Parallel CFD of a prototype car with OpenFOAM

Full text

5th OpenFOAM Workshop, Chalmers, Gothenburg, Sweden, June 21-24, 2010
Parallel CFD of a prototype car with OpenFOAM
M.Sc. Louis Gagnon, louis.gagnon.10@ulaval.ca
Dr. Marc J. Richard, marc.richard@gmc.ulaval.ca
Dept of Mech. Eng., Laval University
G1V 0A6, Québec, Canada
Abstract
The Alérion Supermileage team at Laval University is a team of engineering students who design and build a
prototype car with the intent of making it the most fuel efficient as possible. One of the major factors that determine fuel
efficiency of a ground vehicle is its aerodynamic drag. Thus, the team was interested to find out which improvements
could be made to the current vehicle body design to reduce the drag. To that end, the OpenFOAM toolbox was compiled
on a 8000 processor cluster located at Laval University for the purpose of modeling the aerodynamics of the car. It was
possible to attain a very small turnover time for the calculations and this indicates that the software is an attractive
option for industry players that have access to a cluster. The k-ω-SST model was used for all of the simulations.
Validation against the Ahmed body showed showed a good agreement between experimental and calculated drag
coefficient and flow characteristics of the vehicle. The simulations were done using a three-dimensional mesh. Different
mesh sizes ranging from 2 to 15 million cells were used. Meshing of the domain was done with the snappyHexMesh
utility which is part of the OpenFOAM package. Drag forces in the range of 1.2 N to 2.0 N were calculated for different
geometries. The effect of boundary conditions was tested. Simulations were also done to study the effect of side winds on
the shell and thus predict the drag that occurs when the car is turning. Side winds were found to have a strong influence
on the drag forces. The study involved different bodies with slightly different features, such as camber in the wheel
covers, different curvatures of the main body, different lengths, etc..
Introduction
The Alérion team has recently been busy planning the replacement of the current body, also referred to as the shell,
of the vehicle and the construction of a whole new mold. The current body is completely made of carbon fiber and a lot
of care was taken to make it as light and as aerodynamically efficient as possible. However, no aerodynamic study was
done on the shape before its fabrication. Therefore, it was deemed necessary to iterate on a new body shape in order to
come up with the lowest drag coefficient possible. The current body was first analyzed using commercial software two
years ago by the team [5] but the results were deemed unsatisfactory. The drag coefficient was lying between 0.17 and
0.18, which does not make sense when compared to a renown vehicle, the PAC-Car-II, which has a drag coefficient of
0.075, according to Santin et al. [11]. The mesh generated back then had 130 000 elements and a steady flow with k-ϵ
turbulence model and wall functions was used. Last year, OpenFOAM with Gmsh, a mesh-generation software
developed by Geuzaine and Remacle [3], were used as reported by Gagnon [4] in a second attempt to analyze the flow
on the Alérion body. More interesting results were obtained but repeatability was not studied and no serious validation
was done. Two meshes were used and one had 350 000 cells while the other had 1.1 million cells. Also, a k- -SSTω
turbulence model with wall functions was used. This year, access to a 8000 CPU supercomputer was granted by the
scientific community. It was thus possible to further study the flow on the Alérion body, fine-tune the model, and
validate it against a classical car body shape. For the Alérion body, the analysis turnover time turned out to be be less
than a day and included the generation of surface and a volume meshes, solution of the flow, and visualization of the
results.
Hardware
The computer used for the calculations is the Colossus, which is part of the Compute Canada high performance
computing platform which makes its computers available to all Canadian researchers. The Colossus has 960
computational nodes and 40 infrastructure nodes. Each node has a pair of quad-core Intel Nehalem-EP processors and
24 gigabytes of RAM. Overall, the Colossus has 8000 cores and 24 terabytes of RAM. The nodes are linked together by
a Infiniband Quad Data Rate of which the nominal rate is 40 gigabits/sec. A 10-gigabit ethernet connexion also links the
infrastructure nodes to the outside world. A Lustre parallel filesystem is used on half of the infrastructure nodes.
