Aero Masters Thesis Delft NL

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Aerodynamic analysis of a

2-man bobsleigh

O. LewisOctober 14, 2006


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Aerodynamic analysis of a 2-man bobsleigh

Master of Science Thesis

For obtaining the degree of Master of Science

in Aerospace Engineering at Delft University of Technology

by

Oscar Lewis

October 14, 2006

Examination Committee:

Prof.dr.ir. P.G. Bakker Delft University of Technology

Dr.ir. L.M.M. Veldhuis Delft University of Technology

Ir. W.A. Timmer Delft University of TechnologyDr. F. Motallebi Queen Mary, University of London

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Contents

Preface v

Abstract vii

List of symbols ix

Chapter 1 Introduction 1

1.1 Brief history 1

1.2 A typical bobsleigh run 3

1.3 Modern bobsleigh design 4

1.4 Thesis goal 5

Chapter 2 Bobsleigh aerodynamics 7

2.1 Bobsleigh run time sensitivity 7

2.2 Preliminary estimation of aerodynamic drag 12

2.3 Drag reduction techniques 17

Chapter 3 Windtunnel experiments 19

3.1 Experimental setup 19

3.2 Measurement apparatus 22

3.3 Windtunnel corrections 26

Chapter 4 CFD calculations 29

4.1 CFD Setup 29

4.2 Grid setup 31

4.3 Grid adaptation 35

4.4 Initial check of CFD results 37

Chapter 5 Results 415.1 General flow description 41

5.2 Gap between front and rear cowling 43

5.3 Crew and pilot helmet 49

5.4 Runners and axles 53

5.5 Other features 54

Chapter 6 Conclusions and recommendations 59

6.1 Conclusions 59

6.2 Recommendations 60

Bibliography 63

Appendices 65

A. International rules 66

B. Parameters 71

C. Bobsleigh equation of motion 74

D. CFD settings and results 78

E. Practical tips 91

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Preface

As final part of the study Aerodynamics, a master variant of Aerospace Engineering at Delft

University of Technology, an individual project has to be undertaken. The past year Iexplored the exciting world of bobsleighing as my master project. The objective was to

analyze the aerodynamic flow around a bobsleigh by doing both scale model windtunnel tests

and performing CFD calculations. Also possible improvements had to be investigated. A side

objective was to help the Dutch bobsleigh teams during their Olympic Campaign in Torino

2006 by adapting their current sleds. The ultimate goal would be to design and build a

completely Dutch sled for the Dutch teams. Hopefully this report is a first step toward that

goal.

Basically this report is written for anyone interested in the aerodynamics of a bobsleigh,

although knowledge of low-speed aerodynamics is presumed. People who are interested in

general aspect of the sport are referred to chapter 1. In chapters 2 to 4 the tools used to

investigate the aerodynamics of a bobsleigh are explained. People only interested in theresults should read chapter 5. In chapter 6 the conclusions are given.

I would like to thank the following people who helped me during this project. Leo Molenwijk

and Stefan Bernardy for their technical assistance during the windtunnel testing. Eric de

Keizer and Nico van Beek for their help with all my computer and software issues. Everyone

involved in the bobsleigh project and specifically NOC*NSF for making the full scale testing

possible, TNO for their work on the helmets and of course all the dutch Olympic bobsleigh

teams, without whose enthusiasm and feedback this project would not have come to fruition.

Next I would like to thank Fariborz Motallebi from Queen Mary, University of London, who

provided the windtunnel model. Naturally a big thank you to my supervisors Nando Timmer

and Leo Veldhuis for their support and guidance. Finally I would like to thank my family andfriends who supported me not only during this project, but during my entire study.

Oscar Lewis

October 14, 2006

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List of symbols

Latin

a,b,c Parabola coefficients [-]

A Maximum cross section area of the bobsleigh [m2]

b Windtunnel width [m]

c1 Cornering factor [-]

CD Drag coefficient [-]

Cf Skin friction coefficient [-]

Cside Side force coefficient [-]

d Equivalent diameter based on cross section area [m]

D Aerodynamic drag [N]

f Max sprint force in Keller equation [m/s2]

f# Focal number [-]

F Runner friction force [N]

g Acceleration of gravity [m/s2]

h Height, windtunnel height [m]

k Turbulence kinetic energy [m2/s2]

l Length of bobsleigh [m]

L Length of track [m]

m Mass [Kg]

M Mach number [N]

N Normal force [N]

r Radius based on maximum cross section area, radius of

axis-symmetric body, general radius

[m]

Re Reynolds number [-]

s Distance along track [m]

t Time [s]

Tu Turbulence level [-]

U Freestream velocity [m/s]

V Bobsleigh velocity [m/s]

Vm Model volume [m3]

x,y,z Cartesian coordinates [m]

y+ Law-of-the-wall scaled y-coordinate [-]

Greek

Track slope [rad] Parameter for calculation of solid blockage [-] Boundary layer thickness [m] Turbulent dissipation [m2/s3]s Solid blockage [-] Boundary layer momentum thickness [m] Air viscosity [N s/m2]k Kinetic coefficient of friction [-] Air kinematic viscosity [m2/s]

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Air density [kg/m3] Sprint decay term in Keller equation [s]

Subscripts

0 Initial conditionend Finish condition

H Human

ISA According to International Standard Atmosphere

trans At transition point Freestream condition

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Chapter 1 Introduction

One of the most exciting and fastest winter sports is bobsleighing or Formula One on ice, as

it is also frequently called. This nickname not only emphasizes the high speeds involved, but

also the close margins between finish times and the importance of having state of the art

material. This chapter deals with general aspects of this sport and a goal for this thesis is

formulated. In the first paragraph the history of bobsleighing and the evolution of the sled is

explored (1.1). The second paragraph describes a typical bobsleigh run (1.2) followed by a

description of the general features of a modern bobsleigh (1.3). Finally the goal of this thesis

is discussed and a chapter guide of this report is given (1.4).

1.1 Brief history

Even though sleds have been around thousands of years, the sport of bobsleighing only

started to take shape at the end of the nineteenth century in Switzerland when a steering

mechanism was attached to a toboggan (a sled without runners or skis). It was named after

the bobbing motion the crew used to make along straights to try to gain speed. The first

competition was held in the Swiss town of Saint Moritz. The first bobsleigh club was

founded here in 1897.

Figure 1.1: Early bobsleighing

Bobsleighing was a part of the first Winter Olympic Games held in 1924 in Chamonix Mont

Blanc one year after the Fdration Internationale de Bobsleigh et de Tobogganing (FIBT)

was founded in 1923. During these first Olympics crews consisted of 4 men. In 1928 both 4

and 5-man crews were allowed. In 1932 the 2-man and 4-man format, that is still used today,

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2 AERODYNAMICANALYSISOFA2-MANBOBSLEIGH

was introduced.

Modern bobsleighing started to develop in the 1950s. Up to then it was mostly an activity for

the wealthy and there was no serious training involved. The importance of the start wasrecognized and strong athletes started to take part in the sport. The tracks, sleds and clothing

were developed. Natural tracks were replaced by artificial tracks. The track at St. Moritz is

the only remaining natural track. In 1952 an important rule limiting the total weight of the

sled and crew was introduced.

Figure 1.2: Bobsleighing development

In the mid eighties the World Cup was introduced. Up to then success in the sport was

determined only by the performance at the Olympics, World and European Championships.

In the beginning of the 1990s a womens event was added to the world cup calendar, but onlyin the two-man discipline. In 2002 women were allowed to compete in the Winter Olympics

for the first time.

Today bobsleighing is one of the fastest and most exciting winters sports around. Speeds of

nearly 150 km/h and G-forces of up to five are reached. It is a sport where every hundredth of

a second is crucial. Although very strict rules apply, teams are always trying to implement the

latest technologies to squeeze every last possible fraction of a second out of the sled.

Therefore, technology from Formula One and NASCAR racing is used to design and build

sleds. The increasing role of technology is causing sleds to become more and more expensive

to build (over 40.000) and are only available for the wealthiest teams. To make the playing

field more even new rules are introduced regularly. An example of a recently introduced newrule is that runners have to be made out of a standard material supplied by the FIBT.


