Introduction to Aerodynamics

Aerodynamic Vehicle Design and Analysis

Table of Contents

Introduction Page 3

Aerodynamic Basics Page 3

BMW Z4 Page 4

Concept Modelling Page 5

Initial Testing Page 6

Addition of Front Splitter, Side Skirts & Rear Diffuser Page 8

Addition of Rear Wing Page 11

Final Concept Page 13

Vehicle Dynamics Page 14

Mathematical Validation Page 15

Conclusion Page 16

Future Work Recommendations Page 17

References Page 18

Appendices Page 19

Introduction

In this project it necessary to build a 3D surface model of a BMW Z4 concept car using industry standard aerodynamic CAE (Computer Aided Engineering) software then import the model CFD (Computational fluid dynamics) software. Using the CFD software an appropriate simulation will be created for accurate post processing. Using the results gathered from the CFD simulation a critical analysis will be made on the vehicles drag, lift and flow characteristics under, over and around the vehicle. After analysing the data from the CFD simulations, improvements will be made to the model to improve downforce while minimise the increase in drag.

Basics of Aerodynamics

Aerodynamics is the study of the interaction between moving bodies and the fluids around, under and though them. Aerodynamics first came from aeronautical engineers studying aircraft wing design for aircrafts that fly within the earth’s atmosphere. Aerodynamics are used in designing many different things including building design, bridge design and motorsports/automotive vehicle design and many more.

(Jim Lucas, 2014)

Drag

Aerodynamic drag is the force opposing the vehicles direction of movement. (See figure 1) The main contributor to vehicle drag is the high pressure acting on the front of the vehicle, surface friction and the relatively negative pressure left behind the vehicle.

(Jim Lucas, 2014)

The formula to mathematically calculate aerodynamic drag is as followed.

1 퐷=푐퐷 ⁄2휌푣2퐴

D = Drag Force N

CD = Drag Coefficient ½ = Mathematical

Constants ρ = Air Density Kg/m3 V2 =

Speed m/s

A = Frontal Area m2

Figure 1 Lift & Drag Direction (NASA, 2014)

(Joseph Katz, 2006)

Lift Lift is force acting perpendicular to the motion of the vehicle. It is essential for aircrafts to create positive lift to fly, this is unwanted in motorsports. In motorsports negative lift it sought after to force the vehicle into the ground, this force acting on the vehicle helps increase vehicle grip which leads to faster

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cornering speed. The formula to mathematically calculate aerodynamic lift is similar to the drag formula 1 although the drag coefficient is replaced with a lift coefficient and is as followed. 퐿=푐퐿 ⁄2휌푣2퐴

L = Lift N

CL = Lift Coefficient

A = Frontal Area (Vehicle) Plan Area (Aerofoil) m2

(NASA, 2016) (Joseph Katz, 2006) Downforce

Downforce is a motorsports/automotive term that applies to negative lift. This is the force that pushes a vehicle into the ground this is a sought after affect in the motorsport industry to increase cornering speeds.

Lift and drag coefficients

Lift and drag coefficients are a number given to a model and is affected by from vehicle shape, surface friction (drag) and angle of attack (lift).

퐷푟푎푔 퐷푟푎푔 퐶표푒푓푓𝑖푐𝑖푒푛푡 = 1⁄2 휌푣2퐴

퐿𝑖푓푡 퐿𝑖푓푡 퐶표푒푓푓𝑖푐𝑖푒푛푡 = 1⁄2 휌푣2퐴

(Joseph Katz, 2006) BMW Z4

The BMW Z4 is a rear wheel drive sports car, with a 3 litre straight six engine mounted at the front. It has a wheel base of 2497mm and an overall length of 4091mm, width of 1781mm and a height of 1268mm. The Z4 weighs 1395Kg and has a 50:50 weight distribution. The quoted drag coefficient of the Z4 is 0.34 and has a frontal area of 1.91m2 given it a drag coefficient/area ratio of 0.65.

