Diffuser Design for PACE Global Formula One Racer

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SAE TECHNICALPAPER SERIES 2008-01-1835

Diffuser Design for PACE GlobalFormula One Racer

Zhen Zhang and Zhengyuan Yang and Zhigang YangTongji University, China

2008 SAE International Powertrains,Fuels and Lubricants Congress

Shanghai, ChinaJune 23-25, 2008

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2008-01-1835

Diffuser Design for PACE Global Formula One Racer Zhen Zhang and Zhengyuan Yang and Zhigang Yang

Tongji University, China

Copyright 2008 SAE International

ABSTRACT

The detailed design process of the diffuser for a Formula one racer is described. It begins with the study of overall aerodynamic performance and follows the basic function of the diffuser. And then forms the strategy for such a diffuser which should perform the maximum downforce. Then is the detailed analysis of diffuser by two different methods of development. The small-scaled wind tunnel data is presented, together with the CFD analysis, describing the major consideration in using these two developing methods and demonstrating the major influence for the diffuser design.

INTRODUCTION

This paper is based on the Tongji University PACE (Partners for the Advancement of Collaborative Engineering Education) Centers 2007-2008 Project Formula One Racers Diffuser Design and Manufacturing in PACE Global Vehicle Collaboration. 20 different universities all around the world design the racer referring to the F.I.A 2009 regulation [1].

REVIEW OF AERODYNAMIC PROGRESS IN FORMULA ONE RACING

Formula one racing is one of the most popular racing in the world. And its technology is ever-changing since its beginning. The winning factor is also changing accordingly. In the past, the Formula one racer is designed inside-out, the winning factor is the engine. The team who designs the most powerful engine is the winner. Ever since Louts added some aerodynamic parts in the racer, the formula of winning has been changing. It is rather an outside-in designing method, which means now the most important thing is to achieve a good aerodynamic performance. Even the engine should be thinner to suit the need for that aerodynamic performance [2].

DISCRIPTION OF THE FORMULA ONE DIFFUSER

The Formula One diffuser [2] is located on each side of the central engine and gearbox fairing and behind the rear axle line. As seen in Figure 1, the diffuser and skid board (blue part) consists of many tunnels and splitters. It is designed to carefully guide and control airflow underneath the racecar.

Figure 1: Design space model for PACE Formula One racer

PRINCIPLE OF A DIFFUSER

Diffuser is an act of Venturi Effect [3], when an incompressible flow through a restriction in a tube, the flow will be accelerated and have a lower pressure. The following CFD experiment will show this effect.

Figure 2: Velocity of flow in Venturi Effect, red is flow with faster velocity and blue with lower. Flow enters from the left and leaves to the right.




Figure 3: Pressure of flow in Venturi Effect, red is flow with higher pressure and blue with lower

This is the reason a Formula Ones diffuser is designed to accumulate the underneath air and accelerate it. This process will cause a huge low pressure area under the racer compared with the upper part of the racer. That will provide a total negative lift force on the Formula Racer to keep it stick to the ground, especially is needed when the racer is cornering with an enormous speed.

Figure 4: The Bernoullis principle at the diffuser

DESIGN GOAL STUDY

COURSE STUDY

Each racer should be designed for a specific racing. And the purpose for Formula One racing is not the top speed or anything else, but only the minimum time of reaching the finishing line [7]. And as Peter G. Wright, the technical director of team Lotus, put it: Driving a car as fast as possible is all about the maintaining the highest possible acceleration level in the appropriate direction [4], it is necessary to analysis at the first place in what condition is the Formula One racer running in.

Here take Shanghai Formula One Course as an example to analysis the design goal for the Formula One diffuser.

Figure 5: The Formula One course in Shanghai (picture taken from the website of www.17uc.com)

As shown in Figure 5, different from the NASCAR course, which is only an eclipse, there are lots of turnings and straight lines with different combination in Formula One course, such as U-shape corner (T14), Corner after a long acceleration (T13), continuous corner (T1-4), corner before a long acceleration (T16 ).

So, without considering the height change during cornering, the course could be conveniently abstracted to two circles with different width between two straight straps, shown in Figure 6.

