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Computational aerodynamic analysis of a rear spoiler on a car in two dimensions.

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- 1. Computational aerodynamic analysis of a rear spoiler on a car in two dimensions By Dibyajyoti Laha (Student No: 1227201) Supervisor Dr. Ahad Ramezanpour A dissertation submitted in partial fulfilment for the degree Of Bachelor of Engineering Honours (Engineering: Mechanical) In Mechanical Engineering Faculty of Science & Technology
- 2. 1 ACKNOWLEDGMENT This research paper is a report of “Aerodynamics of a rear spoiler on a car in 2D using CFD software to analyse the results”. It was only possible through the help of the course moderators including: Lecturers, industrial CFD consultants, and in essence, all sentient beings. On the same occasion, please allow me to dedicate my acknowledgment of gratitude towards the following significant lectures and contributors for the research project. First and foremost, I would like to show my gratitude and thanks to Dr. Ahad Ramezanpour for his dedication to teach the every bits and parts of the thermodynamics and ANSYS Fluent which have been a major use in the research project and devoting his invaluable time along with advice to hold a grip on the report writing. He spent his class lectures to find the best possible solutions to the problems generated while studying and helping to improve the standard of the brainstorming the solutions for the report. Not only being a professor, he has been a great mentor & supervisor for the project with priceless feedback. Secondly I would like to thank Dr. Habtom Mebrahtu in advising to write a research report referring IET publications as my personal tutor at Anglia Ruskin University, Anglia Ruskin University for providing the infrastructure and the ANSYS Laboratory for conducting the research. I would also like to extend my gratitude to my colleague Miss Ambika Samanta for assisting and explaining the research survey, software at times when needed. Alongside my parents, my father Mr. Dilip Kumar Laha, Deputy Site Manager, Jacobs Engineering India Pvt. Ltd, a Jacobs Engineering for briefing me and making me understand the investment of potential in the world of designing and Finite Element Analysis in industrial background and my mother Mrs. Chaitali Laha for boosting my enthusiasm while studying abroad while also funding me financially for the project.
- 3. 2 DECLARATION BY THE AUTHOR I hereby declare that the work in this report is my own except for quotations and summaries which have been duly acknowledged by in citation references. I have clearly stated the contribution of others to the production of this work as a whole. I have read, understood and complied with the Anglia Ruskin University academic regulations regarding the assessment offences, including but not limited to plagiarism. I have not used material contained in this work in any other submission for an academic award or part thereof. I acknowledge and agree that this work may be retained by Anglia Ruskin Ruskin University and made available to others for research and study in either an electronic format or paper format or both of these and also may be available for library or inter-library loan. This is on the understanding that no quotation from this work may be made without proper acknowledgment. Candidate Signature: …………………………………………………….. Candidate Student Number: ………………………………………………. Date: ………………………………………………………………………..
- 4. 3 Table of Contents Table of Figures................................................................................................................................................... 8 List of Tables:................................................................................................................................................ 11 ABSTRACT ..................................................................................................................................................... 12 NOMENCLATURE:............................................................................................................................... 13 Terms used: ....................................................................................................................................... 13 Variables relating to CFD results: ..................................................................................................... 13 CHAPTER - 1 ................................................................................................................................................... 14 INTRODUCTION......................................................................................................................................... 14 1.1 PROJECT INTRODUCTION.................................................................................................... 15 1.2 PROBLEM BACKGROUND..................................................................................................... 16 1.3 PROJECT AIM & OBJECTIVE............................................................................................... 17 1.4 DISSERTATION DESCRIPTION ............................................................................................ 17 1.5 PROJECT SURVEY & OBSERVATION ................................................................................ 18 1.6 PROJECT LIMITATION .......................................................................................................... 19 CHAPTER 2...................................................................................................................................................... 20 LITERATURE REVIEW & THEORITICAL BACKGROUND ................................................................ 20 2.1 LITERATURE REVIEW........................................................................................................... 21 2.2 GENERAL CONCEPTS............................................................................................................. 24 2.2.1 LIFT CONCEPT ................................................................................................................... 24 2.2.2 DRAG CONCEPT................................................................................................................. 25 2.2.3 BERNOULLI’S EQUATION ............................................................................................... 26 Application in the research model:.................................................................................................. 27 2.3 AERODYNAMIC FORCES....................................................................................................... 28 2.3.1 DRAG FORCE...................................................................................................................... 28 2.2.2 LIFT FORCE......................................................................................................................... 28 2.3.3 DOWNFORCE...................................................................................................................... 29 2.4 AERODYNAMIC PRESSURE DISTRIBUTION.................................................................... 30 Application in the research work:...................................................................................................... 34 2.5 RELATION BETWEEN COFFICIENTS OF DRAG & LIFT............................................... 34 2.6 AERODYNAMIC PRODUCT - REAR SPOILERS................................................................ 34 2.6.1 HEIGHT OF REAR SPOLIERS ........................................................................................... 35
- 5. 4 2.7 CONTINUTY EQUATION........................................................................................................ 37 Application in the research:............................................................................................................... 38 2.8 NAVIER STOKES EQUATION................................................................................................ 38 Application in the research:............................................................................................................... 40 2.9 DIMENSIONAL ANALYSIS & SIMILITUDE ....................................................................... 40 Application in the research:............................................................................................................... 40 CHAPTER 3...................................................................................................................................................... 41 METHODOLOGY........................................................................................................................................ 41 3.1 INTRODUCTION ...................................................................................................................... 42 3.1.1 QUALITATIVE VS. QUANTITATIVE: QUESTIONS & APPROACH............................ 42 Qualitative Methods: ..................................................................................................................... 42 Coherence of qualitative method in the research work: .................................................................... 42 Quantitative Methods: ................................................................................................................... 43 Coherence of qualitative method in the research work: .................................................................... 43 3.2 ENGINEERING DETERMINING METHODS ..................................................................... 44 3.2.1 EXPERIMENTAL METHOD: ............................................................................................. 44 3.2.2 ANALYTICAL METHOD: .................................................................................................. 45 3.2.3 NUMERICAL METHOD: .................................................................................................... 45 1. Finite Difference Method: ......................................................................................................... 45 2. Finite Element Method:............................................................................................................. 46 3. Finite Volume Method: ............................................................................................................. 46 3.3 COMPUTATIONAL FLUID DYNAMICS ............................................................................. 47 3.3.1 INTRODUCTION TO CFD.................................................................................................. 47 3.3.2 HOW DOES CFD MAKE PREDICTIONS?........................................................................ 47 3.3.3 CFD ANALYSIS PROCESS ................................................................................................ 48 3.3.4 MESHING............................................................................................................................. 49 1. Structured mesh generation:.............................................................................................................. 49 a. Algebraic grid generation: ............................................................................................................. 50 b. PDE Mesh generation:................................................................................................................... 50 2. Unstructured mesh generation:...................................................................................................... 51 3.3.5 MESH QUALITY ................................................................................................................. 53 1. Mesh Element Distribution:.......................................................................................................... 53 2. Cell Quality: ................................................................................................................................. 54 3.3.6 BOUNDARY CONDITIONS ............................................................................................... 54
- 6. 5 Inlet & Outlet Boundary:................................................................................................................... 54 3.3.7 COMPUTING SETUP .......................................................................................................... 55 3.3.8 CONVERGENCE ................................................................................................................. 56 3.3.9 ERRORS................................................................................................................................ 56 Physical Errors: ................................................................................................................................. 56 Discretization Error: .......................................................................................................................... 57 Programming Errors:......................................................................................................................... 57 Computer-round off Errors:............................................................................................................... 57 Iterative Convergence Error: ............................................................................................................. 57 CHAPTER 4...................................................................................................................................................... 58 NUMERICAL SETUP.................................................................................................................................. 58 4.1 INTRODUCTION ....................................................................................................................... 59 4.2 DEVELOPING THE DIGITAL BASE LINE MODEL .......................................................... 60 4.2.1 GEOMETRY......................................................................................................................... 60 4.3 MODELING IN THE INVENTOR 2014...................................................................................... 61 4.4 DESIGNING THE BLM............................................................................................................... 61 Original Specifications:......................................................................................................................... 61 Inventor Steps:....................................................................................................................................... 62 Step 1: Initial Setup ........................................................................................................................... 62 Step 2: Selecting the design sketch.................................................................................................... 62 Step 3: Selecting the work plane ....................................................................................................... 63 Step 4: Importing Image based design .............................................................................................. 63 Step 5: Designing using points.......................................................................................................... 64 Step 6: Finalising the sketch and dimensioning ................................................................................ 64 Step 7: Creating the boundary walls.................................................................................................. 65 Step 8: Generating the Boundary surface.......................................................................................... 65 4.4.1. BLM PRESENTATION........................................................................................................ 67 4.5 MODEL WITH BUILT-IN SPOILER BY MANUFACTURER............................................ 68 4.6 MODEL WITH DECKLID SPOILER...................................................................................... 69 4.7 MODEL WITH OPEN TYPE SPOILER ................................................................................. 71 4.8 ANSYS WORKBENCH SETUP................................................................................................ 72 Step 1: Extracting the CAD file......................................................................................................... 72 Step 2: Updating the boundary condition for the FLUENT .............................................................. 73 Step 3: Setting the Meshing........................................................................................................... 76