(Car Foilo, 2006)

Figure 2 BMW Z4 (BMW, 2016)

Concept Modelling

A concept model was designed using the basic dimension and canvas images of the BMW Z4. The software chosen for this was Autodesk Alias SpeedForm 2016. Autodesk Alias is an industry standard

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surface modelling package, Alias is a great visualization tool for automotive design and has powerful rendering features.

(Autodesk, 2016)

See figure 3 below for an image of the Z4 concept during the modelling stage. During this design process a symmetry plane was used (Green line though the vehicle in figure 3), this was used to help keep the vehicle symmetrical, any modifications made to one side would automatically update on the other side. See appendix 1 for more images of the Z4 concept during the design process.

Figure 3 Z4 Concept Design Stage

See figure 4 below for a rendered image of the BMW Z4 concept design rendered in Alias SpeedForm with added wheels designed in Autodesk Inventor. See appendix 2 for more rendered images of the conecept.

Figure 4 Z4 Concept Render image

Initial Testing

Initial testing was carried out on the Z4 concept vehicle using CD-Adapco’s Star CCM+ CFD (Computational Fluid Dynamics) Software. Star CCM+ is a powerful CFD solver that can handle multiple physics and complex geometries, as well as being a CFD solver Star CCM+ solve for heat transfer and stress.

(CD-Adapco, 2016)

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All tests were carried out at 120kph, and in a wind tunnel measuring 65m in length, 10m wide and 10m high. The air density used for testing is 1.2255kg/m3 which is the air density at sea level at 10°C.

(Richard Shelquist, 2016)

Analysing Results

The result from initial testing are as followed,

퐹표푟푐푒 푊𝑖푒푔ℎ푡 퐹표푟푐푒 (퐾푔) = 9.81 (퐺푟푎푣𝑖푡푦) Drag 506.33 N (51.61Kg) Lift 314.48 N (32.06Kg) Frontal Area 1.74 m Drag Coefficient 0.43 Lift Coefficient 0.27 Drag/Lift Ratio 1.61 Lift/Drag Ratio 0.62 After analysing the results from initial testing its shown that the Z4 concept is actually creating lift, this is unwanted in a sports type vehicle, this could lead to undesirable handling characteristics e.g. under/over steer. When analysing the vector scene (see figure 5) it is clearly visable what the main contributers to the vehices lift are. The first being the large amount slow velocity air traveling under the vehicle, this low velocity will be creating a high pressure area which will try to force the vehicle upwards. The second biggest area creating lift is the high velocity air passing over the roof of the vehicle, this high velocity creates a low pressure passing over the vehicle, the low pressure area pulls the car upwards creating lift.

Flow Separation

Figure 5 Initial Testing Vector Scene

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Figure 6 Initial Testing Resampled Volume Scene

After further post processing its clear what the main areas that are creating drag are. The biggest contributor to the vehicles drag is the wake, a large, slow speed turbulent area of air behind the vehicle trying to pull the vehicle back this can be seen in the vector scene and the resampled volume scene. (See figure 5 & 6) Another area creating vehicle drag is the high pressure zone on the front of the vehicle this can be seen in the scalar scene (see figure 7). The pressure acting on the front of the vehicle tries to push the vehicle in the opposing direction to the vehicles movement.

Figure 7 Initial Testing Scalar Scene

Another part creating drag is the flow separation areas at the bottom of the windscreen and over the rear window these are highlighted in the vector scene. (See figure 5) The flow separation areas create turbulence on the surface of the vehicle, also within these separation areas the velocity of the air almost becomes zero. The final main area to cause drag are the vehicles wheel arches, the wheel arches reduce the velocity of the air creating high pressure zone. These high pressure zones try pushing the vehicle in the direction opposing its motion in the same way it occurs on the front of the vehicle. This can be seen in the resampled volume scene. (See figure 6) For more images from initial testing see appendix 3.