Figure 6: A course model study

CORNERING ANALYSIS

By observing Formula One racing, we can find that there are several different ways to turn the corner. One is to go the shortest path by driving along the inner side of the corner. Another is the out-in-out style, which takes fully advantage of the width of the course by following the red track line in Figure 6. These two are the most common turning methods. And as long as the course is wide enough, it is always recommended to take the second method [7, 8].




Here is a basic analysis based on the abstracted course model shown in Figure 4. As for the first corner, with a wide track width, the racer could take fully advantage of the width, so what the driver wants is maximum deceleration to acquire the cornering speed as fast as possible. And now slight under steering is preferred to keep stability. When driving out of the corner, a slight over steering is recommended to put the head straight as fast as possible [8].

However, deceleration would cause the force increase on front wheels and force decrease on rear wheels, which is inclined to over-steering, and vice versa. F.I.A [1] doesnt allow variable aerodynamic parts, so one way is to use the position change of the body to the ground. Obviously, the body will pitch forward while braking and pitch backward while accelerating, so Tongji engineers decide to analyze this kind of change.

Figure 7: Schematic of force analogy when decelerating

As for the second corner, most drivers would choose to turn it in a steady speed along the inner circle. No matter what kind of corner, increasing the cornering speed is always being sought; this requires the racer to acquire high downforce with the change of ground clearance.

STRAIGHT LINE ANALYSIS

Straight lines are mainly about top speed, acceleration, deceleration and stability.

From the formation ZF Fj j= we can see that the more downforce (Fz) the more torque engine could provide ( tF F rj= , r is the tyre radius) which means faster speed. However, another formation of t f w i jF F F F F= + + + , in which

21/ 2w d rF C A ur= tells us that the increasing speed of drag force is far more quickly than that of torture, or more precisely, not in the same scale. So, the purpose is not maximum downforce, rather the proper ratio of downforce to drag.

As for stability, one important thing is the place of CofP (center of pressure) related to CofG (center of gravity). Lets now make an analysis according to the situation shown in Figure 8. If CofP is in front of CofG (Figure 8-(a)), then if the some slip occurs and form some angle between AB, which is the line of CofP and CofG, and the direction of velocity, than the drag force would cause the increasing of AC and serve as a positive feedback, which would cause over steering or even make the racer

spin. However, if the CofP is behind CofG (Figure 8-(b)), then it would serve as a negative feedback which could increase the ride stability. However, it doesnt mean that CofP is the after the better, only a little behind is enough, or it will cause too much under steering.

(a) (b)

(a) CofP is in front of CofG

(b) CofP is behind CofG

Figure 8: Schematic of moment analogy of the relative position of CofP and CofG

So CofP should be slightly behind CofG. So according to the CofG of this years PACE Formula one racer and the down force provided by other two major aerodynamic parts, the diffuser should provide about 40% of the total down force.

With the increasing of speed, the downforce of every aerodynamic part increases and their acceleration rate is not the same, which will cause the CofP to change. Since the diffuser has higher efficiency than front and rear wings, CofP will slide a little backward as the increasing of speed. Thus one job is improving the efficiency of diffuser at lower speed.

CAE ANALYSIS

The CAE analysis in Adams validates the requirements above.

Figure 9: Course analysis in Adams




MAJOR INFLUENCES STUDY

Having had the requirement, or criteria, the next job is to find out the design factors influencing the performance. Two methods are taken here, start from a CFD preliminary analysis for a basic idea and followed by a wind tunnel experiment for a practical idea.

CFD PRELIMINARY ANALYSIS

This step explains with CFD results the importance of the diffuser with a Formula One racer.

Figure 10: Pressure on racer with diffuser, blue is low pressure area. This is a diffuser with 900 mm length, 25 angle and a 50 mm ground clearance.

Figure 11: Pressure on racer without diffuser with a 50 mm ground clearance.

The models are based on a PACE racer model according to the 2009 Formula One Technical Regulations.

It is showed in the above 2 plots that a racer with diffuser has lower pressure underneath compared to one without diffuser.

The CFD experiment result shows the lift force on racer in Figure 3 is -1790N while racer in Figure 4 only is -401. That the previous negative lift force is 4 times more than the later one.

Figure 12: Pressure distribution along the length of a racer with diffuser

The pressure distribution indicates the negative life force created by the diffuser is mainly acted on the 2.2 m to 4 m area from the nose point.