- 7. 6 Step 4: FLUENT Setup................................................................................................................. 79 4.9 POST PROCESSING SET UP................................................................................................... 80 4.10 RESIDUALS & ERRORS ......................................................................................................... 86 CHAPTER 5...................................................................................................................................................... 87 ANSYS FLUENT RESULTS & ANALYSIS............................................................................................... 87 5.1 INTRODUCTION ....................................................................................................................... 88 5.2 ANALYSIS FOR BLM ............................................................................................................... 88 Velocity Contours:............................................................................................................................. 88 Pressure Contours:............................................................................................................................. 89 Static pressure.................................................................................................................................... 90 Turbulence Contours: ........................................................................................................................ 90 5.3 ANALYSIS FOR MANUFACTURER MODEL...................................................................... 91 Velocity Contours:............................................................................................................................. 91 Pressure Contours:............................................................................................................................. 92 Turbulence Contours: ........................................................................................................................ 94 5.4 ANALYSIS FOR DECK LID SPOILER .................................................................................. 96 Velocity Contours:............................................................................................................................. 96 Pressure Contours:............................................................................................................................. 97 Turbulence Contours: ........................................................................................................................ 98 5.5 ANALYSIS FOR OPEN STYLE SPOILER............................................................................. 99 Velocity Contours:............................................................................................................................. 99 Pressure Contours:........................................................................................................................... 100 Turbulence Contours: ...................................................................................................................... 101 5.6 VELOCITY MAGNITUDE COMPARISION TABLE: ....................................................... 102 5.7 PRESSURE COMPARISION:................................................................................................. 104 5.8 TURBULENCE COMPARISION........................................................................................... 107 5.9 RESULTANT FORCES............................................................................................................ 109 CHAPTER 6.................................................................................................................................................... 111 CONCLUSION & FUTURE SCOPE ......................................................................................................... 111 Conclusions ............................................................................................................................................ 112 Future Scope .......................................................................................................................................... 113 REFERENCES................................................................................................................................................ 114 APPENDICES................................................................................................................................................. 118 APPENDIX 1 ......................................................................................................................................... 118
- 8. 7 What Are the Navier-Stokes Equations?............................................................................................. 118 How Do They Apply to Simulation and Modeling?................................................................................ 118 Example: Laminar Flow Past a Backstep................................................................................................ 118 Different Flavours of the Navier-Stokes Equations................................................................................. 120 About the Reynolds and Mach Numbers............................................................................................. 120 Low Reynolds Number/Creeping Flow............................................................................................... 120 About the Experiment...................................................................................................................... 121 Modeling the Experiment................................................................................................................ 121 Flow Compressibility .......................................................................................................................... 123 Incompressible Flow ....................................................................................................................... 123 Compressible Flow.......................................................................................................................... 123 What Flow Regimes Cannot Be Solved by the Navier-Stokes Equations?............................................. 125 APPENDIX 2 ......................................................................................................................................... 127 RESEARCH PROPOSAL .................................................................................................................... 127 1. RESEARCH INTRODUCTION ................................................................................................. 127 2. RESEARCH AIM ................................................................................................................... 128 3. RESEARCH OBJECTIVE...................................................................................................... 128 4. RESEARCH LITERATURE REVIEW .................................................................................. 129 5. RESEARCH METHODOLOGY ............................................................................................ 130 PROJECT LIMITATIONS.......................................................................................................... 130 6. OBSERVATIONS & CALCULATIONS ............................................................................... 131 7. RESEARCH CONCLUSION.................................................................................................. 131 RESEARCH ETHICS APPLICATION FORM................................................................................. 132 CV, Cover Letter and Exit Plan........................................................................................................... 138
- 9. 8 Table of Figures Figure 1 Showing spoiler at the back of a sedan car ......................................................................................... 15 Figure 2 Front Spoiler on Maserati ................................................................................................................... 15 Figure 3 Open type rear spoiler......................................................................................................................... 15 Figure 4 Flow of air around a car generating pressure areas & lift directions .................................................. 16 Figure 5 Built-in spoiler .................................................................................................................................... 18 Figure 6 Aftermarket deck lid spoiler................................................................................................................ 18 Figure 7 Different types of spoilers available in market. .................................................................................. 18 Figure 8 Wind tunnel test .................................................................................................................................. 20 Figure 9 Failed La Bomba car........................................................................................................................... 21 Figure 10 Dimitris first aerodynamic car design............................................................................................... 21 Figure 11 Water drop shape .............................................................................................................................. 21 Figure 12 Water drop shaped car Persu............................................................................................................. 21 Figure 13 Porsche 911 streamline car................................................................................................................ 22 Figure 14 Volkswagen Beetle ........................................................................................................................... 22 Figure 15 Coefficient of drag value of cars changing over decade ................................................................... 22 Figure 16 Opel's GT a failure model with spoiler ............................................................................................. 23 Figure 17 shows the direction of flow, Lift and drag ........................................................................................ 25 Figure 18 Flow of air/ fluid around a spherical body to demonstrate low and high pressure regions............... 26 Figure 19 a.) Left shows the low pressure. b) Values of coefficient of pressure around the geometry .......... 27 Figure 20 shows downforce generated due to spoiler. ...................................................................................... 29 Figure 21 shows airflow in profile for the Nissan R35 GTR ............................................................................ 30 Figure 22 shows region of high (blue) & low (yellow) pressure of a corvette Stingray ................................... 31 Figure 23 Pressure Coefficients Plotted Normal to surface............................................................................... 32 Figure 24 Region of high & low pressure around a car..................................................................................... 32 Figure 25 Variation of Cp along with the geometry.......................................................................................... 33 Figure 26 shows the region of high & low pressure along with the car geometry. ........................................... 33 Figure 27 Gillespie experiment of how height of spoiler affects the pressure. ................................................. 35 Figure 28 Variance of pressure coefficient along.............................................................................................. 35 Figure 29 Pressure coefficient along the front end and rear end with & without spoiler.................................. 36 Figure 30 shows values change when spoiler retracts and in action ................................................................. 36 Figure 31 shows different mounting of the rear spoilers affect the Lift and the Drag coffieicient value.......... 36 Figure 32 Body used to show equation of continuity........................................................................................ 37 Figure 33 showing the use of continuity in ANSYS Fluent.............................................................................. 38 Figure 34 Wind Tunnel test of spoiler on Porsche 911 Carrera ........................................................................ 41 Figure 35 Pie chart showing the three different methods of prediction ............................................................ 44 Figure 36 shows a fine structured mesh on a model.......................................................................................... 50 Figure 37 mapping of the physical coordinates on the x, y coordinates............................................................ 50 Figure 38 Generation of unstructured mesh of BMW 3 series model............................................................... 51 Figure 40 adjusting the element sizes and finding the number of elements...................................................... 52 Figure 39 Meshing of the model with minimum 2 & maximum 4 mm element size........................................ 52 Figure 41 meshing with default configurations................................................................................................. 53 Figure 42 meshing obtained adjusting sizing .................................................................................................... 53
