiles. The two computer programs used were selecte d because these panel method

based codes are powerful tools that can be used during the preliminary stages of the design process

where a quick estimate of the aerodynamic performance of the airfoil profile is required. In this

sense, the use of viscous-inviscid interaction available in these programs can be used to get a general

idea of the pressure distribution over a range of angles of attack for different profiles. Finally, some

of the most desirable geometries based on the results from the 2-D XFLR5 study were selected to

further analyze their performance using higher order modeling techniques such as CFD.

A database of 58 different airfoils was collected from several sources. The most common

airfoils were collected from the University of Illinois UIUC Airfoil Coordinates Database36. The rest

were retrieved from Enrico Benzing’s Ali Wings10, a book that lists the coordinates of airfoil profiles

with special pressure distributions. Some of these profiles were used in Formula 2 and Formula 3

during 1970s and 1980s. The profiles were simulated in free -stream and the ground effects were

ignored. It has been mentioned before the importance that ground effect plays on wing

aerodynamics but a program such as JavaFoil, which includes ground effect, is more time consuming

than XFLR5 where the entire database of profiles can be imported, a number of co nditions are

prescribed (e.g. Reynolds number, transition location) and then a batch simulation can be

implemented to analyze all the airfoils at once.

XFOIL and XFLR5 are in essence the same panel code but the former is written in fortran and

the latter in C programming language. XFLR5 also includes a more user friendly GUI that enables the

visualization of the airfoil geometry and different parameters such as the L/D, the variation of lift and

drag with angle of attack all in the same window. XFOIL was mainly used to smoothen the panel

distribution of some of the airfoils. Specifically, the profiles (Be) given in Benzing ’s book did not

include enough points to have a correct panel distribution. XFOIL was used to re -panel the airfoils

while ensuring that the original geometry was kept intact. Once the airfoils were re -paneled, the

database was imported into XFLR5 where the analysis was performed.

Before analyzing the results it is worth discussing the different approaches that can be taken to

select an appropriate airfoil for the front wing. Clearly multi-element wings are significantly different

than single element wings so that the approach for selecting the airfoils must be different. From

Smith11 it is known that in general, the more elements in a multi -element configuration the more lift

but no design guidelines are given by the author. However McBeath37 presents a detailed discussion

of wing set up and wing design for high lift. The first topic that is discussed is camber, which as

36 Urbana-Champaign, Department of Aerospace Engineering | University of Illinois. UIUC Airfoil Coordinates Database.

Retrieved on 17 February 2013

37 McBeath, S. Competition Car Aerodynamics: A Practical Handbook. 2nd edition. s.l. : Haynes Publishing, 2011

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mentioned on the literature review section has a significant effect on lift. According to McBeath, if a

low drag set up is required, the point of maximum camber should be shifted forwards. Rearward

camber induces a more progressive stall and in general has a greater effect on stall. Then the author

lists some criteria for single-element wings from which it becomes apparent that airfoils with a

camber of approximately 9% give good performance for maximum downforce configuration. Also

profiles with 18-20% thickness are said to give maximum downforce according to the author. Then

for dual element wings McBeath explains that the overlap and gap between the wings are very

important parameters for maximizing the performance of the given configuration. In this regard, the

overlap is not too critical and it is best around 1~4% of the chord of the wing. The gap should be

between 1 and 2% of the chord. The author also mentions that a thicker mainplane section works

better with flaps, especially when the flap chord is high. Then for multi-element wings the author

suggests:

The first flap is usually smaller and thicker than the second flap

Usually only a maximum of two flaps is used because optimizing a configuration with

3 or more flaps is time consuming

The combined chord of the two flaps should be around 30~40% of the total chord

The first flap angle of attack usually placed at 25~30 degrees while the second flap is

usually at 30~70 degrees relative to the mainplane

Adding a slat may prevent leading edge separation.

Finally the book includes a brief discussion on multi -tier wings. The author states that multi-

tier wings can be useful if the beam wing is placed in such a place so that it augments the low-

pressure production. This in turn aids the diffuser performance since the pressure pumping within

the diffuser could increase significantly.

The profiles tested along with the thickness and camber characteristics are included in the of

the report. The airfoil database included the LS(1)-0413 profile that is used by the baseline car in all

of the three elements that compose the front wing. In addition, it also includes the section NACA

9618 used by the 2011 GDP group on each of the three elements and by the 2012 GDP group in the

mainplane. The Eppler 423, which was used on both the flaps of the front wing by the 2012 GDP, has

also been analyzed. It is worth mentioning that the vast majority of the Be profiles are highly

cambered and present significant thickness when compared to other profiles. Camber is known to be

a significant lift contributor while thickness has a more profound impact on the pressure distribution

but a lesser effect on lift when compared to camber. The Reynolds numbe r used for the calculation

corresponds to the Reynolds number of the front wing of the car based on the full chord (leading

edge of main element to trailing edge of the third flap). For a velocity of 30 m/s and a total chord of

0.168 meters, the Reynolds number is approximately 3.22 x 105. XFLR5 uses the en method as the

transition prediction, and in the simulations carried out, the transition was forced at approximately

5% of the chord from the leading edge. This was done because in the CFD calculations the majority

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of the boundary layer developed on the wing would be turbulent. Forcing transition effectively

means that the airfoil profiles will likely stall at lower angles of attack because the boundary layer is

thicker.

Figure 60 presents the maximum coefficient of lift predicted by XFLR5 versus the camber of the

airfoils. As predicted with increasing camber, the maximum coefficient of lift should increase. It is

noteworthy that the airfoil profile selected for the baseline car has the lowest camber, but it achieves

a good level of lift. The Be airfoils populate the right hand side of the plot with most of them

obtaining significant lift at the expense of maximum curvature. These highly cambered airfoils, while

predictably obtaining significant amounts of lift, must be treated with caution because in ground

effect they could stall at low ride heights because of the pronounced curvature and the likely sharp

gradient that would form on the suction surface of the airfoil. Nevertheless this figure shows some

airfoil profiles that are good candidates to be further tested in CFD and in ground effect in an

attempt to increase the downforce levels of the front wing compared to those obtained in the

baseline car.

Figure 60: Maximum Coefficient of Lift versus camber.

Figure 61 shows the variation of coefficient of lift with angle of attack for some of the airfoils

shown previously. As it can be seen, the baseline car profile does not perform well when compared

to the other airfoils. It appears that for moderate angles of attack, such as those found on the

mainplane section, the S1210, S1223, Be 152-175 and the Be 153-126 perform much better than the

baseline profile with more than twice the lift augmentation. However it is noted that the Be 153-126

and Be 152-175 profiles have significantly higher camber than the baseline profile. The Be 183-105

and the Be 152-075 appear to be in between those profiles that show a big improvement from the

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baseline profile. They still achieve a higher lift coefficient and the camber of these profiles is not as

pronounced as for those mentioned before.

Figure 61: Coefficient of Lift against Angle of Attack.

Finally, simple 2-D RANS calculations in STAR-CCM+ were carried out to validate the results

given by the panel codes. Some of the airfoils tested were selected and run at different angles of

attack with the same conditions: free-stream velocity of 30 m/s, Reynolds number of 3.22x105, and

turbulence characteristics used on other simulations for the full car. The meshes generated for the

airfoils were for a wall y+ of 1 or lower to resolve the viscous sublayer. Realizable K -Epsilon

turbulence model was used in the simulations. The maximum boundary thickness w as estimated

analytically by using known results for a flat plate in turbulent flow. This was a highly iterative

process and sample equations used are shown in the of this report. Special attention was placed on

the prism layer of the airfoil with 20 layers within the estimated prism layer thickness to ensure that

the boundary layer was resolved correctly. Then, refinements were added at the leading and trailing

edges as well as in the wake of the airfoil in a similar manner as in the Front Wing Study and the full

car. Table 1 shows the comparison of results between the panel code and the CFD.

As it can be seen, the discrepancy of results between the CFD simulations and XFLR5 is

always below 12% error for the cases tested. The drag results are slightly worse in some instances

especially at high angles of attack for some airfoils where discrepancies are much higher. This is

expected because the drag prediction of a panel code is not as accurate as the drag prediction of

CFD. Nevertheless, taking into account that the XFLR5 simulations only took an hour and that all the

CFD process took an entire day of simulations and post-processing on Lyceum 2, it is concluded that

the low order modeling is a faster yet reliable way to obtain quick performance data of the airfoils.

This data can be analyzed and a few of the airfoils that show promising performances can be used to

perform much more detailed modeling in CFD.

The main objective of this study was to investigate and compare the performance of a

database of aerodynamic profiles using low order modeling. CFD in this instance could not be used to

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analyze the entire database due to the time restrictions of the project and the large amount of data

that 58 airfoils at 20 angles of attack would have generated. However, a panel method was selected

because of its ability to predict in general terms the pressure distributions of the airfoils and their

overall lift characteristics in a timely manner, making it the ideal preliminary design tool. An

additional goal of this study was to find profiles that have better lifting characteristics than the

baseline car profile. Finally, the study revealed that Benzing’s highly cambered airfoils generate a

significant amount of lift when compared to the baseline car front wing profile. Both of the Selig

profiles tested showed high values of lift without the high camber levels of some of the Be profiles.

Table 11: Comparison of CFD and Panel Method Results.

Airfoil AOA CL (XFLR5) CL (CFD) Error % CD (XFLR5) CD (CFD) Error %

LS(1)-0413 0 0.429 0.4242 1.131 0.015 0.0143 4.895

5 0.967 0.9543 1.331 0.018 0.0186 3.381

10 1.368 1.3935 1.2829 0.027 0.0295 8.598

17 1.583 1.48 6.959 0.075 0.0927 19.09

S1223 0 1.106 1.13097 2.217 0.0196 0.02 1.75

5 1.595 1.6265 1.967 0.0256 0.028 8.643

10 1.899 2.0154 5.751 0.0416 0.042 0.857

Be 122-185 0 1.299 1.4647 11.31 0.04236 0.0382 11.04

5 1.623 1.737 6.572 0.0697 0.0625 11.58

10 1.854 2.02 8.218 0.1095 0.105 4.362

Be 123-075 0 0.928 0.9775 5.074 0.0178 0.0182 2.143

5 1.366 1.456 6.14 0.0246 0.0255 3.529

10 1.643 1.793 8.365 0.0475 0.0429 10.65

4.2. Wing Study

Following the promising results of the 2-D airfoil study, CFD simulations of different wing

configurations have been tested in ground effect. To recall, the main objective of the airfoil study was

to investigate and compare the performance of a database of aerodynamic profiles using low order

modeling. CFD in this instance could not be used to analyze the entire database due to the time

restrictions of the project and the large amount of data that 58 airfoils at 20 angles of attack would

have imposed. However, a panel method was selected because of its ability to predict in general

terms the pressure distributions of the airfoils and their overall lift characteristics in a timely manner,

making it the ideal preliminary design tool. The study revealed that Be nzing’s highly cambered

airfoils generate a significant amount of lift when compared to the baseline car front wing airfoil or

any other conventional aerodynamic profile.

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In this study, 2-D simulations of multi-element wing structures with the addition of ground

effects were performed to investigate the performance of the Benzing profiles in multi -element

configurations and their behavior in ground effect. From the bibliographical review, it is known that

the ground has a powerful effect on the stalling and the lifting characteristics of the wing profiles. In

this sense, it was considered risky to base the decisions on whether to modify the front wing

configuration solely on the airfoil study because of the obvious assumptions that went into that

investigation (e.g. Free-stream, single-element). Hence some further testing in ground effect was

deemed important to assess the true potential of the Benzing profiles.

A total of 3 different wings were tested. The first wing configuration is the baseline

configuration. Wing 1 refers to the wing that uses the Be 152-075 as the main element, Be 152-155

for the first flap and the Be 152-125 for the second flap. On the other hand, Wing 2 uses a NACA

9618 for the main element and a Be 122-125 for the first and second flaps. The specific parameters

used are shown in Table 12 while Figure 62 shows the wing configurations. It can be seen that the

baseline wing is somewhat conservative with the lowest cambered profiles on the airfoil database.

The angles of attack are measured with respect to the ground and are also moderate. On the other

hand, Wing 1 and 2 are more aggressive configurations that aim to maximize the downforce levels of

the front wing configuration. These two wings have higher overall camber than the baseline wing

and the main elements are longer aiming to obtain higher downforce. The main elements for both

Wing 1 and Wing 2 were chosen because the camber is not as high as for the other Be profiles and

they are similar profiles to those found on the main element of the baseline wing. The first flap

changes from Wing 1 to Wing 2 from 14% to 11%. The second flap camber is about the same for

Wing 1 and Wing 2 but the former is much thicker. Furthermore, the second flap for the two designs

is about 20% shorter than in the baseline configuration. Including a longer mainplane with more

thickness and shorter flaps was done following McBeath37 recommendations. The gap and overlaps

were kept very similar to the baseline configuration. Figure 62 shows the wing configurations.

Table 12: Wing Configurations for CFD study.

Angle of Attack % of Chord Gap [mm] Overlap [mm]

Baseline Mainplane LS(1)-0413 0.35 44.7 - -

1st Flap LS(1)-0413 10.35 31.5 1 9.5

2nd Flap LS(1)-0413 20.35 23.8 1.38 8.39

Wing 1 Mainplane Be 152-075 0 48.7 - -

1st Flap Be 152-155 11 32.7 1.37 10

2nd Flap Be 152-125 23 18.6 1.18 5.9

Wing 2 Mainplane NACA 9618 -2 48.7 - -

1st Flap Be 122-125 15 32.7 1.37 10

2nd Flap Be 122-125 30 18.6 1.18 5.9

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The set up of the simulations is the same as for the airfoil study and the Front Wing study.

The same number of prism layers and boundary conditions introduced in the full car analysis were

applied. Just as before, the Realizable K-epsilon two layer all y+ treatment was used with a wall y+ of

1. Refinements near the wing and on the wake were applied to ensure the sharp gradients in these

regions were captured properly. The wing was placed at the ride height of the full car analysis and

the same domain dimensions in the streamwise direction were used (e.g. 3 car lengths in front of the

wing and 5 cars in length behind). Finally, the ground was given a velocity of 30 m/s to simulate the

same conditions of the full car. Figure 63 shows the pressure coefficient distribution on the surface of

the wing.

Clearly the pressure distribution is very different from the baseline configuration to the other

two setups simulated. Because this study is 2-D the flow characteristics simulated are similar to

those seen by the wing in the mid-plane of the full car, where the flow can be approximated as two-

dimensional. For clarity purposes the x-coordinate has been normalized. The baseline wing obtains a

suction peak on the leading edge of the main element while the other two wing configurations

obtain this peak further downstream. This is the effect of the camber of the wings. Furthermore,

Wing 2 has the suction peak further downstream because of the angle of attack at which it was

placed. As expected ground effect effectively causes the pressure surface to not feel the presence of

the ground, which appears to be similar for all the wing configurations and that is somewhat flat. It is

observed that Wing 1 main element is generating a significant amount of lift compared to the other

two configurations. The adverse pressure gradient of the main element appears to be more

demanding for Wing 1 because the suction peak is higher in magnitude and unlike the baseline wing

configuration, Wing 1 does not have a plateau where pressure is nearly constant. The pressure

recovery for Wing 1 is more demanding than for the baseline configuration. The apparent plateau

seen in the baseline configuration is slightly present in Wing 2 although not as clear. The adverse

pressure gradient of the main element in Wing 2 is very sharp and it possibly shows flow separation

at the trailing edge where the pressure is flat. Also it is noticed that making the chord of the main

element larger has a profound effect on the lift generated increasing it significantly. The effective

increase in suction for Wing 1 can be due to the camber and the two flaps that complete the

configuration. The effect of the flap is to introduce a finite pressure at the trailing edge of the main

element as it can clearly be seen. This induces a higher pressure on either surface. The aerodynamic

behavior of the flaps compared to the main element is very clear. The pressure recovery in the flaps

is more modest compared to that of the main element. The first flap of Wing 2 is generating

significantly more lift than the first flaps of the other two designs. The second flap for Wing 1 and 2 is

also generating more downforce than the baseline design especially Wing 2. From the overall

pressure coefficient it is obvious that making the main element and the first flap longer and the

second flap shorter is more beneficial. This predictably imposes a larger pressure recovery on either

the main element or the second flap but if designed carefully, it can improve the performance of the

configuration.

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Figure 62: 2-D Front Wing Configurations used for Baseline (top), Wing 1 (Centre) and Wing 2 (bottom) .

Figure 64 shows the wake velocity profiles of the wings. The velocity is measured half of the

chord downstream of the second flap where a zone of possible recirculation can be found and it is

normalized by the free-stream velocity. The vertical distance at zero corresponds to the ground. The

wake of the front wing is a very important variable that must be carefully monitored because the

performance of downstream components such as the diffuser or the sidepods depends on the flow

characteristics downstream of the front wing. In a real scenario there are mainly two types of wakes

that the front wing can produce: a wake with discrete vortex shedding due to the turbulent nature of

the boundary layer or a wake with flapping motion due possibly to large scale separation which is

detrimental to the performance of the diffuser because this component will suffer from inconstant

mass flow. As shown in the figure the velocity profiles downstream of the wing are similar. A big

difference is seen between the baseline wing and the other two wings in that there appears to be

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some recirculation immediately behind of the wing. This recirculation bubble is much more

significant for Wing 2. Clearly the wake downstream of the any of the wing configurations is not very

favorable because behind the second flap there is always a zone of very low velocity fluid. These

results possibly indicate that the flap angles for Wing 1 and 2 are too high. Furthermore Figure 65

shows a contour of the velocity in x-direction where the recirculation zones downstream of the main

element are clearly seen. The baseline configuration appears to have the best-behaved wake. Wing 2

gives the worst wake and the separation on the trailing edge of the main element is clearly observed

with a wall jet. The appearance of the wall jet is a clear indicative that the wing is possibly stalled and

is not obtaining as much downforce as it could be possible. The wall jet is not observed on either the

baseline or Wing 1 configurations. The velocity contour clearly gives a strong evidence for discarding

Wing 2 for the front wing because of the poor aerodynamic characteristics of the wake it produces.

Figure 63: Pressure Coefficient of Different Wings Tested in CFD.

Figure 64: Wake Survey Velocity Profiles for the Wings.

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Finally the skin friction coefficient is plotted in Figure 66. The baseline wing gives a very

different skin friction distribution compared to the other wing configurations. Because of the higher

camber and thickness both Wing 1 and 2 appear to have obtained higher values of skin friction on

the surface. In addition, there is a big difference between the upper and lower surfaces of the wings.