Although the cluster has 7680 cores available, the simulations were ran using 64 and 128 cores for reasons of lower
queue times for jobs that require fewer processors. The OpenFOAM source code was compiled in order to link the code
to the precompiled OpenMPI librairies available on the cluster that have embed InfiniBand support. The mesh was
decomposed for parallel computations using the METIS algorithm available in OpenFOAM. A quasi-linear relationship
between the number of processors used and the computation time was observed.

5th OpenFOAM Workshop, Chalmers, Gothenburg, Sweden, June 21-24, 2010
Validation
As expected, using different approaches to the problem
yielded different drag forces on the same geometry. The same
happens when the mesh is modified. It was thus desirable to
validate the model that was chosen for the analyses. Due to
the lack of wind-tunnel access it was chosen to validate using
a combination of Ahmed body flow resolution and
comparison with the expected drag coefficient on the
Alérion. The Ahmed body was chosen for its proven CFD
data availability and the existence of at least two
experimental reports on its flow from Ahmed, Ramm, and
Faltinn [1] and Lienhart and Becker [2]. Since the flow
behind the Ahmed body is known to be difficult to model, the
validation was done more on the comparison of the flow on
other zones and the separation or non-separation of the flow
on the slant angle was seen as a advantage but not a
necessity. The goal here is not to tune the model to the
Ahmed flow but rather to validate the flow characteristics on
the overall Alérion body, which only has large slant angles in
the small rear zones were no ambiguity is present with
regards to whether the flow is attached or not: it separates. It
is also known that for RANS models, it is difficult to
precisely predict the shape of a detached vortex and it was
chosen to accept that as an uncertainty of the model. It was also tested whether the results agreed more with the
experimental flows when using a slip condition or a fixed floor one and the difference between the two conditions was
found to be negligible. Furthermore, this condition is not considered important when comparing two different shapes
with the intent to test which one has the lowest drag and get their flow properties. According to Franck et al. [6], the
flow on the 12.5 degree slant angle Ahmed body is expected, from experiments, to behave as shown in Figure 1 where
there is apparition of a bubble on the slant surface and the streamlines there are well aligned with the slant side edges.
Simulations or the 12.5 degree slant angle Ahmed body were done on a 15.1 million cells mesh which is shown in
Figures 4 and 8. A y+ value ranging between 2 and 88 on the vehicle body and above 125 on the floor was found.
Different wall models were tested and are, in OpenFOAM language, a Low Reynolds Number (LRN) wall model; a wall
function approach; and a Spalding wall function. Drag forces for these different wall models, are reported in Table 1.
The experimental drag coefficient value found by Ahmed, Ramm, and Faltin [1] is 0.23 and the contributions are 76
percent from pressure and 24 percent from friction. In the simulations, lift forces were roughly between one tenth and
one fifth of the drag forces. As expected, the influence of having a slip floor is very small and, also as expected, a small
increase in friction forces was noticed for the slip condition and it is explained by the flow underneath the body not
being slowed down by a fixed floor. A stronger pressure force accompanied by a smaller friction force was noticed when
using a LRN model and this agrees with the generally accepted idea that log-law wall functions on low y+ values tend to
overestimate friction forces. Figures 2 and 3 show the vortices behind the Ahmed body when using the LRN wall
model. Here and throughout this paper, the units of p are pressure in Pascals over density in kilograms and the values
are capped for a better graphical comprehension. The other wall functions yielded the same vortex geometry and are
thus not shown here.
Table 1: Drag coefficients on the Ahmed body using different wall models.
Body/floor condition Drag coeff. Diff. from measured Contribution press./frict.
1. Spalding/Spalding 0.280 22% 82/18
2. Spalding/slip 0.278 21% 81/19
3. Wall funct./wall funct. 0.275 20% 84/16
4. Low Re./wall funct. 0.254 10% 96/4
Figure 1: Flow structure expected for a 12.5
degree slant angle. Image taken from Franck
et al. [6].

5th OpenFOAM Workshop, Chalmers, Gothenburg, Sweden, June 21-24, 2010
Figure 3: Vortex C of Figure 1 and two-dimensionnality of the streamlines
on the slant plane from the simulation with the low Reynolds wall model.
Figure 2: The two spanwise vortices from the simulation with the low Reynolds wall model.