Addition of Front Splitter, Side Skirts & Rear Diffuser

To create more downforce from the underbody design of the vehicle the amout of air allowed to travel under the vehicle must be reduced and the velocity of the air that is allowed to travel under the vehicle needs to be increased which will create a low pressure area which will pull the car into the ground. In

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an attempt to increase vehicle downforce a front splitter, side skirts and rear diffuser where designed and added to the Z4 concept.

Front Splitter

A front splitter consists of a parallel extension attached at the bottom of the front bumper. The way the front splitter creates downforce is by creating a high pressure area above the splitter and low pressure below, this high pressure is drawn to the low pressure forcing the front end of the vehicle into the ground.

(Formula 1, 2016)

Side Skirts

Side skirts are used to minimise the clearance between the vehicle body and the ground at the side of the vehicle. The reason for side skirts is to help aerodynamic downforce this is done by reducing the amount of high pressure from around the vehicle being drawn to the low pressure area under the vehicle. The effectiveness of the side skirts depend on the clearance from the ground, 2cm or less is best practice anything above this any bigger ground clearance diminishes quickly. (Formula 1, 2016)

Diffusers

Diffusers are designed to increase the volume at the rear of the under body of the vehicle, this increase in volume creates a void which needs to be filled this increases the velocity of the air traveling at the rear of the vehicle. This high velocity air will create a low pressure area which increases the downforce.

(Racecar Engineering, 2016)

There are different types of diffusers that very for the normal design (see figure 8). One of the designs is a blown diffuser, this design uses the high velocity gases from the exhaust to help draw the air from under the vehicle. The downside to this design is that it can increase the size of the wake behind the vehicle.

Figure 8 Diffuser Design

Modelling of the Front Splitter, Side Skirts and Rear Diffuser

To model the front splitter, side skirts and rear diffuser additions Autodesk alias this can be seen in figure 9 the red wire frame shows the additions added to the initial design. The chosen diffuser design was a blown diffuser the reason this was chosen was because this design can have the biggest increase in vehicle downforce is correctly designed.

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Figure 9 Wire frame model of Splitter, Side Skirts & Blown Diffuser

Results from the addition of front splitter, side skirts & rear diffuser

The results from the second test are in the table below, Drag 778.15 N (97.32Kg) Lift -410.82 N (-41.87Kg) Frontal Area 1.88 m Drag Coefficient 0.61 Lift Coefficient -0.32 Drag/Lift Ratio -1.89 Lift/Drag Ratio -0.53

After anaylising the results with the additional componets added, there is a noticable increase in vehicle downforce but also an increase in vehicle drag. One area where downforce was created is at the front splitter as you can see in figure 10 that there much higher pressure acting on the top of the splitter compared to the low pressure under the splitter therefore creating downforce.

Figure 10 Scalar Scene Showing Pressure Between -2500 & 600 Pa on a the XZ Plane

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In figure 10 it is visible the reduced ground clearance compared to the initial test this reduced ground clearance which consequently reduces the air allowed to flow under the vehicle, the less amount of air allowed under the vehicle the more down force can be created. In figure 11 you can see the air velocity tremendously increased around the blow diffuser where the high velocity exhaust gases draw the air around. The outer diffuser channels are not working affectively as the centre channels, this is because there is no exhaust gases to help increase the flow. These outer channels could be improved by reducing the steepness of the angle the diffuser was designed at. Another area of interest is the effect the vehicles wheels and tyres have on the velocity behind them creating very low velocity areas.

Slow Velocity

Figure 11 Velocity Scalar Applied to the Vehicles Surface

As you can see in figure 12 the side ski r t design has effectively stopped the slow turbulent air flow from the side of the vehicle bleeding under the vehicle and disturbing the underbody flow. After further post processing it is apparent there has been an increase in the vehicle drag and drag coefficient the main contributors to this are the increase in frontal area and also the increase in the vehicles wake. For further images from post processing for the added front splitter , side skirts and rear diffuser see appendices 4.