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INTRODUCTION 3

Figure 1.3 Modern bobsleighing

1.2 A typical bobsleigh run

A modern bobsleigh competition is held over several runs down an iced track; two runs for

world cup events and four runs for European and World championships and the Olympic

Games. All times are added and the team with the fastest total time is the winner.

Even though all tracks have individual designs they all are approximately 1.5 km long and

have a vertical drop of approximately 120m. A bobsleigh track consists of three different

areas: the start area, the main track and a deceleration area. These different sections and the

impact on the run will be discussed briefly.

The start area can be divided in the push off stretch and the actual starting area. The push off

stretch is 15m long and is the section from the start block to the first photoelectric cell. This

is where the start line is, so where the clock starts running. After these first 15m a straight

downhill section follows. In this section the changeover from pushing phase to gliding phase

takes place; the athletes take their places in the sled and the push-bar is retracted. After 50m

another photoelectric cell is placed that determines the starting time. Speeds of over 40 km/hare reached in this first section. A generally accepted rule of thumb is that one tenth of a

second reduction of the start time leads to three tenths at the finish, so the first few meters are

of crucial importance.

After the start area the main track follows. The track where the Olympic Games in 2006 were

held has 19 bends (see figure 1.4). The bob gains more and more speed as it continues the

run. Usually maximum speeds are reached before the end of the track since the last part of the

track can be slightly uphill. The high speed part of the track is where the aerodynamics of the

bob is most important. An approximate variation of drag during a run will be given in

paragraph 2.1. To convert a good start time into a good final time it is of vital importance that

no momentum is lost by hitting the wall or slipping.

After the finish line there is a straight deceleration stretch, where the sleds come to a


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Chapter 2 Bobsleigh aerodynamics

In this chapter the aerodynamics of bobsleighing is discussed. First of all an estimation will

be made of the impact drag has on the final times (2.1). This will be compared with the

influence of the start and ice friction. In the following paragraph an estimation of drag will be

given (2.2) and it will be shown that typical drag variations have a significant influence on

final times. Finally some typical drag reduction techniques found in literature and their

applicability to bobsleigh design will be discussed (2.3).

Before starting with section 2.1 a general remark must be made. In this report drag will

usually be given in terms of drag coefficient using the maximum cross section area of the bob

as reference area. The reason for this is that scaled windtunnel tests need to be compared

with full scale windtunnel tests and CFD calculations. Since the same bobsleigh shape isused, this is no problem. When comparing different shapes, looking only at the drag

coefficient can be very dangerous, because increasing the area may reduce the drag

coefficient but not the absolute drag. A better parameter to compare the sleds is the drag area.

The scale of the tested models must be the same in this case.

2.1 Bobsleigh run time sensitivity

Results in bobsleigh competitions are based on final times. As described in the previous

chapter two forces act against a bobsleigh; aerodynamic drag and friction with the ice. The

purpose of this section is to relate these two forces to the final time of a run and comparetheir influence.

Calculation procedure

A run down a track is complex. All forces acting on the sled vary constantly. To obtain a

global estimate of the influence of drag the exact details of these forces are not needed. The

following assumptions are made to calculate global variation of the forces:

The track is a parabolic downhill stretch without corners.

The kinetic friction coefficient (k), air density () and air viscosity () are assumed

to be constant.

The airflow around the bobsleigh does not produce lift or downforce. Usually there isa small amount of downforce but this is relatively small when compared with the

normal force due to gravity, and especially when compared with normal forces due to

cornering (up to 5g).

With these assumptions a simple equation of motion can be derived for a bobsleigh (see

appendix C) wheresis the distance traveled along the track:

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Figure 2.2: Forces during a bobsleigh run

Parameter variation

Now that the equation has been solved different parameters can be varied. In figure 2.3 the

influence of drag area (a), kinetic friction coefficient (b), mass (c) and start times (d) on final

times are shown. In table 2.3 the change of the same parameters that is needed to reduce the

final time by one tenth of a second is given. The first three parameters may change the start

time but this effect is not modeled.

An equal variation in kinetic friction coefficient has more influence than changing drag

coefficient, but both have significant effect. However, the rules allow more room to reduce

drag than to reduce the kinetic friction coefficient. It is essential that the mass of the sled is as

close a possible to the allowed maximum of 390 kg. When mass is reduced its influence

increases; for a woman's sled with a maximum mass of 340kg it is even more essential tomake the sleigh as heavy as possible.

Of course a good start is equally important. Using the model, an improvement of a tenth of a

second leads to a reduction in finish time of 0.303s or three tenths which corresponds exactly

with the rule of thumb given in paragraph 1.2.

All factors examined here are important to win races and aerodynamic drag is one of them.

Having a 3% higher drag than your opponent means that you have to make up one tenth of a

second somewhere along the way, either at the start or by hoping your opponent makes a

mistake somewhere down the track.

0 10 20 30 40 50 600

50

100

150

200

250

300

350

400

t [s]

Force[N]

Aerodynamic drag

Ice friction

Tangential component gravity

Resultant force


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BOBSLEIGHAERODYNAMICS 11

0 0.1 0.2 0.3 0.451

52

53

54

55

56

57

58

CD

tend

[s]

(a) (b)

(c) (d)

Figure 2.3: Influence of parameters on final time, the final time for the original situation is indicated

by the dashed line

Table 2.3: Change needed for t = -0.1s

Parameter Original value Change Percentage

CD 0.409 - 0.0042 - 3.00%

k 0.014 - 0.0003 - 2.14%t0 4.81 s - 0.033s - 0.69%

m 390 kg + 12.2 kg + 3.12%

200 300 400 50051

52

53

54

55

56

57

58

m [kg]

tend

[s]

4 4.5 5 5.5 651

52

53

54

55

56

57

58

tstart

[s]

tend

[s]

0 0.005 0.01 0.015 0.0251

52

53

54

55

56

57

58

tend

[s]

mkk


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2.2 Preliminary estimation of aerodynamic drag

In this section the drag of the different parts of a bobsleigh will be estimated. If possible anestimate of the variation of drag will be given. This will be related to a change in time with

the relations given in the previous section to show that typical differences in drag have a

significant influence on final times.

Main cowling

To get a rough estimate of the cowling drag it is assumed the bob is an axis-symmetric body

with the following dimensions (see figure 2.6):

r=0.331-1-x

1.12

for 0x1.1m

r=0.33 for 1.1 mx1.5m

x-1.52-r8,712=8.882 for 1.5m 2.7m

(2-2)

The large cavity is absent and there is no influence of the bumpers, the runners, the joint

between the front and back part or any other parts or disturbances. There is no influence of

the ground or sidewalls. Then the drag of the cowling has the following components:

Skin friction drag

Forebody pressure drag Base pressure drag

To predict the skin friction drag it is assumed that the boundary layer develops like on a flat

plate. For a laminar boundary layer on a flat plate the skin friction coefficient is given by

[White, 1991]:

Cf=0.664

Res(2-3)

The coordinate s is the coordinate along the body. For a turbulent flat plate:

Cf=0.027

Res1/7 (2-4)

The drag coefficient for the turbulent or laminar case can be found by integrating the value of

the skin friction coefficient over the area of the body and dividing by the reference area:

CD=2

A

0

send

Cf r ds (2-5)

When transition occurs, the calculation can start with the formula for laminar skin friction. At


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the transition point the thickness of the turbulent boundary layer needs to be matched to the

laminar boundary layer. This gives a virtual starting point (sV0) for the turbulent boundary

layer (see appendix B.2) and for the drag coefficient:

CD=

2

A0s

transition

Cf

laminar

r dss

transition-s

V0

send-s

V0

Cf

turbulent

r ds (2-6)With this equation the skin friction can be calculated for different locations of the transition

point(see figure 2.4). According to literature the position where transition occurs can be

approximated by accepting a critical Reynolds number of [Anderson, 1989]:

Res critical=5105

(2-7)

In figure 2.5 the position of transition is given at various velocities for the same atmospheric

conditions as used previously. At U = 35 m/s transition occurs at s = 0.22m. This point is

indicated in figure 2.4. It is obvious that skin friction drag can be reduced by moving

transition backward. Due to roughness on the nose from inspection hatches it is expected that

transition occurs even earlier, but that will not change the drag much according to the figure

2.5. If transition occurs at s = 0.22m a skin friction drag coefficient of 0.047 is found. In

figure 2.6 the boundary layer thickness development is given for this case.