5th OpenFOAM Workshop, Chalmers, Gothenburg, Sweden, June 21-24, 2010
Mesh
The utility SnappyHexMesh was used for the generation of the different meshes. The shape of the shell was
imported as a surface mesh from a shape created with a commercial CAD software. It was then converted to a
stereolithography (STL) file with a 0.7 mm to 7 mm element size varying according to the curvature of the shape. The
STL file was then linked to snappyHexMesh for the creation of the volume of fluid. The volume consists of a simple
box, created by Gmsh where the vehicle rests at 3 cm above the floor. The wheels are not included in the shape. Refined
zones were also defined for the volume mesh in the snappyHexMeshDict file and they are near the vehicle body and the
anticipated wake. Special care had to be taken in order to remove all possible holes in the STL file because otherwise
the meshing utility would mesh both the inside and the outside of the shell and thus render a realistic analysis
impossible. AdMesh was used to fill holes in the surface geometry. The mesh used for the validation case is shown in
Figure 4 and it has 15 million cells. The mesh could obviously contain fewer cells if a mesh optimization procedure had
been done but this was not the goal of the validation process. The use of the layer addition process of the
snappyHexMesh utility was used as a means to reduce the number of skewed cells present in the mesh. The influence of
using layers was tested and found to have an influence on the overall drag and lift coefficients of less than 3 percent. It
was also noticed that, for the settings used, the layer addition process did not produce a noticeably different mesh but
excessively skewed faces were fixed in the process.
One of the issues that came from snappyHexMesh is its curious tendency to refine some parts of the surface mesh
with no apparent reason. One such example is shown in Figure 8 where one can see the refined line that crosses the top
of the Ahmed body and goes all round it. The issue was not considered as a problem for the validity of the results. It
does however force the user to have slightly more cells than necessary and undesired y+ values.
For the Alérion body the meshing procedure was similar. Essentially, the idea is to have a mesh which is fine enough
to capture the vortices and pressure zones that come from the vehicle. To that end, a very slow mesh expansion factor
was set in the snappyHexMesh controls, asking that 7 cells be present between each refinement level. Also, refined
zones were defined from STL geometries created in zones of expected separation, in the wake, and on the floor. These
zones were initially set as shown in Figure 7. Each plane defines the center of a distance-based cell refinement zone.
However, it was found from the results obtained that a finer resolution of the wake could be considered because the
downwind part of the wake was slightly coarsely resolved, as seen in Figure 5. To that end, a second wake control was
Figure 4: Slice at z=0 for the mesh used on the 12.5 degree slant angle Ahmed body. Three different
zoom ratios.

5th OpenFOAM Workshop, Chalmers, Gothenburg, Sweden, June 21-24, 2010
added to gain a better resolution of the full wake
behind the body. For similar reasons, a refinement
zone was also added on the front of the body to have
a finer resolution of the pressure zone caused by the
nose of the body.
Getting y+ on the Ahmed body to a similar value
than for the Alérion body was a hard to reach goal
because the velocities are four times higher on the
former and thus four times smaller cells are needed.
However, it was reasonably feasible to reach y+
values in the order of 1-8 for the Alérion body, and
this is mainly what motivated the study of different
wall functions. However, there was, in certain cases,
an issue in properly analyzing the y+ values on the
walls because the yPlusRAS tool yielded min, max,
and average y+ values but they did not agree with the
ones created in the field files. Further investigation
with ParaView showed that the y+ values written in
the field files can be incoherent and thus the values
given by the yPlusRAS tool output were considered
as the valid ones. An example of this incoherence is
shown in Figure 6 where the cell sizes and flow
velocities are visibly constant but the y+ values
change sporadically.
Figure 8: Mesh generated by SnappyHexMesh on the Ahmed body.
Figure 6: Nose of the Alérion body colored by y+
values and nearby flow field colored by velocity
magnitude.
Figure 5: Slightly coarse wake mesh seen on the
plane normal to spanwise axis and at the middle of
the Alérion body.
Figure 7: Snapshot of the Alérion body with
its refinement planes.