WIND TUNNEL TEST

From the CFD simulation, weve got an idea of the role of diffuser. Then, here is a wind tunnel test to analyze the outer field of one model Ferrari 248F1 racer (The 1:18 model is an official licensed product by Ferrari whose license number is AN2737PS.) in an experimental way; to systematically describe its unstable variation characteristic by test and collect the transient data, which provides the statistical ground for understanding and designing the diffuser.

Facility and testing method

1. Small scaled wind tunnel

Figure 13: Small scaled wind tunnel




Basic parameters for the small scaled wind tunnel:

Scale 1:15

Testing room dimensionmm 1515x1185x820

Injection area (m2) 0.12

Maximum wind speed (km/h) 170

Injection flow length (mm) 1160

Fan power (kw) 7.5

2. CPS-3303/C Multi Output DC Power Supply

CPS-3303/C (Figure 14) is an adjustable and portable multi functional work station, which has two independent output channels and one stable 5V DC voltage output. It also has 3 modes of power output which are independent, series and parallel connection. In this experiment, positive/negative series connection power output is chosen.

Figure 14: DC Power Supply

Figure 15: positive/negative series connection power output mode

3. Mechanical pressure scanner system

The mechanical pressure scanner system is major consisted of mechanical scanner, pressure sensor, pitot tube, channel switcher and code displayer (Figure 16).

(a) (b)

(c) (d)

(e)

(a) mechanical scanner, (b) pressure sensor, (c) pitot tube, (d) channel switcher, (e) code displayer

Figure 16: Main parts of the mechanical pressure scanner system.

In this experiment, a scanner with 49 pressure channels, in which 48 channels are for pressure testing and one is for output, and one pressure sensor is chosen. As driven by the channel switcher, the scanner rotor sequentially connects the testing point pressure with the pressure sensor to switch the pressure channel. Meanwhile, the code displayer will display the current pressure channel. The digital signal which is converted by D/A converter from amplified output signal is then transmitted to the computer by USB2.0 interface and is saved. The detailed mechanical pressure scanner system is shown in Figure 17.

1. Scanner 2. Pressure channels 3. Pressure sensor

Figure 17: Mechanical pressure scanner system

4. Data collecting system

The data collecting system is mainly consisted of PAMP726-8/200 preamplifier, PMD-1608FS data




collector and PMD-1608FS data collecting system program.

Figure 18: PMD-1608FS data collector

PMD-1608FS data collector (Figure 18) is a data collecting device compatible to both USB 2.0 and USB 1.1. It provides 8- channel 16-digit simultaneous analogy input. The collecting rate of each channel is 50kS/s (single channel), the full capacity is 100KS/s, the 32K byte collecting rate could reach 200KS/s. In addition, it also provides a 32-digit counter and a 8-channel digital I/O.

Here is specification for PMD-1608FS data collector:

Dimension 3.1(L)3.2(W)1(H)

Input Configuration One A/D converter each channel

Channel 8 channels one end input

Convert Accuracy

16-digit 1/65536 15-digit (no miscode)

Input Range 10V5V2V1V

10 V 5.66 mV

5 V 2.98 mV

2 V 1.31 mV

Absolute Accuracy mV

1 V 0.68 mV

PMD-1608FS system program (Figure 19) is specifically written for the PMD-1608FS data collector. Its purpose is to selectively collect and display the data according to the demand of one experiment. While running, it displays the real-time graph and save the data for data processing.

Figure 19: PMD-1608FS program interface of data collecting system

Experiment Process

This experiment is mainly consisted by three parts. Former two are shown by data and the third part should be observed by eyes.

1. The Cd, CL, and pitch moment

These three parameters, which are tested under the wind speed of 0Km/h, 100km/h, 130km/h and 150km/h (the speeds are controlled by the fan control software shown in Figure 20) in the yaw degree of 0, show the main statistics one need to know about the overall aerodynamic performance of an Formula One racer.

The method is to test 100 values after the wind speed is stable for 10 seconds.

Figure 20: interface of fan control software

2. The pressure distribution behind the racer

Take a square of 140mmX140mmX140mm behind the racer to observe the pressure distribution of the flow when leave the diffuser.

For the wind angle is zero and the distribution of left and right is theoretically symmetric. Only half of the square is tested. This method can also minimize the influence by the mechanical pressure scanner system to the flow field.




