Aerodynamic analysis of a 2-man bobsleigh

Transcription

Aerodynamic analysis of a
2-man bobsleigh
October 14, 2006
O. Lewis
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
Dr.ir. L.M.M. Veldhuis
Ir. W.A. Timmer
Dr. F. Motallebi
Delft University of Technology
Queen Mary, University of London
i
ii
Contents
Preface
v
Abstract
vii
List of symbols
ix
Chapter 1
1.1
1.2
1.3
1.4
Introduction
Brief history
A typical bobsleigh run
Modern bobsleigh design
Thesis goal
1
1
3
4
5
Chapter 2
2.1
2.2
2.3
Bobsleigh aerodynamics
Bobsleigh run time sensitivity
Preliminary estimation of aerodynamic drag
Drag reduction techniques
7
7
12
17
Chapter 3
3.1
3.2
3.3
Windtunnel experiments
Experimental setup
Measurement apparatus
Windtunnel corrections
19
19
22
26
Chapter 4
4.1
4.2
4.3
4.4
CFD calculations
CFD Setup
Grid setup
Grid adaptation
Initial check of CFD results
29
29
31
35
37
Chapter 5
5.1
5.2
5.3
5.4
5.5
Results
General flow description
Gap between front and rear cowling
Crew and pilot helmet
Runners and axles
Other features
41
41
43
49
53
54
Chapter 6
6.1
6.2
Conclusions and recommendations
Conclusions
Recommendations
59
59
60
Bibliography
63
Appendices
International rules
Parameters
Bobsleigh equation of motion
CFD settings and results
Practical tips
65
66
71
74
78
91
A.
B.
C.
D.
E.
iii
iv
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 I
explored 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 the
results 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 and
friends who supported me not only during this project, but during my entire study.
Oscar Lewis
October 14, 2006
v
vi
Abstract
One of the fastest and most exciting winter sports is bobsleighing. Every last one hundredth
of a second is of importance. Boblsleighing originally started in the end of the 19th century
and especially since the 1950's has developed into a hi-tech sport. Today NASCAR and
Formula One technology is used to build the fastest sleds.
After the start the only force propelling a bobsleigh is the force of gravity and if no driving
mistakes are made only the aerodynamic drag and friction with the ice act against the sled. A
simple bobsleigh equation of motion shows that the aerodynamic force during a run has a
significant influence on the finish times. A drag reduction of three percent is predicted to
reduce the final time by one tenth of a second.
The basic shape of a bobsleigh is determined by the rules. Slight changes can be made to for
instance the bumpers, the gap between front and rear cowling, the shape of the nose and the
edges of the spring leafs and runner carriers. What severely limits changes to an existing bob
is the fact that the bob should have convex shape and that no holes or vortex generators are
allowed.
To study the flow several measurement and visualization techniques have been applied. To
measure the forces a six component balance was used. Oil flow visualization has been
applied to investigate the surface flow. PIV has been used to get both qualitative and
quantitative information. Wool tufts and a microphone were used to localize vortices and
finally CFD calculations have been performed. The steady RANS equations with the
realizable k-ε turbulence model were solved on half the model, because it is assumed the flow
is symmetrical. The calculated flow shows good agreement with theory and windtunnel
results, both qualitatively and quantitatively.
Much effort was concentrated on the transition between front and rear cowling. This is
because it is an area that is relatively easy to adapt, so any found improvements could be
applied at the Olympic Games by the Dutch bobsleigh teams. Also numerous other variations
have been researched, like the position of the crew and rotation of the nose.
From the results found it can be concluded that the gap between front and rear cowling
should be partially closed, leaving a gap at the top. Other factors that can reduce the drag of a
bobsleigh are selecting a low drag helmet, optimizing the position of the crew, rounding the
edges of the runner carriers and keeping the nose as smooth as possible.
Several topics require further research. For instance the effect of the shape of the nose on
aerodynamic drag. Also the drag of the axles, leaf springs, runners and runner carriers should
be analyzed and improved if possible.
vii
viii
List of symbols
Latin
a,b,c
A
b
c1
CD
Cf
Cside
d
D
f
f#
F
g
h
k
l
L
m
M
N
r
Re
s
t
Tu
U
V
Vm
x,y,z
y+
Parabola coefficients
Maximum cross section area of the bobsleigh
Windtunnel width
Cornering factor
Drag coefficient
Skin friction coefficient
Side force coefficient
Equivalent diameter based on cross section area
Aerodynamic drag
Max sprint force in Keller equation
Focal number
Runner friction force
Acceleration of gravity
Height, windtunnel height
Turbulence kinetic energy
Length of bobsleigh
Length of track
Mass
Mach number
Normal force
Radius based on maximum cross section area, radius of
axis-symmetric body, general radius
Reynolds number
Distance along track
Time
Turbulence level
Freestream velocity
Bobsleigh velocity
Model volume
Cartesian coordinates
Law-of-the-wall scaled y-coordinate
[-]
[m2]
[m]
[-]
[-]
[-]
[-]
[m]
[N]
[m/s2]
[-]
[N]
[m/s2]
[m]
[m2/s2]
[m]
[m]
[Kg]
[N]
[N]
[m]
Track slope
Parameter for calculation of solid blockage
Boundary layer thickness
Turbulent dissipation
Solid blockage
Boundary layer momentum thickness
Air viscosity
Kinetic coefficient of friction
Air kinematic viscosity
[rad]
[-]
[m]
[m2/s3]
[-]
[m]
[N s/m2]
[-]
[m2/s]
[-]
[m]
[s]
[-]
[m/s]
[m/s]
[m3]
[m]
[-]
Greek