5th OpenFOAM Workshop, Chalmers, Gothenburg, Sweden, June 21-24, 2010
Boundary Conditions
The floor condition does influence the flow and for that reason it was chosen to model it as if the Alérion was
actually driving on a road, thus a moving or slip floor condition was used. k and inlet boundary conditions wereω
chosen for the Ahmed body as calculated from known data and generally accepted formulas. The data being a turbulent
intensity of less than 0.5 percent and an incoming boundary layer of 1.5 cm. Air viscosity and pressure were taken at
21.5 °C. For the Alérion body, the inlet k value was calculated similarly while the was initially calculated from anω
eddy viscosity ratio of 0.2. This approach gave a very large value for the inlet and it simply increased the convergenceω
time without changing the results obtained with a smaller inlet . It was thus chosen to take the calculated from anω ω
imaginary boundary layer thickness of 1.5 cm, as had been done for the Ahmed body. From the validation process it
was found that classical log-law wall function boundary conditions on the walls were most appropriate. There are two
walls in the analysis: the shell of the vehicle and the floor. The other walls of the volume are modeled as symmetry
planes. A fixed velocity inlet at 9 m/s and a fixed pressure outlet at 0 Pa are used. The choice between a slip or wall
function floor boundary condition was found to have little influence on the drag and lift coefficients. The influence was
measured at below 0.65 percent. This is explicable by the fact that the difference between a slip and a moving floor is
fairly small considering that only the part of the floor that is
affected by the vehicle will behave differently. This is seen in
Figure 9 where a floor using a slip boundary condition is shown
and one can see that only the floor velocity under the wheel
fairings is visibly affected, and not by much. A moving floor is
also, incidentally, known to emulate wind tunnel tests with
boundary layer control, as pointed out by Franck et al. [6].
However, the choice between a LRN and a High Reynolds
Number (HRN) model at the walls of the vehicle was considered
to be worth studying. Its influence on the drag coefficient was
measured at 16 percent and of this influence came from the
friction forces. This confirms the generally accepted idea that
friction forces are what is mostly influenced by the choice of wall
modeling. More care was thus taken in order to choose which
approach to use and it was decided to test an adaptable wall
function which switches between LRN and HRN approaches
depending on the velocity of the ambient flow as discussed in the validation and turbulence sections. Contrary to
Möller, Suzzi, and Meile [12] and Hemida and Krajnović [13], a slip boundary condition was not used on the floor
upstream of the Ahmed body as a means to control the boundary layer thickness. This could have proven useful for the
Ahmed body since the boundary layer thickness is known upstream of the vehicle but it is not the case for the Alérion
body, for which no wind tunnel tests are available and the best option remains to model it using on-track conditions.
Turbulence Modeling
All of the simulations took turbulence into account with the k- -SST turbulence model. This model was used for itsω
proven reliability in separation zones and its ability to blend a good freestream model to a good boundary layer model.
The k- -SST model used by OpenFOAM is described in a paper by Menter and Esch [7]. ωThe newly implemented wall
conditions available in OpenFOAM-1.6.x were tested. At first, it was unclear whether a model using classical wall
functions, with y+ values greater than 30 or a LRN model with y+ values ~1 was more appropriate. It was also question
of using an adaptive model which would either rely on the LRN approach in regions where y+ values calculated from the
velocity field were low or a HRN approach in regions of higher y+. The Spalding wall function was tested because of its
great flexibility for a mesh where y+ is neither consistently below 1 nor above 30. It sets k and ω wall values according
to the distance from the wall. For the Spalding wall function, a little tweak had to be done to the wall velocities and they
were set to a very small number in order to avoid division by zero. Finally, in view of the results of the validation
process, it was decided that the classical log-law wall function approach will be used for the Alérion body simulations.
Further details on the comparison of different wall functions are given in the discussion section and details on the wall
functions tested are available in the OpenFOAM source code [8].
Convergence
Most of the cases tested converged directly without the need to change the numerical schemes or refine the mesh
even though some meshes contained a few skewed cells. The model was also ran right away with turbulence turned on
Figure 9: Centered side plane of the
Alérion body and slip floor.