Figure 2.4: Influence of transition point on drag

coefficient at U = 35 m/s

Figure 2.5: Influence of freestream velocity on

transition point

The base and forebody drag have been estimated from ESDU data units [ESDU, 1980] and

[ESDU, 1996]. For the data from these references to be valid the base and boat-tail drag need

to be independent of the forebody drag. To achieve this it is suggested the cylindrical body

between forebody and boat-tail should be at least three body diameters. This is not the case,

but for this preliminary estimation these data are used anyway. For the forebody a drag

coefficient of -0.003 is found. The base drag for the circular boat-tail with the given geometry

a total base drag (including boat-tail) of 0.06 was found. Without a boat-tail this can be as

high as 0.14. Since a bobsleigh does not have a complete boat-tail all the way around theaverage of these is taken, so the estimated drag coefficient becomes 0.10.

0 1 2 30

0.01

0.02

0.03

0.04

CD

stransition

[m] 10 20 30 40

0

0.2

0.4

0.6

0.8

1

U [m/s]

strans

[m]


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Figure 2.6: Geometry of the axis-symmetric body and boundary layer development at U = 35 m/s

Bumpers

In this section the drag of the bumper will be estimated, based on simple 2D shapes. For a

rectangular shape with sharp edges the drag coefficient can be as high as 1.4. If the edges

have a small radius this can be reduced significantly to about 0.5. If the trailing edge is

streamlined this value can be reduced to 0.2. These values have been estimated from data in

[Hoerner, 1965]. An overview is given in table 2.4.

Table 2.4: Bumper drag

Shape Cross-section CD CD, front bumperA = 0.008 m2

CD, rear bumperA = 0.005 m2

Rectangle 1.4 0.033 0.020

Rectangle,

streamlined back1.2 0.028 0.017

Rectangle rounded

edges0.5 0.012 0.007

Streamlined back,

rounded edges0.2 0.005 0.003

Streamlined body 0.1 0.002 0.001

These values have to be multiplied by 2 to get the drag of both left and right bumpers. For the

estimation the rectangle with rounded edges and streamlined back is taken. The total drag

coefficient then becomes 0.016.

Based on the numbers in table 2.4 it seems the drag can be halved by further streamlining the

shape. However streamlining the bumpers would mean an increase in height of the bumper,

because it has to have a certain thickness over a prescribed length. Since the listed drag

coefficients are based on height the actual drag is not halved. Streamlined shapes usually

have a sharp trailing edge. This is not desirable for a bobsleigh bumper. Rounding the trailing

edge will usually increase the drag coefficient.

0 0.5 1 1.5 2 2.5 30

0.2

0.4

x [m]

y[m]

Boundary layer thickness

Geometry shape

Transition point


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Figure 2.8: Contribution of bobsleigh parts to the total drag

2.3 Drag reduction techniques

In this section some drag reduction techniques that have been found in literature are

discussed. According to [Motallebi, 2004], there are three main areas that add to the total

drag:

Formation of the wake inside the bobsleigh cavity. The low pressure in the wakecauses an influx of air over the side of the cowling, which creates large trailing

vortices.

Brakeman position. An angle of approximately 45 of the brakeman results in thelowest drag.

The shape of the nose. Although the forebody pressure drag is not very large and doesnot change much at low speeds for different shapes, it has great influence on the flow

over the rest of the sled. It has influence on the transition from laminar to turbulent

flow.

In the same paper [Motallebi, 2004] two modifications are discussed and tested on a quarter

scale model:

Flared sidewalls: by gradually accelerating the flow over the sidewall, it should flowalong the wall further without being diverted and sucked into the cavity. For the

unmanned situation a small reduction in drag was made. In the manned case thisadvantage disappeared at higher Reynold's numbers, which are applicable to the real

Cowling skin friction15%

Cowlingpressure

30%

Bumpers5%

Crew5%

Axles, runnercarriers and runners

46%


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situation.

Shark nose: by energizing the boundary layer, the pressure drag was expected to

reduce in two ways. The boundary layer can better withstand a higher adversepressure gradient induced by the driver's head, which should decrease the size of the

separated area. The air over the sidewall will be accelerated reducing the size of the

separated area over and after the crew. It was tried to achieve this by changing the

smooth curved configuration into slightly broken parts, by adding three peaks across

the nose. For low Reynold's number the drag was lower in both the manned and

unmanned case, but once again this advantage was lost at higher Reynold's numbers.

Other means of reducing drag of bluff bodies are [Sovran, 1978]:

Base bleed: by injecting gas in the low pressure wake region, the pressure can beincreased and thus the drag should decrease. Keeping a gas cannister on board is not

allowed but a kind of base bleed might be achieved by allowing air to flow into the

the bob through the gap between the front and back parts of the cowling.

Trailing edge notches: by adding trailing edge notches the big vortices are broken

down into smaller vortices that should reduce the drag. These shapes are not allowed

under the rules.

Splitter plates: a feature often used for bluff bodies is the addition of splitter plates,but these are also not allowed.


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Chapter 3 Windtunnel experiments

In this chapter the hardware and software used for the experimental analysis will be

discussed. In the section 3.1 details of the windtunnel will be given. Also details and features

of the bobsleigh model will be discussed. In section 3.2 the apparatus used for the different

measurements is handled. Finally in section 3.3 corrections to the force measurements are

discussed.

3.1 Experimental setup

In this section the windtunnel setup is discussed. First of all some details of the windtunnelare given. Then the model is described and the way it is attached in the tunnel.

LTT Windtunnel facility

The windtunnel experiments have been performed in the Low Turbulence Tunnel at the Low

Speed Laboratory of the Aerodynamics section at the Faculty of Aerospace engineering of

Delft University of Technology (see figure 3.1). This windtunnel has the following

characteristics:

Test section: 1.25 x 1.80m Turbulence level < 0.1% Maximum speed 120 m/s

19

Figure 3.1: Low Turbulence Tunnel at TU Delft Low Speed Lab

0 2 3 4 5 6 7 8 9 101meter

1

2

34

5

6

78

9

1011

121314

Fan and straighteners

Motor

Corner vanesSettling chamber

Expansion screen

7 Anti-turbulence screens

Screen store roomContraction

Exchangeable test section

DiffuserSecurity screen

Spider webScreenSix-component balance

Exchangeable test section 1.80 x 1.25 meter

V max. = 120 m/sec

Tu = 0.02 - 0.1 %

23b

3a

1

12

3b 10

14

9

13

6

8

4

7

5

3d

3c


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Model of the bobsleigh

For the windtunnel tests a plastic scale model (1:3.17) was used of a bobsleigh (see figure

3.3). It has been painted black, using blackboard paint, to limit the reflections of the laser

light during the PIV measurements. Axles were present and used to attach the bob to the

measurement plate. No holding runner carriers or runners were modeled, but there is a brace

present that connects the bob to the measurement plate. The windtunnel test section is

equipped with a reflection plate to reduce the thickness of the boundary layer. To align the

bobsleigh with the flow measurements were done at different yaw angles. The model was

fixed in the position where the sideforce was zero (-0.19, see figure 3.2).

Figure 3.2: Sideforce coefficient at different yaw

angles at Re = 0.6106

The inside of the bob is not completely open; the nose section is reinforced with a wooden

plate and filled with insulation foam. The gap between front and rear cowling in the

bobsleigh is a little further to the front than is usual for a bobsleigh. In a later stage of the

experiments a brakehole was added as well.

Figure 3.3: Model (1:3.17) of the bobsleigh in the low speed

windtunnel

2 1 0 1 20.2

0.15

0.1

0.05

0

0.05

0.1

0.15

Yaw angle [deg.]

CSide


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The results are shown in figure 3.7. The instability region can be seen clearly. For the case

with zig zag tape this instability disappears. The drag at lower speeds is reduced significantly.

The laminar boundary layer is tripped by the zig zag tape to a turbulent boundary layer. This

suppresses laminar separation on the sphere, which causes a decrease in the size of the wake.This difference disappears at higher speeds because of natural free transition.

