Conference PaperPDF Available

Parallel CFD of a prototype car with OpenFOAM

5th OpenFOAM Workshop, Chalmers, Gothenburg, Sweden, June 21-24, 2010
Parallel CFD of a prototype car with OpenFOAM
M.Sc. Louis Gagnon,
Dr. Marc J. Richard,
Dept of Mech. Eng., Laval University
G1V 0A6, Québec, Canada
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..
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
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
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
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
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].
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
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.
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.
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,
5th OpenFOAM Workshop, Chalmers, Gothenburg, Sweden, June 21-24, 2010
[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.
... The simulation properties follows the prescribed method of setup conducted by Gagnon and Richard (2010) for the OpenFOAM implementation of the simpleFOAM steadystate algorithm. They were tested against the Ahmed body (a simplified, standardised car body used in CFD testing) wind tunnel data. ...
... The Ahmed body model also has an angled front section which allows for a defined comparison of lift and drag coefficients. The conclusion from Gagnon and Richard (2010) showed that the chosen simulation's setup using the simpleFOAM algorithm had a 10 % difference from experimental wind tunnel testing data. A time-varying velocity was applied from 5 to 25 m s −1 in steps of 0.5 m s −1 at the inlet boundary condition, which is a spatial specification of values at the domain inlet. ...
... thus the most significant boundary conditions are the vessel surface and the floor surface (the lower boundary of the simulation domain). In accordance with Gagnon and Richard (2010), a classical log-law wall function was applied to the domain floor and vessel's surface for the turbulence characteristics of k (specific kinematic viscosity) and (specific dissipation rate). The k − shear stress transport (SST) turbulence model (Menter, 1993) was used for a turbulent intensity of 4 % for all boundary conditions. ...
Full-text available
Wind speed measurements over the ocean on ships or buoys are affected by flow distortion from the platform and by the anemometer itself. This can lead to errors in direct measurements and the derived parametrisations. Here we computational fluid dynamics (CFD) to simulate the errors in wind speed measurements caused by flow distortion on the RV Celtic Explorer. Numerical measurements were obtained from the finite-volume CFD code OpenFOAM, which was used to simulate the velocity fields. This was done over a range of orientations in the test domain from −60 to +60° in increments of 10°. The simulation was also set up for a range of velocities, ranging from 5 to 25 m s−1 in increments of 0.5 m s−1. The numerical analysis showed close agreement to experimental measurements.
... The Laval team was granted access to an eight thousand processor supercomputer and this allowed a quick turnover time between design iterations. While this article tends to focus on the shape optimization process and the various features of the flow on the body, a more complete description of the numerical approach is given in [3]. The new shape of the vehicle was created within an uncoupled iterative process between the aerodynamics analysis and the shape creation. ...
... While this section outlined the important aspects of the validation process, more details are given in a previous article [3]. ...
... From testing these wall models, it was decided that the classical log-law function would be most suitable to set the k and ω values at the wall. Further details on the different wall functions tested are given in a previous article [3] and available in the OpenFOAM source code [12]. In fact, the choice of wall function for the Ahmed body had mostly influenced the friction forces. ...
... In the present embodiment the effort is aimed at answering the following question: which solver formulation, from an accuracy point of view, is the best today? Fluent, CFX, PowerFLOW and OpenFOAM have been investigated and compared with findings in the literature for PowerFLOW [5], OpenFOAM [31], [17], [19] and Star-CCM+ [23] . ...
... The temporary fix for this issue is similar to the principle presented in reference [25], except that the flow regime is not supersonic for road vehicles and the sensing function is different. However we still appreciate PowerFLOW for being the only commercially available Lattice Boltzmann Method, so it scores high for innovation and theoretical advantages over the RANS approach [5], [7], [11], [17], [12], [12], [36]. ...
... OpenFOAM is very appealing from an economic, research [31], [17] and development [19] stand point. It is in stark contrast to PowerFLOW's high price. ...
Full-text available
The use of numerical simulations is nowadays drawing an increasing interest in aerodynamic shape optimization. We firstly present a thorough benchmark of different numerical experiments done with Fluent, CFX, OpenFOAM and PowerFLOW on the Ahmed body in order to select the proper model and numerical scheme for our needs. Numerical strategies for reducing preparation, discretization, simulation and time optimization are also shown. Secondly, results around a NACA airfoil are discussed. As an application we consider the air flow around a notchback race car. The results presented show that the chosen strategy is able to accurately predict drag, lift and aerodynamic efficiency with low computational cost.
... The simulation properties outlined follows the prescribed method of setup conducted by Gagnon and Richard (2010) for the OpenFOAM implementation of the simpleFOAM 10 steady state algorithm. The simulation properties were tested against the Ahmed body (a simplified, standardised car body used in CFD testing) wind tunnel data. ...
... The Ahmed body model also has an angled front section which allows a defined comparison of lift and drag coefficients. The conclusion from Gagnon and Richard (2010) showed that the chosen simulations setup using the simpleFOAM algorithm had a 10 % difference from experimental wind tunnel testing data. Using this setup thus gave us initial accuracy levels within 10 % of experi-20 mental data from the in-situ wind speed measurements on the R/V Celtic Explorer as validated by the Gagnon and Richard (2010) simulations. ...