5th OpenFOAM Workshop, Chalmers, Gothenburg, Sweden, June 21-24, 2010
and OpenFOAM was able to withstand the initial chaos created
by the flow trying to reach equilibrium. However, some cases
needed particular attention and it was sometimes necessary to
change the size of the elements on the surface mesh generated by
the commercial software because of the presence of
discontinuities. They could cause divergence beyond the control
of the bounding functions on k and ω. Such a case of problematic
cells is shown in Figure 10 where diverging cells are highlighted.
Shape Iterations
Having no access to the previous shape parametric definition
due to it having been created with a different CAD software, a
new shape was thus iteratively created and the
flow properties were compared to the initial
model. The iterative process first only yielded
shapes that did not perform as well as the initial
one. Thus, to help the surface designers,
ParaView was used to visualize surface
differences between different shapes. An example
of this procedure is show in Figure 11 where the
blue shows protuberances of the new shape.
An attempt at automatically calculating the
frontal area of the shell was made in OpenFOAM
by calculating the sum of the magnitudes of the
projected areas of all the cells on the surface and
dividing it by two. Unfortunately, this leaves the
issue of discerning between frontal area
contributions and redundant contributions from
concavities in the geometry unresolved.
Yaw Angles
The analysis of side winds is also of concern to the team. According to Santin et al. [11], during a typical track lap,
the vehicle is subjected to a non-negligible quantity of side winds. They come from two factors: 1. the ambient winds
affect the apparent flow velocity that the vehicle sees, and 2. the vehicle turns and its movement direction is no longer
along its longitudinal axis. These two factors should be considered separately if the objective was to have a very
accurate idea of their respective influence.
In a simulation where the vehicle is traveling along a straight line and is subjected to a side wind, its drag forces,
which are the forces that slow it down, are calculated as the sum of the forces acting on its longitudinal axis. The
apparent wind is thus the sum of the vehicle velocity and the ambient wind. The floor still moves backwards and along
the longitudinal axis of the vehicle.
Alternatively, in a simulation where the vehicle turns and the ambient winds are absent, the drag forces become the
forces that slow it down and they are thus the sum of all forces acting on its velocity axis. The floor velocity also
becomes in the direction of the vehicle velocity. The velocity magnitude is equal to that of the vehicle, as can be seen
when the conservation of energy laws are applied to the vehicle.
Unfortunately, the vehicle is usually not subjected to only one of the effects but rather to a combination of both at the
same time. From the analyses reported by Santin et al. [11], it is obvious that the 5 degree yaw angle is the one that is
mostly present in a typical track lap. Other angles that seemed worthwhile for an investigation are the 15 and 25 degree
angles.
Results
The different shapes were analyzed with classical wall function approach because they are known, as pointed out by
different authors [9,10], to be tuned for, and behave well with, steady flows and the analyses ran are solving for steady,
Figure 10: Diverging values of k caused by
skewed cells created by unwanted
concavities on the Alérion body.
Figure 11: Comparison of the original shape (white)
with a newly defined one (blue). Model 5.

5th OpenFOAM Workshop, Chalmers, Gothenburg, Sweden, June 21-24, 2010
in average, flows. They are also the ones that seemed to be the most appropriate after the validation process. Also, using
a wall function approach was also chosen because the iterations dealt mainly with analyzing the pressure distribution
and vortex formation around the body. The approximation in a classical log-law wall function approach is made on the
shear stress near the wall, as pointed out by Bredberg and Davidson, [9] and thus one expects a better resolved pressure
than wall friction. Finally, the stronger influence of wall functions on the friction coefficient is also generally accepted
by the CFD community. For the first iteration period, six shapes were created and analyzed. Their respective
performances are compared to the reference shape in the Table 2. Most of the lift is due to pressure. The friction
contribution to the lift is well below 1 percent.
Table 2: Drag and lift forces on the reference and new shapes of the Alérion body.