3.2 Measurement apparatus

During the windtunnel campaign different measurement and flow visualization techniques

have been used. This section will describes used hard and software for each technique.

Particle image velocimetry

One of the techniques used is particle image velocimetry (PIV). Tracer particles are

immersed in the flow and illuminated by a laser sheet. By taking two pictures in rapid

succession the particle displacement can be found. Because the time separation is known the

velocity field can be deduced. For details on this technique see [Raffel, 1998].

The CCD camera used was a PCO sensi cam QE which has a 1376x1040 pixel resolution and

a pixel size of 6.45 mm. The laser was a Spectra-Physics Quanta-Ray PIV 400 Pulse

Nd:YAG, which has a wavelength of 532 nm and an energy output of 400 mJ/pulse. The

seeding device was a Safex double power fog generator. With the normal power mix the

typical particle diameter is 1 mm.

Figure 3.7: Unsteadiness during initial measurements

0 2 4 6 8 10 12 14

x 105

0.39

0.4

0.41

0.42

0.43

0.44

0.45

0.46

0.47

0.48

Re

CD

No zig zag tape pilot helmet

Zig zag tape pilot helmet


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WINDTUNNELEXPERIMENTS 23

The software used to capture the images and process the data was the commercial package

Lavision Davis 7.1. The used settings can be found in table 3.1. The Reynolds number at

which these measurements took place was approximately 6.4105. No zig zag tape was

applied yet. The gap between the front and rear cowling was closed.

Table 3.1: PIV settings

Property Value

t 15s

f# 8

FOV 246x186mm

lens 50mm

Figure 3.8: Seeding system Figure 3.9: Optics

Figure 3.10: Camera Figure 3.11: Model

Unfortunately the data found with this technique in this configuration is limited in use. For

instance the flow around the axles can not be seen with the camera due to the presence of the

brackets. The flow around the bumpers was not captured very well due to reflections from the

bumper but also from the sidewall, despite painting the bob black. Since the laser light has to

come from behind, the flow in front of the helmet going into the bob cannot be seen as well.

The front bumper is partly in the shadow of the rear bumper. The only areas of interest that

could be captured are the separation area behind the pilot's helmet and the wake behind the

bob.


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Balance measurements

To measure the forces on the bobsleigh a six component balance system has been used (fig.

3.12). Because the balance system is placed above the windtunnel the model is mounted

upside down. To capture and process the data the in-house program W3D has been used. This

programs can correct for solid model blockage (see section 3.3), wake blockage, buoyancy

and lift interference. Unless stated otherwise the measurements are averaged over 20 data

points.

Figure 3.12: The six component balance system


37/103


Oil flow visualization

To visualize the surface flow an oil flow visualization technique has been applied. First

petroleum was applied to create a smooth surface. The mixture for the visualization consists

of the following components:

Shell Ondina 68 Paraffin; viscosity thick. A680 fluorescent oil additive.

After the oil is applied the model is illuminated with ultraviolet light. The oil flow

measurements were done at approximately 60 m/s. For an example see figure 3.13.

Figure 3.13: Example of oil flow visualization

Other techniques used

To visualize the flow a woolen tuft was used. It was attached to the end of a metal rod. When

inserted in the flow the tuft follows the streamlines and flow features like vortices can be

detected. Of course the rod influences the flow itself, so care must be taken when interpreting

the results.

A microphone was used to trace flow transition on the bob. When a microphone is placed in a

laminar flow almost no noise is heard. In turbulent flow a distinctive noise can be heard.

Once again the microphone influences the flow and may force the flow to become turbulent

which can make it difficult to pinpoint transition.


38/103


3.3 Windtunnel corrections

Three types of corrections have been applied to the force measurements. These are discussedhere.

Solid model blockage

Due to the presence of the model the air around the model is accelerated. This can be

corrected for with [AGARD, 1966]:

s=V

V

=0.65V

m

3

h2

b

(3-1)

With:

=1-M2=1-0.2272=0.974 (3-2)

The volume of the model is estimated with:

Vm=AL=0.3420.964=0.0328 m3

(3-3)

With the windtunnel area being 2.07 m2and with the width of 1.80 m the blockage becomes9.7 10-3.

Measurement plate

When measuring the drag of the model, the drag of the plate to which the bob is attached is

also included. To be able to determine this drag a dummy run is performed; the bobsleigh is

mounted on four streamlined stakes, instead of the measurement plate (see figure 3.14). Extra

wires were attached to keep the model firmly in place. In this configuration the drag of the

plate is measured. This is an approximation because:

The brackets had to be removed. Otherwise the model would still be touching theplate and therefore influencing the measured forces.

The stakes and wires block the tunnel. Especially wires can have significant wakes.The coefficients have not been corrected for this effect.

For every configuration the drag of the plate will change, so actually a dummy runshould be performed for every one of these configurations. Because it is expected

that the plate drag is influenced only slightly and because setting up the dummy run

is very time consuming this is not done.

The measured plate drag is given in figure 3.15. The drag of the holding brackets was also


39/103


measured, without the bobsleigh present, but it does give an idea of the drag they can produce

(see figure 3.16).

Figure 3.15: Dummy run results Figure 3.16: Bracket drag

Daily variation

Finally, because of temperature differences in the tunnel building, the behavior of the

measurement plate can change slightly every day. Therefore a reference run was performed

daily (see figure 3.17). This reference run consists of measuring the drag of the plate in an

empty tunnel. The reference run done just before the dummy run (on 23-09-2005) is taken asstandard. On other days the difference with this standard run is applied as a correction.

Figure 3.14: Dummy run configuration

0 5 10 15

x 105

0

0.01

0.02

0.03

0.04

0.05

0.06

Re

CD

Dummy run

Empty tunnel

0 5 10 15

x 105

0

0.01

0.02

0.03

0.04

0.05

0.06

Re

CD

Brackets

Empty tunnel


40/103


To calculate the differences an interpolant spline is used since the measurement are not taken

at exactly the same Reynolds numbers. However in the lower Reynolds regime this gives

problems because the drag has steep gradients and the calculated differences become

inaccurate (see figure 3.18). Therefore for Reynold numbers below 5105

the difference is setat the value at Re = 5105 (see figure 3.19).

Figure 3.17: Reference run drag (empty tunnel)

Figure 3.18: Original differences Figure 3.19: Adjusted differences

0 5 10 15

x 105

0.01

0.015

0.02

0.025

0.03

0.035

0.04

Re

CD

20092005

21092005

22092005

23092005

26092005

0 5 10 15

x 105

5

0

5x 10

3

Re

DCD

20092005

21092005

22092005

26092005

0 5 10 15

x 105

5

0

5x 10

3

Re

DCD

20092005

21092005

22092005

26092005

CD

CD


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Chapter 4 CFD calculations

To further analyze the flow around the bob CFD calculations are performed. In section 4.1

the setup of the CFD calculations is discussed. In section 4.2 the setup of the grid is

discussed in more detail. In section 4.3 grid adaptation is discussed. The results are checked

in section 4.4.

4.1 CFD Setup

In this section the general setup of the CFD calculations is discussed. This setup was done by

following theBest practice guidelines for handling automotive external aerodynamics withFLUENT[Lanfrit, 2005]. For a complete overview of the boundary conditions and solver

settings see appendix D.

The CFD calculations have been done using the commercial package Fluent 6.2.16. The setup

was done on a local workstation. The calculations were performed on a Beowulf cluster with

10 computational nodes with two 3 GHz processors each and 4 GB of memory. Also 24 64-

bit nodes were available temporarily, with four processors each and 8 GB of memory.

The geometry used is based on the same bobsleigh as the windtunnel model. They were both

derived from the same scan of a full scale bob. However the scanned geometry had to be

fixed to perform calculations; the surface had to be made completely watertight. This might

have changed the geometry slightly in some areas, but this is also the case for the windtunnelmodel. The inside of the bob was modeled to match the configuration of the windtunnel

model. The geometry can be seen in figure 4.1. Because the flow is considered steady and the

geometry is symmetric only half the geometry is calculated.