s


k

ix


Air density
Sprint decay term in Keller equation
Subscripts
0
end
H
ISA
trans
∞
x
Initial condition
Finish condition
Human
According to International Standard Atmosphere
At transition point
Freestream condition
[kg/m3]
[s]
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 Fédération 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,
1
2 AERODYNAMIC ANALYSIS OF A 2-MAN BOBSLEIGH
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 was
recognized 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 only
in 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 new
rule is that runners have to be made out of a standard material supplied by the FIBT.
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/h
are 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
standstill. This is done by pulling a fork-shaped device through a gap in the cowling of the
bob into the ice. Since this section is after the finish it has no effect on the time.
Figure 1.4 Cesana Pariol track used for 2006 Winter Olympics
1.3 Modern bobsleigh design
Most bobsleighs look alike. This is largely because the rules prescribe most features and their
dimensions (see appendix A). In this paragraph these common features will be described and
it will be mentioned where there is some room for different designs.
The structural backbone of a bobsleigh is a steel frame, which is divided transversally. The
two frame sections are connected by an articulation joint and can rotate approximately 4
degrees along the longitudinal axis. To this frame the steering mechanism, the axles and a
front and back cowling are attached. The cowling is usually made of fiberglass. There are no
seats in the sled and the crew sit on the cowling, although usually some type of padding is
applied (see figs.1.5 and 1.6).
Figure 1.5: Frame and pilot seat
Figure 1.6: Brakehole and brakeman seat
The bob has four runners all made from steel. Under the new rules, the steel is regulated by
INTRODUCTION 5
the F.I.B.T. And because no heating or other treatment is allowed, very little can be done to
improve the friction of the runner with the ice. The runners are connected to the axles by a
leaf spring. The leaf spring and holding brackets may be radiused or chamfered.
Another very noticeable feature are the front and rear bumpers. Even though they may look
like aerodynamic devices, they are only there to prevent the runners from scraping ice from
the sidewalls. Although a minimum thickness over a certain length and a few radii are
prescribed some room for design is present. The bumpers can bee seen in figure 1.7.
The main part of the cowling has to have a convex shape. Furthermore it has to be open from
the shoulder area of the pilot. This means that most bobsleighs alike, but there are some
differences. For instance the way the gap from the front section to the back part is bridged
varies for different bobs. Some teams have a rubber strip to close this gap. Other teams just
leave the gap open.
Another part of the bob that can be quite different is the nose. In recent years noses used to
have quite round shapes, but newer sleds have a somewhat more pointed shape (see figs 1.7
and 1.8). On the sled on the left the carrying handles are sticking out slightly in the middle of
the bumpers. On the sled on the right, the bumpers are completely smooth.
Figure 1.7: Rounded nose
Figure 1.8: Sharp nose
As mentioned in the previous paragraph there must be a hole in the cowling for the brake.
This is a rectangular hole and its dimensions are prescribed. It must be open and no attempts
may be made to reduce the area of the hole with any material. There are some inspection and
access holes, but they can be closed during a run. The edges of the hatches that are used to
close these holes are not always flush with the cowling itself and screws used to fasten them
may stick out a little bit.
1.4 Thesis goal
The following aspects are the most important areas that determine the final time:
•
The track: different tracks have different layouts, but also the track conditions
(temperature, smoothness of surface, weather, etc) have major influence on the final
times. Usually conditions deteriorate during competition.
•
The start: this is mostly down to the athletes' capabilities. Several start tracks exist
around the world where only the start is trained.
•
Steering: for the best times the best lines have to be followed. Pilot skills are very
important but also the driveability (weight distribution, position of runners, etc) of
the sled.
•
Runner friction: one of the two main forces slowing the bobsleigh is the friction of
the runners with the ice. Friction is determined by the weight of the sled and the
kinetic friction factor.
•
Aerodynamic drag: the other main force is the aerodynamic drag. This is the main
focus of this report.
The goal of this report is to analyze the aerodynamics of a 2-man bobsleigh. The first
question that has to be answered is whether changing the aerodynamic forces has a
significant effect on final times. If this is the case, the second question is what improvements
can be made within the rules that have a significant effect on drag and final times.
First of all the influence of drag will be discussed in chapter 2 and be compared with
influence of other parameters. In this chapter a drag build-up estimation is also given and
drag reduction techniques found in literature will be discussed. In chapter 3 and 4 tools used
to analyze the aerodynamic flow around a bobsleigh are discussed; windtunnel testing and
CFD calculations. The used hardware and software is described. For the windtunnel tests,
applied corrections are given and for the CFD calculations initial checks of the results are
performed. In chapter 5 the results are discussed and compared with each other. Finally in
chapter 6 conclusions and recommendations for further research are given.
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 is
used, 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 compare
their 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 is
a 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) where s is the distance traveled along the track:
7
s̈= g sin  k cos 
1 
C A ṡ 2
2m D
(C.1)
To solve this equation initial conditions are needed. Two approaches are possible. The first is
to start the calculation where the velocity is known to be zero (at s = -15m). However the
bobsleigh equation of motion is not valid in the first part of a run since the crew is pushing
the sled. The equation can be extended to include this force but difficulties arise in the
crossover phase, since it takes some time to board the sled. Additional empiric sprint
parameters are also needed. This approach will not be used because of these issues, but the
formulas are given in appendix C.4.
Figure 2.1: Forces acting on a bobsleigh
The approach used in this chapter is to skip the start section and start calculations at s = 50m
where the intermediate times are known for all competitions. However speeds at this point
are not known. Fortunately data from the bob starting track at Harderwijk have been made
available. This track has been modeled after the Cesana Pariol track, which is located in the
north of Italy and was used for the 2006 Olympic Games. In appendix C.2 an equation is
derived which relates the start time with a start speed:
V 0=22.8232.0579⋅t 0
(C.7)
Apart from the initial conditions other parameters need to be defined as well. For the
derivation of atmospheric conditions see appendix B.1. The equation will be solved for a
two-man bobsleigh for which the maximum mass is 390 kg. A drag area of 0.14 is taken,
based on full scale windtunnel tests. As reference area the maximum cross-sectional area is
taken, which is 0.342 m2, resulting in a drag coefficient of 0.409.
For ice friction a kinetic friction factor of 0.014 is used. This value was found in [Zhang,
BOBSLEIGH AERODYNAMICS 9
1995]. This value is multiplied by a constant factor (c1) to include extra friction caused by
centrifugal forces during cornering. This factor will be determined later and used to gain
realistic final time and speed.
The track data are taken from the Cesana Pariol track since the Harderwijk start track is
modeled after this track. Only the drop height and length of the track are used. As mentioned
the track is assumed to have a parabolic shape and the three parabola parameters need to be
determined. Since the beginning and end point of the track are known this leaves just one
parameter to be determined. The track shape is given by:
y=a⋅ x49.62 b⋅ x49.6c
(2-1)
Overall this leaves one parabola parameter and the cornering factor to be determined. They
are chosen such that the final times and speeds correspond with the best time of the Olympic
Games 2006 in Torino. The reason this time is taken is that during the best run down the
track presumably the wall was hit least often and losses because of mistakes are minimal.
Table 2.1: Parameters bobsleigh equation of motion
Parameter
CD
A


k
c1
Value
0.409
0.342
1.085 kg/m3
1.6912·10-5
0.014
1.182
Parameter
m
g
∆h
a
b
c
Value
390 kg
9.81 m/s2
114 m
1.34·10-5
-0.097
-6.00
Terminal
conditions
send
tend
Vend
Value
Table 2.2: Initial and terminal conditions
Initial
conditions
s0
t0
V0
Value
50 m
4.81 s
12.93 m/s
1435 m
55.28 s
36.80 m/s
Now that all parameters of the equation have been determined it can be solved. This is done
using a fourth order Runge Kutta method until the track length L has been reached. Because a
fixed time step is used, the final distance will be larger than the track length L. A cubic
interpolation is made between the last two steps to get the correct final time.
In figure 2.2 the forces during a run are summarized. The resultant force is still positive at the
end of the run in this approximation meaning that the bobsleigh is still accelerating. More
graphs can be found in appendix C.3. The friction with ice is almost constant. The
aerodynamic drag increases constantly and becomes larger than ice friction around half way
down the run.
400
Aerodynamic drag
Ice friction
350
Tangential component gravity
Resultant force
300
Force [N]
250
200
150
100
50
0
0
10
20
30
t [s]
40
50
60
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 to
make 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.
58
58
57
57
56
56
55
55
tend [s]
tend [s]
54
54
53
53
52
52
51
0
0.1
0.2
0.3
51
0.4
0
0.005
CD
58
58
57
57
56
56
55
55
54
53
52
52
51
300
0.02
5.5
6
54
53
51
200
0.015
(b)
tend [s]
tend [s]
(a)
0.01
µk
m
k
400
500
4
m [kg]
(c)
4.5
5
tstart [s]
(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
CD
k
t0
m
Original value
0.409
0.014
4.81 s
390 kg
Change
- 0.0042
- 0.0003
- 0.033s
+ 12.2 kg
Percentage
- 3.00%
- 2.14%
- 0.69%
+ 3.12%
2.2 Preliminary estimation of aerodynamic drag
In this section the drag of the different parts of a bobsleigh will be estimated. If possible an
estimate 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):