Shape Pressure Drag (N) Friction Drag (N) Drag (N) Lift (N)
Ref. 0.772 0.464 1.236 -7.520
1 1.026 0.480 1.506 -5.278
2 1.087 0.650 1.737 -8.877
3 1.421 0.488 1.909 -10.659
4 0.906 0.469 1.375 -4.703
5 0.879 0.49 1.369 -4.730
6 0.750 0.637 1.387 -4.138
The first three models were compared with the reference model with
a focus on the front wheel fairings. The comparison of the pressure
distribution on the body is shown in Figures 13 and 14. Much of the
downforce on the body comes from the low pressure zone created under
the body between the front wheels. Models 5 and 6 are very similar
shapes; the only difference is the tail of the body. It is interesting to note
that the rounded tail induces more friction drag but less pressure drag,
as expected, since the wetted area has been increased but the closure is
smoother. The two tails are shown in Figure 12 where the pressure line
is due to a very small discontinuity on the body shape and was seen to
have very little influence on the flow next to the surface. One can also
see in Figure 16 that the rear longitudinal vortices on model 5 are
stronger than on model 6, this explains the higher pressure drag on
model 5. Lower pressure behind the model 5 is also confirmed in Figure
15 where a longitudinal cut plane of the two models is shown.
Figure 13: Comparison of the pressure distribution on the first three models. Rear view.
Figure 12: Rears of model 5 (front)
and model 6 (back).

5th OpenFOAM Workshop, Chalmers, Gothenburg, Sweden, June 21-24, 2010
Figure 15: Cut plane of the pressure along the centerline of model 6 (top) and model 5 (bottom).
Figure 16: Rear longitudinal vortices on model 6 (left) and model 5 (right) of the Alérion body.
Figure 14: Comparison of the pressure distribution on the first three models. Front view.

5th OpenFOAM Workshop, Chalmers, Gothenburg, Sweden, June 21-24, 2010
An analysis of the Alérion body at a 15 degree yaw angle was done. The floor velocity vector was kept as equal to
the moving velocity of the vehicle and the flow velocity was set to have a magnitude equal to the moving velocity but at
an angle of 15 degrees with respect to the longitudinal axis of the body. Drag forces for the 0 and 15 degree yaw angles
of the reference model are given in Table 3. The forces in the streamwise direction are calculated from a simple
trigonometric rule and one can notice right away that they are much greater than in the velocity-wise direction.
Table 3: Drag and lift forces on the reference Alérion body at 0 and 15 degree yaw angles.
Angle (degrees) Pressure Drag (N) Friction Drag (N) Drag (N) Lift (N)
0 0.772 0.464 1.236 -7.520
15, velocity-wise forces 0.904 0.515 1.418 -7.435
15, streamwise forces 3.237 0.52 3.754 -7.435
A comparison of pressure distributions on the front and rear of the Alérion body subjected to equal velocity
magnitude winds at 0 and 15 degree yaw angles is shown in Figure 17. One can notice that the pressure acting on the
spanwise direction is visibly stronger for the 15 degree yaw angle while the pressure acting on the longitudinal axis is
not visibly weaker, if not actually the other way around, as pointed out by the drag results of Table 3. It is also seen in
Figure 18 that the separation zones and the vortices created in presence of a side wind are not negligible.
Discussion
The validation process showed that the most promising wall model might very well be the LRN approach when one
looks only at the drag coefficient. However, when one looks at the respective contributions of friction and pressure
drags, then a wall function approach seems more appropriate. In both cases, the flow over the rear of the Ahmed body
exhibited very similar structures to the experimental data reported by Franck et al. [6], with the exception of the C
vortex from Figure 1 being much weaker, if at all existent, in the simulation results of all wall models tested. The two
spanwise vortices next to the rear vertical wall and the two-dimensionality of the streamlines reported by Franck et al.
[6] in experimental analyses were seen in the simulations with every wall model tested, as seen in Figures 2 and 3. The
slant angle separation bubble was not well reproduced. Surprisingly, the results from the log-law and Spalding wall
functions were very similar. However, this can be explained by the fact that the on most of the Ahmed body the y+
values were above 30. The initial approach of using a classical log-law wall function was retained for the simulations of
the Ahmed body and will be used at least until further study of the Ahmed body is done and lower y+ values are
reached. The study should include an incoming boundary control using the upstream slip condition on the floor as
Figure 17: Pressure distribution on the rear (left) and front (right) of the reference Alérion body.