The equations to be solved are the steady incompressible Reynolds averaged Navier-Stokes

equations. The flow can be considered incompressible because the Mach number is around

0.1. The steady model is chosen for several reasons. First of all the Reynolds numbers at

which the standard CFD test are done are larger than the instability region discovered in the

windtunnel (figure 3.7) and the wake coming from the pilot helmet is expected to be stable.

Other unsteady features may definitely occur, for instance behind the axles and in the wake.

However, unsteady calculations are computationally very demanding. Therefore it is chosento study the steady solution first. In section 4.4 these steady results are checked to see if they

can be used to predict drag, or at least the drag of certain parts.

To close the RANS equation the realizable k-model with non-equilibrium wall functions is

used. According to [Lanfrit, 2005] industrial applications have shown that it is possible to

achieve drag coefficients that are within 2-5%. Since accurate drag values have been obtained

in the windtunnel, the prediction of the absolute drag coefficient is not very important. It is

more important to compare different cases. Since the model is also known to be very stable

and fast converging this model is chosen.

All boundaries need to be assigned boundary conditions. The inlet is set as velocity inlet and

29


42/103


43/103

CFD CALCULATIONS 31

4.2 Grid setup

The grid was generated with Gridgen 15.09. There are a number of aspects that have to bekept in mind when creating a computational mesh (see [Fluent, 2005]):

Smoothness: the volume of the cells should not change too fast. For the boundarylayer a maximum volume ratio of 1.2 is recommended.

Node clustering: a minimum number of cells is needed to resolve geometric and flowfeatures. Less can be used in less interesting areas. At least 5 cells are recommended

for every flow passage.

Cell shape: to ensure a good quality the cell skewness should not be too high. A

maximum aspect ratio of 5 is recommended.

To minimize numerical diffusion cells should be aligned with the flow, especially inthe boundary layer where the velocity gradients are large.

For non-equilibrium wall functions a wall y+between 30 and 300 is recommended forthe cell centroid of the first cell adjacent to the wall.

Usually a compromise has to be made between these aspects. For example high clustering

can lead to high skewness.

Figure 4.2: Used cell types

An unstructured triangular surface mesh is created on the bob to be able to cope with the

curved surfaces. A prismatic boundary layer is extruded from the bob to align the cells near

the boundary with the flow. First an estimation is made of a first cell height that will give a

good wall y+value. The wall y+is given by:

y+=uy

(4-1)

u=UCf

2 (4-2)

To make an estimate the same formula for skin friction is used as in chapter 2. In figures 4.3and 4.4 the first cell height (is two times the height of the cell centroid) is plotted against the


44/103


length of the bob for different values of wall y+. The chosen value, 1.5 mm, is also plotted in

the figures. For this value wall y+is larger than 30 everywhere at 15 m/s and smaller than 100

for the most part at 35 m/s. Even though most cases have been done at 35 m/s this does make

it possible to do calculations at lower speeds.

Figure 4.3: First cell height at U = 15m/s Figure 4.4: First cell height at U = 35m/s

If it is assumed that the triangles on the surfaces are equilateral where s is the side of the

triangle the aspect ratio is given by:

AR=Atriangle

h =

s2

34

h

(4-3)

With an aspect ratio of 5 and a cell height of 1.5 mm this gives a maximum side of 11.4 mm.

This is the maximum grid spacing used on the surface of the bob. If this grid spacing is

considered, and considering a maximum volume change of 1.2, five layers are needed to

ensure a smooth volume change into a tetrahedron, with which the rest of the domain is

filled.

The smallest chosen grid spacing is 5mm. For this spacing no growth of the cell height is

necessary to match the volume of the tetrahedrons. This spacing is used near edges, the gapin the cowling, the axles, the bumpers, dummy heads and stagnation point. In other places the

larger spacing is chosen, with a smooth transition. In figure 4.5 a 2D example is given of a

boundary layer with these settings.

On the moving wall a prismatic layer is also applied, although a higher wall y+is accepted

further away from the bob. The rest of the domain is filled with tetrahedrons. A maximum

spacing of 250mm is taken.

The size of the domain is determined by once again following the guidelines. The grid

extends approximately three body lengths in front of the bob and five body lengths behind the

bob. The height and width are set at 4.5m. The ratio of (half the) bobsleigh frontal area anddomain frontal area becomes:

0 1 2 30

0.002

0.004

0.006

0.008

0.01

x [m]

y[m]

y+= 30

y+= 100

y+= 300

y = 1.5 mm

0 1 2 30

0.002

0.004

0.006

0.008

0.01

x = [m]

y[m]

y+= 30

y+= 100

y+= 300

y = 1.5 mm


45/103

CFD CALCULATIONS 33

ABoblsleigh

ADomain =

1

20.342

4.54.5=0.8% (4-4)

This is below the recommended maximum value of 1-1.5%. There is an inner square box

present around the bob to have more control over the grid size. It extends half a body length

around the bob, except behind the bob where it extends one body length.

The grid also features non-conformal boundaries where the bobsleigh has sharp edges and the

grid boundary layer cannot be connected without creating highly skewed cells. This can be

seen in figure 4.6. Finally in figure 4.7 the seal can be seen that is used to open and close the

gap in the cowling. It consists of two parts, so it can be opened, partly opened or completely

closed. All in all this results in a grid of approximately 4.5 million cells.

In figures 4.8 and 4.9 parts of the grid can be seen. In the last picture the spacing is indicated

with colors. The smaller the spacing the more red it becomes. The regions where the smaller

grid spacing is used can be seen clearly, for instance around the edges of the bumper and

around the rim of the cowling.

Surface

Figure 4.5: Example grid boundary layer layout


46/103


Figure 4.6: Non-conformal boundaries Figure 4.7: Seal gap top

Figure 4.8: Part of the symmetry plane grid with top part of gap open

Figure 4.9: Grid spacing


47/103

CFD CALCULATIONS 35

4.3 Grid adaptation

A full grid independence study usually involves solving the problem on at least threedifferent grids where the number of cells is increased, sometimes even doubled, every step. A

complete study like this is not performed for this case, since this would lead to a too large

number of cells (>10 million). Also the boundary layer is designed for a good wall y+.

Changing the boundary layer cells might change the solution but not necessarily improve it.

In this case one grid adaptation step is applied. The chosen parameter is the curvature of the

total pressure. By choosing this variable especially the cells in the wake in the cavity and

behind the axles are selected for adaptation. The threshold value is set so that almost no cells

in the boundary layer are adapted. The exact settings are given in appendix D. In figure 4.10

the symmetry plane can be seen after adaptation. The total pressure is shown in this picture.

Refinement regions can be seen clearly, for instance behind the brakeman's head.

In figures 4.11 and 4.12 the variation of the residuals and drag coefficient during the iterating

process are plotted. The final drag coefficient is indicated by the dashed line. The definition

of the residuals can be found in [Fluent, 2005] and they should be as small as possible.

In both plots the adaptation step is clearly visible at 5000 iterations. The residuals decrease

further after the adaptation step. The drag coefficient changes from 0.2778 to 0.2743.

Figure 4.10: Symmetry plane grid after adaptation colored by total pressure


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Figure 4.11: Residuals at U = 35m/s

0 2000 4000 6000 8000 100000.25

0.255

0.26

0.265

0.27

0.275

0.28

0.285

0.29

0.295

0.3

Iterations

CD

Figure 4.12: Convergence of drag coefficient with final value

indicated with dashed line

0 2000 4000 6000 8000 10000

106

104

102

100

Iterations

Continuity

xvelocityyvelocity

zvelocity

epsilon

k


49/103

CFD CALCULATIONS 37

4.4 Initial check of CFD results

With the settings as described in the previous sections a drag curve is made for a standardcase. The gap between the front and rear cowling is closed. The curve can be seen in figure

4.14. The CFD results are compared with the theoretical values found in chapter 2 in table

4.1. The prediction for runner carriers and runners has been left out since these were not

modeled in CFD. The drag predicted by CFD is lower than the drag measured in the tunnel.

There are a number of possible causes for this:

The brackets that are used to attach the bob to the measurement plate are not modeledfor CFD. In an empty windtunnel the brackets have a drag coefficient of around 0.02

(figure 3.16). With the bob present the drag is probably larger since the flow is

accelerated by the presence of the bob.