Figure 12 streamlines down the Side of the Z4 Concept

Figure 13 Vector Scene Showing Velocity on Z4 with Additional Components

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Addition of Rear Wing

To further increase the vehicle downforce a rear wing was designed and attached to the rear of the vehicle. The rear wing design uses an inverted aerofoil shape taken from aircraft creating lift when the aerofoil is inverted this will create downforce. The design will utilize a Gurney flap attached to the top side of the trailing edge of the aerofoil. The gurney flap helps to slow down the air traveling over the top of the aerofoil therefore increasing the pressure needed to create higher downforce.

The AOA (angle of attack) relates to the angle of the chord line of an aerofoil in relation to the direction of motion the vehicle takes. The AOA has a great effect of the amount of drag and lift created by an aerofoil, greater the AOA the greater the drag and downforce. After a certain AOA the aerofoils lift will start to decrease this is called aerodynamic stall. To work out the optimal AOA for the designed aerofoil simulations where carried out on every AOA until stall occurred the result are below. (See figure 14)

After analyising the AOA data it can be seen that the stall point ouccurs at 21°. The choosen angle for the aerofoil on the Z4 concept was 5° this was choosen because it gives the best drag to lift ratio at -0.099.

Now that the optimal angle of attack has been chosen the aerofoil now has to be positioned in an effective area, when analysing figure 13 it is noticeable that the aerofoil position has to extend higher than the slow velocity air traveling down and over the rear of the car.

After the AOA and position has been decided the end plates and aerofoil legs could be designed see figure 15 for the finished rear wing design.

Figure 14 Angle of Attack Data

Figure 15 Aerofoil Design

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Results from the addition of the rear wing

The results from the addition of the rear wing are as followed, Drag 840.65 N (82.02Kg) Lift -1035.86 N (-105.59Kg) Frontal Area 1.92 m Drag Coefficient 0.64 Lift Coefficient -0.79 Drag/Lift Ratio -0.81 Lift/Drag -1.23

Figure 17 Vector Scene Showing the Velocity with the Rear Wing Addition

After analysing the results, it is clear there is a dramatic increase in downforce created from the rear wing. In figure 16 you can see the rear wing working well creating a high velocity area under the wing and a much slower velocity over the wing. The high velocity under the rear wing creates low pressure which draws the high pressure created from the low velocity speed above the wing creating downforce. After further post processing it is visible there is a 62.5 N of drag increase this is due to two factors first is the increase in frontal area but the main factor is the increase in the vehicles wake this can be seen when comparing figure 13 and 16, it’s visible that the slow turbulent area is much larger. After analysing figure 17 it is noticeable that the rear wing support arms are having an effect on the drag creating low velocity air behind them. For more post processing images from the rear wing additions see appendices 5.

Figure 16 Resampled Volume with Rear Wing Addition

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Final Concept

See figure 18 and 19 for a rendered image of the final Z4 concept design, the software used to render the image is Alias SpeedForm. For more images of the final render see appendices 6.

Figure 18 Side Render of Z4 Concept

Figure 19 Rear Diffuser Rendered Images

Vehicle Dynamics

Due to the aerodynamic modification created for Z4 concept the vehicle dynamics have changed these could affect the handling characteristics and the weight distribution. The vehicles as standard had a 50/50 weight distribution while the vehicle is static. To work out the weight force of the vehicle at the simulation speed of 120 kph the lift force figure must be subtracted from the vehicles static weight the formula for this is below.