2
x
r=0.33 1 1
1.1
r=0.33
2
 x1.5 r8,712=8.882
for
0x≤1.1 m
for 1.1 mx≤1.5 m
for 1.5 m x≤2.7 m
(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]:
C f=
0.664
 Re s
(2-3)
The coordinate s is the coordinate along the body. For a turbulent flat plate:
C f=
0.027
Re1/s 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:
send
2⋅
CD=
∫ C r ds
A 0 f
(2-5)
When transition occurs, the calculation can start with the formula for laminar skin friction. At
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⋅
A

send sV0
stransition
∫
0
Cf
r ds
laminar
∫
Cf
stransition sV0
r ds
turbulent

(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 =5⋅105
(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.
1
0.8
0.03
0.6
C
D
strans [m]
0.04
0.02
0.01
0
0.4
0.2
0
1
2
stransition [m]
3
0
10
20
30
40
U [m/s]
Figure 2.4: Influence of transition point on drag Figure 2.5: Influence of freestream velocity on
coefficient at U = 35 m/s
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 the
average of these is taken, so the estimated drag coefficient becomes 0.10.
Boundary layer thickness
Geometry shape
Transition point
y [m]
0.4
0.2
0
0
0.5
1
1.5
2
2.5
3
x [m]
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 bumper
CD, rear bumper
A = 0.008 m2 A = 0.005 m2
Rectangle
1.4
0.033
0.020
Rectangle,
streamlined back
1.2
0.028
0.017
Rectangle rounded
edges
0.5
0.012
0.007
Streamlined back,
rounded edges
0.2
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.
Crew and pilot helmet
Another source of drag is the crew, especially the pilot, who has to stick his head out of the
large cavity. If the pilot helmet is considered and it is assumed it behaves like a sphere its
drag can be estimated. At higher speeds the Reynold’s number is higher than the critical
Reynolds number (approximately 3·105 for a sphere). At 35 m/s or a Re = 5.7·105 the drag
coefficient for a sphere is around 0.1. The frontal area of the sphere is given by;
A=⋅r 2
(2-8)
Related to the frontal area of the bob the drag coefficient of the pilot helmet becomes 0.015.
Since the brakeman is tucked in behind the pilot and the pilot body is inside the cavity of the
bob, their drag is assumed to be very small compared to the drag of the pilot helmet.
Therefore the estimate for the total crew is 0.015.
Axles, runners and runners carriers
The axles are cylinder shaped. The front axles stick out 13.5 cm and the rear axles 12.8 cm.
stick out. The minimum diameter of the front axle is 45mm and of the rear axle 44mm. At the
highest velocity (U = 35 m/s) the Reynolds number is 100.000 which is still subcritical. The
corresponding drag coefficient is 1.2. Related to the frontal area of the bobsleigh the drag
coefficient becomes 0.082.
Figure 2.7 Influence of a rounding radius on CD of various blunt bodies taken
from [Hoerner, 1965]
All holding and guiding brackets are 70mm long. They have a frontal area of 35mm by
50mm. For a rectangle without rounded edges the drag coefficient is around 1.4 (see figure
2.7) . The total drag coefficient for all 12 brackets related to the bobsleigh frontal area
becomes 0.086. The drag coefficient can be halved for a radius height ratio of 0.2. This
would mean a radius of 7mm. The rules allow all edges of the holding and guiding brackets
to be chamfered or radiused with a maximum of 8mm so this is a real possibility. It would
result in a total drag coefficient of 0.043. Because the edges are slightly radiused and because
the brackets are in each others wakes an average value is chosen which results in a drag
coefficient estimate of 0.065.
The spring leafs may also be radiused. This could provide a further advantage. The runners
themselves contribute to the drag but have a very small frontal area. The total contribution of
the runners, axles and runner carriers to the drag coefficient is 0.147.
Total drag
In table 2.5 and figure 2.8 an overview of the total drag is given. Also listed are possible
variations with corresponding time differences. The cowling pressure drag variation is based
on the case with and without boat-tail. The variation for runners is based on rounding the
edges of the runner carriers. The variation of bumpers is based on the difference between a
streamlined body and a rectangle with rounded edges and a streamlined back.
Overall it seems that gains can be made, although the differences listed cannot be interpreted
as possible gains, since most modern bobsleighs already have good designs and will most
likely have values near the lower end of these estimates. The two most important contributors
to drag are base drag and the drag of the axles and runner carriers.
Table 2.5 Drag estimation overview at U = 35 m/s
Cowling skin friction
Cowling pressure drag
Bumpers
Crew
Runners, runner carriers and axles
Total
CD
0.047
0.097
0.016
0.015
0.147
0.322
Variation
0.057 - 0.137
0.008 - 0.016
0.125 - 0.168
∆t [s]
0.64
0.06
0.34
1.04
15%
Axles, runner
carriers and runners
46%
Cowling
pressure
30%
Bumpers Crew
5%
5%
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 wake
causes an influx of air over the side of the cowling, which creates large trailing
vortices.
• Brakeman position. An angle of approximately 45º of the brakeman results in the
lowest drag.
• The shape of the nose. Although the forebody pressure drag is not very large and does
not 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 flow
along 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 this
advantage disappeared at higher Reynold's numbers, which are applicable to the real
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 adverse
pressure 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 be
increased 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.
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 windtunnel
are 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
Exchangeable test section 1.80 x 1.25 meter
V max. = 120 m/sec
Tu
= 0.02 - 0.1 %
7
14
4
5
8
3b
10
3a
3d
9
6
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Fan and straighteners
Motor
Corner vanes
Settling chamber
Expansion screen
7 Anti-turbulence screens
Screen store room
Contraction
Exchangeable test section
Diffuser
Security screen
Spider web
Screen
Six-component balance
1
2
3b
3c
12
0
1
2
3
4
5
6
7
8
9 10
meter
13
Figure 3.1: Low Turbulence Tunnel at TU Delft Low Speed Lab
19
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).
0.15
0.1
C
Side
0.05
0
−0.05
−0.1
−0.15
−0.2
−2
−1
0
1
2
Yaw angle [deg.]
Figure 3.2: Sideforce coefficient at different yaw
angles at Re = 0.6·106
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
WINDTUNNEL EXPERIMENTS 21
The crew has been modeled with simple dummies (figure 3.4) with spherical heads as
helmets. They are not permanently fixed to the bob. They can be removed and their position
can be varied, both in height by adding or removing spacer plates, and to the front and the
back because of the slot in the attachment plate. The brakeman's back is at an angle of 45º,
which according to [Motallebi, 2004] should produce a low drag.
Figure 3.4: Crew dummies
During the initial measurements it was found that the forces on the bob showed unstable
behavior between 55 and 65m/s (see figure 3.7). The critical Reynolds number for a sphere is
approximately 300.000. The Reynolds number at 60m/s for the dummy head, also a sphere,
during the measurements was
Re=
V d