The CFD flow is modeled completely turbulent. This will result in higher skinfriction than in the windtunnel. However the drag predicted by CFD for the axles

might be much lower. Even though the drag of the axles in the windtunnel is

unknown, the Reynolds number is subcritical for a 2D situation. In chapter 2 a drag

coefficient of 0.082 was predicted for the subcritical case. The value predicted by the

turbulent CFD calculations is 0.038.

Another big difference between the CFD model and the windtunnel test is that thefloor is moving in CFD while it is standing still in the windtunnel. A CFD calculation

was done without the moving wall, but the total drag hardly changed. The lift was

different.

In the back of the bob there is a brace to reinforce the sidewalls. This may havecaused extra drag. Despite this brace the walls were still vibrating. This and other

unsteadiness may have increased the drag. For the CFD calculation a steady model

was used.

In the windtunnel model the nose is completely closed (see figure 4.13). Thegeometry used for CFD has a hollow nose.

If the estimates from the first two points are added a difference of 0.06 is already found

which makes up for a large part of the difference. As mentioned the realizable k-model is

known to produce errors of up to 5%. It is encouraging that the trend of the curves aresimilar.

If compared with the theoretical values it can be seen that for most cases the results agree

reasonably well, especially considering the crude 2D approximations made for some cases.

The biggest difference is found for the front bumpers. This is because the value for the drag

was based on an average frontal area. However this area changes considerably and the

leading edge, where a stagnation pressure is found, is quite large. The other big difference,

already mentioned, is found for the axles.


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Figure 4.13: Plate inside rear cowling

Figure 4.14: Windtunnel drag versus CFD

Table 4.1 Drag comparison overview standard case at U = 35 m/s

CD Theory CD CFD CD

Cowling skin friction 0.047 0.041 -0.006

Cowling pressure drag 0.097 0.106 +0.009

Front bumpers 0.010 0.064 +0.054

Rear bumpers 0.006 0.012 +0.006

Pilot helmet 0.015 0.024 +0.009

Rest of crew - -0.002 -0.002

Front axles 0.043 0.019 -0.024

Rear axles 0.040 0.018 -0.022

Total 0.257 0.274 -0.048

0 5 10 15

x 105

0.25

0.3

0.35

0.4

Re

CD

CFD

Windtunnel


51/103

CFD CALCULATIONS 39

Apart from the forces, it is important that the flow is qualitatively the same. The absolute

drag coefficient was measured in the windtunnel so it does not have to be calculated by CFD.

The purpose of the CFD calculations is to get more insight in the flow and the ability to break

the drag down into the drag of the different parts and into viscous and pressure forces. If theflow is qualitatively the same, there is more confidence that drag differences found with

CFD will also be found on the real bobsleigh.

The flow in the windtunnel was visualized with oil flow. Surface flows can also be made for

the CFD calculations. The flow patterns found are very similar. Some are shown in figures

4.15 to 4.18. More will be shown in the next chapter, where all the results will be discussed

for every part individually.

Apart from the drag and flow features there are other parameters that can give more

confidence in the results, for instance correct wall y+values. These can be seen in table 4.2.

They are well within the range of 30 and 300, especially for the outside of the cowling.

Finally some results from PIV will be compared with CFD results (see figures 4.19 to 4.22).

Unfortunately the PIV measurements were done at approximately 45 m/s, which is still

subcritical. It can be clearly seen in figures 4.21 and 4.22 that the complete wake is unsteady.

As already mentioned in the previous chapter zig zag tape was applied to the pilot's head, but

this was not yet the case when the PIV measurements were performed. There were a few

burnt pixels in the camera. This area has been covered with a white dot.

Table 4.2: Average wall y+values

U [m/s] Avg. y

+

cowling outside Avg. y

+

complete bob15 30.1 19.9

35 64.2 42.1

Figure 4.15: Oil flow visualization rear Figure 4.16: Surface flow CFD rear, colored by

cp


52/103


Figure 4.17: Oil flow visualization bottom Figure 4.18: Surface flow CFD bottom, colored

by cp

Figure 4.19: CFD results helmet symmetry plane Figure 4.20: PIV results helmet symmetry plane,average of 100 pictures

Figure 4.21: Instantaneous PIV result wake Figure 4.22: Instantaneous PIV result wake


53/103

Chapter 5 Results

Now that all the used tools have been described the results can be discussed. First of all the

general features will be discussed in section 5.1. In sections 5.2 to 5.8 the different parts of

the bob are studied in more detail. All the data are given in Reynolds numbers to be able to

compare windtunnel results with full scale tests and CFD results. In figure 5.1 the Reynolds

numbers are related to the bobsleigh velocity. Just as a reminder; all drag coefficients are

related to the same (frontal) area. For full scale this is 0.342m2and for the scale model

0.0340m2.

Figure 5.1: Free stream velocity vs.

corresponding Reynolds number

5.1 General flow description

The air flow is mainly determined by the bob's main feature; the cavity. First the flow hits the

nose and bumpers. The flow is accelerated over the nose. Under the bob a venturi-like flow

occurs, which creates a low pressure under the bob. Because of this the bobsleigh has a small

lift coefficient or even downforce. Windtunnel test show a little downforce. The CFDcalculations predict a quite large downforce coefficient of around -0.3, completely caused by

the underside of the bob. These differences were probably caused by height difference and

because the windtunnel does not have a moving wall. For CFD the downforce coefficient is

0.07 lower if a stationary wall is used instead of a moving wall (see appendix D).

The air that flows over the side of the wall hits the bumpers and axles. Where the axles meet

the cowling a large vortex starts. This was both seen in the windtunnel with a woolen tuft and

in the CFD calculations. A smaller vortex originates from the bumper. Once again this was

both seen in the windtunnel and in the CFD results. These vortices can be seen in figure 5.2

and in appendix D.3.

41

0 0.5 1 1.5 2x 10

6

0

10

20

30

40

Re

U[m/s]


54/103


The flow over the top of the nose is probably the most interesting. It separates from the

cowling where the cavity begins and hits the pilot helmet. A large amount flows into the

cowling, around the pilot and then hits the brakeman. The flow around the side of the helmetis pushed to the outside and is partly forced out of the cowling. Behind the pilot helmet two

large vortices exist in the CFD calculations. The case that only half a bob was chosen

probably has most effect in this area, so caution must be taken when studying the wake as

predicted by CFD. However the fact that the flow behind the helmet above the cavity moves

fairly straight is confirmed by the PIV results. The wake is shown in figure 5.3. Once again

more pictures can be found in appendix D.3.

Figure 5.2: Cross section x-vorticity at Re = 1.48106 [s-1] around

brakeman's head

Figure 5.3: Iso-surface of zero total pressure at Re = 1.48106


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RESULTS 43

5.2 Gap between front and rear cowling

A large part of research has been focused on the gap between front and rear cowling. Thereare a numbers of reasons for this. Although they have already been mentioned they are

summarized here again:

One goal was to try to help the Dutch bobsleigh teams in preparation for the OlympicGames in 2006 by adapting their existing bobsleighs. Possible changes to the

configuration of the gap should be easy to implement without changing the complete

cowling.

The drag of a bobsleigh consists largely of pressure drag. One of the largestcontributors to the pressure drag is the drag of the inside of the nose. It is expected

that the pressure in the nose cowling can be changed by changing the configuration

of the gap, thereby significantly changing the drag.

The gap has been investigated during the scale model windtunnel testing as described in this

report. Also several configurations were tested full scale [Timmer, 2006]. Finally different

options were calculated with CFD.

First of all the results from the windtunnel measurements on the scale model will be

discussed. On the next two pages the results of variation of the gap are shown. First of all the

results for a case with five big holes in the plate in the cowling (see figure 4.13) are given.

Then the results are given with additional small holes in the plate. Unless stated otherwise

when there is a gap present its size is 3 mm.

In both cases the situation where only the underside is closed gives the best result, even

though the behavior is quite different. For the case with only the big holes the drag is lower

over the whole Reynolds range, where for the case with additional holes, the drag is only

lower for a part of the range. When the gap size is increased from three to five millimeter the

same behavior is found as for the case with only five holes. It is not exactly known what

caused these differences in behavior, but it may be related to the way the different situations

influence the flow over the dummies (see section 5.3). Overall though the situation where the

bottom is closed gives the best result.