The skin friction distribution on the lower surface is very similar for every configuration. It is noted

that both Wing 1 and 2 have significant portions of the wing with skin friction close to zero, which

may indicate a fragile state of the boundary layer. No evidence of flow separation for Wing 1 was

found from the pressure distribution and velocity contours. On the other hand, separation on the

trailing edge of the main element of Wing 2 was clearly seen in Figure 65 and in the figure below the

skin friction is zero. Wing 1 clearly obtains a risky skin friction distribution since any changes to the

boundary layer can precipitate sudden flow separation. Now, the upper surface skin friction

distribution is very different. Because of the sharp suction peak of the baseline wing, the skin friction

in the leading edge is very high. The same applies to Wing 1 where the skin fricti on is highest on the

leading edge and drops progressively downstream for the main element. It is noted the rapid drop in

skin friction for all the elements which is clearly seen in Figure 65 where a “coat” of very low velocity

fluid is developed around the flaps. This is not observed in the other two wing configurations. Wing 2

is very different due to the angle of attack of the main element and the position of the suction peak:

On the leading edge the skin friction is moderate to then increase further downstream in the main

element. The flap skin friction behavior is very different as well depending on the wing analyzed.

Perhaps the most noteworthy effect is the sudden increase in skin friction for Wing 1 on the leading

edge of the flaps. This could be due to the shape of the flaps, which are highly cambered causing the

leading edge of the profile to be out of the region of influence of the wing underneath so that the

flaps are in a region of higher fluid velocity that would increase the skin friction. Also it is observed

that for Wing 2 the skin friction on the trailing edge of the flaps is significantly higher. Looking at

Figure 65, this appears to be due to the wall jet that is formed. It is seen that both flaps have higher

velocity in the vicinity region because the boundary layer of the main element is not directed

towards the flaps as seen in the other two wing configurations.

This study has shown that the Benzing profiles also perform well in ground effect significantly

maximizing the downforce of a possible front wing configuration. With this being said, it has also

been observed that the configurations tested do not produce a nicely behaved wake that would

enhance the performance of the components downstream of the front wing. Especially Wing 2 has

given a wake with a large recirculation area and a wall jet that could potenti ally worsen the

performance of the diffuser by affecting the mass flow rate entering this component. Wing 1 gave a

slight better wake with no wall jet but with a recirculation area bigger than that found on the

baseline configuration.

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Figure 65: Contours of Velocity on Streamwise Direction for Baseline Wing (top), First wing (center) and Second Wing

(bottom).

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Figure 66: Skin Friction Coefficient for the Wing Configurations.

The next step on the design process would be to test these same configurations on 3-D to

gain more realistic insight of the flow behavior and it would show whether what has been proven in

the 2-D studies is correct. However, this was not attempted as full 3-D studies are more CAD and CFD

demanding and the large time restrictions of this project did not allow this investigation to be carried

out. The question remained whether or not to move forward by changing the front wing

configuration to the Wing 1 configuration that had shown some promising results by increasing

significantly the downforce of the front wing. The team however, decided that the evidences of poor

flow characteristics on the wake of the wings tested were clear enough to discard the use of a

modified wing on the full car. It could have been possible to investigate a bit further different flap

configurations with different angles and gap/overlap values but once again this was time demanding

and the design of the full car had to move forward as the investigation of the airfoils and the design

of the car could not be done in parallel since the flow characteristics of the car are highly dependent

on the front wing. Furthermore, at the time the decision was made to abandon this airfoil research,

several components such as the diffuser and the sidepod channels appeared to be generating high

levels of downforce (significantly higher than the baseline car) and the team decided that investing

the time on optimizing the performance of these components could be more beneficial than seeking

downforce gains solely by modifying the wing profiles. Lastly, the rear wing profiles were not

investigated in isolation because the Reynolds number is different than for the front wing and it is

complicated to predict as there is an induced effective angle of attack in the region where the rear

wing is located and moreover the velocity distribution there is likely to not be constant. Hence the

airfoil profiles were not used in the front or the rear wings and the improvement in downforce of th e

car was sought in other components, primarily the sidepods and the diffuser.

4.3. Meshing Settings

Following the baseline analysis and the front wing study results, it was attempted to modify

the prism layer characteristics around the wings of the baseline car aiming to improve the quality of

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the mesh, especially in the gap regions between the wing elements. The post -processing of the

baseline car revealed that part of the prism layer was not being used to resolve the boundary layer

around the wings. The purpose of this study was to examine if with a reduction of prism layers on the

wings, hence reducing the cell count, the same results could be obtained. Three different

configurations were meshed and simulated. Aiming for a y1+ of more than 30 the number of prism

layers was reduced from the initial estimate of five to two layers for the front wing and from five to

three layers on the rear wing, attending to what is mentioned above. Two simulations were set: one

using 5 points in gaps and another using 10 points in gaps, to test as well the variation of the mesh

quality in the critical regions between the wings. In addition to this, a third simulation was carried

out looking for y+ less than unity on the front and rear wings surfaces, hence resolving the viscous

sub-layer instead of using wall functions there, to compare these results with cases using higher wall

y+ values.

Even though the viscous sub-layer was fully resolved around the wings, results for y1+ less

than unity on the wings were unexpected. The CL for the baseline car with these settings decreased

from 2.25 to 1.95, which corresponds to a 14 percent difference. This can be attributed to the

interaction of the fine prism layer on the wings’ surfaces with the much thicker prism layers on the

end-plates and the struts. Analogously, there is a fine resolution of the boundary layer on the

surfaces of the wings which is interacting with boundary layers of the end -plates and struts which

have been modelled with wall functions. The interaction of a well resolved boundary layer around

wings with under resolved boundary layers around the rest of the car was proved to not work

properly. In addition to this, the resolution of the viscous sublayer around the wings may induce

slightly different flow patterns causing deviations in the results for the full car. A sample view of the

mesh is shown below in Figure 67. Using 20 prism layers, 1.6 mm thickness and near wall prism

thickness of 2e-5 m the cell count is increased by 25% compared to the mesh using a wall y 1+ of more

than 30 (new cell count of 15 million cells). Ideally a wall y1+ of around or less than unity should be

employed for the full car to increase the fidelity of the results, however this approach was not

pursued further, as it would be significantly more expensive in terms of computational effort,

meshing and simulation times. This was thought to not be affordable by the team and the use of wall

functions was further exploited.

After the baseline simulations were run, the post-processing of results showed a boundary layer

thickness of approximately 1.5 mm for the front wing. This thickness is in accordance with the first

JavaFoil boundary layer thickness estimation that was calculated during the front wing study. As

mentioned before, the baseline car used a prism layer thickness of 5 mm, which produced poor

quality grids in the gap regions between the elements of the front wing. Similarly, the rear wing

boundary layer thickness simulated was afterwards measured to be below 3 mm. However, the gaps

between the wing elements of the rear wing (4 and 5 mm) are larger than those of the front wing

(1.2 mm and 2.55 mm), and as a consequence it is observed that each element in the rear wing has a

complete fresh boundary layer. It was assumed that the boundary layer could be visualised as the

region with velocity magnitude below the 99% of the freestream velocity, and the above mentioned

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features are observable on the suction surface of the wing and flaps. Moreover, a separation region

is seen near the trailing edge of the third element of the rear wing. It is believed that decreasing the

number of prism layers there would not result in a detriment in the resolution, since the template

growth rate was set at medium and smooth transition cells would help to resolve this high pressure

gradient region. The maximum boundary layer thicknesses for the body of the car, whose main areas

of interest are the sidepods and diffuser lower surfaces, were seen to be close to or slightly over 5

mm. With all the spotted possible improvements a postulated study was conducted on the prism

layers around the car, paying special attention to the main downforce generating elements (front

wing, rear wing, diffuser and sidepods) for the baseline half car simulations.

Figure 67: Wing-endplate prism layers interaction.

Unlike the front wing, the rear wing is not in ground effect, however it is located in a region

where the air is not entirely in freestream conditions; therefore there is an induced effective

incidence angle of the flow. By the use of a user defined field function, the flow incidence

immediately upstream of the rear wing, as shown below, was observed to be negative everywhere.

An increase in the angle of attack would derive in a thicker boundary layer, and by monitoring the

flow incidence it can be sorted out where the thicker boundary layer would developed. As seen in

figure Figure 68 the effective angle of attack is higher near the mid-plane. The resolved boundary

layer in the rear wing was therefore analysed in a plane close to the symmetry plane.

A strategy adopted in order to keep a y+ roughly over 30 and using the same physics settings of

the baseline simulations, the thickness of the first cell adjacent to the surface was set to 1 mm.

Furthermore, to simplify the prism mesh all the prism layers were set to 1 mm as well, avoiding cell

stretching in wall-normal direction and a consequently thicker prism layer (for example going from 5

to 6.1051 mm with a stretching factor of 1.1). At the trailing edges of the multi -element wings the

prism layers are subsequently chopped to fit the specified number of prism layers in the gap with the

next flap element, as seen in Figure 69. It was observed that by reducing the number of prism layers

in the front and rear wings the quality of the mesh could be increased and the results could be

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improved. The transition and volume ratios of cells in these mentioned regions were intended to

ameliorate by introducing those slight changes to the mesh.

Figure 68: flow incidence angle (9 cm upstream of main element leading edge).

The results obtained in this study were consistent with the baseline simulations. The principal

investigation was focused on the lift coefficient of the full car for each simulation, since downforce is

the major variable of interest of the project. For the simulations aiming at y + above 30 the CL

obtained were 2.245 and 2.281, using 5 and 10 points in gap respectively. The total cell count for

both meshes is almost the same with about 12 million cells and the increase in C L is synchronous

with the increase in resolution of the mesh in the gaps, but with this the prism layers have worse

quality in the gaps. Hence as previously predicted, the best approach for future analyses is to attain a

y1+ of 30 with 5 prism layers (1 mm thick each) in the full car, with 2 and 3 prism layers in the front

and rear wings respectively. Five points in gap with a search floor of 1mm was finalised. I n figures

Figure 69 and Figure 70 the simulated boundary layers are shown for the three approaches both for

the front and rear wings, and compared the five points in gap give better results. Note the improved

cell transition and resolution at the trailing edge of the rear wing first element.

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Figure 69: Front Wing simulated boundary layers (from top to bottom: baseline, new setup with 10 points in gap, new setup with 5 points in gap).

The effective angle of attack was visualised as the flow incidence angle on an upstream plane,

where the flow field approaching the rear wing is only altered by upstream geometries. This

influential parameter affecting the rear wing performance serves also to monitor whether the

solution is obtained accordingly to the baseline. For the newly tested meshes the comparison is

shown in the images below, where the minimum angle has been fixed at -15 degrees and the

maximum is auto ranged. This permits to easily check the differences between the two solutions,

presented in Figure 71 which have fairly similar distributions but with reduced overall incidence

(maximum changing from -3.6789° to -3.6318°) in the case using ten points in gap. This shows that

the new settings do not affect the flow field solution and it further supports the decision to

implement five points in gaps.

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Figure 70: Rear Wing simulated boundary layers (from top to bottom: baseline, new setup with 10 points in gap, new setup with 5 points in gap).

Figure 71: Flow incidence angle with 5 points in gap (left) and 10 points in gap (right) .

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4.4. First Design Cycle – Iteration A

4.4.1. A01 Car Introduction

Following the baseline analysis, it was evident that the car needed a major redesign in

almost all its constituent parts. It was decided to put most of the effort in the front section, in order

to remodel flow behaviour downstream, and to perfect diffuser and sidepods accordingly in a further

iteration. First, the front wing aerofoils and endplate remained unchanged. A tri-dimensional view of

the A01 Car is shown in Figure 72. The two struts were redesigned, making them slightly narrower.

They were also placed further apart as a result of a wider nose, to improve the quality and the

amount of the flow being ingested by the Venturi channel (see Figure 73). The nosecone accounts,

arguably, for the most substantial alteration to the initial design. It was, as a matter of fact,

considerably raised, giving birth to a flat, and almost completely horizontal, top surface. The nose

taper was significantly reduced, in an attempt of straightening the flow directed into the sidepods. It

was also attempted to move the stagnation point and reduce the separation on the top of the nose:

therefore, a more pointy shape was adopted in the front part.

The bottom surface was completely redesigned as well, now including a more gentle

contraction section, which was permitted by the employment of a longer nosecone. The two splitters

were moved upstream, in order to have a longer effective Venturi; they were made to be narrower

and pointier, striving to obtain a higher, and less turbulent, mass flow. It can be noted that the nozzle

section now features an increased width, coupled with a further contraction created by the splitters,

which define a channel. The front wheels were moved forward, in an effort to close the detrimental

gap created between them and the front wing. It can be observed that now the contact patch is

simulated differently from before: instead of simply adding a plinth on the bottom surface, now the

wheel is somehow “spread” on the ground, which means that the ground clearance obtained by

matching the wind tunnel ground and the contact patch is appreciably more accurate. Mesh

precision was also taken into account while designing this part.

The sidepods underwent a complete redesign, during which it was tried to eliminate the

numerous flaws detected in the baseline design. Primarily, they were stretched, exploiting the

increased length of the car, to obtain a better pressure recovery. A sideplate was added in an attempt

to generate an edge vortex, with a ramp at the end, to direct the flow over the wheel and regain

some downforce. The outlet position was modified, in order to elimate the rear wheel blockage

effect. The sidepod inlet was reduced in size, after considering that cooling is not a big issue in

hillclimb races, given the length of the courses. The diffuser showed some noteworthy changes too

as well: as anticipated, a proper channel was dug into the bottom, to avoid spillage (see Figure 74).

The diffuser was divided into two different sections, in order to get a better pumping effect, and

exploit the possibilities left open by the regulations. As it can be seen, the diffuser is now extending

more behind the rear wheels than in the baseline, and two different expansion sections can be

observed in the bottom view, in an attempt of generating two negative pressure peaks, which would

significantly increase downforce

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Figure 72: Tri-dimensional views of the A01 Car.

The top section of the car was object of a redesign that aimed principally at reducing drag

and feeding the rear wing with better flow. A little windshield was added in front of the driver to

direct airflow above the driver’s head, and two lateral elements were added, effectively surrounding

the driver, to connect the windshield and the engine cover, as shown in Figure 75 The driver was

lowered further into the car, to reduce the drag; this was made possible by a small increase in the

height of the car. The engine cover can be observed to be gentler in its streamwise curvature, and

extends well behind the rear wheel whose integration with the sidepod is again more gradual.

Further downstream, the rear wing remained unchanged in its main features, just like the front one.

The struts were redesigned, using a NACA 0012 profile to minimise drag. They were also positioned

slanted, to reduce the upwash on the beam wing. It is to be observed how, from a structural

standpoint, these struts look unquestionably more realistic than the ones employed on the baseline.

Finally, the semitrack was increased in order to maintain a similar wheelbase to track ratio.

Notable changes were introduced in this new design, and the quantity of new parts can be

quantified to be over 80%, with the wings remaining almost untouched. This was a precise design

choice: the aim of the whole process was to try to approach design issues like a modern F1

aerodynamicist, i.e. considering how to manage vortices and the vast, large -scale structures present

in the flow. Although being recognised as relevant sources of downforce, and as important

discriminants for overall performance, the aerofoils were left outside the mainstream improvement

process, and the main features of the flow were deemed to be more interesting, and their

investigation capable of resulting in higher improvements. It is here acknowledged that, altering the

aerofoils right from the beginning, could have led to a more pronounced increase in downforce in the

immediate; nonetheless, the team agreed that, on the long run, a more organic approach

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represented an alternative which could prove itself better and more adherent to actual industrial

problems.

Figure 73: The nosecone of A01, with the ideal channel created by repositioning the struts.

Figure 74: Nosecone and diffuser for A01. Highlighted in red, the contraction-expansion zone created in the central part

of the underbody.

Figure 75: Middle section of the A01, coloured in blue. Highlighted in green, the windshield. The splitter is circled in

black.

4.4.2. A01 Car Conclusion

As mentioned in the 1.3 Section, after each new car simulation on the First Design Cycle the

group had a post-processing section, from the post-processing discussion of the A01 car it was easy

to conclude that it had improved the overall performance of the baseline design. The overall

downforce was increased by more than 4% and the drag increased by 3%, resulting in an

aerodynamic efficiency increase of more than 1%. The increase was considered satisfactory since the

results presented in previous years reports were negative in the first iteration.

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The modifications implemented to improve the flow underneath the car increased the

downforce generation by the sidepods underchannels; however still not much of the flow was going

through the diffuser. The conclusion reached at this stage was that the lower pressure formed behind

the front wheels were still diverting some of the flow from its path under the car. The following

design would have to be focused on managing the flow on the front wing and front wheels;

subsequently the group agreed on testing some form of bargeboards. The group also agreed that the

A01 car made a considerable step forward on the frontal section, therefore some effort was placed in

further modifying the rear part elements of the car. The beam wing was observed to produce

positive values of lift and hence neither contributing on the overall downforce generation nor

improving the flow on the diffuser, so it was decided to remove it. A few modifications that were

suggested after the baseline car post processing were decided to be implemented in the next design,

such as the louvres on the rear endplates and the position of the rear wing, which was moved in

order to place it in a region of cleaner flow.

It was hoped that with the envisioned modifications an increase of lift would be obtained by

the increase of mass flow under the diffuser and the sidepods, and by a better positioning of th e rear

wing. A reduction of the drag would also to be expected by better managing the flow on the front

wheel and by removing the beam wing, which would allow a better design of the rear endplates

reducing its wetted area. In addition, a great expectation was placed on how the bargeboards would

perform.


The purpose of the A02 was dual: refining the features introduced in the A01, especially in

the rear section, and implementing a bargeboard to redirect flow in the sidepod area. Tri-

dimensional views of the A02-1 Car are shown in Figure 76. The first major modifications to the A01

design were attempted in the front endplate (Figure 77), which was completely changed, and was

assigned with increased flow management tasks. The endplate is now effectively made of two

parallel plates, connected by a horizontal plane on the bottom. The purpose of this configuration is

to create a channel that, aided by the additional downward-directed ramp and by the outward

curvature, blows directly on the air that is being sucked in the gap between wing and wheel,

preventing this phenomenon to happen, or at least reducing its magnitude. The enlarged horizontal

plate, in turn, is supposed to enhance the formation of the lower edge vortex. Moreover, the upper

edge is designed to reduce the strength of the vortex it forms. The onl y drawback individuated for

this component, at least in the design process, was the probable formation of two upper edge

vortices to impinge on the wheel. It was postulated that the increase in frontal area and drag would

have been negligible, since the immediate presence of the wheel downstream.

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Figure 76: Tri-dimensional views of the A02-1 car.