=
1.2⋅60⋅0.08
1.824⋅10
5
=3.16⋅10 5 , so the Reynolds
number of the dummy head is near the critical Reynolds number and this may cause this
instability. To eliminate this instability zig zag tape was applied on the head, which can be
seen in pictures 3.5 and 3.6. The applied tape has a thickness of 0.5mm, is 6.0mm wide and
the wedge angle is 70 .
Figure 3.5 Zig zag tape head
Figure 3.6 Zig zag tape head side view
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.
0.48
No zig zag tape pilot helmet
Zig zag tape pilot helmet
0.47
0.46
0.45
CD
0.44
0.43
0.42
0.41
0.4
0.39
0
2
4
6
8
10
Re
12
14
5
x 10
Figure 3.7: Unsteadiness during initial measurements
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.
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 6.4·105. No zig zag tape was
applied yet. The gap between the front and rear cowling was closed.
Table 3.1: PIV settings
Property
∆t
f#
FOV
lens
Value
15µs
8
246x186mm
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.
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
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.
3.3 Windtunnel corrections
Three types of corrections have been applied to the force measurements. These are discussed
here.
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
=
0.65⋅V m
3 h 2 b
(3-1)
With:
=  1M 2=  10.2272 =0.974
(3-2)
The volume of the model is estimated with:
V m =A⋅L=0.342⋅0.964=0.0328 m3
(3-3)
With the windtunnel area being 2.07 m2 and with the width of 1.80 m the blockage becomes
9.7 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 the
plate 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 run
should 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
measured, without the bobsleigh present, but it does give an idea of the drag they can produce
(see figure 3.16).
0.06
0.06
0.05
0.05
0.04
0.04
CD
CD
Figure 3.14: Dummy run configuration
0.03
0.02
0.02
Dummy run
Empty tunnel
0.01
0
0.03
Brackets
Empty tunnel
0.01
0
5
10
Re
Figure 3.15: Dummy run results
15
5
x 10
0
0
5
10
Re
Figure 3.16: Bracket drag
15
5
x 10
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 as
standard. On other days the difference with this standard run is applied as a correction.
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 5·105 the difference is set
at the value at Re = 5·105 (see figure 3.19).
0.04
0.035
C
D
0.03
0.025
20−09−2005
21−09−2005
22−09−2005
23−09−2005
26−09−2005
0.02
0.015
0.01
0
5
10
15
Re
5
x 10
Figure 3.17: Reference run drag (empty tunnel)
−3
5
−3
x 10
5
x 10
D
∆CD
DC
20−09−2005
21−09−2005
22−09−2005
26−09−2005
D
∆CD
DC
20−09−2005
21−09−2005
22−09−2005
26−09−2005
0
−5
0
5
10
Re
Figure 3.18: Original differences
15
5
x 10
0
−5
0
5
10
Re
Figure 3.19: Adjusted differences
15
5
x 10
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 the Best practice guidelines for handling automotive external aerodynamics with
FLUENT [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 64bit 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 windtunnel
model. 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 chosen
to 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-ε 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
the outlet as pressure outlet. The ground is modeled as a moving wall. The bob and crew are
set as stationary walls. The top, side and symmetry planes are all set as symmetry planes.
Figure 4.1: CFD Geometry
CFD CALCULATIONS 31
4.2 Grid setup
The grid was generated with Gridgen 15.09. There are a number of aspects that have to be
kept in mind when creating a computational mesh (see [Fluent, 2005]):
•
Smoothness: the volume of the cells should not change too fast. For the boundary
layer a maximum volume ratio of 1.2 is recommended.
•
Node clustering: a minimum number of cells is needed to resolve geometric and flow
features. 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 in
the boundary layer where the velocity gradients are large.
•
For non-equilibrium wall functions a wall y+ between 30 and 300 is recommended for
the 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 +=
 u y

(4-1)

(4-2)
u =U 
Cf

2
To make an estimate the same formula for skin friction is used as in chapter 2. In figures 4.3
and 4.4 the first cell height (is two times the height of the cell centroid) is plotted against the
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.
0.01
0.01
y+ = 30
y+ = 30
y+ = 100
0.008
y = 300
y = 1.5 mm
y[m]
y [m]
0.006
0.004
0.002
0.002
0
1
2
0
3
y+ = 300
y = 1.5 mm
0.006
0.004
0
y+ = 100
0.008
+
2
3
x = [m]
Figure 4.4: First cell height at U = 35m/s
x [m]
Figure 4.3: First cell height at U = 15m/s
0
1
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:

s2  3
A
4
AR= triangle =
h
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 gap
in 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 and
domain frontal area becomes:
CFD CALCULATIONS 33
1
0.342
A Boblsleigh 2
=
=0.8%
A Domain
4.5⋅4.5
(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
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
CFD CALCULATIONS 35
4.3 Grid adaptation
A full grid independence study usually involves solving the problem on at least three
different 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
10
10
10
10
0
Continuity
x−velocity
y−velocity
z−velocity
epsilon
k
−2
−4
−6
0
2000
4000
6000
Iterations
8000
10000
8000
10000
Figure 4.11: Residuals at U = 35m/s
0.3
0.295
0.29
0.285
CD
0.28
0.275
0.27
0.265
0.26
0.255
0.25
0
2000
4000
6000
Iterations
Figure 4.12: Convergence of drag coefficient with final value
indicated with dashed line
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 standard
case. 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 modeled
for 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 skin
friction 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 the
floor 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 have
caused 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). The
geometry 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-є model is
known to produce errors of up to 5%. It is encouraging that the trend of the curves are
similar.
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.
Figure 4.13: Plate inside rear cowling
0.4
0.35
CD
CFD
Windtunnel
0.3
0.25
0
5
10
Re
Figure 4.14: Windtunnel drag versus CFD
15
5
x 10
Table 4.1 Drag comparison overview standard case at U = 35 m/s
Cowling pressure drag
Front bumpers
Rear bumpers
Pilot helmet
Rest of crew
Front axles
Rear axles
Total
CD Theory
0.047
0.097
0.010
0.006
0.015
0.043
0.040
0.257
CD CFD
0.041
0.106
0.064
0.012
0.024
-0.002
0.019
0.018
0.274
∆CD
-0.006
+0.009
+0.054
+0.006
+0.009
-0.002
-0.024
-0.022
-0.048
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 the
flow 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]
15
35
Avg. y+ cowling outside
30.1
64.2
Figure 4.15: Oil flow visualization rear
Avg. y+ complete bob
19.9
42.1
Figure 4.16: Surface flow CFD rear, colored by
cp
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
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 0.342m2 and for the scale model
0.0340m2.
40
U [m/s]
30
20
10
0
0
0.5
1
Re
1.5
Figure 5.1: Free stream velocity vs.
corresponding Reynolds number
2
x 10
6
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 CFD
calculations 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
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 helmet
is 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 = 1.48·106 [s-1] around
brakeman's head
Figure 5.3: Iso-surface of zero total pressure at Re = 1.48·106
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. There
are 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 Olympic
Games 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 largest
contributors 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 closed
gap 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.
0.4
Standard
Gap
Gap bottom taped
0.39
CD
0.38
0.37
0.36
0.35
0
5
10
Re
15
x 10
5
Figure 5.4: Gap variation
Table 5.1 Gap variation
Case
Diagram
Time [s]
Underside
taped
-0.07
Gap
-0.01
Standard
54.71
RESULTS 45
0.4
Standard
Gap
Gap bottom taped
Larger gap
0.39
CD
0.38
0.37
0.36
0.35
0
5
10
Re
15
x 10
5
Figure 5.5: Gap variation, extra holes
Table 5.2 Gap variation, extra holes
Case
Diagram
Time [s]
Underside
taped
-0.04
Gap
-0.04
Larger gap
(5mm)
-0.01
Standard
54.71
0.4
Gap filled with plasticine
Gap taped
0.39
CD
0.38
0.37
0.36
0.35
0
5
10
15
Re
Figure 5.6: Gap variation, closed (with brakehole)
x 10
5
Table 5.3 Gap variation, closed (with brakehole)
Case
Diagram
Time [s]
Gap taped
-0.04
Gap filled with
plasticine
54.71
Figure 5.7: Gap taped
Figure 5.8: Gap with plasticine
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 can
be 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
Closed
Open
Bottom closed
Top closed
Small opening top
CD total
0.2743
0.2753
0.2745
0.2753
0.2732
CD front cowling inside
0.1262
0.1235
0.1238
0.1254
0.1243
CD gap
0.0034
0.0058
0.0047
0.0046
0.0035
Time [s]
53.90
+0.01
+0.00
+0.01
-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 CD this 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.
CD·A
Figure 5.10: Gap variation, full scale test
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 crew
are 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 52º.
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 Figure 5.12: Surface flow CFD helmet, colored by
cp
cp
Figure 5.13: Oil flow visualization helmet
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 calculations
is 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
Theory
CFD
Windtunnel
CD Helmet
0.015
0.024
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 is
reduced. 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. Whether
this 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.
RESULTS 51
0.4
z = 13 mm
z = 6.5 mm
z = 0 mm
z = −6.5 mm
z = −13 mm
0.39
CD
0.38
0.37
0.36
0.35
0
5
10
Re
Figure 5.14: Pilot height variation
15
x 10
5
Table 5.6 Pilot height variation
Pilot z [mm]
-13
Diagram
Time [s]
-0.07
-6.5
-0.04
Standard
54.71
6.5
+0.01
13
+0.01
0.39
Standard
Pilot only
No crew
0.38
CD
0.37
0.36
0.35
0.34
0
5
10
Re
Figure 5.15: Crew variation
15
x 10
5
Table 5.7: Crew variation
Case
Diagram
Time [s]
No crew
-0.17
Pilot only
-0.02
Standard
54.71
RESULTS 53
5.4 Runners and axles
In this section the result from the axles and runners will be discussed. The axles were
modeled 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 the
difference 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
Front axles
Rear axles
CD Theory
0.043
0.040
CD CFD
0.019
0.018
5.5 Other features
In this section the remaining features will be discussed. Not much research was invested in
these 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 a
completely 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
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
Zig zag tape bumper
Standard
0.39
CD
0.38
0.37
0.36
0.35
0
2
4
6
8
Re
Figure 5.20: Results zig zag tape front bumper
10
12
14
x 10
5
Table 5.9: Results zig zag tape front bumper
Case
Standard
Zig zag tape bumper
Time [s]
54.71
54.73
∆t [s]
+0.02
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
0.4
With brakehole
Without brakehole
0.39
CD
0.38
0.37
0.36
0.35
0
5
10
Re
Figure 5.22: Influence of brakehole
15
x 10
5
Table 5.10: Results nose rotation
Case
With brakehole
Standard
Time [s]
54.66
54.71
∆t [s]
+0.05
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
Rotated nose
Normal nose
0.39
CD
0.38
0.37
0.36
0.35
0
2
4
6
8
Re
10
12
14
x 10
5
Figure 5.25: Influence of nose rotation (5º)
Table 5.11: Results nose rotation (5º)
Case
No rotation
Rotated nose
Time [s]
54.70
54.76
∆t [s]
+0.06
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
0.4
No rim
Straight rim
Rim under angle
0.39
CD
0.38
0.37
0.36
0.35
0
2
4
6
8
Re
Figure 5.28: Influence of rim along cutout
10
12
14
x 10
5
Table 5.12: Results rim along cutout edge
Case
Standard
Rim
Rim under angle
Time [s]
54.71
54.75
54.75
∆t [s]
+0.04
+0.04
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 very
easy 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 having
a 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 also
called 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 is
largely 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.
59
So the first question can be answered. Changing the drag can have a significant influence on
final times. Numerous variations have been applied while other possible variations were only
based on theory. Variations that were found to significantly change the drag and thus answer
the second question are given here:
•
Leaving the transition between front and rear cowling partially open at the top
produces the lowest drag. Leaving a small gap reduces the pressure drag of the inside
of the front cowling. However opening the gap produces drag on the front edge of the
rear cowling so it should not be open completely. Differences found were very small.
•
For a low drag configuration of the crew, the biggest component of the drag is the
drag of the pilot's helmet. Measurements [Venema, 2005] have established that there
are significant drag differences between different helmets. The location of the pilot
head is more or less fixed because the pilot needs to be comfortable and must be able
to see out of the bob. Sticking the pilot's helmet further out the bob for better sight is
not necessarily bad for drag; it depends on the position of the brakeman relative to
the pilot. So the position of the brakeman should be optimized for a given position of
the pilot. Different positions have a significant effect on drag [Timmer, 2006].
•
The total drag of the axles, leaf springs, runner holding brackets, runner guiding
brackets and the runners themselves is significant. Theoretically speaking this drag
can be reduced significantly by rounding the edges of all the brackets. It is also
allowed to round the edges of the leaf springs which could provide a further
advantage.
6.2 Recommendations
In this section recommendations are given. They are quite different in nature. First of all
some recommendations are given that have to do with the setup of the windtunnel
measurements and model:
•
The windtunnel model had a wooden plate in front of the rear cowling for
reinforcement and for attachment to the nose. Holes have been made in this plate to
let air through but it would be better it the gap is completely open. Of course another
attachment system will be needed. It would also be better if the gap is further to the
back like on real bobsleighs.
•
The brackets that attach the bobsleigh to the windtunnel produce a lot of drag. It
would be better to have something that resembles the runners and holding brackets
more closely or a streamlined bracket that has a lower drag.
It is recommended to further investigate the following topics:
•
As mentioned the previous section the holding and guiding brackets may be radiused.
In theory this could provide a very big advantage. This is definitely something that
should be investigated, preferably in a windtunnel, since prediction of separation on
the rounded edges is typically poorly predicted by CFD codes.
CONCLUSIONS AND RECOMMENDATIONS 61
•
If a completely new bobsleigh is designed one of the first investigations should
probably be to determine the effect of the shape of the nose.
•
Although the performed CFD calculations seem to produce reasonable results and
perform 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 on
final 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 a
rubber 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 windtunnel
measurements 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 careful
application of sponsor stickers.