- 10. 9 Figure 43 defining the boundary conditions on geometry in ANSYS............................................................... 55 Figure 44 obtaining convergence of the operating equations in ANSYS Fluent before post processing.......... 56 Figure 45 Top and bottom shows analysis of the models in the ANSYS.......................................................... 58 Figure 46 BMW 3 series dimensions ................................................................................................................ 61 Figure 47 Initial steps using inventor ................................................................................................................ 62 Figure 48 generating a 2D sketch on inventor................................................................................................... 62 Figure 49 creating a sketch................................................................................................................................ 63 Figure 50 using image pointing system to generate BMW 3 series model ....................................................... 63 Figure 51 importing the image .......................................................................................................................... 64 Figure 52 creating the constrained sketch ......................................................................................................... 64 Figure 53 creating the boundary walls for ANSYS........................................................................................... 65 Figure 54 creating the boundary patch for boundary walls............................................................................... 66 Figure 55 finishing the boundary patch............................................................................................................. 66 Figure 56 Deck-lid model spoiler...................................................................................................................... 70 Figure 57 ANSYS workbench........................................................................................................................... 72 Figure 58 generating the named boundaries...................................................................................................... 73 Figure 59 generating the named boundary and geometry condition in built-in the model................................ 74 Figure 61 generating the boundaries for Open Spoiler model........................................................................... 75 Figure 60 generating boundary conditions for deck-lid spoiler model.............................................................. 75 Figure 62 default mesh...................................................................................................................................... 76 Figure 63 adjusting the mesh to 1 mm minimum and 2 mm maximum............................................................ 76 Figure 64 Updated mesh of BLM...................................................................................................................... 77 Figure 65 updated mesh of built-in model spoiler............................................................................................. 77 Figure 66 updated mesh of deck-lid spoiler ...................................................................................................... 78 Figure 67 updated mesh for open spoiler .......................................................................................................... 78 Figure 68 Fluent setup....................................................................................................................................... 79 Figure 69 applying the general settings............................................................................................................. 80 Figure 70 changing the velocity formulation .................................................................................................... 81 Figure 71 adjusting the model settings.............................................................................................................. 82 Figure 72 adjusting the fluid selection .............................................................................................................. 82 Figure 73 assigning the input velocity (similar for all 4 cases)......................................................................... 83 Figure 74 selecting the initialization ................................................................................................................. 83 Figure 75 selecting number of iterations for accuracy ...................................................................................... 84 Figure 76 shows converging the equations........................................................................................................ 85 Figure 77 showing the converged equations ..................................................................................................... 85 Figure 78 Velocity magnitude picture from Fluent........................................................................................... 88 Figure 79 pressure contours............................................................................................................................... 89 Figure 80 shows static pressure graph............................................................................................................... 89 Figure 81 shows the stagnation point ................................................................................................................ 90 Figure 82 shows turbulence graph of the BMW Body and the tyres (in red).................................................... 90 Figure 83 Velocity in X axis ............................................................................................................................. 91 Figure 84 Velocity magnitude in manufacturer’s –built in model .................................................................... 91 Figure 85 shows velocity in Y direction............................................................................................................ 92 Figure 86 shows the pressure contours.............................................................................................................. 92 Figure 87 shows the static pressure graph......................................................................................................... 93
- 11. 10 Figure 88 shows same stagnation region as the base line model....................................................................... 93 Figure 89 shows the turbulence in case 2.......................................................................................................... 94 Figure 90 shows the kinetic energy of the turbulence region............................................................................ 95 Figure 91 shows velocity magnitude in deck-lid spoiler................................................................................... 96 Figure 92 shows velocity in x direction ............................................................................................................ 96 Figure 93 enlarged picture showing the lesser velocity around the model........................................................ 97 Figure 94 showing the pressure contours for deck-lid model............................................................................ 97 Figure 95 showing the static pressure region in graph ...................................................................................... 98 Figure 96 shows turbulence in the deck-lid spoiler car..................................................................................... 98 Figure 97 shows the velocity contours for open style spoiler model car........................................................... 99 Figure 98 shows the velocity in x direction....................................................................................................... 99 Figure 99 shows enlarged image of the velocity magnitude ........................................................................... 100 Figure 100 shows the pressure contours in open style spoiler model.............................................................. 100 Figure 101 shows the graph for the static pressure along with the geometry.................................................. 101 Figure 102 shows the turbulence contours for the open style spoiler model................................................... 101 Figure 103 shows the velocity magnitude. From top to bottom Case 1, 2, 3, 4 respectively......................... 102 Figure 104 shows the pressure contours for cases 1, 2, 3, 4 respectively........................................................ 104 Figure 105 shows the pressure graphs for cases 1, 2, 3, 4 respectively........................................................... 105 Figure 106 shows the turbulence regions in cases 1, 2, 3, 4 respectively........................................................ 107 Figure 107 shows region of wake turbulence.................................................................................................. 108 Figure 108 figure of a deck-lid spoiler at rear of BMW 3 series..................................................................... 111
- 12. 11 List of Tables: Table 1 Upper body velocity magnitude for case 1, 2, 3, 4............................................................................. 103 Table 2 Lower body velocity magnitude for cases 1, 2, 3, 4........................................................................... 103 Table 3: Upper body pressure comparison for cases 1, 2, 3, 4....................................................................... 106 Table 4: Lower body pressure comparison for cases 1, 2, 3, 4........................................................................ 106 Table 5: Comparison table for turbulence in cases 1, 2, 3, 4........................................................................... 108 Table 6: Resultant forces on the model car body for cases 1, 2, 3, 4 .............................................................. 109 Table 7: Resultant forces from tyres for cases 1, 2, 3, 4.................................................................................. 109 Table 8: Total drag and lift forces in cases 1, 2, 3, 4....................................................................................... 110
- 13. 12 ABSTRACT Performance, safety, manoeuvrability of a car depends on multi-disciplinary elements/ factors such as car engine, tyres, aerodynamics, and ergonomics of design and most proficiently the driver. With the recent years, inflation in the fuel prices & the demand to have reduced greenhouse emissions has played a significant role in redefining the car aerodynamics. This concentrated on the utilization of negative lift called the down force and resulting in several improvements. Aerodynamic drag created by the car results in the maximum fuel consumption on highway, almost 50%. These aerodynamic properties are used to study the drag & stability of car’s performance. Improvement in the aerodynamic drag can be achieved in multiple ways of introducing active and passive air flow control. Rear spoilers are an example of the passive air flow control of the aerodynamic drag. Generally rear spoilers are used to slower down the air flow and accumulate air which helps increasing the pressure around the trunk and removing any chance of low pressure. The research investigates on the effect of the rear spoiler in the aerodynamic drag, stability and efficiency. The research focuses on 2D model of BMW 3 series sedan car with & without spoilers and the iterations of the rear spoilers are designed in Auto desk inventor software. Modifications in the rear spoilers are done to obtain the minimal drag and maximum downward force. The 2D surface model is extracted as CAD file with, without on the car and individual rear spoilers are analysed on the CFD software ANSYS Fluent. The use of CFD software is to calculate the estimated drag and lift values acting on the car as well as the drag force and the coefficient of lift to improve the drag & stability. It involves understanding the basic applications of the post processing tools. The results showed that the rear spoilers help in reducing drag by creating high pressure at the rear of the car. Key Words: CFD, Fluent, Aerodynamics, Drag, Lift, Meshing, FVM, Inventor, Pressure, Velocity, Turbulence.
- 14. 13 NOMENCLATURE: CD : Coefficient of drag CL : Coefficient of Lift CP : Coefficient of Pressure P : Pressure ρ : Density v : Velocity φ : Quantity A : Area m : Mass 𝛻 : Divergence 𝜕 : Partial Diffentiation t : Time ε : Epsilon ω : Omega Terms used: CFD : Computational Fluid Dynamics CAD : Computer Aided Engineering BLM : Base Line Model Free Stream : Stream line fluid flow 2D : Two dimensional object having length and breadth. Variables relating to CFD results: Drag Force : Component of force acting in the x direction Lift Force : Component of force acting in the Y direction Downforce : Negative of lift force.