The nose was tapered slightly more, in an effort to reduce drag; this implied the front wing

to be marginally moved downstream to keep the same distance between the struts. The same

happened to the front wheel, in order to keep the same gap between wheel and wing. The splitter

can be seen to be better integrated in the nosecone design, with a flatter surface on the side, to

prevent vortices from being created in that zone. The sidepod was again increased in length, a

process which involved bringing the entry more upstream, closer to the front wheel: its cross -section

was also increased, by expanding its width. The lowest point of the throat was moved upstream as

well, to get a better pressure recovery. The size of the inlet was slightly reduced as well. The Venturi,

in turn, saw no changes in the central section, with the first expansion area remaining untouched.

The windshield introduced in A01, as mentioned before, directed the flow directly on the helmet,

accounting for large portions of drag. As a consequence, the entire cockpit was redesigned. A new,

gentler windshield was inserted, and moved upstream, with respect to the previous one. The lateral

elements of the cockpit were lowered and connected to the engine cover, which saw its fillets on the

top removed, in an attempt to induce premature turbulence and alleviate possible separation. As a

result of the different proportions of the car, it was considered possible to lower the helmet, which in

turn resulted in a lower engine cover. The helmet was also tilted, to some extent, backwards, to

obtain a position more similar to the real one. The air scoop kept the same area. As shown in Figure

80.

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Figure 77: Views of the endplate: on the left, the channel is highlighted in red. In the middle, a section of the endplate

showing the ramp is presented. On the right, the ramp is circled in blue, and the particular shape of the endplate at the edges is circled in green

The rear section accounted for the highest number of modifications, following the path that

was decided when designing A01. The rear wing was raised and moved downstream, in an attempt

of putting it in a region of clean air, and reducing the upwash effect from the engine cover. The

engine cover itself was extruded all the way to the end of the top surface of the diffuse r, in order to

reduce the drag induced by the recirculation created in A01. The second expansion region of the

diffuser was increased in length, and a significant angle (around 5 degrees) was introduced in the yz

plane, in order to obtain better pressure recovery and increase the pressure pumping. Regarding the

rear wing elements, they were again conserved. The beam wing was eliminated, since it produced lift

in A01, and it did not seem to help diffuser performance. This allowed to drastically reduce the s ize

of the endplates, and their effect on the wake of the rear wheel. It was therefore decided to redesign

the endplates, which ended up being more refined than the baseline. To get the optimal endplate

height, the pressure distribution on the internal side of the initial endplate was observed, and the cut

was made where the gradient was almost negligible, thus effectively keeping the principle for which

the suction surface should not “see” the pressure surface. The top and bottom edges were shaped to

reduce the downwash vortices, which are responsible of high amounts of drag. Last, louvers were

added to induce a circulation running counter to the top edge vortex, again for drag reduction

purposes, at the price of a possible small reduction in downforce, as shown in Figure 81.

As anticipated, a new element was introduced in the A02 design: the bargeboard. Its main

objective was to increment the mass flow in the sidepod e ntry. Three versions were prepared,

conceptually similar, but realised in different ways. The first bargeboard was made by protruding

forward the lateral and side plates of the sidepod, thus creating a longer channel which would feed

the sidepod, and at the same time start to accelerate the flow. The idea behind this design was to

seal the gap between the sidepod entry and the front wheel, to prevent flow from escaping on the

outside of the car. The second design was almost identical to the second, with the only change

consisting in how the sidepod was swept forward: the height of the plate was decreased while

marching upstream, which meant the flow hit a lower cross-sectional area. The third design was

much less intrusive, and involved a different functioning mechanism to obtain the same result: the

curved element just behind the front wheel has the role of curving the flow coming of the wheel

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towards the outside, preventing the wake vortices from entraining more flow coming from the

centre of the car. This bargeboard is connected to the body by a NACA 0012 aerofoil with a slight

negative (pitch-up) angle of attack, which would create lift, but at the same time curve the flow and

prepare it for the sidepod. Figure 82 shows the A02-1 and A02-3 bargeboards.

The concept behind this iteration was to improve single parts of the car that showed room

for development in the A01 car, assuming that small changes would not significantly affect the flow,

at least not enough to nullify the relevance of the observations made. It was also recognised the

importance of directing the flow around the front wheel and into the sidepod, and the bargeboards

were added as a consequence.

Figure 78: Sidepods for A02 cars. Highlighted: in red the sideplate, in orange the sidepod inlet, in blue the ramp. In the

bottom figure, the aerofoil-like shape can be appreciated.

Figure 79: Isometric view of the A02-3 car.

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Figure 80: Middle section of the A02 cars, coloured in blue. Highlighted in green, the new windshield. In the red oval, the

prolonged engine cover and the new diffuser can be seen.

Figure 81: New rear wing endplates (A02), with louvres (blue) and cuts on the upper edge to reduce drag (red).

Figure 82: Bargeboards for A02-1 (left) and A02-3 (right).

4.4.4. A02 Conclusion

The execution of the second iteration of the First Design Cycle with three cars being

designed, meshed, simulated and post processed, presented an evolution on the direction of the

concept of implementing the newly customized methodology, since the group showed the ability to

execute multiple designs in a short amount of time. The results obtained from the second iteration

however were negative in terms of lift and drag generation. All three cars tested presented a higher

drag than the baseline car and two presented considerable less downforce (more than 10%) than the

baseline car; the third one only presented a very modest increase in downforce (0.2% of increase

when compared to the baseline car). In terms of the design objectives, the second iteration was a

step back.

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The bargeboards were implemented to improve the flow underneath the car and behind the

front wheels; two of the bargeboards designed were too cumbersome, they were designed as

barriers on the flow trying to force it on the desired directions. The third design was a simple flow

diverter behind the front wheel and it presented a better result than the two others. The conclusion

was that simple modifications can generate better aerodynamic results than too intrusive ones,

moreover the modifications implemented in other parts of the car were hidden under the radical

change on the flow field caused by the sidepods. It was assessed that a further investigation of the

bargeboards, although beneficial, would be incredibly time-consuming, and therefore this route was

abandoned. Consequently, the group in unison decided the removal of the bargeboards to check

whether the other modifications that had been implemented in the second iteration would yield

positive results without the bargeboard. This was the main idea implemented in the A03 concept.


The results from the two different A02 cars showed two opposing results: the first outcome

was that the bargeboards are very delicate components, and that a very precise and rigorous study is

needed to make them work properly. The second consequence was that, apart from the

bargeboards, the rest of the car seemed to work better, and more in unison. With this premise in

mind, it was decided to remove the bargeboards and apply some very small modifications, to

discover what the real potential of the car was. Figure 83 shows tri-dimensional views of the A03 Car.

The shape of the windshield was slightly modified: the part facing the flow was made flatter. As

shown in Figure 84. Differently from A02, the fillets on the engine cover, behind the helmet, were

reintroduced. Another fillet was also added on the front edge of the splitters, in order to relieve the

pressure rise and increment the mass flow into the diffuser. The nosecone and the diffuser for the

A03 car are shown in Figure 85

Figure 83: Tri-dimensional views of the A03 Car.

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Figure 84: Particular of the windshield and the engine cover.

Figure 85: Nosecone and diffuser for A03. Highlighted in red, the improved contraction-expansion zone created in the underbody.

4.4.6. Analysis and Discussion of Results of the A03 Car

The component-wise coefficient for downforce are presented in Figure 86. The value for total

car climbed up to 2.81, distinctly outperforming all previous designs: in particular, a +25% was

obtained with respect to the baseline, and a +19% was registered against the best car at the time,

the A01. Overall, all the components, no one excluded, saw an improvement in downforce by

removing the bargeboards: specifically, the diffuser and the sidepod contributed decisively to this

leap in performance. The front wing downforce was raised over the levels of A01, with the first and

in particular the second element (+20%) to benefit more from the removal of the bargeboard, which

made possible to reach better pressure peaks on the suction surface. The endplate itself seemed to

work better, clinching a remarkable lift coefficient of 0.07, ten fold the baseline endplate. The

positive lift on front wheel decreased from the A02 designs of around 40%, but still remained higher

than A01, arguably because of the different vortices created on the inboard side of the wheel itself.

Still, it produced almost half of the lift of the rear wheel, which reached a value as low as the

baseline. Remarkably, the sum of lift generated by all the wheels is virtually the same for A 01 and

A03.

For the rest of the car, nose and body continued to produce lift, even thus to a lesser extent if

compared to the A02 series. The sidepod now receives much better-behaved flow, boasting a +10%

with respect to A01, but foremost almost double downforce when compared to the A02-1, this to

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reflect how detrimental the presence of the bargeboard was. The new diffuser, basically the only

part that showed any improvement from A01 and A02, raised its contribution to even higher figures,

reaching a total coefficient of 0.62 (almost one quarter of the total car) and a staggering +42% from

A01. The rear wing recovered some of the lost downforce, in the order of some percentage points

from both A01 and A02s. Still, it fell much behind the values of the baseline car. Overall, the removal

of the bargeboard has been beneficial for all the components, and an impressive value has been

reached for the total downforce.

The values for the drag coefficient, in percentage, can be found in Figure 87. The total value

for this iteration decrease to 0.84, as a result of the improvements on the body and around the

wheels. With respect to A01, the only component to significantly increase drag was the sidepod, with

the wheels values dropping of as much as 15%. With respect to the A02 iteration, the wings produce

more drag, both in percentage and in absolute value: this happens possibly as a result of the

increased downforce in these two components. The sidepod saw its drag to be reduced as well, both

from A01 and A02s: the difference with the first is in the shape of the upper surface that now

prevents huge amounts of separation; for the second, the disappearance of the bargeboard led to a

nicer flow which dramatically reduces drag The really surprising result from this car was,

undoubtedly, the figure achieved for the overall efficiency: the psychological barrier of 3 was broken,

and a value of 3.36 was reached, which puts the A03, at least from a theoretical point of view, in

modern F1 cars territory. This dramatic improvement is mainly to be linked to all the updates already

introduced in the A02 designs, that were however spoilt by the presence of the bargeboard, which

nullified all the possible advancements.

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Figure 86: Downforce Breakdown for Each Component of A03 and Comparison with A02-3.

As a recap, the downforce-generating components that sky-rocketed their efficiency were

predominantly two: the sidepod and the diffuser. The modifications in size for the former, and the

revision of the second expansion zone for the latter, made possible to reach high levels of downforce

without exaggeratedly worsening the drag, and without any apparent detrimental impact on the rest

of the car. In opposition to what was expected, raising the wing did not yield any significant

improvement, perhaps as a result of the reduced effective angle of attack neutralising the beneficial

effect of a cleaner flow. The balance is also lowered to a value of 30%, as a consequence of the

increased importance of sidepod and diffuser.

Figure 87: Drag Breakdown for A03.

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4.4.7. Post-processing of Results

As usual, different plots and figures are put forward, in order to better understand the

mechanism that gave rise to the differences observed in the previous paragraphs. It is to remarked

how that only plots that yielded significant differences with any of the A02 designs will be presented,

leaving aside all the figures that would not lead to any original conclusion or discovery.

The fillets applied on the splitter relieved the pressure rise in the inlet of the Venturi ( Figure

88) in the middle part of the car, the little modification in the windshield led to a reduction in the low

pressure area on top of the engine cover. In the same figure, it can be observed how the suction

peak in the diffuser increased from previous designs, and moved somewhat upstream. The biggest

improvements were obtained in the sidepod where, as it can be noted, the suction peak reaches

levels very similar to the diffuser itself, meaning that no extensive cross-stream pressure gradient

exists, which is beneficial to the performance of both components. A second suction peak is

observed more downstream in the sidepod, perhaps as an effect of the sudden expansion. A region

of low pressure is still present on the top surface of the sidepod, but it has been reduced in size.

The streamlines in Figure 89 show most of the improvements that have been made in this

car. The channelling effect is very visible one again, but this time has a significant effect on the

Venturi inlet as well, by further accelerating the flow directed towards the contraction section. The

flow behind the front wheel is remarkably cleaner than before, with some flow still escaping out of

the sidepod entry, but a reduced rate with respect to previous cars. The amount of flow displaced

around the car is definitely lower, with straighter streamlines outside the wheels. The flow into the

diffuser seems to be better than before, with the streamline clearly showing no separation taking

place, at least on the side walls.

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Figure 88: Mid-Plane Coefficient of Pressure for A03 Front section (top) and Rear section (centre). Sidepod Coefficient of Pressure (bottom).

In Figure 90 it can be seen how the fixed pressure at the sidepod inlet is affecting the area

around it: being at a nominal pressure coefficient of 0, this boundary has a pressure that is higher

than the flow that surrounds it, meaning that reverse flow takes place at the interface, rather

unphysically. This induces a chain of effects which finally results in a recirculation bubble just at the

entry of the sidepod, evidently reducing the performance of thi s part. A study has been carried out

on this phenomenon, and an account can be found in the correspondent chapter.

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Figure 89: Streamlines for A03: from the top (top image) and from the bottom.

Figure 91 shows the vorticty and velocity vectors for the wake of the front and rear wheels.

The former shows a wake that is very different from the one that was seen with the bargeboards in

their position. Many vortices can be observed, generally smaller and more coherent than what was

observed previously. The presence of the edge vortex can be seen between the body and the wheel.

In the second figure, the only difference from A02 is seen at the external side of the diffuser, where a

positive vortex is observed, pushing air into the diffuser itself and promoting the formation of the

edge vortex, which is clearly beneficial to overall performance, as confirmed by the data presented

before.

In Figure 92, the skin friction is shown for the bottom of the car, for the purpose of finding

out whether any separation is taking place on the underbody. Critical zones are observed to be the

sidepod outlet, the change in inclination between the two expansion stages in the diffuser, and the

two side walls in this component too. This suggests that a reduction in the expansion in the diffuser

could even turn out to be advantageous. This image shows also how efficient is to generate

downforce from a contraction-expansion process, i.e. the diffuser and the sidepod: less skin friction

is involved, and the form drag is, doubtlessly, higher for the wings.

Figure 90: Velocity vectors and contours at sidepod inlet.

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Figure 91: Vorticity and Velocity Vectors for the wake of the front (top, x=0.48) and rear (bottom, x=1.54) wheel.

Figure 92: Skin Friction for A03.

It can be interesting to compare the Q-criterion figures (Figure 93) with what was obtained in

A02. Thanks to this analysis, many reasons for the dramatic improvement can be found. What is seen

is that the the positive vorticity is pushed outside of the sidepod entry, helping to form an earlier

edge vortex more downstream, pushing down the side plate and improving the performance of the

sidepod. The two C vortices are smaller than before, which means that they interfere less with

sidepod and diffuser, allowing cleaner air to be fed into these two components. The two edge

vortices (E and F) in the diffuser and sidepod appear to be bigger and stronger, which explains the

great improvement obtained. From a drag point of view, the wake of the wheels appears to be less

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complex, with weaker and smaller-scale vortices: in particular, D and H are greatly reduced in

intensity with respect to the A02 designs: drag is therefore reduced, and a nicer airflow is sent to the

rear section of the car. The isometric view shows that the vortex (O) that developed on the top

surface of the sidepod is now unmistakably reduced in size, and that the D’ vortex on the upper edge

of the sidepod is smaller too. All the remaining vortices show little to no variation from A02.

In this iteration, two more quantities were investigated: the turbulent kinetic energy and the

turbulent dissipation rate. Two images that supplied fruitful information can be seen in Figure 94 and

Figure 95. In Figure 94, Just at the exit of the diffuser it is possible to see a large vortex formed inside

of the sidepod. This vortex has a low TKE which implies that it is probably convecting downstream

without too many changes, so that the fluctuations are small (steady). This is beneficial in an

expansion section because if it were unsteady this could lead to asymmetric unsteadiness and

possibly vortex burst. This also implies that the expansion angle could be increased. The higher TKE

seen outside of the diffuser and below of the flat plate is very unsteady because of the increasing

slope that induces a sharp gradient. In the following picture, the diffuser vortex can clearly be seen.

This vortex is created by the leakage of air from the outside to the inside of the diffuser. The sharp

edge where separation occurs (hence the edge vortex) creates a shear layer which divides the high-

vorticity structure on the flow and the diffuser edge vortex, causing relevant amounts of drag from

friction.

Figure 93: Q-criterion Colored by Vorticity in Stream-wise Direction for Lower Surface of the Car (top) and Isometric View

(bottom) – Q = 10,000.

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Figure 94: Turbulent Kinetic Energy for A03, x=1.24.

Figure 95: Turbulent Kinetic Energy for A03, x=1.54.

4.4.8. A03 Car Conclusion

Despite the evolution obtained by bolstering the productivity of the design process cycle

shown in the previous iteration, the results obtained were somewhat disappointing from the

aerodynamic efficiency point of view. The results that have been presented for the A03 car were

undoubtedly encouraging. It was proved that the bargeboards had “disguised” the improvements

obtained by the other changes implemented in the car and this fact represented a boost of moral, as

the changes proposed in previous iterations were moving the design in the right direction. From this

it is clear that the car designer has to be cautious when introducing significant changes into a car and

it is a better alternative to introduce little changes and assessing its performance before

implementing large amount of changes at once.

The performance of the elements was improved by a good management of the flow around

the car. The changes implemented in the front wing, nose and the splitter plates throughout this

optimisation cycle had caused a positive impact downstream. Comparing the streamlines from the

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A01 and A03 it is possible to see that the outer streamlines that were being deflected from the

centreline of the car, in the current design really were being pushed inwards, resulting in more mass

flow being fed to the diffuser and sidepod and a reduced perturbation of the flow on the vicinities of

the car.

The sidepods and the diffuser have proven to be the backbones of the downforce generation

for the full car by generating together most of the downforce. The result have shown that the

approach adopted in the first interaction by maintaining the Venturis instead of trying to implement

a modern F1 solution was proven a good design choice, since a big modification in the underfloor of

the car would have been time consuming and it would have not paid dividends in such a short time

span.

4.5. Optimisation Methodology

4.5.1. Introduction

Everyday people make predictions based on assumptions. For example when a bottle is

rolling over a table and it is about to fall one can almost instantaneously predi ct the trajectory that

the bottle is going to follow and hence intercept it before reaches the floor. Without even knowing,

the human brain has constructed a model which predicts the trajectory of the bottle based on some

assumptions such as the bottle’s velocity, acceleration, weight, etc. Obviously this model does not

exactly represent the bottle real trajectory, in fact as it happens many times the model is completely

wrong and the bottle ends up falling over. The real trajectory can be obtained by doing the proper

calculations for the acceleration depending on the time and integrating twice with respect to time to

get the bottle’s position at all instants of time. Although doing the proper calculations would lead to

the exact solution, the penalty in time would render the bottle fallen anyways. At the end, it turns

out that the prediction based on the assumptions is more effective since, it might be not as accurate

as the proper calculation, but it is faster and closer enough to save the bottle from falli ng over most

of the time.