Bibliography
Anderson, J.D. Jr., Introduction to flight. Third edition. Singapore: McGraw-Hill, 1989.
ESDU, Data item 80021b Pressure drag of blunt forebodies at zero incidence for Mach
numbers up to 10. London: ESDU, 1980.
ESDU, Data item 96012 Subsonic and transsonic base and boat-tail pressure drag of
cylindrical bodies with circular-arc boat-tails. London: ESDU, 1996.
FIBT, International Rules. Italy: FIBT, 2005.
Fluent, Fluent 6.2 User's Guide. USA: Fluent Inc., 2005.
Garner, H.C., E.W.E. Rogers, W.E.A. Acum, E.C. Maskell, Subsonic wind tunnel wall
corrections. : AGARDograph 109, 1966.
Hoerner, S.F., Fluid-dynamic drag. Bakersfield: Hoerner fluid dynamic, 1965.
Keller, J.B., 'A theory of competitive running'. Physics Today, 26, 1973.
Kyle, C.R., V.J. Caiozzo, 'The effect of athletic clothing upon running speed'. Medicine and
science in sport and exercise, Volume 18(5), 1986.
Lanfrit, M., Best practice guidelines for handling automotive external aerodynamics with
FLUENT. Version 1.2. Darmstadt: FLUENT, 2005.
Meriam, J.L., L.G. Kraige, Engineering Mechanics, statics. Fourth edition. New York: John
wiley & sons, inc., 1998.
Motallebi, F., P. Dabnichki, D. Luck, 'Advanced bobsleigh design. Part 2: aerodynamic
modifications to a two-man bobsleigh'. Proceedings institution of mechanical engineers,
Volume 218 Part L: Journal of materials; Design and applications, 2004.
Quinn, M.D., 'Modeling the effect of wind resistance in the 200-m sprint'. International
Journal of Computer Science in Sport, Volume 3, edition 1, 2004.
Raffel, M., C. Willert, J. Kompenhans, Particle image velocimetry. Berlin Heidelberg:
Springer-Verlag, 1998.
Ruijgrok, G.J.J., Elements of Airplane Performance. Delft: Delft University Press, 1996.
Sovran, G., T. Morel, W.T. Mason, Aerodynamic drag mechanisms of bluff bodies and road
63
vehicles. New York: Plenum Press, 1978.
Timmer, W.A., L.L.M. Veldhuis, O. Lewis, Voorlopige conclusies naar aanleiding van de
metingen in de LST van DNW op dinsdag 31 januari 2006. Delft: TU Delft, 2006.
Venema, Lars, Weerstandsvermindering bij het bobsleeen - de ideale helm. : , 2005.
White, F.M., Viscous Fluid Flow. Second edition. Singapore: McGraw-Hill, 1991.
Zhang, Y.L., M. Hubbard, R.K. Huffman, 'Optimum control of bobsled steering'. Journal of
optimization theory and applications, Volume 85, No. 1, 1995.
Appendices
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 meters
long, 1200 meters of which shall be sloping downhill.
• The last approximately 100-150 meters may consist, depending on speed, of an uphill
stretch that shall have bends. The maximum gradient if this stretch must not exceed
12%.
• After time-keeping at the finish, the stopping stretch shall be straight and not have any
further bends.
Starting area (2.9)
• Bob push off stretch: Bob push-off stretch means the part of the track between the
start block and the first photo-electric cell. This stretch shall be 15m long and have a
gradient of 2%.
• Starting area: After the first photo-electric cell (start-line), the track must follow a
straight path so that bobsleds starting off may reach a speed of 35 km/h. The track
must be sufficiently wide in order, not to obstruct teams. The gradient of a 60m
stretch must be equal to 12%. The stretch between the first photo-electric station must
be 50m long (start time).
Bends (2.11)
• The bends must be constructed in such a way as to allow sleds to move not only along
a single trajectory , but to provide a band of possible trajectories from which to
choose. In a central part of the bend , the trajectory should extend along the upper half
of the bend. Entries and exists from bends must be rounded so that the sleds can take
them smoothly with no risk of capsizing, if no mistake is made in driving.
Centrifugal force (2.13)
•
The maximum time for which a centrifugal force of '4G' may occur is 3 seconds . The
maximum centrifugal force allowed is '5G'; this centrifugal force must not last for
more than 2 seconds.
Straights (2.14)
• The iced construction maximum width is 140cm. The external part of the side walls of
the straight stretches should not be higher than 80-100cm, including any raised
section. In the iced state, the inside part of the side walls must be at least 50cm high.
The side wall of straight stretches must be at a right-angle to the track base. The
66
A. INTERNATIONAL RULES 67
transition between the side wall and the base of the track must be provided with a
channel . In the iced state its radius must be 10cm. In transition linking a bend to a
straight, the raised part of the bend must run into the side wall of the straight
gradually in a sufficiently long section.
Figure A.1: Track geometry
A.2 Bobsleigh Geometry
Principles (3.1)
• Bobs must be cowled within the guidelines specified by these rules.
• The rear part of the bobs must be open.
• From the start, (green light signal) no specifications of the bob may be changed,
(damages excluded). The driver's and side push bar must be fully retracted, in
accordance with 3.5.
Weights (3.2)
• Minimum and maximum weight of the bob are limited. The following is allowed:
minimum weight (including runners, excluding any ballast):
– two man bob: 170kg
• To achieve minimum weight, additional steel may be firmly welded to the frame.
• Maximum Weight (including crew members and equipment required according to
8.7.):
– two man bob: 390kg
– women's bob: 340kg
• Maximum weight may be achieved by means of ballast. Ballast must be firmly bolted
or clamped to the bob.
Dimensions and construction (3.3)
• The gauge (centre to centre of opposite runners)is the same for front and rear runners:
670mm plus or minus 5mm.
• Every bob frame must be divided transversally between front axle and rear axle. The
angle between said longitudinal pivot axis and the horizontal standing surface must
not exceed 5 .
• The cowling must also be divided transversally.
• The front/rear axle must not be clad, cased or streamlined.
• The front (rear) runner carriers must not be cased, clad, faired or streamlined. All
edges of the spring leaf(s), guiding brackets and holding brackets may be radiused or
chamfered to a maximum of 8mm.
Cowling (3.3)
• It is not allowed to use any additional material on the cowling cutout.
• The cowling must be open – starting from the region of the driver's shoulders, through
to the back.
• The rectangular, symmetrical inspection hole situated beneath the front axle must be
at least 440mm long and at least 160mm wide.
• The cowling must be convex with the following exceptions:
– The bumpers
– The brake cutout
– The impression for the driver's push handle
– The articulation joint
– The holes for the front and back axles
– The brakeman's push handles
• Any unusual additions to the shape that are clearly vortex generators are not allowed.
• Additional holes that may give improved aerodynamic effects are also not allowed.
• The brakeman's handles must be immovable (3.5).
• The brake cutout must be open. No attempt may be made to reduce the area of the
cutout with any material.
Bumpers (3.3)
• In a top view the bumpers must be arc shaped.
• The rear bumpers must have a minimum height of 50mm (measurement taken
•
•
•
•
vertically with regard to the standing surface) over a length of minimum 200mm. The
upper and lower edges of the bumpers must have a radius of between 5 and 8mm.
The lower edge of the front bumpers must have a radius of no less than 10mm for a
minimum length of 300mm. In an upward direction they must be straight for a
minimum length of 35mm, subsequently passing into the upper edge with a minimum
radius of 35mm (fig A.2).
The connecting elements between the front bumpers and the bob cowling must have a
height of a minimum of 80mm over the minimal length of the front bumpers. The
connecting elements between the rear bumpers and the cowling must have a height of
a minimum of 50mm over the minimal length of the rear bumpers.
In a top view and in a side view the front of the connecting elements of the front
bumpers must form a continuous, not concave line with the tip of the cowling.
The front tips of the front runners must be covered by the cowling in any position of
the runners.
Runners (3.4)
• All runners must be produced in a solid piece of standard material according to FIBT
specifications.
• All types of treatment are forbidden, including those which even cause only a local
variation of the physical characteristics and/or of the compostion of the material
and/or structure of the material.
A. INTERNATIONAL RULES 69
• Any aerodynamic covering of the runners is prohibited.
• The nuts (attaching runners to runner carriers) must not be cased, clad, faired or
streamlined.
Figure A.2: Bumper geometry
Figure A.3: Bobsleigh allowed dimensions
A.3 Surfaces and materials
Principles (3.1)
• For the purpose of the FIBT, the term “steel” means an alloy of iron and carbon with
an iron (Fe) content of more than 50%, or an alloy which reacts positively to the FIBT
chemical test.
• For building bobs it is forbidden to use transparent material, or any other material
which may shatter as a result of an impact.
A.4 Clothing and helmet
Helmet (8.6.1.3)
•
During training and races, all bobsledders must wear a fully protective helmet, which
has to comply with the minimum EEC safety rules, respectively OKM or DOT and is
available and can be purchased on the market. It is forbidden to apply additional
aerodynamic elements to helmets. This is the task ans responsibility of the National
Associations and they undertake to comply with the safety rules.
Clothing (8.6.1.4)
• Shorts and short sleeves are forbidden in all races.
• It is forbidden to apply any extra aerodynamic element to the outside and/or beneath
the competition clothing.
A.5 Other
Principles (3.1)
• To propel the bob, only the pushing force of the team, when starting, and the force of
gravity are allowed.
Electronics (3.8)
• No electronic, electric, electronically activated or wave activated components are
allowed on the bob or the crew during official training or competition. The exception
are those components approved by the FIBT and he relevant Jury.
Measurement apparatus and devices (8.6.1.6) (during competition)
• It is forbidden to use any kinds of non-official measuring gauge or device on the sleds
or on the track during the period when the track is under the control of the F.I.B.T.
Teams (8.6.2)
• During descents the sitting position only is permitted.
B. Parameters
B.1 Air characteristics
The Cesana Pariol track is located between 1500 and 1700 m altitude. According to the
International Standard Atmosphere the conditions at 1600m are given in table B.1 [Ruijgrok,
1996]. However the actual temperature during a bobsleigh competition is usually lower (fig
B.1). At the the Torino 2006 Winter Games the bobsleigh competitions were held in the early
evening when temperatures were approximately -5 C. With the following formula the density
can be calculated [Ruijgrok, 1996]:
=
 ISA
T
1
T ISA
(B.1)
With:
T =T ISA T
(B.2)
For viscosity Sutherland’s law is used (for air S = 111K) [White, 1991]:
 