- 15. 14 CHAPTER - 1 INTRODUCTION
- 16. 15 1.1 PROJECT INTRODUCTION The 20th century has seen some of the finest sedan cars. From highest speed Hennessey Venom GT reaching up to 270.49 mph, Bugatti Veyron to the luxurious Rolls Royce phantom and much more. Personal cars ranging from hatch backs, sedans & SUV have seen major changes in their design and ergonomics depending on their customer’s choice. Aerodynamics for the cars has changed gradually from initial designers to the manufacturers’ to obtain more power under the hood. This means more stability; better performance, better grip and most prominently increase the comfort of the car. People seem to have sportier look to have the best output performance. This certainly does mean that the cars are equipped with more additional parts such as air dams, front and rear spoilers, and use of VGs (vortex generators) on the surface of the cars. Most widely used are the rear spoilers in the passenger cars. This aids in greater drag reduction and in the same occasion increases the stability of the car. Mostly mounted on the car’s rear depending on the fixing location of the car rear (figure 1,3 ) either a fastback, notch-back or square back. Spoilers can even be mounted in the front of the car as air dams with the bumpers (figure 2). However rear spoilers provide the maximum contribution to the aerodynamic drag and lift. This occurs as rear spoilers stagnant the flow of the air at the rear of the car generating a high pressure region and reducing the low pressure. This directs the flow and offer greater drag reduction, increasing the downward force at the rear and more stability. Figure 1 Showing spoiler at the back of a sedan car Figure 2 Front Spoiler on Maserati Figure 3 Open type rear spoiler
- 17. 16 1.2 PROBLEM BACKGROUND Usually when a person drives the car, the car breaks through the barrier of the air. This creates a region of high pressure as the air flows from the windscreen to the top surface of the car. Gradually there is a region of the low pressure created at the rear of the car. In a worst case scenario, the air which possibly makes way to the rear window creates a notch due to the window dropping down to the trunk, creates a region of vacuum or low pressure which lifts the car and acts on the surface area of the trunk. This is possibly because of the lack of the air being refilled in that region. Technically a spoiler regulates the flow of air around the rear end by accumulating more air refill in the region of the low pressure so that more high pressure region is created with better stability and the car always sticks to the ground. Use of spoiler is quite unique and impressive as most of the sedan & hatch back cars tends to become light at the rear end lifts the car while the spoilers help acting as an air barrier. This also allows reducing the axle-lift and reduction of dirt in the rear surfaces of the car. Figure 4 Flow of air around a car generating pressure areas & lift directions
- 18. 17 1.3 PROJECT AIM & OBJECTIVE The research project aims to accumulate all possible information & Knowledge of a model car BMW 3 series sedan class aerodynamics focusing on the rear spoiler use. Aerodynamic forces can be used to improve the tyre adhesive nature and find the vehicle performance. It describes the side slipping forces acting on the tyre. Using three different types of the rear spoilers & their CFD analysis results to achieve the aim using following objectives in the research project. Analysis of the air flow around the car without the rear spoiler,. Analysis of the air flow around the car with a concept rear spoiler. Effect of the aerodynamics on the car Analysis with the variation of the rear spoilers on the down force, drag and the stability of the car. Estimating the CD (Coefficient of Drift) & CL (Coefficient of Lift) on a high speed run of the car. Comparison of the CD and CL values with (variations in rear spoiler designs) and without rear spoilers. Analysis of all the models on the CFD software ANSYS Fluent. Drawing out the possible outcomes comparing the results & establishing the relation of using rear spoilers for better performance, reduced lift and drag. 1.4 DISSERTATION DESCRIPTION The dissertation report focuses on the investigation of the rear spoiler uses and its effect to the aerodynamic drag, stability and lift as calculated by CD and CL. This obtained by a series of consecutive tests and steps and research. The dissertation report starts with a literature review covering the basic standard principles of aerodynamics which is easy to be understood by a layman. This is followed by theory which focuses of the laws of physics and engineering of aerodynamics governing the equations and results. This also includes the predominant theories and concepts used in the project. As the title reflects Aerodynamics of a car using rear spoiler, a series of the CAD files are generated of the different types of spoilers. This also includes the design of the model car with and without the rear spoiler along with the spoilers. All the designs are generated on the Auto Desk Inventor 2014 as 2D surface. The designs are exported as .iges or .step file to be extracted to the CFD package. ANSYS Fluent is used to run the models for analysis. The CFD software interprets and results the value of CD & CL which is explained in the
- 19. 18 observations & calculations. The obtained results are explained and plotted on a graph. Iteration of the spoilers is compared to the base model. Finally finishing the report with conclusion, future works are also included to underpin the potentials of the further research that could be extended by potential candidates. 1.5 PROJECT SURVEY & OBSERVATION According to a recent study (Stavros, 1995-2015) survey observation, a prominent feature was observed that most of the passenger cars have started using spoilers with ranges from variation in their height. Besides the research reports, surveys from different leading magazines like Car magazine UK, (Tim Pollard, 2015) and observing the inbuilt spoilers built by the car manufacturers were studied. It was found that there were many different types of spoilers that could be used on the cars. Our study focuses on the fast sedan car which has sufficient rear space to have the spoilers mounted on it. Since the fast sedan cars have rear boot space called the notchback, spoilers like deck-lid and free standing spoilers can be used. This results in eliminating the square hatchback car and hatchback spoilers. Most of the fast sedan car manufacturers provide with deck-lid spoilers. This is usually done to minimize any errors during analysing. Figure 6 Aftermarket deck lid spoilerFigure 5 Built-in spoiler Figure 7 Different types of spoilers available in market.
- 20. 19 1.6 PROJECT LIMITATION One of the major limitations of the project was the system requirements. Most of the designs were generated and simulated on a 4 core processor computer with 4 GB of ram. This underscored and limited the designs to be in 2D surface models. As making in 3D would consume more memory power and the lab was equipped with only above specification computers. Using 2D geometry has a major drawback as a restriction of boundary. Other major dependencies were the designs were generated on the Auto Desk inventor professional 2014. The researcher has previous knowledge of using auto desk inventor instead of the designing geometry in ANSYS Fluent. This consumed a major time as modifications and iterations based on the basic model, the researcher had to refer back to the initial models in the CAD format in inventor. Although the project started with a delay in analysis, much of the major time loss was a result of the initial geometry design and using ANSYS Fluent.
- 21. 20 CHAPTER 2 LITERATURE REVIEW & THEORITICAL BACKGROUND Figure 8 Wind tunnel test Picture Courtesy: GTR Blog, 2015
- 22. 21 2.1 LITERATURE REVIEW The purpose of this chapter is to have a generic view on the background of spoilers in the automobile industry. The evolution of the spoilers from a mere product to a must need requirement in the modern period. Alongside with the changes, it also describes the basic concepts and theories of aerodynamics that play a crucial role in the research. It all started in late 1890. The earliest design of a car based on the concepts of aerodynamics was made by Camille Jenatzy, a Belgium race car driver (Dimitris, 2007). This was followed by a conceptual design by Alfa Romeo in 1914. The car was “La Bomba” which was an aerodynamically designed but failed because of world war era and its weird design (Altecc, 2001-2015) After the post-world war era the concept of the aerodynamics on the cars were more focused. Number of concept designs was analysed. This resulted in water dropped shaped cars as, water drops were considered to be aerodynamically perfect (Patrascu, 2011). Figure 11 Water drop shape Figure 10 Dimitris first aerodynamic car design Figure 9 Failed La Bomba car. Figure 12 Water drop shaped car Persu
- 23. 22 In the same era, Germany played an active role in understanding the aerodynamics involved in a car. Infact Germany was forbidden in building aircrafts after the war. This led the aerodyamic engineers to convert their aero ideas into cars and make it an aeronautical flavored (World War planes, 2001). Edmund Rumpler an Viennese pioneer in aerodynamics in cars tested the first car in wind tunnel. The car he tested was Trophenwagen which showed a drag of about 1/3rd of the contenporary vechiles. In the same period Paul Jaray, an Austo-Hungarian designer well know for his aerodynamic and streamline design of cars. He innovated the smooth surfaces of the body of the car, headlamps and cambered windsheilds. Much of his work were copied or adopted in big car manufacturing players like BMW, Mercedes, Audi, Diamler-Benz (Dimitris, 2007). However the streamline shaped cars were never a hit since they generated a high drag cofficient of around 0.4. Some of the streamline designs still in use are like Porsche 911, Vokswagen Beetle. In early 1970’s the crisis for petrol and more efficiency resulted in Kammback cars. Wunibald Kamm an aero- dynamist from Germany brought the concept of aerodynamics in cars, which was the use of air foils. He showed that the air foils with slight truncated tailing edge have slightly lesser drag coefficient compared to completely air foil shaped cars. The post-world war 2 era saw a drastic change in the automobile shapes from brick designs to rain drop and streamline shapes. Figure 14 Volkswagen BeetleFigure 13 Porsche 911 streamline car Figure 15 Coefficient of drag value of cars changing over decade
- 24. 23 All these changes in the car designs were the result of the detailed optimization of the drag improvement in 1970s. It was based on the numerous minor and major modifications in the drag reductions. Detail optimization included the modifications in curvatures, pillars, location of spoilers and much more but reached it limits quiet early. Some of the failure example was Opel’s GT which had a drag coefficient of 0.42 even with streamline design and spoiler. Figure 16 Opel's GT a failure model with spoiler Even yet the detail optimization resulted in the dramatic change but the prior concentration of the car manufacturers was in the reduction of the drag. By this time, shape optimization was given more priority. Re- evaluation of work by the aero dynamists from early 1930s was conducted. This led to a realistic car design and shape with lower drag coefficient. Audi 100 was the first manufactured which a drag coefficient of 0.3 (Edgar, 2006). Current State of Art The current state of art in aerodynamics utilizes both the detail and the shape optimization. The reasonable drag coefficient can vary from 0.25 to 0.35 for modern cars. For future aspects and reasonable target a drag coefficient of 0.25 is idealistic. The evolution of the car spoilers involved use of general concepts & theories of physics. These were flow of air around the streamlined body, effect of the pressure, way the air as a fluid acts when the car is in motion and much more. It is hence very important to discuss them in brief to get a clearer view of the working science behind the aerodynamic product spoiler and the car. From the aircrafts to the cars, the aerodynamicists have invested a mixture of aeronautics in cars that has resulted in more efficient models. Much of the credit in the
- 25. 24 research work of the evolution is involved in experimental coherence with the laws of physics and computational analysis. 2.2 GENERAL CONCEPTS To provide a clear view to the literature review, the whole literature review has been sub categorized into different parts. Each part defines & makes the concepts of the theory easier to be understood. 2.2.1 LIFT CONCEPT In aerodynamics lift (figure 17) is a force that holds an object in the air. In automobiles the pressure difference of the high pressured frontal end to the low pressure rear end generates the lift. But how actually it is generated with velocity? The answer lies in simple physics. Whenever air flows over an object or vice versa, the molecules of the gas move freely. According to David Bernoulli (Bernoulli’s concept explained: 2.1.*) the pressure is directly proportional and relates to the local velocity of the air (NASA, 2013). This explains why velocity varies and pressure too. Lift is always perpendicular to the flow of the air on the automobiles. It is explained by the following equation in aerodynamics: 𝑳 𝑫 = 𝟏 𝟐 𝛒𝐯 𝟐 𝑪𝒍 𝑨 Equation 1 Where 𝑳 𝑫 is the Lift force 𝛒 is the density of the fluid. v speed of the object CL is the lift Coffieicient A is the cross sectional area. This equation will be used further in the chapter of results to find the lift force obtained in the car body. Generally the lift force will be the total force of the forces in y direction in addition to the viscous forces in the y direction.