Engineers face these kinds of situations when optimising some design. During an

optimisation process, engineers need to know how the design variables affect the performance of

what they are trying to optimise. But, as it happens in the bottle ’s example mentioned above, the

exact behaviour, or response of the design to the variables is usually unknown a priori, or at least too

expensive to calculate in terms of time or resources available. As a consequence in most cases

optimisation schemes rely on models of the problem space they are exploring. These models are

usually called surrogate models, meta-models or response surfaces. In the particular case of this

project, the flow behaviour around an open-wheeled race car is so complicated that the use of a

surrogate model becomes necessary.

As it has been mentioned before, it was decided to implement an optimisation cycle for the

second and third iterations of the car. The aim for this optimisation cycle was to fine -tune some

variables of the first iteration design using a surrogate-based approach. In this optimisation cycle two

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iterations were planned, one affected the front part of the car whereas the other affected the rear

part.

4.5.2. Optimisation Procedure

The procedure followed in this optimisation cycle can be observed in Figure 96. The first task

in an optimisation process is to decide which are the variables or parameters that are going to be

varied. This is an important decision since the design has to be sensitive enough to these parameters

so that varying them produces a wide range of solutions.

Once the variables have been chosen, some initial samples are created in CAD and analysed

in a CFD environment. After that, the results obtained from the first design population are used to

construct the surrogate model, which is then investigated seeking for a zone where the model

suggests the design can be improved. A loop then begins using the new design points suggested by

the surrogate analysis to update the model and analyse its response. This is called adaptive sampling

(box 6 in Figure 96). The additional points are not only to validate the surrogate, but also to enhance

its accuracy (Forrester38). Once the design seems to be converged i.e. it does not improve, the

process ends selecting the best design tested and not the last suggested by the surrogate model.

Figure 96: Optimisation process.

38 Forrester, A. I . J. "SESG6019 notes: Design Search and optimisation - case study 1:Fast global optimisation", 2013.

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As there is a CFD calculation involved in the process, it becomes incredibly tedious if it is not

automated in some manner. The team’s Mesh department consequently spent a significant amount

of time in automating the entire process of meshing and preparing the models for simulating on the

Lyceum2 cluster. A Java macro was developed for this purpose whose details are explained in

Appendix 5 – Macros. It is worth saying that all the process showed in Figure 96 could have not being

achieved (36 car designs were involved in this optimisation cycle) without the Java tools mentioned

above and the ease with which it can be recorded or implemented in STAR CCM+.

4.5.3. Sampling Plans

In a design environment, there always exists a possibility for improvement. Varying small

parameters of the design may increase the possibility to arrive at an ‘optimum’ – a trade-off between

the various design and performance parameters that gives an ideal result . Having arrived at the A03

design, it was decided to implement an optimisation procedure to explore this possibility of

improvement in performance of the car. With the constraints of time and computational power, a

multi-parameter optimisation involving more than two variables was ruled out as it meant

performing a large number of simulations.

The first step in an optimisation procedure is to select various values of the design variables

to be tested. Ideally, it is best to test all the possible combinations of the design variable in the

domain, but in a situation where there are constraints on the computational resources, it is wise to

select a few points in the domain to represent the entire population. The process of selecting the

representative subset within a population is defined as sampling. For any sort of optimisation, the

way in which sampling is done, is called sampling plan. The plan chosen greatly influences the result

and hence great care must be taken while populating the initial design space. There are many types

of sampling plans that are used in real life; the simplest being a random sampling. For the purpose of

optimisation, a sampling plan with a uniform but not regular spread of points across the design space

must be selected; as it would be counter intuitive to sample the same variable more than once at the

same value. This stratification is achieved by using the Latin Hypercube where the points are spread

in the manner described above. The Dr. Andras Sobester’s39 MATLAB code for Latin Hypercube

sampling is bestlh.m, provided as a part of the syllabus.

4.5.4. Surrogate Model

As it was mentioned above, when a surrogate model technique is used some assumptions

need to be made. The first assumption made here is to suppose the optimized function subject to be

continuous, which is a well-founded assumption in most engineering problems (Forrester38). The

second assumption is that the function is smooth, which is again a common characteristic of the

engineering functions1.The purpose of using surrogate models in this project was to conf irm if results

coming from the initial samples could be improved. The team then decided new design points based

on the resulting response surfaces.

39 Lecturer, University of Southampton; EPSRC/Royal Academy of Engineering Research Fellow.

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The team members acknowledge that the procedure chosen for this optimisation may not be

the best approach that could have been taken but considering the time constraints and the fact that

the project was developing at the same pace as the collective knowledge of the team, the process

was concluded satisfactorily. The car was improved during this optimisation cycle as it can be seen in

following chapters.

4.5.5. Kriging

In this project the surrogate modelling method used was Kriging (Krige40), which seems to be

the most effective and versatile method for use in engineering design and more particularly for

intensive CFD based calculations (Forrester38). In Figure 97 it can be seen how accurate the Kriging

prediction can be with only 20 points.

Figure 97: Kriging prediction for the Branin function with 20 sample points (left) compared with the true Branin function (right).

Kriging is a statistical interpolation method suggested by Krige in 1951 and mathematically

formulated by Matheron in 1963. Kriging was widely used in the context of geo-statistical problems.

In 1989, this method was extended by Sacks et al. for the design and analysis of deterministic

computer experiments41. Then it was widely used as a surrogate modelling technique for predicting

the output of computer codes in simulation-based analysis and optimisation. Kriging is based on the

idea that the value at an unknown point should be the ave rage of the known values at its

neighbours; weighted by the neighbours' distance to the unknown point. The method is

mathematically closely related to regression analysis, with the difference that where this is made for

the estimation of a single realization of a random field, regression models are based on multiple

observations of a multivariate dataset instead. Kriging is used as a basis function in optimisation

when the true objective function is computationally intensive; which is true in the case of th e

40 D. G. Krige, "A s tatistical approach to some mine va luation and a llied problems on the Witwatersrand", MSc thesis.,

University of the Witwatersrand, Johannesburg, 1951.

41 Jerome Sacks, William J. Welch, Toby J. Mitchell & Henry P. Wynn; Design and Analysis of Computer Experiments;

Statistical Science, 1989, Vol . 4 No. 4; Pages 409 – 435.

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project; the predictor and the expected improvement are obtained using the Dr Alexander

Forrester’s42 MATLAB codes predictor.m and likelihood.m

4.5.6. Infill Criteria

In the process of the Kriging-based optimisation, the global optimum can’t be found if the

user only utilizes the Kriging models built from initially sampled data, since the models are not

accurate globally. Hence, new sample points in the promising regions should be added, then the

Kriging models can be refined; this process is repeated until the global optimum is found or some

stop criteria are met. This process is so-called iterative sampling refinement (or adaptive sampling)

and the criteria to sample the promising regions are so-called infill sampling criteria (ISC). There are

many infill sampling plans, which make various assumptions to simplify the update of the response

surface. The most straightforward assumption is that the surrogate model is globally accurate and all

that is required is to evaluate the optimum of this surrogate at this point. This assumption may not

converge at the global maximum for a deceptive function. Another way is by using the expected

improvement from the Kriging to update the surface. Expected improvement may be defined as the

improvement that is expected to be achieved at an untried point. The pursuit and practice of proper

infill methods requires a fair amount of prior knowledge that the team did not possess at the time of

implementation and hence, for the first optimisation cycle in the project the team updated the

response surface by selecting the maxima in the initial surface. It was realised at a later stage in time

that it may not have been the best approach for updating the surface as the Kriging may never

converge at a global maximum. Nonetheless, this technique is still considered to fit the requirements

of the project, i.e. to improve the aerodynamic performance through a systematic and rigorous

mathematical tool.

4.6. Second Design Cycle – B Iteration

4.6.1. Optimisation Variables and Initial Sampling

For the first optimisation cycle, the two variables chosen had to be very influential on the

performance of the car and in turn had to involve a major downforce generating component.

Moreover, the variables should not be time consuming to change at the CAD level. Hence, after a

thorough bibliographical review, and also based on prior knowledge, in the first optimisation cycle,

the CAD department decided to investigate the effects of altering the gap and overlap of the front

wing and wheel as shown in Figure 98. Initial samples of 20 points were generated in the population

space, including A03 design discussed in the previous chapters as the baseline. They were distributed

as randomly as possible in the design space. Some points were stratified as it was deemed

interesting to test the physics at that design point.

Figure 99 shows the sampling plan adopted with the naming convention and also the

normalised (non-dimensionalised) values of gap and overlap. Note that B0 is the baseline (A03). The

points represent the parameterised variables (ranging from 0 to 1) in the design space. Each point

42 Lecturer, University of Southampton.

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represents the non-dimensionalised combination of the variables to be tested. The reason for this

choice is that the edge vortices and the wheel wake are greatly affected by the relative position of

these two elements. The overlap was adjusted by extending the front wing width. As it can be

noticed, increasing the front wing’s width increases its AR and hence its downforce generation. The

overlap was varied (with respect to the initial position in A03) between -27.5mm to +7.5mm, with

the gap from 0mm to 100mm. The reasons behind this choice can be found in the CAD section. The

baseline car is indicated as B0, and has coordinates (0, 0.79). The use of macros functions in STAR -

CCM+, explained in upcoming chapters, automated the entire procedure from the CAD import to the

final CFD calculation, including mesh and simulation set up.

Figure 98: Gap and Overlap between the front wing and wheel.

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Figure 99: Initial sample for iteration B.

4.6.2. Results

Figure 100 shows the surrogate model created based on the initial population (20 design

points). In addition, the location of the maximum predicted for each contour map is represented by a

red dot. It can be seen that there are two regions where the model predicts high C L. The first one,

which is the absolute maximum, located at the left upper corner of the figure, in the maximum

overlap and the minimum gap zone. The second one, which is a local maximum, located at an

intermediate overlap combined with minimum gap. This indicates that the downforce of the car

seems to be greater when the distance between the wheel and the front wing is reduced. In addition

to the CL surrogate, an L/D surrogate was created and as it can be seen in Figure 100 the L/D

prediction looks very similar to the CL surrogate prediction. This can be attributed to the fact that the

lift is the primary variable for computing efficiency in this case since the variation in C D is less than

6% whereas the variation in CL goes up to 23%. This distinct behaviour in drag and lift also leads to

the conclusion that both the variables investigated have a stronger influence on lift than on drag.

Having this in mind, a new design point (B20) was incorporated in the population with the

gap and overlap configuration of the maximum predicted CL (red dot). Additionally a second update

(B21) was defined based on the configuration suggested for the maximum aerodynamic efficiency.

Lastly, a third update (B22) was placed near the vicinity of the local CL maximum mentioned above in

order to investigate whether that predicted local maxima could be actually an absolute optimum

design of the real function. Besides updating the surface, the three new points will increase the

accuracy of its former predictions significantly.

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Figure 100: Surrogate model prediction (20 samples).

Figure 101 shows the recalculated response surface after adding the three new design

points. None of the infill points had any improvement in terms of lift or efficiency (results can be

seen in Table 13) but their inclusion in the surrogate clarified the zone where the maximum lift was

predicted. The inclusion of point B22 resolved the uncertainty about the local maximum and both

B20 and B21 shifted the zone of maximum lift in the south-east direction. This means that a

configuration with less overlap but more gap than the baseline (B0) could have been a wiser

decision.

Figure 101: Surrogate model prediction (20 samples + 3 updates).

As none of the new design points managed to improve the results of the initial population

the team decided that updating the surrogate at least with one more point would lead to the desired

optimum solution. Consequently a new design point (B23) was defined to be in the area where both

lift and efficiency was predicted. Unfortunately the team was with B23 as unlucky as it was with the

three previous updates as Table 13 and Figure 103, Figure 104 and Figure 105 can show.

Nevertheless this last update was useful in the sense that it helped to further improve the reliability

of the model and showed that probably the optimum solution had already been found in the initial

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population, since the area suggested for maximum lift and efficiency seems to be surrounding the B6

design (Figure 102).

Figure 102 shows how the variation in downforce is directly proportional to the overlap and

inversely proportional to the gap distance. Increasing the overlap between wheel and front wing

means that the front wing span is being increased too. In conjunction with this, a higher value of

overlap means that the distance travelled by the incoming air towards the symmetry plane of the car

increases. This fact combined with a low overlap distance reduces the amount of air entering the

channel formed by both wheels and enhances the quality of the air entering the sidepod. One

interesting feature that can be extracted from Figure 102 is that the worst design in terms of CL (B12)

has the same overlap configuration as the best design (B6) has. It seems that although both

parameters affect the downforce of the car the gap seems to have a greater impact. That is, the

gradient in the gap direction is bigger than the gradient in the overlap direction. After 4 updates the

first optimisation cycle was concluded with the best design being B6 which attained an increase of

more than 4% in both lift coefficient and efficiency. This design was then used as the baseline for the

second optimisation cycle accomplished in this project.


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Figure 103: Iteration B CL results.

Figure 104: Iteration B CD results.

Figure 105: Iteration B L/D results.

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Table 13: Iteration B data and results.

Design Gap [mm]

Overlap [mm]

Norm Gap

Norm Overlap

CL CD L/D

B0 "A03" 0.00 0.00 0.00 0.79 2.808 0.836 3.359

B1 0.00 7.50 0.00 1.00 2.891 0.833 3.470

B2 0.00 -13.00 0.00 0.41 2.870 0.827 3.471

B3 0.00 -27.50 0.00 0.00 2.501 0.800 3.126

B4 100.00 -6.00 1.00 0.61 2.289 0.844 2.711

B5 100.00 -27.50 1.00 0.00 2.256 0.838 2.693

B6 12.00 2.00 0.12 0.84 2.917 0.835 3.496

B7 9.00 -22.00 0.09 0.16 2.510 0.809 3.103

B8 35.00 -16.00 0.35 0.33 2.393 0.809 2.957

B9 46.00 -21.00 0.46 0.19 2.522 0.835 3.021

B10 96.00 -21.00 0.96 0.19 2.453 0.846 2.899

B11 29.00 2.00 0.29 0.84 2.800 0.839 3.338

B12 80.00 2.00 0.80 0.84 2.224 0.833 2.670

B13 37.00 -7.00 0.37 0.59 2.718 0.835 3.256

B14 66.00 -25.00 0.66 0.07 2.451 0.835 2.936

B15 78.00 6.00 0.78 0.96 2.530 0.856 2.955

B16 90.00 7.00 0.90 0.99 2.453 0.863 2.844

B17 54.00 4.00 0.54 0.90 2.694 0.843 3.196

B18 61.00 -18.00 0.61 0.27 2.387 0.835 2.857

B19 88.00 -9.00 0.88 0.53 2.318 0.843 2.751

B20 6.00 5.40 0.06 0.94 2.882 0.838 3.441

B21 2.00 5.40 0.02 0.94 2.877 0.832 3.458

B22 10.00 -9.00 0.10 0.53 2.862 0.828 3.455

B23 18.00 -3.00 0.18 0.70 2.867 0.825 3.473

4.7. Third Design Cycle –C Iteration

4.7.1. Optimisation Variables and Initial Sample

Having performed an optimisation cycle in the front half of the car, the team then focussed

on the rear part of the vehicle. Again, the variables chosen had to have a large effect on the overall

aerodynamic performance of the car. Backed by bibliographical review, the diffuser was individuated

for optimisation. In this direction the C Iteration had a primary goal of optimizing the performance of

the diffuser.

The two variables selected to be the base for this optimisation cycle were the width of the

Venturi-channel’s throat and the diffuser’s exit (see Figure 106). The forethought behind having the

throat’s width as an optimisation parameter was to modify the velocity and hence the pressure in

the middle zone of the underbody. It was comprehended that optimising this variable would lead to

the optimum design for the double stage diffuser installed on the car. In conjunction with the

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throat’s width, the exit of the diffuser was set as an optimisation parameter since it is responsible for

the pressure recovery. Depending on how this pressure recovery is carried out, the diffuser may have

a beneficial pressure pumping effect or may end up having separation in the ramp zone.

Figure 106: Width of throat and diffuser exit.

In contrast with what it was done in the last optimisation cycle, the initial sample space was

populated using Dr. Andras Sobester42 bestlh.m MATLAB function, which generates an optimised

Latin Hypercube sampling plan. The throat width was varied within a range of 30mm and the diffuser

width within a range of 60mm, to produce an initial sample of design points, including B6. Only 11

designs were defined to be the initial population this time as it was thought that using the Latin

Hypercube could optimise the sampling plan so that using 20 designs (like in the B iteration) was

unnecessary. As it has been pointed out in the introduction part of this chapter, a noticeable

assumption was made between the two optimisation iterations. The rear wing of the B6 design was

moved down and it was taken as the baseline design for the C iteration, hence it can be noticed in

the following pages that the results for this model differ from those shown in the last chapter.

However, the assumption made was that the general trend between the results of each design would

be the same had all the designs been modified in the same manner (lowered rear wing), i.e. that the

B6 design would still be the best one performance-wise. This hypothesis is strongly confirmed by CFD

data, as explained later. The modified B6 was then taken as a baseline, which had the width of its

throat as 106mm and a diffuser’s as 220mm. all the other designs were defined within ranges of

30mm for the throat and 60mm for the diffuser exit taking the values of B6 as the centre for both the

ranges. As it happened during the previous optimisation cycle, the variables were normalised - the

minimum value for each variable was represented by 0 whereas the maximum was represented by 1

(see Figure 107). The values for the rest of the car configurations can be seen in Table 14.

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Figure 107: Initial sample for iteration C.

4.7.2. Results

Once the 11 initial car designs were prepared in by the CAD department, they were meshed

and run for 4000 iterations. The results were fed into the MATLAB code and the Kriging predictions of

both the downforce and the aerodynamic efficiency were built as shown in Figure 108. It can be

observed that both models look very similar, so the parameters chosen for the C iteration have

presumably more impact on the downforce than on the drag, as it happened with the previous

optimisation cycle. One can see that the point C7 is located in a zone of predicted maximum

performance, very close to the predicted maximum in both cases. Nevertheless the team was

reluctant to have a best design from the initial population again so it was decided to inspect the area

around C7 meticulously. In that sense the CAD department prepared three more designs (C11, C12

and C13) to be the updates for the surrogate model.