Top representation has no yaw angle and bottom representation has a 15 degree yaw angle.

5th OpenFOAM Workshop, Chalmers, Gothenburg, Sweden, June 21-24, 2010
pointed out earlier in this paper, a mesh that will not have the cell size variation problems pointed out in Figure 8, and
tests at more slant angles to study the consistency of the accuracy of each wall model. Overall, what the validation
process showed is that the pressure on the Alérion body will be well calculated from any of the wall models tested. As
for the friction forces, they turned out to be dependent on the wall model, but they are also dependent on the wall finish,
which was not considered in the simulations and does have a great impact on the actual drag forces. When comparing
the relative performance of different bodies, any of the wall models tested should be effective.
From the results of the iteration over the different body shapes a few points ought to be made. First, the results
consistently show a downforce on the body, which apparently is caused by the increased velocity and decreased pressure
between the two front wheel fairings. An increase in the angle of attack of the vehicle is worth testing because it will
likely cancel out the negative lift and its associated drag. Second, it is also visible that the drag coefficient decreases
with the smoothness of the shape. The closure of the flow behind each obstacle to the flow is very important for drag
reduction. This is shown especially with model 6 that has lower pressure coefficient than the reference model. Third, the
features of the body tend to have a lower drag when they are symmetric and contain no unnecessary curves. It seems
useless to have curves, even in the wheel fairings where it could be beneficial to modify the flow in order to remove the
negative lift. Fourth, friction plays an important role and even if it is fairly difficult to accurately measure it, care should
be taken to have the lowest wetted area as possible. It is necessary to postpone turbulence as much as possible and avoid
zones where the velocity increases drastically.
Figure 18: Velocity streamlines on the reference Alérion body with a 15 degree yaw angle.

5th OpenFOAM Workshop, Chalmers, Gothenburg, Sweden, June 21-24, 2010
Now, with regards to the simulations done at a 15 degree yaw angle, if the vehicle was moving along a straight line
and only the ambient wind influenced the flow direction, the flow velocity vector in the longitudinal direction should
have been kept equal to the moving velocity of the vehicle instead of keeping the magnitude of the flow velocity equal
to the moving velocity of the body. On the other hand, if the vehicle had been turning, the floor velocity should have
had the same direction as the stream, 15 degrees. Thus, the simulations are close to a case where the vehicle is turning.
However, because the purpose of these simulations is to get an first overview of the effect of side winds, the accuracy
provided by this model is deemed very reasonable. A further study should include an energy based analysis of how
much energy is spent fighting aerodynamic forces during a typical lap. It should also consider the percentage of time
spent at each velocity and yaw angle. The data to start such an analysis is made available by Santin et al. [11].
The results from the yaw angle study mean that the Alérion body will experience stronger aerodynamic forces when
turning and it suggests that trying to cut down on the turning forces can be a winning strategy considering that a typical
track has many curves. They also show that the drag forces are stronger when a side wind is present, even if the stream
velocity magnitude is not increased. Surprisingly, even the friction forces are increased, which is somewhat counter-
intuitive because one would expect that a lower stream velocity along the longitudinal axis of the vehicle would imply
lower friction drag forces. This effect is likely due to the flow being heavily diverted by the vehicle which becomes an
obstacle to the side wind and thus creates stronger friction forces on the shell. It should also be noted that for the Ahmed
body, Möeller, Suzzi, and Meile [12] reported a roughly 50 percent increased drag force for both measured and
simulated 15 degree yaw angles when compared to no yaw angle. With regards to that finding, the side wind results on
the Alérion body are not so surprising. Stronger drag forces at a 15 degree yaw angle were also found by Hemida and
Krajnović [13] from the DES simulations of a bus model. Contrasting with the Ahmed Body findings of Möeller, Suzzi,
and Meile [12], the lift coefficient of the Alérion body was not influenced by the yaw angle.
Finally, further tests will need to be made to weight the respective importance of the different yaw angles and an
energy-based evaluation procedure as the one pointed out earlier in this paper seems to be the most promising approach
to select between similarly efficient shapes. Also, on a practical note, the Alérion body will usually slow down very
quickly when turning because of the strong tire losses.