- 26. 25 2.2.2 DRAG CONCEPT Drag in general physics is referred or defined as the resistive force experienced by an object/ body when it is in motion with respect to the fluid surrounding it. Drag forces are dependent on the velocity of the object and is shown by a formula defined as: 𝑭 𝑫 = 𝟏 𝟐 𝛒𝐯 𝟐 𝑪 𝑫 𝑨 Equation 2 Where FD is the drag force 𝛒 is the density of the fluid v is the speed of the object in the fluid CD is the drag Coffieicient A is the cross sectional area Drag force is highly dependent on the density of the fluid, velocity of the object and cross sectional area of the body acting with the fluid. This means the sleeker the body is less the drag coefficient (which is a dimensionless value) less is the drag force is. However the velocity and density is also proportional to the drag force. This will be used to calculate the net force acting on the x direction on the car body along with the viscous forces. Figure 17 shows the direction of flow, Lift and drag
- 27. 26 2.2.3 BERNOULLI’S EQUATION 𝐏 + 𝟏 𝟐 𝛒𝐯 𝟐 + 𝛒𝐠𝐡 = 𝐂𝐨𝐧𝐬𝐭𝐚𝐧𝐭 Equation 3 The Swiss mathematician & physicist (1700 – 1782) put forward a principle called Bernoulli’s equation (Eqn 3) which held for fluids in ideal state; pressure and density are inversely related: in other terms slowing moving fluids exert more pressure than fast moving fluids. This equation is the fundamentals of the study of the airflow around vehicles. Bernoulli’s equation obtained by integrating Newton’s law F = ma (Munson, Young, and Okishi. 2006) is supported with the following assumptions: Air density does not change with the pressure. Viscous flow of the fluid is neglected. Steady state flow is assumed and always maintained. The fluid flow is compressible. The formula can be applied at any point in the streamline flow. This resulted in the formula being derived to 𝐏 + 𝟏 𝟐 𝛒𝐯 𝟐 + γz = Constant Equation 4 (Munson 2006) Or can be written as 𝐏 𝛒 + 𝟏 𝟐 𝐯 𝟐 = 𝒌 Equation 5 (Katz 1995) The above equation is valid when height is not accountable. Region of Low pressure Region of high pressure. Figure 18 Flow of air/ fluid around a spherical body to demonstrate low and high pressure regions
- 28. 27 Whenever the air flows over the body, it generates a velocity distribution resulting in the aerodynamic loads acting on the body of the vehicle. The first is the shear force acting tangentially on the surface of the vehicle body generating the drag force which is because of the viscous boundary layer. The second force is the pressure force. The pressure force acts perpendicular to the surface of the body and has a contribution to both drag and lift. Technically the vehicle’s downforce is the added effect of the pressure distribution (Katz, 1995) Application in the research model: As the model car/ car pass through a region of fluid, velocity changes with the geometry. This means the geometry will have regions of high velocity and low pressure or vice versa. This is established by the equation 3, that when pressure is maximum, the velocity is zero as they equate to constant and vice versa. Figure 19 a.) Left shows the low pressure. b) Values of coefficient of pressure around the geometry
- 29. 28 2.3 AERODYNAMIC FORCES 2.3.1 DRAG FORCE As already explained in 2.2.2 drag force opposes the motion of the car which is travelling. This ultimately affects performance of the car, fuel economy as well as greater power is required to overcome the force. As usually given by the expression in which is 𝑭 𝑫 = 𝟏 𝟐 𝛒𝐯 𝟐 𝑪 𝑫 𝑨 A: “A” is the frontal area in square of meter (m2 ). The size of vehicle is directly related to the drag properties and is characterised by the value of CDA. However the frontal area is slightly less than the total width & length of the car measured in (m2 ) CD: Coefficient of Drag is a function of Shape, Reynold number (Re), Mach number (Ma), Froude number (Fr) and relative roughness ε/l and is given mathematically by: CD = Ø (Re, Ma, Fr, ε/l) (Munson, 2006) The density of the air ρ is dependent on the temperature, humidity, altitude and pressure. On in any standard condition the density of the air is 1.23 kg/m3 . Any change in the pressure is denoted by PX and temperature by TX using the equation to find the density ρ (Gillespie, 1995). 𝛒 = 𝟏. 𝟐𝟐𝟓 [( 𝑷 𝑿 𝟏𝟎𝟏.𝟑𝟐𝟓 ) ( 𝟐𝟖𝟖.𝟏𝟔 𝟐𝟕𝟑.𝟏𝟔+𝑻𝒙 )] In the eqn [ ] the term 1 2 ρv2 is the dynamic pressure of the air and v is the final velocity of the car. 2.2.2 LIFT FORCE With the Drag force there is one more component of the force called the Lift force which tends lift the car and reduces the friction between the tyres and the road. This means the force acts as the stability of the car and handling too. Given by the eqn 1, i.e. 𝑳 = 𝟏 𝟐 𝛒𝐯 𝟐 𝑪 𝑳 𝑨 , lift force plays a significant role in the aerodynamic optimization of the car.
- 30. 29 The lift force is a dependent on the shape of the car. In the present modern day passenger cars, the coefficient of lift ranges from 0.3 – 0.5 for any wind angle at zero degrees (Huco, 1998). However in crosswind conditions the value of CL can vary from 1 and increases on. This clears that even L is a function of geometry i.e. Ø (geometry). 2.3.3 DOWNFORCE The force that is exerted on to the car by the aerodynamic properties of the rear spoiler is called the downforce. This actually follows Newton’s third law. Every action has equal and opposite reaction. Hence the downforce is the opposite force to the lift and is usually greater. The downforce is responsible for the car to keep on to the track and provide more traction to the wheels. Downforce is usually generated when air mover through and over the parts of the car (Fig ). This occurs when the wing pans are set at angle which forces the air up and through it naturally generating a force downwards – or the opposite force. The positive aspect of having a downforce is that since it adds traction to the wheel, it also adds more stability to the car. The down force can be given by the formula (T. Glossop, S. Jinks, R. Hopton, 2011): 𝑭 𝒘𝒊𝒏𝒈 = 𝟏 𝟐 (𝑾𝑯𝑨𝒐𝑨)(𝑪 𝑫 𝝆𝒗 𝟐 ) Equation 6 Figure 20 shows downforce generated due to spoiler.
- 31. 30 Where Fwing is downforce per wing W is the wing span H is the height of the spoiler. AoA is the angle of attack. CD is the coefficient of drag 𝝆 Is the density 𝒗 𝟐 Is the velocity, squared. However the equation can be simplified as ß the effective area of each wing. 𝑭 𝒘𝒊𝒏𝒈 = 𝟏 𝟐 (𝑨𝒐𝑨)(𝑪 𝑫 𝝆𝒗 𝟐 )ß Equation 7 With the number of the spoilers (front & rear usually ranging from 3 to 5 this equation changes to 𝑭 𝒘𝒊𝒏𝒈 = 𝟏 𝟐 (𝑨𝒐𝑨)(𝑪 𝑫 𝝆𝒗 𝟐 )(ß 𝟏 + ß 𝟐 + ß 𝒏) Equation 8 2.4 AERODYNAMIC PRESSURE DISTRIBUTION As the car moves through an ambient mass of air, the body of the car displaces bundle of imaginary streamline filaments that constituent of the airflow field. Now as the stream line is displaced these streamlines are made to accelerate from rest up to a velocity. This creates a pressure distribution across the air field and the boundary of the body of the car (fig 22 ). The high static pressure also referred as the zero velocity is Figure 21 shows airflow in profile for the Nissan R35 GTR
- 32. 31 generally the stagnation point in the front of the car while the low static pressure area is the wind screen header and the top roof peak of the car. (John D. Smidth, 2014) The coefficient of pressure at any point on the surface of the car is characterised by the following equation given by: 𝑪 𝒑 = (𝐩−𝐩 𝟎) ( 𝟏 𝟐 𝝆 𝒗 𝟐) [Eqn ] where Cp is the coefficient of pressure, p is the static pressure at the vehicle surface, p0 is the free stream static pressure and rest of the variables are defined earlier. Usually the value of Cp at the stagnation point is 1 & zero when the local as well as free static pressure is same all over the flat section of the car body. The negative pressure coefficients can be obtained in certain cases when the local velocities are greater than the free stream velocities. The coefficient of the pressure depends upon the geometry of the car, hence is a function of the shape. The distribution of pressure on most of the surface of the car is done by using Bernoulli’s equation [Eq. ]. The net upward force is calculated by the integration of the total pressure distribution. The force obtained (Which is usually negative) means that there is no requirement to enhance the stability of the car. The exact opposite reactive force is the downforce (explained in 2.2.3) (Duysinx, 2014-2015) Certain experiments on the pressure distribution calculated by different car manufactures and individual research analyses are shown below. This will help to generate a clear concept of the pressure distribution around a car. Region of stagnation Region of low pressure Corvette Stingray. Figure 22 shows region of high (blue) & low (yellow) pressure of a corvette Stingray
- 33. 32 Figure 23 Pressure Coefficients Plotted Normal to surface Figure 24 Region of high & low pressure around a car
- 34. 33 Figure 25 Variation of Cp along with the geometry Figure 26 shows the region of high & low pressure along with the car geometry.