Figure 109 confirms that the C7 design was very close to, or it was, the optimum design from

the very beginning. It can be seen that the three updates clarified the overall picture of the model

and the area predicting an improvement around the C7 design was considerably reduced. The fact

that the C7 was the best configuration could be attributed to the fact that it was beneficial in some

manner for the sidepod. The leakage of air coming from the sidepod lower surface towards the

central channel may have been decreased, due to the increased pressure in the diffuser throat area

(increase in width). The detailed analysis of the C7 design and the reasons for these enhancements

are discussed in the post-processing section. Results for the second optimization cycle are shown in

Figure 110, Figure 111, Figure 112and Table 14.

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Figure 108: Surrogate model prediction (11 samples).


The second optimisation cycle was considered finished being C7 the best design out of the

40 cars tested so far. The optimisation process successfully managed to increase the general

performance of the car. Starting from A03, which was the optimisation -baseline model, the

optimized C7 design increased downforce (4.79%) with only 1.67% increase in drag, which l ed to an

increase in the aerodynamic efficiency of 3.07%. The evolution over the two iteration cycles can be

seen in Error! Reference source not found. Error! Reference source not found. shows that the

downforce produced by the car was increased each stage of the optimisation cycle. On the other

hand it can be appreciated that the aerodynamic efficiency of the car was reduced in the second

stage of the optimisation cycle, but this is due to the fact that the rear wing was moved down after

the iteration B was finished as it is mentioned at the beginning of this. Despite the loss in the car’s

performance because of this rear wing modification it can be seen that it was not only recovered but

augmented indeed after the second optimisation. It can be safely stated that shifting the rear wing

down in the A03 design would have smoothed the evolution of optimisation shown in Figure 107.

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Table 14: Iteration C data and results.

Design Throat [mm] Diffuser [mm] Norm Throat Norm Diffuser CL CD L/D

C0 "B6" 106.00 220.00 0.50 0.50 2.828 0.848 3.336

C1 92.50 211.00 0.05 0.35 2.888 0.850 3.398

C2 98.50 223.00 0.25 0.55 2.844 0.851 3.342

C3 113.50 193.00 0.75 0.05 2.930 0.851 3.443

C4 104.50 235.00 0.45 0.75 2.847 0.850 3.348

C5 110.50 247.00 0.65 0.95 2.846 0.849 3.352

C6 107.50 217.00 0.55 0.45 2.890 0.850 3.400

C7 119.50 205.00 0.95 0.25 2.943 0.850 3.462

C8 101.50 199.00 0.35 0.15 2.912 0.848 3.432

C9 116.50 229.00 0.85 0.65 2.886 0.850 3.395

C10 95.50 241.00 0.15 0.85 2.850 0.849 3.357

C11 121.00 205.00 1.00 0.25 2.911 0.847 3.436

C12 118.00 205.00 0.90 0.25 2.916 0.846 3.449

C13 119.50 208.00 0.95 0.30 2.916 0.848 3.440

Figure 110: Iteration C CL results.

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Figure 111: Iteration C CD results.

Figure 112: Iteration C L/D results.

Figure 113: Optimisation Evolution.

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Table 15: Optimisation Evolution.

Design CL CD L/D Difference % CL Difference % CD Difference % L/D

A03 2.808 0.836 3.359 - - -

B6 2.828 0.848 3.336 0.69 1.39 -0.69

C7 2.943 0.850 3.462 4.79 1.67 3.07

4.7.3. Additional comments

Apart from being used as an optimisation tool, the response surface offers the unique

opportunity of deciding which configurations could be the most appropriate depending on the track

the car is going to race on. In this sense, the analysis of the response surfaces of both optimisation

iterations points out B3 as the design with least drag (see Figure 114) and hence most suited for

racing in circuits where straights and fast corners are dominant.

Figure 114: surrogate model prediction for drag (Iteration B left, Iteration C right) .

However, the investigation of Figure 104 shows that there are other designs that produce

less drag than the final design (C7). B7 designs has a CD coefficient close to the minimum (B3) but at

the same time its downforce is higher than the B3 model as seen in Figure 103. It should be pointed

out that, although B7 has slightly higher downforce, the aerodynamic efficiency is slightly lower.

Taking into account that the bigger difference between B7 and B3 is the drag they produce and that

they have similar downforce and efficiency, B3 stands as the best design with respect to drag

reduction.

4.8. FINAL CAR INTRODUCTION

The final car resulted from the outcome of the two optimisation processes performed on the

A03 car. Tri-dimensional views of the car are shown in Figure 115. The two optimisation cycles were

implemented to show the effect of systematic modifications to a car that had been already

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thoroughly studied in its major aerodynamic features. Once it is decided to undergo a parametric

study of this kind, it is left to the designer’s abilities and knowledge to fully understand which areas

of the car have the highest margin for betterment.

Figure 115: Tri-dimensional views of the Final car.

The preliminary resolution was to perform the first investigation on a subassembly in the

front part of the car, owing to the assumption that the second cycle, which in turn would be carried

out on the rear section, would not greatly affect the outcome of the first study. This being stated,

following also what was studied in the bibliographical review, it was decided to act on the front wing-

front wheel interaction. A simple 2D response surface (see optimisation chapter) was indicated as

the optimal trade-off between improvement potential and complexity. The two parameters were

individuated to be the overlap and the gap between these two parts. It is straightforward to grasp

the reason for this choice: the edge vortices and the wheel wake are greatly affected by the relative

position of these two elements, as it is the channelling effect. Consequently, unde rstanding how

performance is affected by the different flow structures and their paths within the flow can lead to

major improvements. In order to modify the overlap, the front wheel was kept in the same position,

and the front wing was cut or extended, according that what was needed. Both the operations were

performed, for what regards the third element of the front wing, on the maximum -chord section.

The overlap was adjusted by moving the front wheel fore and aft, keeping the front wing in the same

position as A03. As it can be easily understood, this kind of parametric study can be carried out in a

simulation-environment only, since changing the position of the wheel would, in real life, involve

major modification to the entire car.

After a more careful analysis of A03, and before the second optimisation cycle, it was

decided to lower the rear wing again, to regain the beneficial effect it had on the body (it decreased

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the lift) and improve the downforce generation on the wing itself. A very important assumption was

made in this case, i.e. the results for the first optimisation cycle were considered to be independent

from the rear wing height. Since the downforce figures for the rear wing were almost unchanged

throughout the entire iteration, this conclusion is supported by evidence. Next, it was determined

that the second cycle had to include the diffuser. The definition of the two parameters was, in a

sense, more debated, because of the vast number of possibilities, and the constraints represented by

the remaining parts of the car. At the end, the choice was to simply modify the widths of the channel

throat, right behind the nosecone, and of the final section of the diffuser ( Figure 106).

Since this is the last car, it can be valuable to briefly sum up all the important modification

that have taken place during the entire design process. The nose was raised and its top surface made

almost horizontal, and the front wing struts were replaced, to increase the mass flow to the

underbody. The front endplate was completely redesigned, to better manage the flow around the

tyre. The two splitters were modified in shape and their width was increased. Sidepods and diffuser

were redesigned from scratch, with the creation of a channel for the latter. The engine cover was

slightly raised and its cross-section, as well as the curvature, were altered. A windshield was

positioned in front of the helmet which, in turn, was sunken more into the chassis and til ted

backward. The rear wing saw its struts and endplate substituted with new elements, and the position

relative to the rest of the car was changed. The beam wing was eliminated. It is obvious, even by a

quick glance, that the baseline car and the final version are completely different. All parts were

addressed, with radical modifications or simple revisions taking place, according to the individual

case. The only parts left totally untouched were the aerofoils. As explained before, the team

considered any intervention on the aerofoil not to be worth of attention, for the reason explained

earlier on. No Gurney flaps, or other devices, were added, since the ultimate goal was not pure

performance, but a better understanding of the flow characteristics around an open-wheel race car,

and the mutual interaction between the various parts.

4.8.1. Analysis and Discussion of Results (C07-Final DESIGN)

The final (C07) car showed improvement in downforce for the vast majority of components.

Being the results of two different optimisation processes, two separate steps can be individuated.

The result of the first optimisation process yielded a maximum downforce of 2.83 with the low wing

and 2.91 with the raised wing. The increase in downforce was found in the front wing main element

and the diffuser, with the sidepod slightly increasing its values as well. The second cycle, based on

the diffuser, brought the maximum downforce to 2.94 (low wing); interestingly, only about 10% of

the improvement was obtained from the diffuser itself, with the sidepod accounting for the highest

increase, with more than 10% raise over the A03 configuration.It is possible to summarise,

component by component, the evolution in downforce coefficient for every car, from the baseline to

the final one: the graphical outcome of this study is shown in Figure 116. Two things are immediately

noticed: the sidepod allowed balancing and overcoming, the downforce loss in the rear wing; and

continuous improvement was obtained in the rest of the car. Specifically, the entire sidepod

transitioned from a downforce coefficient of 0.25 to a staggering 0.71, as a result of the different

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shape of the sidepod itself, and of the adjustments made upstream of it. The diffuser produced a

coefficient of 0.35 in the baseline, which moved up to 0.60 in the final car, documenting the

incredible significance that the Venturi effect can have over a racing car. It is also very interesting to

see how the downforce generated by the front wing changed solely as a result of the upgrades

introduced downstream, and on the endplate: the main plane (+12% from the baseline) and the first

flap (+11%) achieved better results without compromising the components downstream of them. As

already mentioned, the very complex endplate managed to get more than ten times the initial

downforce, while managing the flow around the front wheel very efficiently, representing a major

improvement for the performance of the entire car.

Figure 116: Downforce Breakdown for Each Component of C07 and Comparison with other iterations.

The objective for the body and the nose was to keep the lift as low as possible, a result

partially obtained considering that the figures are almost unchanged from the baseline to the C07.

Nonetheless, the flow was better managed, and the drag dropped, especially for the body. The only

really relevant loss in downforce was observed in all the elements of rear wing, whose angles of

attack evidently were specifically tuned-up for the particular position in the baseline car.

Nonetheless, the approach of not addressing these reductions and focussing on the large -scale

features of the flow proved itself to be more efficient that working on the aerofoils, judging by the

results obtained throughout the design process. The positive lift generated by the wheels was kept to

a minimum as well, and the attention was shifted more to the effect of the wake of the wheels on

the rest of the vehicle, rather than on these elements themselves.

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It is worth considering the fact that, until now, only the force coefficient has been

investigated, in order to keep consistency throughout the entire analysis. It is to be pointed out that

the reference area, and the actual dimensional numbers for drag and downforce with it, generally

increased from car to car. In order to understand the magnitude of this variation, it can be said that,

from the baseline to the final car, the lift coefficient increase of 30%; at the same time, owing to the

an higher frontal area, the total lift (computed with the conditions mentioned in the CFD chapter)

raised of 42%, from 100 N to 142 N. For the drag, a reduction in the drag coefficient did not match a

decrease in the total drag force, which increased from 39 N to 41 N. These results are maybe less

relevant than the coefficients from a design point of view, but in racing conditions what really

matters are the forces that can be transmitted to the ground, which justifies this brief detour.

The values for the drag coefficient can be found in Figure 117. The final car managed to

reduce the total figure from the 0.87 (baseline) to 0.85. Although the variation for the overall

coefficient is small, the variations in the single components are, in same cases, even of a higher order

of magnitude. For example, the body, which was streamlined and accurately studied, almost halved

its drag (from 0.07 to 0.04). To testify the great upgrade obtained with the front endplate and the

sidepod in managing the flow around the wheels, it can be stated that the drag coefficient dropped

from 0.15 to 0.09 for the front wheel, and from 0.21 to 0.18 for the rear wheel. The diffuser, as a

result of the highly increase downforce, saw an escalation of 50%, from 0.07 to almost 0.12. A similar

effect was observed in the sidepod, with an increase in drag coefficient close to 30%. As expected, it

was not observed any relevant variation in the front wing, as the aerofoils did not change; the

endplate drag raised threefold, from 0.004 to 0.012, a change anyway almost negligible in

magnitude, and more than compensated by its effect on the rest of the car. It was said that the rear

wing lost copious amounts of downforce; nonetheless, the introduction of louvres, decreased the

drag for the three elements from 0.26 to 0.23. Finally, the efficiency showed constant progresses

throughout the various iterations. The initial value of 2.6 increased of 1% for the A01, dropped for

the A02 iteration, and then jumped to a totally unexpected 3.36 for the A03. Starting from this

already outstanding value, the optimisation cycles managed to slowly but consistently increase it,

and the efficiency for the last car was set at a value of 3.46. Finally, the ratio of the front wing

downforce to total downforce (roughly approximated to be the balance) was found to be at 29%, a

common for open-wheeled race cars.

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Figure 117: Drag Breakdown for C07.

4.8.2. Post-processing of Results

Being this the final car, the team strived to put together a pos-processing consistent with

previous cars, and at the same time with some additional features, to explain, from a rigorous

physical standpoint, how the improvement were achieved.

Figure 118 shows the coefficient of pressure in multiple locations. The splitter zone has

obtained a decrease in overall pressure, signifying that the flow is less likely to escape the

contraction section. The Venturi channel seems to be working better with an extended area of low

pressure, which kept the same position but improved the suction peak, with a more effective

acceleration of the flow. On the rear part of the car, it can be noticed that a regi on of high pressure is

present on the engine cover, probably as a result of lowering the rear wing, thus decreasing the lift

generated by the body. With this being said, the results indicate that this effect is not too big, but still

relevant. Furthermore lowering the rear wing creates a zone of low pressure near the suction side of

the wing that affects the engine cover sucking it upwards. Clearly these two effects balance each

other and not a clear gain is observed.

Comparing the A03 design to the C07, it can be seen that the stagnation region on the front

wheels has decreased. As expected, no radical changes on the pressure distribution on the front

wheels are observed despite the optimization cycle that modify the gap and overlap of the front

wing. It is to be remembered that small variations in pressure coefficient cannot be investigated in

this kind of plots, where only large-scale variations can be observed. The bottom side of the car

reveals a slight ‘C’ shape type of distribution on the sidepods and the diffuser. In any case, the cross-

stream pressures are very similar in these two components, meaning that the flow tends to simply

move downstream, without meandering from the diffuser channel outwards, or viceversa. From this

perspective, it is also possible to state an that the endplates and edge plates generate a significant

amount of downforce, as a result of the vortices that are present beneath them. A particular

observation can be made, regarding the sidepod plates: the complex shape involves a change in

width, with the plate growing from the front to the rear of the car. It is postulated that the increase

of width of the edge plate contributes towards the increase in downforce: the initially weak vortex

grows while convecting downstream, and can therefore travel a higher distance below the edge

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plate, increasing the area of low pressure and consequently downforce. The top side of the car

reveals that this vortex is breaking down as a consequence of the high pressure induced by the

wheel at the ramp, which, in turn, pushes the edge plate down. This a peculiarly complex interaction

between different parts (sidepod, wheel, side plate), and it is almost impossible to grasp the full

meaning from a simple RANS simulation. Nonetheless, it can be said that in this case a flat plate close

to the wheel (with no ramp) would further increase the high pressure on the edge plate without

disrupting the beneficial edge vortex.

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Figure 118: Coefficient of Pressure for C07, from top to bottom: mid-plane, bottom, sidepod and rear wheel, top.

Going back to the pressure coefficient seen from the bottom, the front wheel jetting

phenomenon is finally observed on the entire car, probably as a consequence of the better physical

approximation obtained with this type of plinth on the wheel. From the top is it also made possible

to report the effect of the windshield on the pressure distribution of the nosecone: a higher value is

induced where separation happened on the baseline, reducing lift for this component.

Figure 119 shows a vorticity and velocity vectors at three different positions in the car. The

top figure is taken at a plane just behind the front wing endplate, and shows how the negative vortex

(indicated with B in previous cars) is created: the flow is curved downwards by the channel in the

endplate, and blown into the relatively uniform flow outside, which tends to straighten the air and to

curve it back into the gap between the wheels; this creates a very small vortex that separates the

lower edge vortex and the wheel inboard vortex, allowing to manage them better. It can be seen that

the solution employed is cleverly not influencing the formation of the edge vortex itself (positive

vorticity under the endplate), which is the main cause of downforce enhancement in ground effect.

In the sidepod plot, it can be observed how the wake of the wheel promotes flow to be pushed

under the edge plate, thus directly increasing downforce, and from here to the sidepod, where a

massive vortex is formed. The magnitude of this vorticity is so high that the flow is being pushed

even more, under the diffuser side and into the diffuser: a chain of greatly advantageo us flow

features is being promoted by the refined relative position of the sidepod, the front wheel and the

side plate. For the wake of the rear wheel, the two vortices can be easily spotted, very close to what

it would be seen for a wheel in isolation. The wake seems to be very clean, and therefore a drag

reduction would be expected; as it is already been shown, this is actually the case. Differently from

A03, the inboard vortex is displaced more to the outside.It is noted that streamlines are not

displayed, since no difference can be discerned from A03.

A feature that has not been analysed in detail yet is the presence of the louvres in the rear

wing endplate, which can be observed in Figure 120. Figures show that the introduction of these

cuts, or, more properly, gills, in the endplate have reduced drag of a good amount (around 8%). Both

in the wide picture and in the close-up, the regions of negative vorticity, coloured in blue, can be

detected. Especially the little vortex from the highest louvre seems to contain, to some extent, the

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upper edge vortex, thus reducing the strength of this and the consequent drag. It is worth

mentioning now, that the design of the louvers is a time-consuming task that was not investigated in

detail. However their effectiveness has been proven.

Figure 119: Vorticity and Velocity Vectors for endplate (top, x=0.28), sidepod (middle, x=1.02), wake of the rear wheel (bottom, x=1.54).

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Figure 120: Vorticity for rear section of the car (top), Vorticity and Velocity Vectors for rear endplate (bottom) .

Figure 121 displays the negative value of wall shear stress on the car, on x -direction. Despite

not being a final conclusion on the absence of separation in the sidepod and diffuser, it can be safely

assumed that the x-component of velocity, in these two parts, is dominant, from which follows that

not having a negative shear stress implied no negative velocity on the walls, therefore no separation.

This is particularly important because the eventual presence of recirculation bubbles would imply a

great loss in efficiency.

Figure 121: Wall-shear stress, x-component, for C07.

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It is probably required, for the sake of completeness, to sum up all the vortices, and their

main effect, present on the car: Figure 122 displays the well-known Q-criterion isosurface at 10,000.