Conclusion
The goal of gaining a better understanding of the flow around the body of the Alérion was fulfilled successfully and
it was possible to validate the model used. Having access to a high performance computer was essential in order to be
able to study different simulation parameters. The turnover time was very low. Better accuracy was obtained than what
had been previously possible for the Alérion Supermileage team. It is considered that for future tests a strictly LRN
approach with an appropriate mesh could be used but not during a process where many different shapes are tested.
The convergence of OpenFOAM was, in most cases, very satisfactory. Some minor issues were pointed out with
snappyHexMesh mesh generation software but it otherwise showed a strong reliability. The shape generation process in
the commercial software turned out to be an important step and future shapes should be made with more care taken to
avoid discontinuities between the different surfaces of the shape.
If the Alérion Supermileage team wishes to increase the accuracy of the simulations, the approach should be to
switch to an unsteady model, possibly a DES in combination with a LRN number or an adaptive wall function.
However, it is believed that such simulations would have a much higher turnover time than the ones covered in this
paper. It might also be pushing the accuracy of the numerical model too far without being able to verify the results
against experimental data. Comparison with wind tunnel tests would increase the reliability of the simulations.
Finally, a fairly consistent improvement in the drag coefficient as the iterations of the Alérion body shape went on
shows that the aerodynamic analyses did help the shape designer improve the aerodynamic efficiency of the body.
Future work involves iterating over more shapes until a good compromise between surface friction and pressure drag can
be attained. An energy based yaw angle analysis is also planned.
Key words: Drag coefficient, Automotive, Streamlined, Cluster, Wall functions, Ahmed body, Supermileage,
OpenFOAM.

5th OpenFOAM Workshop, Chalmers, Gothenburg, Sweden, June 21-24, 2010
References
[1] S. R. Ahmed, G. Ramm, and G. Faltin. Some salient features of the time averaged ground vehicle wake. Technical
Report TP-840300, Society of Automotive Engineers, Warrendale, Pa., 1984.
[2] H. Lienhart and S. Becker. Flow and turbulence structures in the wake of a simplified car model. SAE Technical
Paper, 2003-01-0656, 2003.
[3] C. Geuzaine and J.-F. Remacle. Gmsh : a three-dimensional finite element mesh generator with built-in pre- and
post-processing facilities. Int. J. Numer. Meth. Engng, 79(11) :1309–1331, 2009.
[4] L. Gagnon. Calcul de la résistance aérodynamique d'un véhicule muni de pièces en mouvement. M.Sc. Thesis,
Laval University, 2010.
[5] Alérion Supermileage. Supermileage design report, SAE Collegiate Design Series. Unpublished Report. 2008.
[6] G. Franck, N. Nigro, M. Storti, and J. D’Elia. Numerical simulation of the Ahmed vehicle model near-wake.
Technical report, Instituto de Desarrollo Tecnologico para la Industria Quimica, Argentina, 2007.
[7] F. R. Menter and T. Esch. Elements of industrial heat transfer predictions. Proceedings of the 16th Brazilian
congress of mechanical engineering, 2001.
[8] OpenCFD. OpenFOAM-1.6.x source code. OpenCFD Limited, Berkshire, UK, 2009.
[9] J. Bredberg and L. Davidson. Low-Reynolds Number Turbulence Models: An Approach for Reducing Mesh
Sensitivity. J. Fluids Eng., 126(14), 2004.
[10] W. Gyllenram and H. Nilsson. Design and Validation of a Scale-Adaptive Filtering Technique for LRN Turbulence
Modeling of Unsteady Flow. J. Fluids Eng., 130(5), 2008.
[11] J.-J. Santin et al.. The world's most fuel efficient vehicle. ETH Zurich. 2007.
[12] S. Möller, D. Suzzi, and W. Meile. Investigation of the flow around the Ahmed body using RANS and URANS
with various turbulence models. 3rd OpenFOAM Workshop, 2008.
[13] H. Hemida and S. Krajnovic. DES of the Flow Around a Realistic Bus Model Subjected to a Side Wind with 30°
Yaw Angle. The fifth IASME/WSEAS International Conference on Fluid Mechanics and Aerodynamics, 2007.