Though we want continuous filed value, the scanner can only test discrete points. Our method is to test one point every 20mm the three directions, totally 256 points in the square.

3. Streamline around the body

Meanwhile, streamlines around the body should also be shown so as to observe the characteristic to time of this unstable filed.

The method is adhere some light colored strings on the body and observe its behavior under wind flow. Figure 21 shows one instance of the observation.

Figure 21: 248F1 under test in small scaled wind tunnel

Experiment Results and data process

1. Results for Cd, CL, and pitch moment

After the experiment, three sets of data under the wind speed of 100km/h, 130km/h and 150km/h (0Km/h is for adjusting of the equipment) are taken; each data has 100 points respectively for three parameters.

So the data processing method is the average of the 100 values, which are shown below:

Cd CL pitch moment

100km/h 0.04857 -0.18205 -0.01161

130km/h 0.08877 -0.222 -0.01449

150km/h 0.15762 -0.33614 -0.01532

(Unit: N)

2. Results for the pressure distribution behind the racer

Through the experiment, we got the value for these 128 points.

(a) Pressure distribution on Plane of Y=0

(b) Pressure distribution on Plane of Y=20

(c) Pressure distribution on Plane of Y=40




(d) Pressure distribution on Plane of Y=70

Figure 22: Pressure distribution of the flow field behind the racer. (Plane XZ is the symmetric plane and the coordination is right-handed.)

3. Results for streamlines around the body

The observation shows that the streamlines of the side of the body is rather stable while those behind the racer have obvious fluctuation, which the frequency about half 5 times a second.

RESULTS VALIDATION

From the CFD simulation we can see that the situation is quite different with and without a diffuser. The results from wind tunnel test is not quite accuracy, due to some reasons in which one major factor is the ground clearance is to high and weakens the ground effect. However, we can still get the general effect from this experiment.

From both CFD analysis and wind tunnel test, the design factors are chosen. They are: diffuser length, diffuser angle, and ground clearance.

DESIGN

Then shall make clear what is the main factors that influence the performance of the diffuser. Three major variables are considered.

All of the below results are based on CFD experiment on models with variables.

VISCOUS MODEL

Viscous Model: k-epsilon Model Constants:

CMU: 0.09 C1-epsilon: 1.44 C2-epsilon: 1.92 TKE Prandtl Number: 1 TDR Prandtl Number: 1.3

K-epsilon Model: Realizable Near Wall Treatment: Enhanced Wall Treatment Materials: Air

Density (kg/m3): 1.225 Viscosity(kg/m-s): 1.7894e-05

Boundary Conditions: Inlet (m/s): 80 Temperature(K): 300 Ground (Moving Wall, m/s): 80

DIFFUSER LENGTH

When length is a variable, angle is set to 25 and ground clearance is set to 50 mm.

Length is calculated with reference to the nose point.

L (MM) 1400 1150 900 700 450

LF (N) -439 -793 -1789 -343 -518

LF stands for lift force.

DIFFUSER ANGLE

When angle is a variable, length is set to 900 and ground clearance is set to 50 mm.

Angle is calculated with the reference plane.

A() 35 30 25 20 10

LF (N) +2030 -1257 -1789 -610 -2535

The results show that downforce increasing is not lineal to the increasing of angle. This is because the vacuum effect is not clear when the angle is too small, while if the angle is too large, the air would split from the surface which will weaken the effect. Thus one job of the diffuser design is to find its limit angle.




GROUND CLEARANCE

When ground clearance is a variable, angle is set to 25 and length is set to 900 mm.

Ground clearance is calculated from the ground to the undertray part of diffuser.

GC() 100 75 50 25 15

LF (N) -1924 -2865 -1789 -1343 -82

RESULTS

To getting the parameters, the best way is to make them change in the Fluent, and since you can write some program in this software, it is easy to achieve that.

With a goal of achieving maximized negative lift force and under the current model, each variable shall have its optimized number, diffuser length is best near 900 mm, diffuser angle is best near 10 and ground clearance is best near 75 mm (in 2D analysis).

ANALYSIS ON DIFFERENT CONFIGURATIONS

Here are three basic diffuser types: general, base and outskirt, they are increasing complex models.

Figure 23 Diffuser base type.

Figure 24: diffuser outskirt type.

All the three configurations are based on the 2 dimensional models same as these used in diffuser variable analysis.