Starting from the front of the car, the edge vortex can be isolated (A). Differently from what

happened in previous cars (until A02), the introduction of a new endplate cause a small vortex(B),

rotating in the other sense, to fill the gap between the front wing and wheel, and allowing the

inboard wheel vortex (A’) to develop). With this configuration, the channelling effect is increased, the

edge vortex is efficiently dissipated, and the the wheel vortex is pushed outside the si depod. The

splitter produces two structures that appear to be detrimental to the sidepod and the diffuser (C). A

complex arrangement of vortices can be seen in the wake of the wheel, the biggest of which is

represented by D; it is to be recalled how the dimensions of this vortex shrank as designs progressed,

effectively decreasing the drag from this component. The edge vortex formation for the sidepod (E

and F) is elaborate, and an hypothesis on the phenomena taking place can be found in post -

processing section for A03. The diffuser edge vortex, as a result of the reduction in width of the final

section), is now much closer to the side wall, improving its performance. The wake of the rear wheel

displays the two well-know counter-rotating vortices on the ground (I and H), which do not interfere

with any other part in a significant manner, thanks to the more refined design of the engine cover.

The two endplate vortices for the rear wing are clearly depicted (J). From the isometric view, the

double upper edge endplate vortex is observed. The measures adopted to weaken it appear to work,

as the iso-surface does not touch the wheel anymore. The D’ vortex on the top surface of the

sidepod has been reduced in size as a result of the first optimisation cycle.

Finally, four 2D plots for the pressure coefficient in various part of the car are introduced, in

order to precisely track down the evolution of these components ( Figure 123). All the plots are

normalised with the length of each component. First, the front wing shows a familiar behaviour, with

the main element exhibiting four separate suction peaks: one because of the wing itself, one cause

by ground effect, and the remaining two as a consequence of the two flaps; similar configuration can

be made for the second and third element. It can be seen that a remarkable improvement was

obtained with A01, whereas the presence of the bargeboards ruined wing performance on the A02.

The A03 design still gained some downforce, as a consequence of the improvement downstream.

The optimisation cycle led to an almost indistinguishable enhancement of the pressure peak: this is

due to the fact that this process was just a fine tuning of a component already performing well, and

therefore the advance is minimal, but still valuable. The trends of the pressure distribution are the

same for all the cars, since neither the aerofoils nor the ground height were touched.

The sidepod shows how the introduction of a completely new part dramatically upgraded

performance: despite the suction peak being moved downstream for all new designs, a much more

efficient acceleration of the flow was obtained, and the magnitude of the peak doubled; still, the

long expansion zone allowed to effectively recover pressure to levels similar to the baseline. The

main improvement from A01 to A03 was to move the throat upstream, slightly anticipating the

suction peak. It can be also observed how the bargeboards highly affected the quality, and thus the

downforce generation, of the sidepod. Then, the introduction of a double -stage diffuser allowed to

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reach, as predicted, two different suction peaks, which allowed to decisively outperform the baseline

design. Having a longer expansion section made possible to obtain a better pressure recovery. The

final design gained better performance with respect to the A03 thanks to a better suction peak at the

transition between the two different zones of expansion, coupled with a more efficient pressure

recovery. Following, as mentioned, the only component to lose downforce throughout the designs

was the rear wing, which consistently saw reduced suction peaks on the main element. It has been

speculated that this is a result of moving the wing, which apparently was already in its very optimal

position; nonetheless, this did not affect the final results. After observing these plots, it can be

noticed how the choice of not modifying the aerofoils in the wings allowed to put forward a coherent

comparison, effectively exposing the mutual effect of different components.


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Figure 123: 2D Pressure Coefficient Plots for different components.

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4.9. B and C Interaction Conclusion

The Second Optimisation Cycle (B Iteration) executed in less time than the First Optimisation

Cycle (A Iteration) have proved the viabil ity of testing the full car methodology instead of testing

individual components separately. A total of 24 cars were simulated and the surrogate model

prediction for optimising the design methodology was implemented. In the subsequent Optimisation

Cycle (C Iteration) testing a total of 7 more cars were simulated in even less time. Clearly as the

group got more practice with the software the steep initial learning curve becomes more subtle and

the productivity has been shown to greatly increase from the ini tial stages of the project to the final

stage.

In the second optimisation cycle the chosen variables to create the design population, gap

and overlap between the front wing and the front wheels, have proven to be a good pair of variables

since they presented a considerable variation on the objective functions in the analysis. Values of CL

varied from 2.223 to 2.870, and CD varied from 0.799 to 0.862. The two variables were also

positioned in an upstream position and have been shown to affect the flow over the entire car.

Figure 124 shows the population from all design cycles plotted against lift and drag. It can be seen

that the initial point from the second optimisation cycle, which was the last design from the First

Optimisation Cycle (A03), was already a well optimised design, and that most of the population from

the second optimisation cycle presented worst results in terms of downf orce generation; however

several designs presented a reduction on the total drag.

Figure 124: Design population plotted with lift on the abscissa and drag on the ordinates.

In the third optimisation cycle (C Iteration), the variables selected have proven to play an

important role on the overall production of downforce, which increased from 2.843 to 2.943.

However, a significant variation on the overall drag was not observed. This means that an

optimisation in the diffuser is paramount for the increase on the aerodynamic efficiency of the car.

0.78

0.80

0.82

0.84

0.86

0.88

0.90

0.92

0.94

2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0

Baseline Car First Design Cycle Second Design Cycle Third Design Cycle

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The population distribution was also less scattered over the plot, since the component was

positioned in a downstream position and on the bottom part of the car, influencing less components

downstream when compared to the front wing and wheels. Optimisation in other components could

present an increase on the objective functions but it is believed that a satisfactory result has already

been obtained from the optimisation process.

Both methodologies implemented: the ad-hoc approach of the first optimisation cycle and

the parameterisation study of the second and third optimisation cycles, have presented an

undoubtedly evolution from the baseline car and have shown that the approach adopted trying to

understand and improve the flow features of the baseline car and then carry on a parametric study

to refine the design was very appropriate.

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5. Summary and Conclusions

An investigation into the aerodynamics of an open-wheel racing car has been completed

using computational fluid dynamics (CFD) to visualize the complex flowfield generated by this type of

moving vehicle. The model was a single-seater hill-climb car, which had been designed and wind

tunnel tested at the RJ Mitchell wind tunnel in Southampton University by the 2010 MEng GDP

project. In the present work, steady RANS computations were performed to assess the performance

of the major components of the car with the intention of using basic aerodynamic and design

principles to improve the overall aerodynamic characteristics of the vehicle. The improvement on any

of the attempted designs was measured in terms of an increase in downforce levels and the

aerodynamic efficiency given by lift-to-drag ratio. These improvements were sought through a

clearly defined team strategy that involved industry-like methodology and detailed planning of the

simulations and the design.

The first step in the process was to formulate the objectives of the project, which were

chiefly to understand the complex physics of the problem and to apply the team member’s expertise

to optimize the aerodynamic characteristics of the car. The second step involved formulating a series

of assumptions that would enable the completion of the project in a timely manner while ensuring

that the problem could be solved reliably. Because the design of the car involved both CAD and CFD

work, it was decided to provide a set of assumptions for each of the different aspects of the design.

In terms of CAD, the major assumption was the simplification of the geometry by excluding minor

components of the car that are not found to affect significantly the flowfield such as the suspension

wishbones, or the intake ducts. This was done mainly to simplify the meshing process during the CFD

stage of the design. On the other hand, several CFD key assumptions that are worth mentioning were

considered for this problem. First, the flow was assumed to be incompressible and steady. Only half

of the car was simulated to decrease computational cost and the settings included a velocity of 30

m/s and low turbulence level to match the wind tunnel characteristics. In addition, the internal flows

of the car through the sidepod or engine intakes were not simulated. Some specific remarks about

the inherent uncertainties built in the RANS approach, where the effect of all relevant scales has to

be modelled, were also provided. Primarily RANS was used due to the prohibitive computational cost

of other CFD techniques such as LES, which are clearly not feasible for a problem of this nature, not

only due to the numerical effort required but also due to the time available to complete this work.

Furthermore, RANS gives the statistic mean of the flow highlighting the most significant flow

structures that affect the overall aerodynamic performance of the car. Hence it can be used to

propose different designs and to judge whether the design is improving or not based upon a series of

objectives.

One of the most important components enabling the completion of the project was the

management of the team. Being this a project where team effort represents a significant portion of

the overall work that has been presented, it was regarded as paramount to establish a methodology

that would guarantee the fulfilment of the objectives in the given timeframe. The management also

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intended to ensure that all the team members had significant exposure to a wide range of different

problems within the overall design of the car. The first decision taken management-wise was to split

the project into two different phases. The first phase took place from October to December of 2012.

This phase was mainly dedicated to understanding the problem, formulating objectives and

assumptions, conducting preliminary research and learning to work with the CAD and CFD tools. In

addition, the first phase included preliminary CFD studies for the front wing and wheel in isolation

and concluded with the generation of a suitable mesh, and subsequent simulation, for the baseline

car. On the other hand, the second phase of the project was developed during February through the

end of March of 2013. This stage concentrated the biggest design effort and in broad terms included

a cyclical process which started by formulating the desired design approach, followed by detailed

designs in CAD, simulations of the different designs in CFD and post-processing of the design to

identify the improvements being made over the course of the design process. To accomplish all this,

the team was divided into different departments. The engineering department was the heart of the

project with all the team members being a part of it. This department was responsible for the

conceptual design of the car, which in essence had as a primary objective to propose new designs

and modifications to existing cars. The proposal made by the Engineering department was executed

by the Design/CAD department, which generated all the CAD geometries. The geometry was then

used by the Grid Generation Department, which ensured good quality grids were being produced for

each of the new designs with consistent meshing parameters throughout the project. Finally, the CFD

team was responsible for interpreting the results generated by the simulations and to clearly i dentify

areas of the car that were not performing in an optimal manner, creating the premises for the

following cycle.

The design of the car was also divided into three cycles. The main objective was to split the

problem into different smaller problems that would enable constant evaluation of the progress made

by the team. Prior to splitting the design process into different cycles, an important decision

regarding the simulation of the car was taken. As opposed to previous GDP projects, which decided

to split the car into different sections to simulate them in isolation, the team decided to only

simulate the entire car for each design. The main reason for doing this was the significant effect in

overall performance the interactions between the components of the car have. The methodology

used previously by other teams led to optimized performance of a given component in isolation but

yielded poor performance when the component was assembled in the car. It was decided that the

team would be able to have a better perspective of the flowfield and how different components

interact with each other by simulating the car as a whole instead of splitting it. It is noted that a big

leap in the computer power available during the second phase of the project clearly enabl ed the

execution of this methodology. In addition, it must be pointed out that the increase in computational

power was also complemented by the automatization of meshing and simulation procedures that

was accomplished, as a consequence of an extensive use of JAVA macros. This allowed to reduce the

simulation time of the cars while always ensuring that consistent settings were used throughout the

design process.

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With the logistics of the project detailed, the attention is now shifted to the work that has

been completed in the present study. Firstly a detailed literature review was conducted at the

beginning of the project to investigate the major components of the car and the relevant challenges

associated with each part. In a similar fashion to the project methodology, the literature review was

divided in multiple sections. The first major section included the critical review of previous GDP

project reports to obtain information about what other teams had done in the past, the

methodology they used, the designs that worked and the ones that did not work. In particular the

last two GDP projects were carefully investigated and they provided the team with a clearer picture

of how challenging race car design is. The second group of research was focused at race car

aerodynamics. This research was generic and sought to obtain information about the physics

associated with race cars, their most critical aerodynamic components and finally some guidelines

for race car design. The third major research topic was wing and airfoil research, because within this

area there can be a priori significant gain in downforce. The design of wings for race cars, high lift

aerodynamics and some other airfoil-related topics were covered. The aerodynamics of diffuser were

also included as part of the research due to the recent gain in popularity of these components

because of its effectiveness in generating large amounts of downforce. Finally the last topic

researched in depth was wheel aerodynamics, because of the massive effect these mech anical

components have in the overall performance of the car; moreover, the wheel-wing interaction was

regarded as a major component that needed to be properly designed if the performance of the car

was to be improved.

The first CFD studies attempted in this project were the wing and the wheel in isolation.

These studies were performed to test meshing parameters and turbulence models at a small scale

and the main objective was to gain sufficient knowledge with the CFD software to ease the grid

generation of the full car. First, the wing in isolation was tested since it was found to be an

aerodynamic surface representative of what is needed to correctly resolve the boundary layer. The

main goal of this study was to test different meshing approaches (e.g. no prism layer mesh, trimmer

mesh and polyhedral), estimate the boundary layer thickness of the wing and to obtain an

acceptable y+ resolution that could be used in the full car. This was accomplished by first testing the

geometry in 2D to obtain a rough estimate of the boundary layer thickness. Then, a coarse mesh was

generated with refinement in key areas of the domain, such as the wake of the wing, the gaps

between the wings and sharp corners. Next, a grid refinement study was conducted to test the

independency of the results. The results showed that a prism layer is ne eded to obtain correct

pressure and skin friction distribution around the wings, and that a low value y+ to properly resolve

the boundary layer is clearly affordable for a simple geometry such as the wing but not for the entire

car. On the other hand, the study on the wheel in isolation was performed as a consequence of the

pivotal role it plays on the optimisation of components such as the wing and the sidepods. Similar

procedure to that used in the wing in isolation study was followed here with different types of mesh,

grid refinement studies, and use of different turbulence models. No appreciable differences in results

were found with different turbulence models. It was proven difficult to simulate the rotating wheel in

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isolation with pure RANS due to the intrinsic unsteadiness associated with the wheel flow physics.

Hence URANS was implemented and the results were found to be in accordance with literature, with

most important physics, such as the ground longitudinal vortices, being correctly captured by the

simulations. Furthermore it was concluded that a prism layer was not necessary for this type of

geometry. This study was also important to obtain necessary information about the difficult ph ysics

involved with wheel aerodynamics.

The baseline simulation and analysis followed the preliminary studies and as mentioned

earlier most of the settings and outcomes from these studies were used in the baseline simulation. In

order to use the CAD geometry given, the CAD team had to prepare it for CFD first. Once imported

into the CFD package, the approach that was kept throughout the entire project, was to split the car

into major components where different meshing parameters could be implemented or where the

quantities such as lift, drag or pressure could be monitored. Unlike previous GDP projects, in this

occasion a subtract operation was performed to avoid the usage of a surface wrapper, which has

been found to remarkably alter the geometry of the car in the past. The mesh was generated

following the conclusions from the preliminary studies with refinements in key areas of the car such

as the wake and the region near the car. Different control volumes with different grid densities were

used to increase the number of nodes available in the region of interest. The mesh used after the

mesh dependency study was concluded had 12.5 million cells. The domain where the car was

simulated was half of the cross section of the RJ Mitchell wind tunnel. A domain dependency study

was completed to find out the most suitable length of the domain in front and in the rear of the car.

This study demonstrated the best choice to be 3 and 5 car lengths respectively. Simulations were

carried out with the Realizable K-Epsilon turbulence model and with a prism layer resolution aiming

at y+=30. The numerical results for the baseline car yielded a coefficient of lift of 2.27 and a

coefficient of drag of 0.870 based on the frontal area of the car, with the corresponding aerodynamic

efficiency of 2.6. Results were found to not be in accordance with previous year’s GDP project and

this was attributed to the fact that the baseline car this year had a beam wing in the rear wing that

generated lift. The simulation of the baseline car concluded the first phase of the project.

The second phase of the project otherwise referred to as the design stage, was divided into

three design cycles. Some more preliminary studies were conducted to explore different options

prior to the actual design of the cars. The first investigation was centred at studying different wing

profiles to assess their aerodynamic performance. It was believed that changing the aerodynamic

profiles of the baseline wings could yield a significant amount of downforce due to the conservative

nature of the profiles selected for the baseline car. The study made use of some common high lift

aeronautical airfoils. In addition, a database of racing car profiles was studied and compared to the

more common profiles. For this study the airfoils were tested at free-stream conditions using a

viscous-inviscid code. The results showed that a significant improvement in downforce could be

achieved by using the race car airfoils which were highly cambered. A number of the most successful

profiles were selected and tested in CFD. 3 different multi-element configurations were tested in 2D

and results compared to the baseline multi-element configuration. The most important conclusion

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from this study was that the airflow generated by these airfoils was very turbulent and could damage

the performance of components downstream. Since the designs of the cars was well underway when

the results of the airfoil-wing study were obtained, it was decided to not modify the wing profiles

and to seek gains in downforce elsewhere. While significant effort was placed on the wing-airfoil

study it is believed that the success in performance improvement that was achieved at the end of the

project could have not been achieved with the modified profiles because these would have produced

a very different flowfield in the front wing leading to different flow conditions to downstream

components, some of which had already been designed and improved. On the other hand a second

preliminary study further investigating the mesh parameters of the car was also conducted. This

study sought to improve the quality of the simulations by investigating whether different meshing

parameters to those used in the original baseline car could have been used. The focus here was

placed on the prism layer thickness and the mesh settings on the gaps of the wings, which in the

baseline car were observed to produce a poor quality mesh in the gaps of the front and rear wing.

The results demonstrated that the new settings in the gaps produced a better quality mesh and that

a thinner prism layer on the wings could be used without affecting the overall results.

With the second round of preliminary studies concluded, the design process started. The

First Design Cycle intended to improve the baseline design by introducing subtle changes into the

geometry following the post-processing of the baseline car. The post-processing of the cars was

mainly done by inspecting velocity, vorticity and pressure contours, 2D pressure coefficients along

the surfaces of the car, streamlines, velocity vectors and the Q-Criterion. A radical re-design of the

car was not pursued in this cycle primarily because the team wanted to have a clear picture of the

flow and how it was affected by changes made in different sections of the car. The baseline post

processing revealed significant deficits in all the major components of the car. The major flaws

observed were the shape of the nose, the high distance between the front wheels and the front wing

and the underbody. It was clearly identified the sidepod top as one of the components that needed

to be redesigned due to the substantial amount of lift that it generated caused by a separation

bubble near the leading edge of the sidepod. The main rear wing element was the biggest source of

downforce and drag. The observed deficits were addressed on the A01 design by modifying

substantially the shape of the nosecone and the shape of the body work (especially the engine cover

and the sidepod upper surface). In addition a venturi channel was created on the underbody of the

car, which separated the diffuser from the sidepod underbody. The geometrical modifications

introduced in this design yielded very positive results with an increase in downforce of 5%. The

sidepod top surface went from generating li ft to generating downforce. The diffuser and front wing

performance was also improved. However the redesign of the engine cover appeared to have an

impact on the rear wing, which lost downforce. The aerodynamic efficiency of this design improved

1% and the drag only increased by 3%. Furthermore in this design the front wing and the wheel were

brought closer together which improved the flow quality over the frontal section of the car.