The gap has been closed with thin tape. This makes the transition from the front to the rear

cowling smooth. To see what the influence of this smoothing is two situations with a closedgap have been measured. In one case the complete gap was taped (see figure 5.8). For the

other case the gap was filled with plasticine, but not completely, to create a rough transition

(see figure 5.7). In figure 5.6 the results from these cases are shown. It is clear that the

smooth transition produces a significantly lower drag. Part of the advantage found above may

be due to this effect.


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Figure 5.4: Gap variation

Table 5.1 Gap variation

Case Diagram Time [s]

Underside

taped

-0.07

Gap

-0.01

Standard

54.71

0 5 10 15

x 105

0.35

0.36

0.37

0.38

0.39

0.4

Re

CD

Standard

Gap

Gap bottom taped


57/103

RESULTS 45

Table 5.2 Gap variation, extra holes


Underside

taped

-0.04

Gap

-0.04

Larger gap

(5mm)-0.01

Standard

54.71

Figure 5.5: Gap variation, extra holes

0 5 10 15

x 105

0.35

0.36

0.37

0.38

0.39

0.4

Re

CD

Standard

Gap

Gap bottom taped

Larger gap


58/103


Table 5.3 Gap variation, closed (with brakehole)


Gap taped

-0.04

Gap filled with

plasticine

54.71

Figure 5.7: Gap taped Figure 5.8: Gap with plasticine

Figure 5.6: Gap variation, closed (with brakehole)

0 5 10 15

x 105

0.35

0.36

0.37

0.38

0.39

0.4

Re

CD

Gap filled with plasticine

Gap taped


59/103

RESULTS 47

The gap was also varied for the CFD calculations. The results are summarized in table 5.4.

The complete results can be found in appendix D.2. Although variations are small, the drag

from the inside of the front cowling is smaller for all cases where there is an opening.

However the gap itself also creates drag. By making the gap smaller the drag of the gap canbe reduced, while still reducing the drag of the inside of the front cowling. In figure 5.9 the

situation around the gap is shown for a completely open gap. It is clear air is flowing into the

bob. In appendix D.2 it can be seen that the gap configuration also influences the drag of the

other parts of the bob, especially the inside and crew. Overall the situations with a small

opening at the top is the fastest.

Table 5.4 Gap variation, CFD results

Gap CD total CD front cowling inside CD gap Time [s]

Closed 0.2743 0.1262 0.0034 53.90

Open 0.2753 0.1235 0.0058 +0.01Bottom closed 0.2745 0.1238 0.0047 +0.00

Top closed 0.2753 0.1254 0.0046 +0.01

Small opening top 0.2732 0.1243 0.0035 -0.01

Figure 5.9: Open gap, CFD, colored by velocity

Finally the results from the full scale testing are shown in figure 5.10. These are the result for

a women's 2-man bob with crew. The drag is given in drag area. To get the CDthis should be

divided by 0.342. This drag also includes the drag of the support system (CDS 0.043). Once

again the drag for the case where the bottom is closed and the bottom is lowest.

Overall having a gap that is open on the top gives the best results in all cases, although the

found differences are small. Whether the gap is open or closed, care should be taken how the

transition takes place. If the gap is closed, for instance with a rubber strip, it should be as

flush as possible with the cowling to create a smooth transition. If the gap is open a radius on

the front edge of the rear cowling seems to work very well.


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61/103

RESULTS 49

5.3 Crew and pilot helmet

In this section the results for the crew are described. The flow and forces acting on the creware mainly determined by the helmet of the pilot; the bodies and pilot helmet are all in the

wake in the cavity. The position of the pilot is more or less fixed; the pilot needs to see out of

the bob and needs to be comfortable. Still the height of the pilot has been varied during the

scale model windtunnel tests and different helmets were also tested full scale. For a report on

these last measurements see [Venema, 2005]. In [Motallebi, 2004] the angle of the brakeman

is varied and it is found that the drag is minimum in the range from 40 to 52.

In figures 5.11 to 5.13 the surface flows found with CFD and in the windtunnel on a real

helmet are shown. It is clear that the flow does not behave as a sphere in uniform flow,

mainly caused by the existence of the body. The CFD results are similar to the results from

the windtunnel. Separation occurs on more or less the same location and there is an upflow

on the back of the helmet.

Figure 5.11: Surface flow CFD helmet, colored by

cp

Figure 5.12: Surface flow CFD helmet, colored by

cp

Figure 5.13: Oil flow visualization helmet


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In table 5.5 the drag of the helmet is given. The drag for the windtunnel means the full scale

helmet in this case. The measured drag for the full scale helmet is much larger than predicted

for the sphere and as found with CFD. This is because the real helmet is significantly larger

than the sphere, and its shape is more irregular. The fact that the drag of the CFD calculationsis larger than for a a sphere is expected, since the flow is different from a uniform flow

around a sphere.

Table 5.5 Helmet drag

Technique CD Helmet

Theory 0.015

CFD 0.024

Windtunnel 0.047

On the next two pages the results from the scale model windtunnel tests are shown. First of

all the influence of the pilot height is shown. If the pilot gets down in the bob the drag isreduced. This is not surprising; the helmet is pulled down into the wake of the bob, and thus

less exposed to the external flow. In other words, the frontal area is reduced. However when

the pilot gets out of the bob, the drag increases, but only very slightly. This can be explained

by the fact that if the pilot is moved up, the brakeman moves out of the wake of the pilot's

helmet into the wake of the pilot's body. This effect counters the effect of increased drag of

the pilot.

On page 52 the results are given for the case where only the pilot is present and with no crew

at all. The brakeman only starts to produce drag at Re = 400.000. This causes a bump in the

graph, that can also be seen for other results. For instance in figure 5.5 it seems that the

configuration of the gap changes the Reynolds number at which this effect occurs. Whetherthis is really the case cannot be based on only these results. Also, since the dummies are very

simple, it remains to be seen whether this happens on a real crew. In general changing a bob

will change the flow around the crew and therefore the position of the crew should be

optimized for each different situation.


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RESULTS 51

Table 5.6 Pilot height variation

Pilot z [mm] Diagram Time [s]

-13-0.07

-6.5 -0.04

Standard 54.71

6.5 +0.01

13 +0.01

Figure 5.14: Pilot height variation

0 5 10 15

x 105

0.35

0.36

0.37

0.38

0.39

0.4

Re

CD

z = 13 mm

z = 6.5 mm

z = 0 mm

z = 6.5 mm

z = 13 mm


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Figure 5.15: Crew variation

Table 5.7: Crew variation


No crew -0.17

Pilot only -0.02

Standard 54.71

0 5 10 15

x 105

0.34

0.35

0.36

0.37

0.38

0.39

Re

CD

Standard

Pilot only

No crew


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RESULTS 53

5.4 Runners and axles

In this section the result from the axles and runners will be discussed. The axles weremodeled in both the windtunnel and for the CFD calculations. Unfortunately the runners were

not present. Also no leaf springs or runner carriers were modeled. Still the runner carriers and

leaf spring form an interesting area of research, because all the edges may be rounded or

chamfered. At the moment the Dutch bobsleigh teams have nearly straight edges. It has

already been reported that changing the runner carriers may decrease the drag significantly.

This is definitely something that should be investigated further.

In figures 5.16 and 5.17 surface flows obtained by CFD and in the windtunnel are shown.

The pattern on the cowling is quite similar. In section 5.1 the vortex coming from the axle

where it exits the cowling was already described.

In table 5.8 the drag coefficients found for the axles are listed again. As mentioned thedifference is caused because the drag predicted by theory is based on the subcritical situation

whereas the CFD uses a turbulent model. How the flow behaves with the presence of the

runner and runner carriers is unknown and should be investigated further. The rules regarding

the axles are very strict so once again care must be taken to remain within the limits.

Figure 5.16: Surface flow around front axis as

predicted with CFD

Figure 5.17: Oil flow visualization image around

front axis

Table 5.8: Axles results

CD Theory CD CFD

Front axles 0.043 0.019Rear axles 0.040 0.018


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5.5 Other features

In this section the remaining features will be discussed. Not much research was invested inthese features, either because it was not feasible or because the results did not give any

reason to conduct further investigations. The nose, the bumpers, the brakehole, nose rotation

and an extra rim along the cowling cutout will be discussed.