T
≈
T0
0
3 /2
T 0S
T S
(B.3)
The new conditions are given in table B.1.
Table B.1: Air characteristics
Parameter
T [K]
p [N/m2]
 [kg/m3]
 [kg/m s]
ISA
277.75
83523
1.0476
1.7388·10-5
Cesana Pariol
268.15 K
83523
1.085
1.6912·10-5
71
Figure B.1: Temperature and humidity at Cesana Pariol track for average day
B. PARAMETERS 73
B.2 Virtual starting point for a turbulent boundary layer
For a laminar flat plate the boundary layer thickness is given by [White, 1991]:
 5.0
=
x  Rex
(B.4)
 0.16
=
x Re1x /7
(B.5)
And for a turbulent boundary layer:
At the transition point these thicknesses are matched. For the laminar flow this is no problem,
since the thickness is assumed to be zero at the starting point. For the turbulent boundary
layer a virtual starting point is introduced. If the virtual starting point is plugged in the
turbulent boundary layer thickness equation and set equal to the laminar boundary layer
thickness:
0.16 x transition x0
Re
1/ 7
x transition x 0 virtual

virtual
=
5.0
 Re x
(B.6)
transition
For the virtual starting point of the turbulent boundary layer the following relation is found:
Rex
0 virtual
=Rex
transition
 31.25  Re x ,tr , lam 
7/ 6
(B.7)
C. Bobsleigh equation of motion
In this appendix aspects of the equation of motion will be discussed. First of all the general
equation will be derived. Then the equation is extended to include the pushing force during
the start. Finally the initial conditions will be discussed.
C.1 Derivation
The forces acting on a bobsleigh during a run are summarized in figure C.1.
Figure C.1: Forces acting on a bobsleigh
The friction of the runners on the ice is given by [Meriam, 1998]:
F=k N
(C.1)
Where N is the normal component of the gravitational force:
N =mg cos 
(C.2)
The aerodynamic drag is given by:
D= 12 U 2 C D A
For equilibrium in the direction of the track:
74
(C.3)
C. BOBSLEIGH EQUATION OF MOTION 75
∑ F s : m s̈=mg sin DF =mg sin k cos  12  U 2 AC D
(C.4)
U = ṡ
(C.5)
With:
This becomes:
s̈= g sin  k cos 
1 
2
AC D ṡ
2m
(C.6)
C.2 Initial conditions bobsleigh equation of motion
In figure C.2 data from the start track at Harderwijk are given. The velocities in figure C.3
are derived by taking the derivative of the cubic interpolation of the data. A linear fit of the
velocities results in the following relation for start times and velocities:
V 0=22.8232.0579⋅t 0
(C.7)
50
12.6
12.4
30
v [m/s]
x [m]
40
20
12.2
12
11.8
11.6
10
11.4
0
0
2
4
t [s]
Figure C.2: Data start track Harderwijk
6
11.2
5
5.2
5.4
t [s]
Figure C.3: Derived starting velocities
5.6
C.3 Calculation results
1500
40
35
30
S [m]
v [m/s]
1000
500
25
20
15
0
0
20
40
10
60
0
20
t [s]
40
60
1000
1500
t [s]
−50
−50
y [m]
0
y [m]
0
−100
−150
−100
0
20
40
60
−150
t [s]
0
500
x [m]
C.4 Bobsleigh equation of motion with start
During the start another force is acting on the sled; the pushing force of the crew. Also the
weight of the sled changes because the crew is not inside the sled, but the total weight of the
system remains the same.
If a sprinter is considered to be a point mass, a sprint can be described by the following
equation by Keller [Keller, 1973]:
dv
V
=f
dt

(C.8)
In this equation f is assumed to be constant and can be interpreted as the maximum force (per
unit mass) a sprinter can exert during a sprint. The parameter  can be considered a decay
C. BOBSLEIGH EQUATION OF MOTION 77
term. To this equation an aerodynamic drag term can be added [Quinn, 2004]. Rewriting this
equation in terms of forces and x and adding drag:
v
m H s̈=m H  f  12  ṡ 2 AH C D
H

(C.9)
Combining this with the bobsleigh equation of motion gives:
1
ṡ
m s̈=g  msin  k mbob cos   AC D ṡ 22 mH  f  AH C D ṡ 2
H
2