- 35. 34 Application in the research work: We will further use this to find the coefficient of pressure in different models of the BMW 3 series model car. The use of the pressure distribution will be important to understand the region of the high concentration of pressure and low concentration along the geometry of the model car. Apart from the pressure distribution, this topic will help in establishing the concept of topic 2.2.3. 2.5 RELATION BETWEEN COFFICIENTS OF DRAG & LIFT Before we study and the application of the coefficient From an experimental study of a generic car, it was concluded that the coefficients of drag and lift for the flow around the body of the car is predominantly dependent on the slant angle. It was observed with the generic model that from 0o to 29o the growth of the lift is linear and drastically changes to negative when the angle reaches 30o . The drag coefficient is minimum at angle of 15o which means the lift coefficient is close to zero and becomes 50% greater when the slant angle reaches 29o . However beyond the slant angle of 30o the lift and drag becomes nearly constant. (Ivan Dobrev, Fawaz Massouh, 2014). Coefficient of Drag is given by: CD = 𝑭 𝒅 ( 𝟏 𝟐 𝛒𝐯 𝟐 𝑨) ⁄ Equation 9 Coefficient of Lift is given by: CL= 𝑭 𝑳 ( 𝟏 𝟐 𝛒𝐯 𝟐 𝑨) ⁄ Equation 10 Both CD and CL are dimensionless values. 2.6 AERODYNAMIC PRODUCT - REAR SPOILERS The aerodynamic product spoilers are devices that increase the stability of the car, reduce the drag and regulate the pressure difference resulting in the better performance of the car. The spoilers constitute of the front and the rear spoilers. However the rear spoilers contribute to a major aerodynamic stability of the car (Xu-xia Hu, 2011). The aerodynamic devices – rear spoilers acts as a diffuser. Usually mounted on the top surface of the rear trunk to create/ generate pressure difference (explained in 2.3). Rear spoilers provide the following advantages.
- 36. 35 Increases the tires capability to produce the required forces. Offering stability at a very high speed. Better traction generating fuel efficiency Improves braking performance. 2.6.1 HEIGHT OF REAR SPOLIERS The way in which drag and lift happened is depend on the height of the spoiler. The influence on the pressure distribution is shown below. The possibility of reducing drag is comparatively low. In fact on sporty cars, and even more so on racing cars, even an increase in drag is accepted in order to ensure that the rear-axle lift gets low. Figure 28 Variance of pressure coefficient along a.) angle of application b) with spoiler height Figure 27 Gillespie experiment of how height of spoiler affects the pressure.
- 37. 36 The extended rear spoiler can increase the pressure on hatch; as a result, rear axle lift is reduced about a third. Figure shows how a rear spoiler influences in reducing lift force at rear. The spoiler causes a clear rise in pressure on the rear slope in front of it. If the pressure is plotted versus the vehicle’s z/h for the centre cross section, the reduction in drag is obvious Figure 29 Pressure coefficient along the front end and rear end with & without spoiler Figure 31 shows different mounting of the rear spoilers affect the Lift and the Drag coffieicient value Figure 30 shows values change when spoiler retracts and in action
- 38. 37 The relation between the spoiler height, lift and drag follows a linear predictable trend obtained from a research work on BMW sport 6 series at Johannesburg (Aberu, 2013). Increasing the spoiler height further slows down the flow field passing over the roof line reducing the dynamic pressure drop to decrease the total lift. 2.7 CONTINUTY EQUATION According to the law of conservation, it can be stated that the mass can neither be created nor be destroyed. This law can be used in the steady flow process which means that there is no change in the flow rate with time through a control volume when the stored mass of the control does not change. (Engineering Tool, 2014) This means inflow is equal to the outflow. The equation for the continuity equation can be shown as: m = ρi1 vi1 Ai1 + ρi2 vi2 Ai2 + ρin vin Aim = ρo1 vo1 Ao1 + ρo2 vo2 Ao2 + ρom vom Aom Equation 11 Where: m = mass flow rate (kg/s) ρ = density (kg/m3 ) v = speed (m/s) A = area (m2 ) With uniform density equation (1) can be modified to q = vi1 Ai1 + vi2 Ai2 +vin Aim = vo1 Ao1 + vo2 Ao2 + vom Aom (2) Where: q = flow rate (m3 /s) ρi1 = ρi2 = ρin = ρo1 = ρo2 = ρom Figure 32 Body used to show equation of continuity
- 39. 38 Application in the research: For all flows, FLUENT solves conservation equations for mass and momentum. For flows involving heat transfer or compressibility, an additional equation for energy conservation is solved. For flows involving species mixing or reactions, a species conservation equation is solved or, if the non-premixed combustion model is used, conservation equations for the mixture fraction and its variance are solved. Additional transport equations are also solved when the flow is turbulent (figure 33). Figure 33 showing the use of continuity in ANSYS Fluent Now since we will use the model of an original car, we will obtain the results for the model. To compare the model with the original car, the easiest and the fastest way is dimensionally analyse the model and the car. This will help in obtaining the values for the original car. Let’s discuss dimensional analysis and similitude in brief. 2.8 NAVIER STOKES EQUATION The Navier Stokes equation provides the foundation for fluids in motion. It is one more important topic along with equation of continuity. It is important to discuss Navier Stokes equation as it forms the base of the analysis if the fluid flows in CFD. Fluid has no limits for distortion when forces are applied. This means that the fluid goes through number of forces. To simplify Navier derived an equation for the viscous fluid Stokes slightly modified the equation to form a basic equation called Navier-Stokes equation:
- 40. 39 The easy way to remember Navier Stokes equation is by understanding the concept1 . The whole process is categorised into following three sections: Transient Convection Diffusion. Transient: It refers to the rate of change of the quantity in an infinite volume for a temporary time. Assuming φ is any random physical quantity like mass, pressure, density, temperature or any other factor. Hence mathematically transient process can be defined as 𝜕 𝜌φ 𝜕𝑡 Convection: If there is any presence of the velocity within the field, the quantity is transported. This is defined as the convection method and is the first derivative multiplied by the velocity. Mathematically represented as 𝛻. ( 𝝆𝒖 𝛗) Diffusion: It refers to the transport of the quantity due to the presence of gradients of that quantity. It is referred in the mathematical terms as 𝛻. λ𝛻𝛗 Where λ refers to the diffusion constant. This is equal to the thermal conductivity in the heat transfer. Finally all the three equations are combined to obtain an accumulated equation referred to general transport equation shown as . Transient + Convection = Diffusion + Source 𝜕 𝜌φ 𝜕𝑡 + 𝛻. ( 𝝆𝒖 𝛗) = 𝛻. λ𝛻𝛗 + 𝑆𝑜𝑢𝑟𝑐𝑒 𝛗 When obtaining the equation of continuity it can be said that 𝛗 is 1 (for compressible flows). When the diffusion is not present and absence of the source all the terms can be set to 0. 𝜕 𝜌 𝜕𝑡 + 𝛻. ( 𝝆𝒖) = 0 To obtain the Navier Stokes equation the physical factor φ can be replaced by the velocity component at the time t. This represents the Navier Stokes equation as: 1 Shown in Patankar’s brief for understanding Navier Stokes Equation.