Nose shape

As mentioned in chapter 1, quite some different nose shapes are used by different teams. A

variation of the shape of the nose was investigated in [Motallebi, 2004]. The nose has not

been investigated further in this report because it is hard to modify an existing nose, both in

the windtunnel and on the real bob, and has therefore not been a priority. However if acompletely new bob is designed, this is definitely something that should be investigated.

Apart from the shape the surface itself is also important. Usually transition from laminar to

turbulent flow will occur on the nose. To delay this transition it is recommended to make the

nose as smooth as possible. Special care must be taken to incorporate the compulsory

inspection holes; prevent screws from sticking out and make the hatches as flush as possible

with the cowling.

Bumpers

In figure 5.18 the oil flow over the front bumper can be seen. On the rear bumper the oil

disappears immediately, because it is in the turbulent wake of the front bumper and axle. As

discussed probably little can be done to reduce the drag of the bumpers. Streamlining the

bumper means an increase in thickness because of the specification of a minimum thickness

over a certain length. Even though the drag coefficient may be reduced, the drag itself may

not decrease much. Also the trailing edge cannot be made too sharp for safety reasons.

Figure 5.18: Oil flow visualization front bumper


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RESULTS 55

One modification was measured; the addition of zig zag tape on the font bumper (figure

5.19). The idea was to remove any possible laminar separation. However the drag only

increased (figure 5.20). So no laminar separation occurred on the nose of the bumper and the

zig zag tape only caused extra drag.

Figure 5.19: Zig zag tape applied on front bumper

Table 5.9: Results zig zag tape front bumper

Case Time [s] t [s]

Standard 54.71 -

Zig zag tape bumper 54.73 +0.02

Figure 5.20: Results zig zag tape front bumper

0 2 4 6 8 10 12 14

x 10

5

0.35

0.36

0.37

0.38

0.39

Re

CD

Zig zag tape bumper

Standard


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Brakehole

In the latter stages of the experiments a brakehole was added to the bob. It can be seen in

figure 5.21. In figure 5.25 the results with and without a brakehole can be seen. There was no

gap during these measurements. Surprisingly the addition of the brakehole decreases the drag

over a large Reynolds range. This has not been investigated further since the fact that the

windtunnel wall is not moving probably has a large effect on these results. Furthermore the

brakehole cannot be changed. The results do resemble the results found for the variation of

the gap (figure 5.5) and the variation found here may also have to do with how the flow

behaves around the crew.

Figure 5.21: Brakehole

Figure 5.22: Influence of brakehole

Table 5.10: Results nose rotation

Case Time [s] t [s]

With brakehole 54.66 -

Standard 54.71 +0.05

0 5 10 15

x 105

0.35

0.36

0.37

0.38

0.39

0.4

Re

CD

With brakehole

Without brakehole


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RESULTS 57

Nose rotation

The influence of the gap between front and rear cowling has already been described. Now the

effect of actually rotating the front part of the cowling will be discussed. In figures 5.23 and

5.24 the applied rotation of approximately five degrees can be seen. A gap of 3mm between

front and rear cowling was present during these measurements. Because the nose is rotated a

step is introduced. On a real bob this step would be rounded or even covered with a rubber

strip. Therefore the results given in figure 5.28 are probably not representative for what

happens on a real sled. The drag increases when the nose is rotated.

Figure 5.23: Rotate nose Figure 5.24: Step due to rotation

Figure 5.25: Influence of nose rotation (5)

Table 5.11: Results nose rotation (5)

Case Time [s] t [s]

No rotation 54.70 -

Rotated nose 54.76 +0.06

0 2 4 6 8 10 12 14

x 105

0.35

0.36

0.37

0.38

0.39

Re

CD

Rotated nose

Normal nose


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Cowling cutout edge

Another applied modification was the addition of a rim along the cowling cutout. This rim

can be seen in figure 5.26. This rim has been tested in two positions. In one case it was

straight up, in the other case it was under an angle of approximately 45 degrees as shown in

figure 5.27. The rim only increases the drag. This is probably mostly due to extra friction

drag. Looking at the figures in appendix D.3 is clear that not much happens along the cutout,

especially at the back.

Figure 5.26: Rim along cowling edge Figure 5.27: Rim bent inside

Figure 5.28: Influence of rim along cutout

Table 5.12: Results rim along cutout edge

Case Time [s] t [s]

Standard 54.71 -

Rim 54.75 +0.04

Rim under angle 54.75 +0.04

0 2 4 6 8 10 12 14

x 105

0.35

0.36

0.37

0.38

0.39

0.4

Re

CD

No rimStraight rim

Rim under angle


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Chapter 6 Conclusions and recommendations

In this chapter the questions posed in paragraph 1.4 will be answered. The main questions

were whether changing the aerodynamic forces by adapting the sled could have a positive

effect on the final times and if so, what possible changes could establish this. These questions

will be answered in section 6.1. Finally in section 6.2 recommendations to improve the used

investigation methods and further areas of research are given. Also recommendations on how

to adapt a bobsleigh, based on this research, are given.

6.1 Conclusions

Based on the simple model as described in chapter 2 the following general points are found to

be important to achieve a good final time:

The combination of crew and bob must be as heavy as allowed. This should be veryeasy to implement and should for this reason only already have a high priority. It

should be investigated how extra weight influences (and maybe even improves) the

dynamic behavior of the bob.

The start is very important as it determines the initial momentum. Even when havinga lower drag or friction it will take some distance to make up for this. Fortunately a

good starting track is available in the Netherlands where starts can be trained to

perfection.

The ice friction must be as low as possible. The art of making good runners is alsocalled the black art in bobsleighing. The ice friction depends on a large number of

parameters and research into this is far beyond the scope of this report. However

rules regarding the runners are becoming very strict indeed. Standard materials will

be prescribed and runners are cleaned and sanded bu the jury before every run to

prevent special treatments. Therefore it is expected that in the future very little can be

won in this area.

The aerodynamic drag must be as small as possible. The shape of the cowling islargely prescribed by the rules but some different shapes are possible. However the

convexity rule and the fact that no holes or vortex generators may be added makes it

hard to improve a given bobsleigh. However varying different parts of the bob which

results in a decreased drag can have a significant effect on the final time. Typical

differences found are only in the order of a few hundredths of a second, but scraping

every hundredth of a second of the final time is what bobsleighing is all about.

Although improving aerodynamics cannot perform miracles and all other factors

need to be optimal as well, it is certainly something that has to be considered.

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CONCLUSIONSANDRECOMMENDATIONS 61

If a completely new bobsleigh is designed one of the first investigations shouldprobably be to determine the effect of the shape of the nose.

Although the performed CFD calculations seem to produce reasonable results andperform the task they were intended for, an interesting study would be to move to

unsteady calculations. This could provide more details about the flow phenomena

that occur on the bob and this may help to further reduce the drag.

A full 3D dynamic equation of motion could help to refine the exact effect of drag onfinal times. It could also be determined whether lift has any effect on the steering

behavior. An interesting spin-off could be a training simulator for bobsleigh pilots.

Finally the recommendations for reducing the drag on a bobsleigh are given:

Close the gap between front and rear cowling partially, leaving the top open. If arubber strip is used make it as flush a possible with the surface. If it is open drag can

be minimized by having a large radiused edge at the start of the rear cowling.

Use a helmet with low drag.

Round the edges of the runner holding and guiding brackets. Although no windtunnelmeasurements or CFD calculations have been done, that confirm this will reduce

drag, it is unlikely that it will increase it.

Keep the whole bob but especially the nose as smooth as possible. This includes

preventing screws from inspection hatches from sticking out, but also carefulapplication of sponsor stickers.


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Appendices


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A. International rules

In this appendix the rules that are applicable to this report are listed. They have been taken

from [FIBT, 2005].

A.1 Track layout

Length of track (2.7)

New artificial combined bob, luge and skeleton tracks shall be 1200-1650 meterslong, 1200 meters of which shall be sloping downhill.

The last approximately 100-150 meters may consist, depending on spee

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