(C.10)
The friction term has changed, because the mass of the bob is reduced. All the sprinter force
terms are multiplied by two, because the crew consists of two people. A complete run can
now be simulated once the empiric sprint parameters are determined. For the starting phase
equation C.10 is used and equation C.6 can take over when this acceleration becomes larger
for instance.
The drag of the sprinters has to be determined as well. Gains may be made here by applying
roughness on the legs of the sprinters thereby decreasing the size of the wake and thus
reducing drag. Reynolds ranges for the legs are listed in table. They were derived with the
program Biomech (http://www.health.uottawa.ca/biomech/csb/software/biomech.htm) which
includes sample data. According to [Kyle, 1986] wind resistance of a runner can be improved
by 0.5% to 6%. A reduction of 2% was predicted to save 0.01s in the 100m dash.
Table C.1 Reynolds range legs
Situation
man 6 m/s
man 12 m/s
woman 6 m/s
woman 10 m/s
Re range
0 ~ 85000
-75000 ~ 170000
-35000 ~ 70000
-45000 ~ 110000
D. CFD settings and results
D.1 Fluent settings
Grid
Object:
Bobsleigh
Boundary layer:
Yes
No. cells:
Approx. 4.5 million
Domain size:
27 x 4.5 x 4.5 m
Boundary Conditions
Sled:
Wall
Inlet:
Velocity inlet
Ground:
Moving wall
Inlet turb. intensity:
0.05%
Top:
Symmetry
Inlet turb. viscosity
ratio:
1
Side:
Symmetry
Outlet:
Pressure outlet
Symmetry plane:
Symmetry
Outlet gauge pressure:
0
Material and reference values
Material:
Air
Operating pressure:
83523 N/m2
Density:
1.085 kg/m3
Area:
0.171 m2
Viscosity:
1.6912 ⋅10-5 kg/m⋅s
Model and solver settings
Solver:
Segregated
Time:
Steady
Space:
3D
Formulation:
Implicit
Gradient option:
Node based
Viscous model:
Realizable k-
Near wall treatment:
Non-equilibrium wall
functions
Grid adaptation
After no. iterations:
5000
Gradient of:
Total pressure
Remaining iterations:
5000
Coarsen:
No
Method:
Curvature
Refine threshold:
0.1
Normalization:
Normalize
Iterations
Pressure
Pressure-vel. coupling
Momentum
TKE
Turb. dissipation rate
Relaxation factors
78
Discretization scheme
0-50
50-100
100-...
Standard
Standard
Standard
SIMPLE
SIMPLE
SIMPLEC
1st order upwind
1st order upwind
2nd order upwind
1st order upwind
1st order upwind
2nd order upwind
st
st
1 order upwind
1 order upwind
2nd order upwind
0.5-1-1-0.2-0.2-0.2-1 0.65-1-1-0.35-0.5-0.5-1 0.65-1-1-0.35-0.5-0.5-1
D. CFD SETTINGS AND RESULTS 79
D.2 CFD Test overview
Simulation number
Velocity inlet
Moving Ground
Gap
CL
CD
CD front bumpers
CD rear bumpers
CD front axles
CD rear axles
CD pilot's helmet
CD pilot's body
CD brakeman's helmet
CD brakeman's body
CD front cowling outside
CD rear cowling outside
CD rear cowling inside
CD gap
CD step
01*
35 m/s
35 m/s
Closed
-0.3544
0.2743
0.056079
0.010538
0.019009
0.017731
0.023619
-0.00271
-0.00084
0.000626
-0.01922
0.126199
0.071574
-0.03298
0.003401
0.001292
Simulation number
Velocity inlet
Moving Ground
Gap
03e
25 m/s
25 m/s
Closed
03f
30 m/s
30 m/s
Closed
04a
35 m/s
35 m/s
Open
CL
CD
-0.3534
0.2777
0.056834
0.010662
0.018832
0.017293
0.023705
-0.00257
-0.00063
0.000524
-0.01776
0.125763
0.073178
-0.03287
0.003410
0.001353
-0.3541
0.2761
0.056415
0.010596
0.018948
0.017587
0.023657
-0.00262
-0.00056
0.000540
-0.01857
0.125915
0.072308
-0.03295
0.003404
0.001392
-0.3570
0.2753
0.056076
0.010505
0.019085
0.017708
0.023502
-0.00220
-0.00106
0.001545
-0.01921
0.123473
0.071253
-0.03247
0.005793
0.001292
CD front bumpers
CD rear bumpers
CD front axles
CD rear axles
CD pilot's helmet
CD pilot's body
CD brakeman's helmet
CD brakeman's body
CD front cowling outside
CD rear cowling outside
CD rear cowling inside
CD gap
CD step
* = Standard case
02
03a
35 m/s
5 m/s
No
5 m/s
Closed
Closed
-0.2873
-0.3451
0.2742
0.3029
0.057198 0.064197
0.010369 0.011493
0.018911 0.018345
0.017573 0.014579
0.023494 0.025486
-0.00211 -0.00165
-0.00085 -0.00032
0.001492 0.002009
-0.01006 -0.00715
0.118228 0.120962
0.066944 0.082852
-0.03088 -0.03192
0.003241 0.003414
0.000671 0.000566
03b
10 m/s
10 m/s
Closed
-0.3498
0.2901
0.059557
0.01125
0.018433
0.016626
0.023698
-0.00160
-0.00042
0.001566
-0.01277
0.123640
0.078189
-0.03237
0.003413
0.000833
03c
15 m/s
15 m/s
Closed
-0.3516
0.2843
0.058194
0.010951
0.018653
0.01689
0.023511
-0.00195
-0.00039
0.001287
-0.01522
0.124484
0.075918
-0.03257
0.003408
0.001107
03d
20 m/s
20 m/s
Closed
-0.3523
0.2806
0.057399
0.01078
0.018779
0.016996
0.023678
-0.00231
-0.00047
0.000898
-0.0167
0.125099
0.074367
-0.03269
0.003409
0.001347
04b
04c
04d
35 m/s
35 m/s
35 m/s
35 m/s
35 m/s
35 m/s
Bottom Top open
Small
open
opening top
-0.3573
-0.3551
-0.3718
0.2745
0.2753
0.2732
0.056075 0.056081 0.055877
0.010521 0.010542 0.010467
0.019078 0.018992 0.019935
0.017714 0.017719 0.016772
0.023304 0.023793 0.023507
-0.00213 -0.00275 -0.00229
-0.00115 -0.00051 -0.00087
0.001479 0.000591 0.000973
-0.01922 -0.01923 -0.019377
0.123848 0.125437 0.124276
0.071593 0.071378 0.071717
-0.03258 -0.03281 -0.03258
0.004674 0.004588 0.003526
0.001328 0.001434 0.001281
D.3 CFD Pictures standard case
Streamline pictures, colored by velocity
Figure D.1: Streamlines front, colored by velocity [m/s]
Figure D.2: Streamlines cavity, colored by velocity [m/s]
Figure D.3: Streamlines side , colored by velocity [m/s]
Figure D.4: Streamlines top, colored by velocity [m/s]
Figure D.5: Streamlines bottom, colored by velocity [m/s]
Surface flows, colored by cp
yz-vectors, colored by x-vorticity, side
Figure D.6: x-vorticity at x = 0.3m [s-1]
Figure D.7: x-vorticity at x=0.5m [s-1]
Figure D.12: x-vorticity at x=0.675 [s-1]
yz-vectors, colored by x-vorticity, cowling edge
Symmetry plane
Figure D.48: Velocity [m/s]
Figure D.49: Pressure coefficient
Figure D.50: Total pressure [Pa]
E. Practical tips
PIV
•
During the PIV tests blackboard paint was used to make the model black to limit the
reflections of the laser. The use of this paint has some drawbacks; it tends to have a
rough structure and needs to be sanded. However this makes the model shinier again
and shows a structure when the laser light reflects on it. This made a lot of images
hard or even impossible to process.
Model
•
The used model was made of plastic. If changes are made to the model and it needs
to painted a primer has to be used in order for the paint to form a smooth layer.
Gridgen
•
In Gridgen there is a possibility to use user made scripts or glyphs as they are called
by Gridgen. A very useful glyph is called SymmetryPlane.glf. This Glyph script
projects connectors and domains onto a user specified symmetry plane. Its intended
use is to correct the lack of precision often found in the symmetry plane geometry in
a CAD file that is inherited by the grid. More glyphs can be found on:
http://www.pointwise.com/glyph/
Fluent:
•
The number of FLUENT licenses is limited. Apart from the full licenses needed post
process licenses are available. These can be used to set up a case and examine the
results. The post process version of fluent can be started by typing the following
command command in the terminal window:
fluent -post
91

Aerodynamic analysis of a 2-man bobsleigh

Transcription

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