- 41. 40 𝜕 𝜌 𝑢 𝜕𝑡 + 𝛻. ( 𝝆𝒖 𝑢) = 𝛻. 𝜇𝛻𝑢 − 𝜕 𝜌 𝜕𝑥 + 𝜌𝑔 𝑥 Equation 12 Similarly in the equation if u is replaced by v and w for y and z coordinates’. Application in the research: In the ANSYS Fluent, the software that will be used to analyse the results in CFD, uses Navier Stokes equations in the final volume discretization method. This equation provides a filtering operation. Mainly used in the mesh grid sizing and grid spacing. This largely affects the mesh quality too. The background of the meshing runs the Navier Stokes equations as in form of Fourier series to obtain a high quality mesh. The literature review focused on the background history of the research product – spoilers along with the basic laws & concepts of physics and aerodynamics acting on the product. This helped to give a depth idea of the mechanism of the spoiler and how these laws still govern the digital analysis for the product. The next chapter introduces and familiarizes with the use of different methods for comparative analysis and introduces CFD. 2.9 DIMENSIONAL ANALYSIS & SIMILITUDE Generally very few real flows can be solved by analytical methods. It requires huge laboratories and more consumption of energy to run a wind tunnel as for example in this research project. Generating huge forces in the wind tunnel can alone consume electricity of an entire village. As a result alternately, models of the prototypes are generated and tested. This means the models and the prototypes need to match certain criteria which are geometrical similarity and kinematic similarity. Satisfying the above mentioned criteria results in dynamic similarity which means the results of the model can be equated to the prototype to find the results of the forces in the prototype. Application in the research: In the research results we will try to dimensionally analyse and similitude the actual value of the force in the car from the obtained values of the model. There will be a limitation since, the model being used in the research work is 2D has limitation on the results as they would have absence of forces in z coordinates.
- 42. 41 CHAPTER 3 METHODOLOGY Figure 34 Wind Tunnel test of spoiler on Porsche 911 Carrera Picture Courtesy: website Pressebox.
- 43. 42 3.1 INTRODUCTION The research focuses on the application of the rear spoilers on the personal cars. Hence it was important to discuss the vital aspects of the aerodynamics involved in the car and the effect of the spoilers on the aerodynamics of the car in the literature review. The research work is meant to be aerodynamics of a rear spoiler on a car in two dimension using Computational Fluid Dynamics software to analyse the results. Throughout the research work there will be application of two approaches to compare and illustrate the results. It is important to have an appropriate methodology of both qualitative and quantitative methodology to obtain the final result. 3.1.1 QUALITATIVE VS. QUANTITATIVE: QUESTIONS & APPROACH When compared to both qualitative and quantitative research work both methodology enquires & implements statements of philosophy, enquiring strategies, surveying to collect the data, analysing and interpreting the results. Qualitative approach emphasises on the essence and the ambience of the entities of the research work. Putting the statement in other way means that qualitative approach focuses on the quality, intensity of the matter, and amount that cannot be experimentally determined. This means that the concentration is led on to the concepts, theories, metaphors, symbols and description. The research statement often stressed on how socio – economic experience is obtained by giving a meaningful name to the research work. The quantitative methodology on the other hand focuses on the analytical approach, statistics and data, use of the numerical methods to interpret the research and approach the results with validation. This includes the use of different numerical software to calculate the values and document the research work for future use. Qualitative Methods: Quantitative method is the narrative way to explain the research work. This includes the theories, concepts implications in everyday applications, decontructivism, phenomenon, past research, industry practice, standards, implications, explore processes, the cultural studies, market research, products descriptions and implementations. The researcher focuses on the best methods to draw the results for the research work. Coherence of qualitative method in the research work: The research work on aerodynamics of a rear spoiler on a car in two dimension using Computational Fluid Dynamics software to analyse the results has explained the main qualitative methods. The entire research work focuses on the use of the spoiler by the automotive industry from market point of research to the
- 44. 43 factual reasons of using the product. Chapter 1 introduces the research project, and supports the socio economic need for the product in the modern automotive industry, ways to design and analyse the product as well as the project limitation. This is followed by Chapter 2, which emphasizes on the history of the spoiler to evolution and practical implementation as a literature review & the general concepts and theories of fluid dynamics working behind the product. The method of qualitative analysis is not only restricted to the first two chapters instead it follows with the market survey and data collection of applications of most used spoiler in industry and after market in chapter 3 as well as comparing the obtained results with the quantitative methods. Quantitative Methods: The quantitative method is more independent of the qualitative method. This implies that the researcher has greater influence on the qualitative method. Quantitative method focuses on the application of techniques to solve the problem statement of the project, conducting the research with different software tools, illustrating the results, documenting the results, comparing with the historiography and stating the conclusions. Coherence of qualitative method in the research work: The research uses more quantitative method to find the solutions. This focuses on the use of designing software for the BLM and spoiler designs, using different methods of flow simulation, explaining the use of ANSYS Fluent, comparing the methods of numerical flow analysis, importance of meshing and selection the method, validating the simulation results and comparing it with the qualitative methods. Each method has advantages and limitations depending on the level of illustration, opportunity to review the collection process, proximity to obtained values and amount of biased based on the researcher. The next topic discuses on the CFD in general.
- 45. 44 3.2 ENGINEERING DETERMINING METHODS Engineers have always been interested in understanding and predicting the behaviour of fluid flow system behaviour & variables. There are three way of predicting methods which are included below: Figure 35 Pie chart showing the three different methods of prediction 3.2.1 EXPERIMENTAL METHOD: The most reliable and easiest way to predict the natural phenomenon is usually done by gathering the information about the measurements. This is the common way of gathering the information of the full scale equipment and predicts how the equipment would behave in real life application. Pros: The actual model can be used for the experimental analysis for prediction. Accurate results can be used to understand the phenomenon This method plays an important role in deriving the statistics and data for future use. Cons: Sometimes the actual equipment costs too much. This can be expensive method to apply in large applications like in aeronautics or automobile industry. Experimen tal Method Analytical / Mathametical Methods Numerical Methods
- 46. 45 This method of using actually collecting the information can result time loss as rigorous experiments needs to be conducted to find the minute changes. Application: In small scale product development, in using the past data for future design and development. Examples include: Aeroplanes. 3.2.2 ANALYTICAL METHOD: This method works on the consequences of the mathematical model. These mathematical models describe the behaviour of the system. Usually the mathematical model is a set of differential equations which are used to solve the problem. Pros: Use of pre-set/ pre-defined differential equations These methods help engineers’ fundamentals of controlling and behaviour of engineering systems. Cons: Limitations of validity of the solutions if too many assumptions and simplifications are made. 3.2.3 NUMERICAL METHOD: It use the to find the behaviour of the physical properties on the product using set of defined differential equations by means of digital computing. It uses the physical properties of the product from the experimental data and pre-defined set of differential equations to understand the behaviours and effects. It breaks the problem into discrete parts where it uses set of equations on each discrete part. Numerical method can be classified into three categories of discretization methods to understand the meshing: 1. Finite Difference Method: This is the simplest procedure used to derive the discrete form of differential equations. The finite difference method uses Taylor series using approximate derivatives. It is the simplest form to apply differential equations on the uniform grids.
- 47. 46 2. Finite Element Method: This method was developed at the time of 1960, especially to analyse the structural dynamics problems. In other terms is based on the weigh residual method. This is a beneficial over the difference method as it can handle complex geometries and use arbitraries on irregular shapes. 3. Finite Volume Method: The Finite Volume Method (FVM) is one of the most robust discretization techniques used in CFD. FVM usually divides the domain into small control volumes (cells, elements) where the variable of interest is located at the centroid of the control volume. The next part is that it integrates the differential form of the governing equations (very similar to the control volume approach) over each control volume using interpolation. The resulting equation that is derive is discretized or discretization equation. In this manner, the discretization equation expresses the conservation principle for the variable inside the control volume. The most prominent feature of the FVM is that the resulting solution satisfies the conservation of quantities such as mass, momentum, energy, and species. This is exactly satisfied for any control volume as well as for the whole computational domain and for any number of control volumes. FVM is the ideal method for computing discontinuous solutions arising in compressible flows. FVM is also preferred while solving partial differential equations containing discontinuous coefficients. Use in the research work: The finite volume method is widely used in the generation of mesh (described below) in ANSYS Fluent. The research focuses on the behavioural properties of a rear spoiler in air. Hence FVM is the only method to be used for it.
- 48. 47 3.3 COMPUTATIONAL FLUID DYNAMICS 3.3.1 INTRODUCTION TO CFD Fluids (gasses and liquid) are governed by partial equations that represent the general laws of conservation of mass, momentum and energy. CFD is the art of replacing such PDE by set of equations which can be solved by the digital computers (Kuzmin, 2013). Computational Fluid Dynamics (CFD) provides quantitative and qualitative predictions of the fluid flow by means of the following: Modelling by applications of mathematics of partial differential equations Use of discretion and solution tools i.e. numerical methods. Use of the software tools like solvers, pre and postprocessing utilities. CFD is essential software which enables the engineers to virtually simulate the numerical experiments carried in the laboratories resulting in less time consuming process and better accurate results. CFD gives an insight to the pattern of the fluid flow that is difficult to predict with regular experiments, expensive to conduct and sometimes impossible to study by the regular experiments. 3.3.2 HOW DOES CFD MAKE PREDICTIONS? The CFD software use mathematical tools to solve the problem which is a pre-set of equations. The main factor of CFD is The researcher who feeds the problem into the computer Scientific knowledge that is expressed mathematically. The computer code that consists of the algorithms that embodies the knowledge Hardware of the computer that performs the calculations The researcher who simulates and interprets the data CFD is a highly disciplinary subject that indulges into the research area and lies at the interface of physics, applied maths and computer science.