With a more clear understanding on how the flow is altered by implementing modifications

into the car, the A02 designs were made slightly more aggressive than the A01 by introducing

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bargeboards. A total of three A02 designs were attempted with A02-01 and A02-02 being very similar

and A02-03 having a different shaped bargeboard. Major changes were pursued on the rear part of

the car by raising the rear wing in an attempt to regain the downforce lost on the A01 design. On the

front section of the car, the endplate was redesigned to improve the flow quality between the wing

and the wheel and different bargeboard designs were introduced to prevent the flow from leaving

the central area of the car. The main conclusions from this iteration were that the introduction of

the bargeboard greatly affected the flow over the entire car worsening the performance with respect

to both the A01 and the baseline car. The bargeboards did not prevent air from spilling out of the

central area of the car, but instead promoted more spillage with the bargeboard creating a very

strong vortex that affected the flow on the upper surface of the sidepod and finally impinged onto

the rear wing. Furthermore, the bargeboards also created very complex wake behind the front

wheel. As a consequence, the sidepod top lost the downforce gained during the A01 design and the

rear wing lost even more downforce. The overall downforce for A02-01 and A02-02 decreased more

significantly than for the A02-03. Despite the negative consequences of introducing the bargeboard,

some positive effects were noticed mainly in the frontal part of the car where the newly designed

flat plate enhanced the flow quality between the wing and the wheel by breaking up the front wing

edge vortex into two structures.

The final car of the first design cycle eliminated the bargeboards and kept all the remaining

of the changes implemented on the A02 cars. This car revealed the profound negative effect that the

bargeboard had on the overall aerodynamic characteristics of the car. The performance of the

sidepod, the rear wing and the diffuser increased significantly when compared to the A02 designs,

enough to achieve a coefficient of downforce of 2.81, a 25% increase with respect to the baseline car.

The front wing endplate introduced in the A02 designs was found to improve the channelling effect

in the frontal section, the wheel wakes were more coherent and less turbulent than those obtained

previously in the A02 design. Furthermore the double expansion diffuser improved the performance

significantly due to the better flow quality in the central section of the car.

With the First Design Cycle concluded, the Second and Third Design Cycles attempted to

implement a more systematic approach by using an optimisation algorithm to enhance the

performance of the front and rear sections of the car respectively. The optimisation process

presented in this project consisted on selecting two different variables followed by the generation of

an initial sample with different designs. Once the designs were created they were simulated in CFD

and the results were used to construct a surrogate model, which sought for a zone of maximum

improvement. Further designs in this area of improvement were generated and the best car was the

chosen. A pre-existing Kriging algorithm was used in this phase. For the front wing the two variables

selected were the gap and overlap between the front wing and the wheel following the research that

was conducted and that indicated these parameters are crucial in car design. A sample of 20 different

designs with different front wing gap and overlap values in the A03 car was produced and simulated

in CFD. The model was then updated with 3 other designs until the best design was found. It was

observed that just by changing these two parameters a wide range of downforce values could be

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obtained highlighting its importance in the design of a race car. The selected design, B6,

accomplished a lift coefficient of 2.917 and an efficiency of 3.496 increasing the values obtained for

the A03 design. On the other hand the third design cycle chose to perform an optimisation of the

diffuser by changing the throat and the expansion angle of this component. The baseline car for this

iteration was the B06 and 11 cars composed the initial sample. Once the results indicated an area

where the maximum could be found, two other designs were generated but they were not found to

improve the downforce of the car. Hence the car chosen increased the downforce up to 2.943. Post-

processing of this final car showed a significant improvement in diffuser performance as well as

sidepod underbody performance caused by the different channels that were created to manage and

separate the flow between these two components. The front wing also increased its performance

despite not altering the airfoil profiles. Also worth mentioning the decrease in lift generated by rear

and front wing due to the better management of front endplate vortex with the re-designed

endplate. Inspection of 2D plots on the diffuser showed that the pressure pumping created by the

double expansion is significantly better than that seen on the baseline car.

Before moving to the final conclusions it is necessary to point out that up to this point little

has been said about the significant changes in height that the rear wing has suffered throughout the

design process. To recall, during the A02 design, the rear wing was raised slightly to improve the flow

quality of this component. However, further inspection of the car geometry in CAD revealed that the

rear wing had been raised to a height that exceeded the maximum allowable height by the hill -climb

regulations. Hence it needed to be lowered in between the two optimisation cycles, but the change

in height of the rear wing did not adversely affect the results, in part due to the fact that the overall

configuration remained untouched as it was not attempted to modify the airfoils.

With the overview of the entire project finalized, it is possible to present some final remarks

that arose from the team's final meetings.

From a performance perspective, there is no doubt that the main goals of the project have

been met. The final car showed a substantial improvement from the baseline, greatly increasing

downforce and reducing drag, as a consequence of the much improved flow management around

the vehicle.

The organic approach to the improvement process proved itself to be a winning concept,

allowing all team members to grasp the main flow physics of a racing car, and to understand how to

influence them via part design. In this view, it was definitely worthwhile to pe rform full-car CFD

simulations only, in order to obtain every time the correct feedback on how the newly introduced

components behaved. This approach required substantial management capabilities, since all the

team needed to work on the same model at the same time, which required all the modifications to

be correctly recorder and notified to all the other members. Nonetheless, once the proper workflow

was established, all the members were able to analyse the post-processed images, propose

adjustments, and appreciate how these affected both numerical results and flow structures. It is also

to be noted how this methodology was made possible by the “work-as-a-company” concept, which

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required team members to work together for an allocated amount of time every week: this boosted

communication and cohesion of the members themselves.

It is also valuable to briefly comment upon the technological resources that were employed.

Right from the start, the team realised how crucial it is to have people that are specialised in some

specific software or field, since they can take the lead for a particular task and jum p-start the

respective departments. In this view, the background of some team members, that included

knowledge of CAD and CFD packages, was beneficial to the completion of the project. Additionally, it

is stressed the importance of having a good quality CAD file of the car, since this smoothens the

exporting and meshing procedures; this did not happen for the baseline car, which led to delays in

the first CFD analyses, since the file needed to be repaired. Eventually, an unsatisfactory CAD file can

hamper the simulations itself, and produce diverging residuals. The team also recognises the

relevance of mesh settings, which greatly affect the final results: in hindsight, it is noticed how it is

better to perform a detailed study on the significance and influence of each mesh parameter instead

that proceeding by trial-and-error. This holds, in general, for all the relevant settings of a CFD

analysis, be those the physical domain or the turbulence model choice. Given the vast amount of

time normally required for a complete simulations, it is easy to guess how a single error can lead to

unacceptable time waste: as usual in engineering, a great attention to detail is required, along with a

hair-splitting mentality. Furthermore, it is to be remarked the impact that computational power has

on the design possibilities: the introduction of a new, faster supercomputer allowed the team to

perform more simulations than initially expected, and unquestionably more than any previous team.

Finally, it is fruitful to examine how the numerical optimisation affected the design process,

since this was arguably the main innovation introduced in the project. First, it is to be record how the

outcome depends on the baseline, and of the choice of the variables: this technique is, as a matter of

fact, efficient when it is used for fine tuning, and cannot be used to seek major improvements in the

initial stages; moreover, it requires a careful and educated selection of the parameters to be

employed: they have to be influential on the overall physics of the car, and the different CAD models

should ideally be easy to prepare. Given these premises, the mathematical tool (Kriging algorithm)

proved to be powerful, allowing significant improvement to be obtained in a relatively short amount

of time, and moreover no engineering knowledge at all is needed, if the variables are already

provided. It is to be stressed how this procedure benefits from the existence of some kind of

software automatisation, which allows for the CAD files and CFD cases to be semi-automatically set

up and used: the JAVA macros employed by the team saved a significant amount of time, made

possible the production of more than 20 simulations in a minimal time span, and ensured

consistency. Same concept holds for the high parameterisation level of the CAD design, which was

pursued from the very beginning of the project.

All in all, a noteworthy improvement in aerodynamic performance was obtained, thanks to

both reverse engineering design approach and numerical optimisation. All team members were

involved in each of the main task required, and built a working knowledge of the main features of

186

the flow around an open-wheel race car, along with an expertise on the main CAD and CFD tools

employed to design and analyse it.

187

6. Further Work

As the project neared completion, the team realised that there were additional studies that

could have been accomplished provided there was no time constraint. This section tries to

encompass briefly some of the approaches that could be performed if the project were to continue.

The addition pertain to two main areas: on one side, the possible improvements in the actual design

of the car, with the introduction of further modified components. On the other, any supplementary

alteration to the general methodology

Concerning the geometry modifications, it is believed that employing new airfoil sections on

the wings of the car could lead to significant advantages, both in sheer numbers and flow

management. As previously discussed, the front wing and rear wing airfoil profiles were left

untouched. The use of these airfoils is especially encouraged for the rear wing elements since they

are in a region of the car where it is possible to generate greater amount of lift without being

detrimental to any other element downstream. Furthermore, it was shown that the performance

could have been improved substantially, had the rear wing been investigated in detail, judging by the

results of the final car, which showed a drop in rear wing performance when compared to the

baseline car. Clearly a more detailed study on the rear wing could be done in a similar fashion to the

two optimisation cycles shown in the present work, perhaps focusing on the optimum angle of attack

of the rear wing which could be proven to be sensitive to the alterations made on the engine cover.

In addition, another optimisation cycle on the rear wing could be conducted with parameters

such as the height and angle of attack of the beam wing with respect to the diffuser, seeking for a

combination that can increase the diffuser’s performance. This is motivated by the fact that the

beam wing is introduced into the car solely aiming to increase diffuser performance. This was not

investigated deeply, and from the only simulation that was carried out with a beam wing, no

significant performance improvement from the interaction of the diffuser and beam wing was

appreciable. Moreover the Louvers that have been introduced did show to have an effect on the

geometry but it would be appropriate to optimize the shape of these louvers to obtain better

performance.

As regards to the front wing, further work on the shape of the front endplates could yield

better results owing to improved handling and channelling of the edge vortex generated. Also, the

wheel analysis was done on the wheel geometry provided from the baseline. Hence, it would be

prudent to try achieving more realistic rim geometry before analysis. In addition, there is always

research to be conducted regarding the wheel’s contact patch. It has to take into consideration many

factors including but not restricted to the sagging, mesh quality in that region and weight of the total

car.

Another suggestion is to implement the airfoil shapes explored in the airfoil study in the

sidepods, effectively making it into an inverted wing in ground effect, thus generating more

downforce. Moreover in the current design, the sidepod, near the rear wheel is in the shape of a

bended plate. It is known that the use of flat plates instead could offer extra downforce taking profi t

188

of the stagnation pressure produced by the rear wheel. Hence this could be further investigated for a

better downforce configuration.

Even after modifying the cockpit in a major way, the team believes that there is more to be

exploited by redesigning the cockpit area, including the helmet. This area is a source of drag and

hence, efficiency of the whole car can be improved by changing the design. A small design

modification to the splitter in the underbody can make a difference in the performance of the

diffuser as a whole and can be redesigned to feed more air into the diffuser. It is noted here that the

design of the splitter in this particular configuration (with absence of a flat underbody) has been

shown to be very complicated and it is worth a deep investigation to improve the flow characteristics

that enter the diffuser. Furthermore, a different configuration with a flat undebody could be also

explored, as this seems to be the standard configuration in most racing series around the world.

Another suggestion would be to include a double-decker diffuser and vertical strakes in the diffuser

exit, which could improve downforce generation by better managing the side vortices. It is to be

noted how many secondary components of the car were completely negle cted, e.g. the suspension

struts, the brake ducts,

As far as CFD is concerned, the obvious suggestion is to try simulating the whole car, and not

just a half section. This may prove beneficial as most of the aerodynamic phenomena around the car

may not be truly symmetrical and when simulated in their entirety, the results may vary. In addition

to this, it may be worthwhile to try and implement a better simulation approach like URANS or

Hybrid RANS/LES. Accuracy of results in such cases is higher than the steady RANS models that

display time averaged results, leading to better design insight and hence more realistic designs. This

probably serves as a long-term suggestion, since their computational is prohibitive. Moreover, the

teams recognises as very important the choice of the turbulence model, and advises the successors

to allow a fair amount of time to discuss and choose it. As time goes by, dynamic meshing in a CFD

environment is becoming simpler to implement and some codes, like STAR-CCM+ have a very user

friendly interface to generate them. Using the same, it is possible to simulate heaving, rotation and

even harmonic motion. This can be implemented in the investigation process to have a better idea of

the performance of the design in realistic scenarios by simulating the car to be heaving when it

passes over uneven surfaces or yawing (turning). The sidepod and engine inlets are simulated as

pressure outlets, which means that once the air enters them, it exits the system and does not re -

enter. This leads to numerical problems like in case of continuity, as there is more than one outlet to

the air that inters through the inlet. Further investigation in this regard, like using porous media

instead of outlets, can be beneficial. inlet. Further investigation in this regard, like using porous

media instead of outlets, can prove to be beneficial.

189

7. References

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Open Wheel Racing Car Model”

Motor Sport Association – United Kingdom – MSA, [online], available: http://

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Zhang, X., Zerihan, J., Aerodynamics of a Double-element Wing in Ground Effect. AIAA Journal,

Vol. 41, 2003 pp. 1007-1015.

Zerihan, J., Zhang, X., Toet, W., Ground Effect Aerodynamics of Race Cars, Annual Review of Fluid

Mechanics, Vol. 59, No. 1, 2006, pp. 33-49.

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Computational Study,” SAE Publication 960909.

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501-530.

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Symposium of the Technology and Science of Low-Speed and Motorless Flight, Soaring Society

of America, Los Angeles, CA, 1974, pp. 97 101; also AIAA Paper 74-1018, Sept. 1974.

Gopalarathnam A. and Selig M. S., “Design of high-lift airfoils for low aspect ratio wings with

endplates”. 15th AIAA Applied Aerodynamics Conference, 1997.

Nelson, D., “Numerical Optimization of Airfoils in Low Reynolds Number Flows”, Journal of

Aircraft, Vol. 46, No. 1, January-February 2009.

Ruhrmann, A. and Zhang, X. Influence of diffuser angle on a bluff body in ground effect. Trans.

ASME, J. Fluids Engng, 2003, 125(2), 332–338.

Zhang, X., Senior, A., and Ruhrmann, A. Vortices behind a bluff body with an upswept aft section

in ground effect. Int. J. Heat Fluid Flow, 2004, 25(1).

Senior, A. and Zhang, X. The force and pressure of a diffuser-equipped bluff body in ground effect.

Trans. ASME, J. Fluids Engng, 2001, 123(1), 105–111.

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Cooper, K. R. Bertenyi, T. Dutil, G. Syms, J. Sovran, G. The Aerodynamic Performance of

Automotive Underbody Diffusers, SAE 980030, 1998

Jowsey L., Passmore M., Experimental study of multiple-channel automotive underbody diffusers,

Proc. IMechE Vol. 224 Part D: J. Automobile, 2010

Puglisevich S., Page G., Large eddy simulation of the flow around a diffuser-equipped bluff body

in ground effect, J. Automobile, Proceedings of the ASME 2011 International Mechanical

Engineering Congress, Denver, 2011

Van den Berg M.A., Aerodynamic Interaction of an Inverted Wing with a Rotating Wheel, PhD

Thesis, University of Southampton, 2007

Bredberg, J., “On the Wall Boundary Condition for Turbulence Models.” Report 00/4, Department

of Thermo and Fluid Dynamics, Chalmers University of Technology, 2000.

STAR-CCM+ Training manual Version 01/12, CD-Adapco.

Zhang X. et al., Ground effect aerodynamics of race cars , Applied Mechanics Review ,

Transactions of the ASME, Vol. 59, 2006.

A. Cogotti, Aerodynamic characteristics of car wheels. Int. J. of Vehicle Design, pages 173 -196,

1983. Special Publication SP3.

Mears, Andrew Paul (2004) The aerodynamic characteristics of an exposed racing car wheel , PhD

Thesis, Durham University.

L. Axon, The Aerodynamic Characteristics of Automobile Wheels - CFD Prediction and Wind

Tunnel Experiment. PhD thesis, Cranfield University: College of Aeronautics, 1999.

W. R. Stapleford and G. W. Carr, Aerodynamic characteristics of exposed rotating wheels

Technical report 1970/2, MIRA, 1970.

Versteeg H.K., Malalasekera W., An Introduction to computational fluid dynamics, 1st edition,

Longman Scientific & Technical

Saddington A.J., Knowles R.D., Knowles K., Laser Doppler anemometry measurements in the

near-wake

Hunt, J. C. R., Wray, A. A. & Moin, P. 1988 Eddies, stream, and convergence zones in turbulent

flows. Center for Turbulence Research Report CTR-S88, pp. 193–208.

Urbana-Champaign, Department of Aerospace Engineering | University of Illinois. UIUC Airfoil

Coordinates Database. Retrieved on 17 February 2013

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Publishing, 2011

FORRESTER, A. I. J. , "SESG6019 notes: Design Search and optimisation - case study 1:Fast global

optimisation", 2013.

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D. G. Krige, "A statistical approach to some mine valuation and allied problems on the

Witwatersrand", MSc thesis., University of the Witwatersrand, Johannesburg, 1951.

Jerome Sacks, William J. Welch, Toby J. Mitchell & Henry P. Wynn; Design and Analysis of

Computer Experiments; Statistical Science, 1989, Vol. 4 No. 4; Pages 409 – 435.

192

8. Appendix 1 - Regulations

The MSA hill climb regulations specified as follows:

Ground clearance 4 cm minimum

Maximum width ahead of the front wheels is 150 cm

Maximum width behind the front wheels is 140 cm

Maximum height of any part wider than 110cm, ahead of front wheels should not

exceed the top of the front wheel rim

Maximum height 90 cm from the ground

Maximum rear overhang of 150 cm behind real wheel axis

Maximum height is measured with the car in any condition and driver aboard, safety

roll-over bars and air boxes are not included in this measurement

193

9. Appendix 2 - Gantt

Figure 111: Gantt chart of the first semester

194

10. Appendix 3 – Grid Convergence Study for the Front Wing

A simple grid convergence study was carried out to demonstrate the grid independent

nature of the results obtained in this study.

Figure 112: Grid convergence for the front wing study

195

11. Appendix 4 – Sample Calculations for Boundary Layer Estimation

of 2-D Profiles

The flow is assumed to be fully turbulent so that the boundary layer thickness is given by

equation (1),

d(x) = 0.37(Rex )- 1/5

(

3)

Where Rex is the Reynolds number. Then, to calculate the first cell size y1, the friction velocity

ut was solved using the following relationship, once again assuming turbulent flow over a smooth

flat plate.

u

u

2

0.0296(Re x )1/5

(

4)

Once the friction velocity is known and a value of y+ is selected the distance y1 is given by

equation (3)

y1 yu

(5)

196

Table 16: Airfoil Database with Maximum Camber and Thickness Values.