푊𝑖푒푔ℎ푡 퐹표푟푐푒 (퐾푔) = 푆푡푎푡𝑖푐 푊푒𝑖푔ℎ푡 (퐾푔) − 퐿𝑖푓푡퐹표푟푐푒 (퐾푔)

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Initial Test

1362.94퐾푔 = 1395퐾푔 − 32.06퐾푔

Addition of Front Splitter, Side Skirts & Rear Diffuser

1436.87퐾푔 = 1395퐾푔 − −41.87Kg

Addition of Rear Wing

1500.59퐾푔 = 1395퐾푔 − −105.59Kg

On the final simulation the new vehicle weight distribution can be calculated with the addition of the rear wing, the addition of the rear wing will increase the weight over the vehicles rear end. To calculate the new weight distribution, it’s first needed to calculate the weight under each axle before the addition of the rear wing.

푊𝑖푒푔ℎ푡 퐹표푟푐푒 푂푣푒푟 퐴푥푙푒 (퐾푔) = 푂푣푒푟푎푙푙 푊𝑖푒푔ℎ푡 퐹표푟푐푒 (퐾푔) × 푊푒𝑖푔ℎ푡 퐷𝑖푠푡푟𝑖푏푢푡𝑖표푛 푂푣푒푟 퐶ℎ표표푠푒푛 퐴푥푙푒

Front Weight = 718.435Kg

Rear Weight = 718.435Kg

To calculate the new weight distribution must add additional weight force from the rear wing to the rear weight. The force weight created from the rear wing is 63.72Kg.

퐹푟표푛푡 푊푒𝑖푔ℎ푡 퐷𝑖푠푡푟𝑖푏푢푡𝑖표푛 = 718.435 ÷ 1500.59 = 0.48

푅푒푎푟 푤푒𝑖푔ℎ푡 퐷𝑖푠푡푟𝑖푏푢푡𝑖표푛 = (718.435 + 63.72) ÷ 1500.59 = 0.52

The Z4 Concept with all additions has a new weight distribution 48/52 bias to the front of the vehicle. This new weight distribution could affect the vehicles handling, depending on other vehicle set up could make the vehicle under steer.

Mathematical Validation

In this section is mathematical validation to back up the CFD simulation software.

Using the simulation from the additional rear wing the lift and drag will be calculated.

Lift

1 퐿=푐퐿 ⁄2휌푣2퐴

L = Lift (N)

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CL = Lift Coefficient

½ = Mathematical Constant

휌 = Density (Kg/m3)

V2 = Velocity (m/s)

A = Area (m)

퐿 = −0.79 × 0.5 × 1.2255 × 33.332 × 1.92 = −1032.48 푁 Drag

1 퐷=푐퐷 ⁄2휌푣2퐴

D = Drag (N)

CD = Drag Coefficient

½ = Mathematical Constant

휌 = Density (Kg/m3)

V2 = Velocity (m/s)

A = Area (m)

퐷 = 0.64 × 0.5 × 1.2255 × 33.332 × 1.92 = 836.44 푁

The mathematical validation is very close to the simulation figures, the reason for slight discrepancies is down to rounding of the figures.

Conclusion

To conclude this project basic aerodynamics principals have been researched thoroughly and applied to CFD simulations data. A concept vehicle was created using industry standard surface modelling software, and then successfully modified to increase vehicle downforce. A detailed analysis of the CFD simulations where done and a critical analysis of the model where made.

After analysing all 3 simulations there had been an increase in downforce of 1350.34 N and an increase in drag of 334.32 N. This increase in downforce and drag will increase fuel consumption by increasing the drag coefficient and the rolling resistance. For motorsports application this increase in fuel consumption is irrelative when downforce is the most important.

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From the three simulations it’s clear that the final model created the highest downforce figure but also the highest drag. Between all three simulations, simulation 2 (addition of front splitter, side skirts and rear diffuser) has the best drag lift ratio.

Due to previous experience with the software packages used there was no potential problems that occurred and with further development, there is possibilities of potential manufacture problems.