- 49. 48 3.3.3 CFD ANALYSIS PROCESS CFD analysis process can be summarised in the following steps: 1. Problem Statement: It deals with the problem statement of the problem and the fastest way to achieve it. It also includes the physical phenomenon to be taken in considerations. Operating conditions and the geometry of the body. Type of fluid flow i.e. Laminar/ Turbulent/ Multiphase. Objective of the CFD analysis i.e. in this research case will be the drag, lift and downforce. 2. Mathematical Model: Defining the symmetries and the flow view. Defining the computational domain. Formulating the law of conservation of mass, energy and momentum 3. Discretization Process It includes the mesh generations, sizing of mesh and inflation Changing the mesh structures. Time discretization Space discretization 4. CFD Simulation Generating the simulation. Changing the quality of the simulation 5. Post Processing and Analysis It is the method of extracting required results from the computation flow field. Visualization and debugging of CFD model. Validation of the CFD model. Using systematic data analysis by means of statistical tools.
- 50. 49 6. Uncertainty and errors Uncertainty includes the lack of knowledge specially the turbulence. Acknowledging the local and the global errors. 7. Validation of the CFD models. Trying different models or iterations with the boundary and geometric conditions. Documenting the findings in report. Assessing the uncertainty and errors by performing sensitivity analysis and parametric study. 8. Validation of CFD Codes Examining the computer program by visually checking it and documenting it Checking the consistency of the trial. Cross checking the results obtained with analytical results. 3.3.4 MESHING Usually the discretion process converts every continuous system to a discrete one. This means that the grids or the mesh generation is done to obtain the approx. solution at each discrete grid. Grid generation of mesh is either of the two types. 1. Structured Mesh generation 2. Unstructured mesh generation 1. Structured mesh generation: Mesh is generated to fit on the boundaries. The benefit of having structured mesh is to generate the high and good quality of mesh. This regulates the fastening go the solution algorithm. It is difficult to have complex domains in mapping from a rectangular grid. Generating the grid is followed by the physical problem discretion and solved on that grid. The most useful method is to convert the equations in to the model problem of computational space (figure 36)
- 51. 50 a. Algebraic grid generation: Algebraic grid generation is called transfinite interpolation. This method uses the interpolation value from the boundaries of the computational domain. This can be a beneficial for the grid/mesh density also in assigning one to one mapping. However this method generates singularity corner into interior of the domain. b. PDE Mesh generation: This method enables the generation of the regular mesh & higher accuracy. There is a single a single value relationship between the generalised coordinates and simple coordinates. Since the model of the car in this research project is in 2 dimensional, it will easier to explain. There is a single value relationship between the generalised coordinates and the simple coordinates. It can be explained as ε =ε (x,y) n=n(x,y) i.e. x=x (ε,n) y=y( ε,n) Figure 37 mapping of the physical coordinates on the x, y coordinates. Usually the functional relationships are determined by the mesh generation process and converted to the governing equations. Figure 36 shows a fine structured mesh on a model
- 52. 51 Conclusion: This method dominated the CFD methods in the early developed codes. It required more computational storage. The old fashioned was replaced by the unstructured mesh generation which generated mesh more automated fashion and is more accurate to determine for the complex geometries. 2. Unstructured mesh generation: They were initially created for the finite element discretion method. However for the variety of applications available in the finite volume discretion they are used in meshing the fluid domain. In the finite volume unstructured meshing there are large possibilities of different mesh sizes ranging from triangles, square in 2D to the prisms, tetrahedral and bricks (figure 38). The instructed meshing in the final volume discretion follows mainly four different methods of mesh/ grid generations. These four different methods follow a basic set of rules mentioned below: 1. Generation of the valid mesh. This means that the mesh should have no holes or self-intersection. 2. Conformation of the mesh with the boundary. 3. Balancing the density of the mesh to control the accuracy and computational requirements. Figure 38 Generation of unstructured mesh of BMW 3 series model. The popular methods to generate finite volume meshing in CFD are: 1. Surface Meshing
- 53. 52 2. Advancing front method 3. Delaunay triangulation method 4. Other methods like paving & plastering, Octree and semi unstructured mesh generation. Application in the research methodology: Automatic unstructured meshing has been used in the mesh generation. However the mesh sizes have been defined to as low values approx. – 1 mm to 2 mm (fig 39, 40) to increase the mesh quantity and quality for better accuracy in results. Figure 39 adjusting the element sizes and finding the number of elements Figure 40 Meshing of the model with minimum 2 & maximum 4 mm element size
- 54. 53 3.3.5 MESH QUALITY Mesh quality plays a crucial role in the determination of the accuracy of the results, irrespective of the types of mesh being used. 1. Mesh Element Distribution: It is important to have a fine mesh element distribution. Since the domain is discretely defined, the salient features of the fluid flow depend on the mesh density and distribution. The mesh distribution in the research is fine and uniform. The automated mesh generated is further modified by the researcher (fig 41, 42). Figure 42 meshing obtained adjusting sizing Figure 41 meshing with default configurations
- 55. 54 2. Cell Quality: It depends on the skewness and aspect ratio. Skewness is defined as the difference between the shape of the cell and shape of the equilateral cell of equivalent volume while aspect ratio is the measure of stretching the cell. In a general rule for a good mesh is to have the triangular mesh with skewness less than 0.95 3.3.6 BOUNDARY CONDITIONS Boundary conditions serve the important and most required conditions for the mathematical model (Bakker, 2002). These direct the motion flow of the fluid in the domain. They are also defined as the face zone in CFD. Application in the research: There has been significant use of the boundary conditions in the research. The boundary conditions in the research work consist of the inlet, outlet, similar symmetries, the model car with or without the spoilers and tyres. Inlet & Outlet Boundary: The inlet & outlet boundary is the condition which serves as the input and output or inlet & outlet of the fluid flow in the domain. They can be of different types, such as: For incompressible flows: Velocity inlet and outflow. General: Pressure inlet and outlet. For compressible flow: Mass inlet and outlet Special cases: Inlet and outlet vent. Most of the time, the selection of the inlet and outlet depends on the type of geometry. Application in the research methodology: Since the geometric model is the car and the study needs to find the significant resistive drag forces, the incompressible flow; input and output boundary condition is applied. This means that the model has an velocity input and output resembling similar to the wind tunnel. The other boundary conditions that have been used are the model car. The car surface is the region of study for the effects of drag forces, down forces, pressure difference. Tyres have also been defined as a
- 56. 55 boundary. The reason for using tyres separate from the car model is to study the similar forces affecting the tyres (fig 43). 3.3.7 COMPUTING SETUP Parallel computing for processing has been used in the processing set up for the models. The reason of using parallel computing is because; single processing allows solving one discrete problem at one time. Parallel processing is used to make more than one processing at a time. This is time efficient while double precision is used to change the magnitude order of the residuals (explained in chapter 4, 4.10). Figure 43 defining the boundary conditions on geometry in ANSYS
- 57. 56 3.3.8 CONVERGENCE Convergence is the way of obtaining accuracy. All the models in the research work have been converged before they are proceeded to post processing analysis. Convergence is the way of obtaining accuracy for the model. Number of iterations is made to run to check the convergence of the governing equations. This is usually estimated by the RMS value depending on the precision of the processor (either single or double). RMS value usually varies between 106 to 1012 . Once the convergence is achieved, the results can be more precise. Application in the research work: Every model before post processing in the ANSYS Fluent is checked for convergence. This is obtained by the successfully running the iterations along with the equations. The solutions once converged (fig 44) results in better accuracy of the results. Figure 44 obtaining convergence of the operating equations in ANSYS Fluent before post processing 3.3.9 ERRORS Physical Errors: Errors that are generated due to the uncertainty in the formulation of the models are called physical errors. They can be mainly due to mathematical rounding off, initial conditions, and mathematical assumptions or form
- 58. 57 Discretization Error: They occur often from the governing flow equations. Discretization errors can be defined as the difference between the perfect solution to the discrete equations and analytical solutions to PDE. They can be classified as: 1. Spatial and temporary discretization of the flow 2. Truncation Error: This error can be defined as the difference between the partial differential equation and the finite equation. Programming Errors: Generally happens due to bugs or referred as mistakes in the programming. Computer-round off Errors: These errors can cause inaccuracy or may prevent convergence. Usually when the exact solution could not be extracted from the discrete equations, they are rounded off as finding the determining the difference between the two discrete points can consumed huge memory. Iterative Convergence Error: This usually happens when slow computing power and time consuming iterations are generally truncated to the final solutions which lead to the numerical error in the solution called the iterative convergence error.
- 59. 58 CHAPTER 4 NUMERICAL SETUP Figure 45 Top and bottom shows analysis of the models in the ANSYS

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