197

12. Appendix 5 – Macros

As it has been mentioned over some chapters of this project, JAVA macro files were used in

order to accelerate the entire process of performing the CFD calculations with STAR CCM+. All the

macros were created using the macro recording tool in STAR CCM+ and they were tuned-up to

enable their usage by all the members of the team. Two main JAVA macros were used in this project:

PreMeshPost.java

Geo.java

PreMeshPost macro

PreMeshPost.java involved the entire process of setting up all the mesh continuum and

parameters, the physics continuum and ahe post-processing scenes that were going to be used after

the calculation. This JAVA code was formed by a class which had 9 methods. The public method

Execute() was in charge of calling all the other private methods. So when one of the private methods

was not to be executed it only needed to be commented in the public method. The reason why

private methods were used is because it allows naming all the objects inside them freely. This

procedure facilitates recording different actions in different simulations and merging them externally

into a unique macro code.

198

Figure 125: Diagram of PreMeshPost.java.

Figure 125 shows a summarized diagram of PreMeshPost.java where Execute() is the piece of

code where all the necessary actions that precedes meshing such as creating the computational

domain, setting custom surface sizes for different parts of the car, or creating the volumetric controls

are performed. In addition, all the physics are also set in Execute0(), e.g. the initial conditions, the

turbulence model, the boundary conditions, etc. Execute1() uses the boundary layer mesh settings

from the boundary layer study (see chapter 4.3). Execute2() contains the code necessary to set up

the force coefficients and the frontal area reports. Execute3() performs all the actions required to

create the derived parts that required to create all the Post-Processing scenes once the computation

was finished. Execute4() was added to the main macro in order to enable change in the base size

inside the Lyceum2 without having to download the file or modifying it in a local computer or using

any X-window. Execute5() is the private method used for execution of the meshing pipeline in

Lyceum2. The implementation of this method was probably the easiest one, but at the same time it

turned out to be the most important because it allowed the team to get rid of the local computers

for meshing purposes and use Lyceum2 cluster with instead. Execute6() could have been avoided but

it was useful in the sense that it allowed the team members to mesh the cars and then immediately

run them. Apart from that, this method provided an option for changing the iteration limit so it was

possible again to modify this parameter with the simple action of modifying a text file such as the

macro, instead of opening the actual simulations file. Finally, the last private method was Execute7(),

199

where all the code needed to create the Post-Processing scenes was included. It turned out to be

very useful as it implemented the exact same configurations for all the scenes taken for each car

design, which is a very good practice indeed. Having the same scene configurations is mandatory

when comparing results from different designs. It is to be noted how this division in different blocks

allowed the team to perform only some determined actions, instead of the entire pipeline, in case it

was needed. In fact, just by commenting or uncommenting the features in the public method, it was

possible to enable or disable the commands: this permitted the investigation of the mesh before

running the case, saving a great amount of time.

Geo macro

Geo.java macro was a much simpler than PreMeshPost.java but equally important. The

Geo.java allowed the team to speed up the initial procedures since it automates the process of

importing the geometry into STAR CCM+ and naming all the surfaces of the car, e.g. Front wing 1st

element, Engine Inlet, etc. When performed manually this simple but tedious process usually leads

to errors in naming the surfaces or in selecting the set of surfaces for being named as one. For this

macro the input is in the form of a CAD car design saved in ParaSolid format and it returns: a DBS file

with the entire car surfaces already named properly, and a STAR CCM+ simulation file properly

formatted to be submitted to Lyceum2 with the PreMeshPost macro attached. This macro proved

itself to be exceptionally useful in the optimisation process, where all the cars featured exactly the

same parts, and consequently consistency, along with time -efficiency, was needed.

200

13. Appendix 6 – Sidepod and engine intake study

When the First Optimisation Cycle was completed and the project carried on evolving at

good pace it was questioned, given the good evolution of the project, whether different boundary

conditions could be employed and what advantages or disadvantages they could deploy. Parallel to

the Second Optimisation Cycle this brief study was undertaken to prove validity of the conditions

used and if better configurations could be found. Specifically it was investigated the effect of

changing the boundary conditions imposed both in the engine intake and sidepod inlet. Initially they

were modelled as pressure outlets, and this brief study helped to outline the differences of using

flow split outlets instead. Ideally the boundary condition desired would be zero pressure gradients at

the outlets, by imposing the same pressure than the immediate precedent cells of the outlet

surfaces, but this option is not found in the current software used.

The pressure outlet boundary condition forces the pressure to be constant at a fixed value

which is set manually. For simplicity all the simulations were run with pressure outlets at 0.0 Pa

(gauge pressure) for the engine intake, sidepod inlet and domain outlet. It was tought that forcing

the pressure to be constant at a determined value could not be correct, and another option was

analysed, which was the flow split outlet, the other possible boundary condition that Star -CCM+

offers. The flow split outlet forces an amount of mass flow to abandon the domain through the part

where it is imposed. This was thought to be more physically accurate for our problem, since it does

not oblige the pressure to be constant. However the flow split quantities needed to be adjusted

amongst the three outlets. For this reason mass flow across these faces was monitored in the

simulations run for this purpose and the flow split corresponding to each part easily computed

afterwards. This makes the process iterative, and a number of simulations were needed to obtain

satisfactory results. The way to check if the results were improving or worsening was counting the

number of faces with reversed flow in the mentioned boundaries. This refers to the amount of mass

flow which is entering the domain instead of exiting it, in order to satisfy the governing equatio ns

whilst obeying the imposed boundary condition. Given the geometry and the flow field associated,

however, there might really exist reversed flow faces both in the engine intake and the sidepod inlet.

The engine intake being downstream of the driver’s helmet and the location of the outlet boundary

just slightly inside of the channel could be the reason for having 50 reversed flow faces, highlighted

in the Figure 126. The sidepod inlet on the other hand presents a much more complex problem,

showing a recirculation region between the splitter and the sidepod under channel. Initially 78

reversed flow faces were encountered with the pressure outlet at 0.0 Pa, as shown in the image

below. These numbers of reversed flow faces was the focus of this study.

201

Figure 126: A03 Car reversed flow faces in engine intake (left) and sidepod inlet (right) .

Although apparently the initial solution seemed not to be very unphysical, a series of

simulations increasing the amount of mass flow exiting the domain through the sidepod and the

engine were run, looking forward to find out if major differences could be obtained. The engine

intake was not increased too much given that the initial solution was considered fairly good, and it

was always around the 0.0002% of the total mass flow that enters the domain. By increasing the

sidepod mass flow from 0.0383 kg/s to 0.04 kg/s a reduction of 2 reversed flow faces was obtai ned.

It was thought that very slight changes in those figures could lead to extreme changes in the flow

field and therefore in the results, however the monitored car lift and drag coefficients showed minor

variations below 1% between each simulation. Then the mass flow was doubled and the reversed

flow faces count was reduced to only 5. This simulation (iteration 5) was considered good enough,

and two more runs were tried: further increasing the flow fraction through the engine and sidepod

intakes (iteration 6) and the analogous case with pressure outlets (iteration 7), by imposing the

average pressures. Iteration 6 gave only 4 reversed flow faces in the sidepod and 1 in the engine

intake, hence this was considered the best solution without an extreme increase in mass flow.

Iteration 7 however presented 40 reversed flow faces in the sidepod, which meant a reduction with

respect to the initial solution, but 54 reversed flow faces in the engine intake, which was the worst

solution in this aspect. A summary of the aforementioned iterations that were carried out is listed in

Table 17.

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Table 17: Summary of the engine intake and sidepods inlet study iterations

The theoretical boundary was calculated to give an estimate of the possible mass flow

allowance in each outlet, computing it for air flow entering the entirety of each outlet at freestream

velocity (30 m/s). This was only a rough guidance, since the flow reaching the outlets is not in

freestream conditions. The first simulation (A03-1) was simply to repeat the simulation for the A03

car using the same flow splits which the solution with pressure outlets gave. The purpose of this

initial run was to figure out the basic differences of the two available outlet boundary conditions. By

directing the same amount of mass flow to each outlet but not forcing a constant pressure, it could

then be checked the pressure distribution computed instead. The exactly same number of reversed

flow faces was encountered, however the average pressure was -8.78 Pa for the domain outlet, 27.12

Pa for the sidepod inlet and 25.50 Pa for the engine intake. The positive average pressures led to

think that the flow might be deflected outwards from the engine and sidepod intakes, and Figure 127

and Figure 128 below show what it looked like, especially for the sidepod.

At sight of the summarised results in Table 17 it is obvious that as the study advanced the

resultant lift and drag coefficients gradually increased. The car used for the current study was the last

design of the First Optimisation Cycle the A03, and three cases of interest were analysed in more

detail: the baseline A03, and the A03-6 and A03-7, referred to the iteration 6 and iteration 7 of this

study. Overall the increase in lift was 0.23% for the A03-6 and 0.3% for the A03-7, whereas the drag

increased by 1.2% and 1.07%, respectively. Those changes combined as aerodynamic efficiency (lift

C_L C_D L/D

2,8084 0,8360 3,3591

Iteration Part Massflow [kg/s] Fraction [%] Avg. pressure [Pa] Reversed flow faces [#] C_L C_D L/D

Domain outlet 168,69168750 0,99902711

Sidepod inlet 0,12710983 0,00075277

Engine intake 0,03716891 0,00022012

Domain outlet 168,62050000 0,99957798 -8,78 - 2,8038 0,8353 3,3565

Sidepod inlet 0,03828847 0,00022697 27,12 78

Engine intake 0,03290363 0,00019505 25,50 1

Domain outlet 168,62049860 0,99957797 -8,78 - 2,8014 0,8348 3,3556

Sidepod inlet 0,03828950 0,00022698 26,88 78

Engine intake 0,03290400 0,00019505 25,53 1

Domain outlet 168,62044210 0,99957763 -8,78 - 2,8040 0,8355 3,3561

Sidepod inlet 0,03830000 0,00022704 26,09 78

Engine intake 0,03295000 0,00019533 23,98 1

Domain outlet 168,61869210 0,99956726 -8,76 - 2,8040 0,8359 3,3545

Sidepod inlet 0,04000000 0,00023712 20,24 76

Engine intake 0,03300000 0,00019562 22,03 1

Domain outlet 168,57669210 0,99931828 -8,45 - 2,8140 0,8430 3,3381

Sidepod inlet 0,08000000 0,00047424 -171,40 5

Engine intake 0,03500000 0,00020748 -52,38 1

Domain outlet 168,55169210 0,99917008 -8,25 - 2,8149 0,8460 3,3273

Sidepod inlet 0,10000000 0,00059280 -302,18 4

Engine intake 0,04000000 0,00023712 -261,96 1

Domain outlet 168,58320000 0,99935686 -8,40 - 2,8170 0,8450 3,3337

Sidepod inlet 0,07450000 0,00044163 -175,00 40

Engine intake 0,03391600 0,00020105 -55,00 54

5

6

A03

7

1

2

3

4

Theoretical

boundary

203

over drag) meant that a drop of 0.95% and 0.75% was finalised for each respective case. To further

understand where the changes came from, the lift coefficient of every part was compared between

cases. In Table 18 below the results for the two final iterations are shown, highlighting in red those

worsened figures, in green those that improved and in orange those that remained roughly around

the same values. All percentages were computed with respect to the A03 numbers.

Figure 127: Streamlines around intakes A03.

204

Figure 128: Streamlines around intakes A03-6.

205

Table 18: Lift coefficient by part comparison between A03, A03-6 and A03-7.

From this table it is clear that unlike the overall values, percentages between the separate

parts are relevant. Very large variations were observed for vertical devices, such as struts or

endplates, which are not designed to directly generate downforce. Not surprisingly, gains and losses

in downforce came exactly from the same parts either with pressure outlets or with flow split

outlets. However, further depicting information about the areas located close to where the changes

were introduced, the lift from the named BODY increased about an order of magnitude whilst the

sidepod is generating more lift on its upper surface but more downforce on its under channel. This

will be depicted throughout this section.

The increase in lift generated by the geometries of the part BODY is closely related to the

engine intake larger suction of air; this derived in two associated effects: a slightly weaker upstream

recirculation around the driver and cockpit region, and more importantly a delayed pressure

recovery downstream (at the engine cover) given the increased amount of air that is sunk through

the engine intake. The former does not seem to be detrimental towards lift generation of the body,

the later however was thought to be the main reason of the increase in the non-desired lift. As an

illustrative guidance, visualisation of streamlines released just upstream of the engine intake are

plotted to compare differences between the initial case A03 and A03-6 in Figure 129.

A03-0 A03-6 A03-7Part Net() Net() [%] Net() [%]

------------------------------ ------------- ------------- -------------------------- -------------

Subtract.BODY -1,11E-01 -1,22E-01 -9,7102 -1,21E-01 -8,8807

Subtract.DIFFUSER 5,35E-01 5,53E-01 3,3928 5,51E-01 2,9790

Subtract.FW 1 6,28E-01 6,39E-01 1,6974 6,34E-01 1,0073

Subtract.FW 2 1,72E-01 1,75E-01 1,9884 1,74E-01 1,1698

Subtract.FW 3 4,40E-02 4,52E-02 2,6155 4,47E-02 1,5320

Subtract.FW_ENDPLATE 7,10E-02 7,33E-02 3,1659 7,24E-02 1,9169

Subtract.FW_STRUT 1,02E-06 1,65E-06 60,8851 1,36E-06 32,9028

Subtract.FWH -6,31E-02 -6,70E-02 -6,1819 -6,61E-02 -4,8208

Subtract.NOSE -7,97E-02 -8,09E-02 -1,5045 -8,22E-02 -3,1675

Subtract.RW 1 6,93E-01 6,94E-01 0,2388 6,94E-01 0,1536

Subtract.RW 2 2,91E-01 2,92E-01 0,1890 2,91E-01 0,1049

Subtract.RW 3 1,29E-01 1,29E-01 0,0298 1,29E-01 0,0376

Subtract.RW_ENDPLATE 3,37E-04 4,14E-04 22,8772 3,79E-04 12,5628

Subtract.RW_STRUT 2,54E-03 2,46E-03 -2,9572 2,49E-03 -1,7437

Subtract.RWH -1,34E-01 -1,41E-01 -5,8561 -1,41E-01 -5,4734

Subtract.SIDEPOD_BOTTOM 4,52E-01 4,53E-01 0,3123 4,58E-01 1,4783

Subtract.SIDEPOD_TOP 1,79E-01 1,70E-01 -5,0166 1,73E-01 -3,5232

------------------------------ ------------- ------------- -------------------------- -------------

Total: 2,808368 2,81489 0,2322 2,81366 0,19

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Figure 129: streamlines around engine cover to show pressure recovery in A03 (top) and A03-6 (bottom).

At sight of the images of figure Figure 127 it was noticed the large separation region present

upstream and below the sidepod inlet. This was not expected a priori and was not clearly understood

physically, but Figure 128 shows the same images for the A03-6 case, highlighting discrepancies with

the initial solution. The engine intake region however also presents separation but this was expected

due to the nature of the geometry of the cockpit modelled. Moreover differences between cases

concerning this region were not noticed in terms of flow field upstream.

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As previously commented a slight difference can be observed between the engine intake

solution in the above Figure 127 and Figure 128. What was noticeable was the reduced recirculation

region in front of the sidepod inlet, clearly motivated by the larger amount of air being sucked

through this outlet. The sidepods performance was analysed in more detail, given that its lower

surface was designed to generate a large suction region. From Table 18 it can be observed that the

downforce generated in the underchannel in slightly increased, but on the other hand the downforce

generated by other surfaces of the sidepod is reduced. The graph on Figure 130 shows where the

differences came from, by comparing the pressure distributions around the sidepod for the three

cases.

Figure 130: pressure distribution around sidepod at z = 0.1m.

Most of the difference is concentrated at the beginning of the sidepod, close to where the

flow field has changed the most. The suction surface pressure peak between x=0.6 and 0.7m was

increased as the physics of the case differ from the initial A03 simulation. How this was produced is

more clearly shown in the Figure 131, where the streamlines released upstream from the sidepod

inlet and the wall shear stress in x-direction are plotted for each of the three analysed cases.

Negative wall shear stress in x-direction was assumed to give a snapshot of the mean flow separation

resolved. It was observed that with the new boundary conditions for iterations 6 and 7 the

recirculation region is much smaller, therefore the airflow incoming the under channel of the sidepod

hits with more strength the suction surface, hence increasing the above mentioned pressure peak.

Solution for A03-7 is closer to the initial case given that it also employs pressure outlet. It can also be

inferred from the streamline images that the flow upstream is slightly better behaved with the new

boundary conditions, incurring in the slight improvement in the front wing performance as well as

the diffuser, whose performance is crucially dependent on how the flow enters it.

Further exploration of the flow field was investigated by the use of Q-criterion, which gives a

more instantaneous image of how the air is behaving around the car under the different conditions.

Visualising regions of high vorticity differences were negligible, and images are not shown due to lack

of interest. This, in addition to the minimal overall differences led to understand that even though

changes were appreciable they were not so crucial on the obtained results.

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Figure 131: A03, A03-6 and A03-7 from top to bottom: streamlines released upstream from the sidepod inlet and wall

shear stress in x-direction.

This study served to understand in more detail the conditions simulated, however the results

did not derive in further actions for the project evolution. When using flow split outlet instead of

pressure outlet as a boundary condition the mass flow can be tuned manually, and even after

doubling the initially simulated mass flow through the sidepod inlet the increase in C L was of 0.23%.

Taking also into account the uncertainty on what the mass flow through the sidepod inlet or engine

intake had to be, assessing what was better or worse was not trivial. After the work done for this

section flow split outlets seemed to be a more realistic option, but still given the very slight changes

in overall performance and the huge doubtfulness around, it was decided to keep the cases as

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initially set up. This is supported from the point of view that trends are more relevant than actual

values, which was stated as one of the assumptions at the beginning of the project. It would have

been ideal to test the use of zero pressure gradient at those boundaries, but the current version of

Star-CCM+ did not allow to do so. A much more complex solution would be to model entirely the

inner flows in the sidepod and the engine, modelling radiators and the engine as porous bodies.

However this route was considered not to be efficient for the team’s purposes and was therefore

discarded. As a recommendation for upcoming years groups a deeper exploration on the effect of

these boundary conditions as well as finding a good tuning of split flows could be advantageous to

carry out at an early stage of the project.

GDP Project 2013 - Final Version

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