Simulation Drag Lift Frontal Cd Cl Drag/Lift Lift/Drag Area Ratio Ratio 1 506.33 314.48 1.74 0.43 0.27 1.610054693 0.621096913 2 778.15 -410.82 1.88 0.61 -0.32 -1.894138552 -0.527944484 3 840.65 -1035.86 1.92 0.64 -0.79 -0.811547893 -1.232213168

Lift & Drag 1000

500

0

-500

-1000

-1500 1 2 3 Drag 506.33 778.15 840.65 Lift 314.48 -410.82 -1035.86

SIMULATION

Drag Lift

Figure 20 Lift & Drag Graph

Future Work & Recommendations

Future work would include trying to optimise the current additional components this would include lower the angle of the outer diffuser channel to reduce the flow separation with these channels.

Another area that would be included in future work would be modification the wheel arches to allow air to flow more freely out of them which would reduce the pressure within them, the way this could be done is by designing vents to release and redirect the air flow smoothly around the vehicle.

One more recommendation would to try and eliminate the flow separation happening around the bottom of the wind screen and down the rear window this could be done by decreasing the angle of the windscreen, and for the rear window it needs to have a less of a recess and to be made more flush with the bodywork.

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References

Autodesk. (2016). Alias. Available: http://www.autodesk.com/products/alias-products/overview. Last accessed 2nd May 2016.

BMW. (2016). Suspension and damping on the BMW Z4 Coupé. Available: http://www.bmw.com/com/en/newvehicles/z4/coupe/2006/allfacts/engine_suspension.html. Last accessed 3rd May 2016.

CD-Adapco. (2016). Star CCM+. Available: http://www.cd-adapco.com/products/star-ccm%C2%AE. Last accessed 2nd May 2016.

Car Foilo. (2006). 2006 BMW Z4 Coupé 3.0si. Available: http://www.carfolio.com/specifications/models/car/?car=137995. Last accessed 3rd May 2016.

Formula 1. (2016). Side Skirts. Available: http://www.formula1-dictionary.net/side_skirts.html. Last accessed 4th may 2016.

Formula 1. (2016). Splitter and air dam. Available: http://www.formula1-dictionary.net/splitter.html. Last accessed 4th May 2016.

Joseph Katz (2006). Race Car Aerodynamics. Cambridge: Bentley.

NASA. (2014). What Is Drag. Available: https://www.grc.nasa.gov/www/k-12/airplane/drag1.html. Last accessed 1st May 2016.

NASA. (2016).What is Lift. Available: https://www.grc.nasa.gov/www/k-12/airplane/lift1.html. Last accessed 3rd May 2016.

Jim Lucas. (2014). What Is Aerodynamics. Available: http://www.livescience.com/47930-what- isaerodynamics.html. Last accessed 1st May 2016.

Racecar Engineering. (2016). Diffusers. Available: http://www.racecar- engineering.com/technologyexplained/diffusers-engineering-basics-aerodynamics/#. Last accessed 4th may 2016.

Richard Shelquist. (2016). An Introduction to Air Density. Available: http://wahiduddin.net/calc/density_altitude.htm. Last accessed 2nd May 2016.

Appendices

Appendix 1 – Z4 Concept Design Stage

Appendix 2 – Z4 Concept Rendered Images

Appendix 3 – Initial Testing

Appendix 4 – Addition of Front Splitter, Side Skirts & Rear Diffuser

Appendix 5 – Addition of Rear Wing

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Appendix 6 – Final Renders

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Appendix 1 – Z4 Concept Design Stage

Below are some extra images of the different views of modelling stages of the BMW Z4 concept.

Appendix 2 – Z4 Concept Rendered Images

Below are more images of the initial design rendered in Alias SpeedForm at different views. Page 18 of 25

Appendix 3 – Initial Testing

Below are more images form post processing from initial testing.

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Appendix 4 – Addition of Front Splitter, Side Skirts & Rear Diffuser Below

Are images from post processing from simulation 2.

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Appendix 5 – Addition of Rear Wing

Below Are images from post processing from simulation 3. Page 21 of 25

Appendix 6 – Final Renders

Final Rendered images with all additional modifications.

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