Figure 25: Diffuser is very close to the ground, in order to get a precise result; a good mesh shall be made.

Type General Base Outskirt

LF(N) -1556 -2023 -2478

The CFD results shows with a correct structure of diffuser, more air will be accumulated into a narrow space for providing negative lift force.

The outskirt set is most suitable for getting the maximized down force purpose.

REAR WINGS EFFECT ON DIFFUSER

A Formula One racer has 3 major aerodynamic components: diffuser, front wing and rear wing.

Following process analyzes the effect of rear wing on the diffuser in 2 dimensional methods.

Figure 26: Pressure analysis by diffuser with rear wing.

When a rear wing is incorporated, it will act with diffuser to make a large area of low pressure not only underneath the racer but at the back of the racer as well.




Figure 27: Pressure distribution on racer by diffuser with rear wing (in 2d).

The distribution of the negative lift force length does not change much with the rear wing.

Rear Wing With Without

LF(N) -4821 -1789

Under the same configuration, the total negative force with a rear wing will increase about 2.7 times compared with a set without rear wing.

FINAL RESULTS

Figure 14 shows the finished diffuser in this years PACE Global formula project.

The major parameters chosen for 07-08 PACE Global Formula Racer are shown below:

Diffuser length: 900mm

Diffuser angle: 10

Ground clearance: 75mm

Flange type: outskirt

Figure 28: The diffuser of the PACE Global Formula

CONCLUSION

This study shows some methods in designing a maximized negative force generate diffuser for a Formula One Racer.

CFD is quite useful in quick making lots of 2D models assessment to indicate a design direction.

In 3 variables that major affects the aerodynamics, diffuser length and ground clearance is quite sensitive to changes, while diffuser angle with a steady variation. That means a little adjustment in length and ground clearance will get a sounding result of enormous increased down force. This area is worth deeper investigation.

A good three dimensional diffuser configuration shall be well proposed as the 3D CFD analysis needs quite a lot of time. This process needs a lot experience and related theories.

As for the aerodynamic parts, you cannot deicide an influence of a part by its size; some small shape changes will make a big difference.

One must view the part by a systematical way. In this case, the front and rear wing and also the shape will influence the performance of the diffuser a lot.

ACKNOWLEDGMENTS

The authors would like to thank Youfu Wang, Wenjun Gu, Yingqin Zhang, Junhui Yu, Ningjian Wang for their continuous support and effort on this project.

The authors would like to thank all the universities involved in this project for their contribution and help, especially BYU for leading the project and Hongik University, Queens University and West University for their collaboration.

The authors would like to thank the entire PACE sponsors, especially GM, for providing the equipments and arranging such an interesting project.

The authors would like to also thank the substantial and ongoing support of School of Automotive Studies, Tongji University.

REFERENCES

1. F.I.A. Sport, 2009 Formula One Technical Regulations.

2. David Tremayne, The Science of Formula 1 Design, Haynes Publishing

3. M. C. Potter and D.C. Wiggert, Mechanics of Fluids,

4. William F. Milliken and Douglas L. Milliken, Race Car Vehicle Dynamics, Society of Automotive Engineers Inc.

5. , Fundamentals of Vehicle Dynamics,




6. Paul Van Valkenburgh, Race Car Engineering & Mechanics,

7. Carroll Smith, Drive to Win, 8. Carroll Smith, Tune to Win, 9. Anderson, Fundamentals of Aerodynamics, 10. J. Blazek, Computational Fluid Dynamics:

Principles and Applications, Elsevier 11. O.C. Zienkiewics, R. L. Taylor, The Finite Element

Method Volume 3: Fluid Dynamics, Fifth Edition, Butterworth Heinemann

12. Wordley, S.J., and Saunders, J.W., Aerodynamics for Formula SAE: A CFD, Wind Tunnel and On- Track Study, SAE Paper 2006-01-0808, 2006.

13. Wordley, S.J., and Saunders, J.W., Aerodynamics for Formula SAE: Initial Design and Performance Prediction, SAE Paper 2006-01-0806, 2006.

CONTACT

Zhen Zhang: [email protected]

Zhengyuan Yang: [email protected]

WEBSITE: www.pacetongji.com.cn

APPENDIX

Schematic of the Tongji small scaled wind tunnel:




Diffuser Design for PACE Global Formula One Racer

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