... This model is a two equation eddy viscosity model and is usable all the way down to the wall through the viscous sub layer. The model was used for its proven reliability in 20 separation zones, and its ability to blend a good free-stream model to a good boundary layer model (Gagnon and Richard, 2010). The outputted calculations from the simulations contain logs for U (velocity), P (pressure) and k. ...
Full-text available
Ocean-Atmosphere Fluxes Eddy correlation (EC) is the most direct method to measure fluxes of trace gases over the Earth's surface. In its simplest form, an EC setup consists of a gas sensor and a sonic anemometer. EC is commonly used on land, but its adaptation at sea has proven difficult because of the marine environment, the motion of the research platform (ship or buoy), and flow distortion. Flow distortion occurs when streamlines circumvent the research platform, which may lead to significant errors in the calculation of the gas transfer velocity. This paper uses computational fluid dynamics (CFD) to simulate the errors in wind speed measurements caused by flow distortion on the R/V Celtic Explorer. Numerical measurements were obtained from the finite volume CFD code OpenFOAM, which was used to simulate the velocity fields. This was done over a range of orientations in the test domain from -60° to +60°, in increments of 10°. The simulation was also set up for a range of velocities, ranging from 5 m s-1 to 25 m s-1 in increments of 0.5 m s-1 The numerical analysis showed close agreement to experimental measurements to within a 12% mean difference prediction of flow distortion effects. Other aspects resulting from flow distortion that were investigated using the CFD tools included development of a correction method for flow distortion effects for in situ wind speed measurements; analysis of ideal positioning of anemometers; vertical tilt orientation of the vessel to inflow; meteorological mast design; and mast instrumentation setups.
... These most important boundary conditions are described with a classical log-law wall function. This follows the prescribed method used by Gagnon and Richard (2010), for external airflow simulations over the Ahmed body test case. The time is non-dimensionalized by the uniform inlet velocity |U| and the largest cell size that will allow numerical stability in the direction of the velocity δx as δt = Co δx |U| . ...
Reynolds-averaged Navier–Stokes (RANS) and large eddy simulation (LES) are two schemes for modeling turbulent flows. Here they are compared for modeling flow distortion over the oceanographic research vessel R/V Knorr, which is important for correcting observations from sonic anemometers. Using the OpenFOAM RANS solver SimpleFOAM and the LES solver PisoFOAM, computations are compared with experimental data taken from various anemometer sites on-board the research vessel. The LES showed mean accuracy levels of ∼3% of the wind speed bias whereas the RANS simulations showed mean accuracies of ∼7%. A LES analysis of the wind speed vector pitch and yaw was also conducted. The dominant forcing was found to be the pitch, which gave a 7% increase to overall magnitude of the wind vector. It was also found that the pitch of the wind speed was the main component responsible for the horizontal flow distortions, found to be due to flow separation in the 10–20 range. We also use the LES simulations over a range of orientations from to , in increments of . The numerical analysis showed close agreement to experimental measurements with a 6% mean difference prediction due to flow distortion effects. We also explore two different methods to define a wave induced flow distortion correction and when finally added to the air-flow distortion correction, improved the overall accuracy of the models by 3%.
Full-text available
Improving vehicle design is essential for esthetic reasons and ensuring better efficiency and lower fuel consumption. The present study intends to provide a computational approach to an actual physical engineering problem: the aerodynamics of automobiles. The focus of this study was to use the open-source software OpenFOAM to study the aerodynamic effects on the external fairing of a Formula SAE vehicle. The vehicle used was the Z03 model of the ZEUS team of the Federal University of Lavras (UFLA). The team participates in university competitions of Formula SAE and, therefore, an aerodynamic improvement of the vehicle for the following versions can be fundamental for the team, increasing efficiency of the vehicle, resulting in a model of greater competitiveness. For analysis purposes, the drag and lift aerodynamic coefficients are analyzed. A procedure for performing aerodynamic simulations of automotive vehicles was systematized, and, in addition, satisfactory results were found for the presented simulation in comparison with results found in literature.
The three-dimensional flow field of a detailed road vehicle model with focus on the importance of engine and underbody representation is studied. Further, issues of vortical flows are explored. Especially the presence of wheels and a detailed underbody has a major impact on the developing flow field. The numerical data provides the necessary insight into the main flow features such as the dominant wake structure typical for a bluff body. URANS simulations accounting for the inherent unsteadiness of the flow were performed in OpenFOAM\(^{{\textregistered }}\) and were validated with experimental force and velocity field measurements using particle image velocimetry at a corresponding Reynolds number of 3 million. The results for the flow field showing a number of secondary effects interacting with the large areas of separated flow along and downstream of the model are discussed in detail. Another emphasis of the analysis is placed on the dependence of the wake structure on the characteristics of the underbody flow and the accuracy of the integral drag and lift coefficients. The study shows the particular importance of considering the impact of model simplifications on the global flow field of a road vehicle model.
Full-text available
The aim of the “Models for Vehicle Aerodynamics” (MOVA) Project is to develop, refine, and validate the latest generation of turbulence models for selected examples encountered in vehicle aerodynamics. The validation of turbulence models requires the availability of detailed experimental data. These quantitative data should cover the most critical flow regions around a bluff car-shaped body and they should give physical quantities that can directly be correlated to the results of numerical simulations. Such experimental data were measured in the LSTM low speed wind tunnel using a 2-component laser-Doppler anemometer (LDA) mounted on a traversing system and a simplified model of a car (Ahmed model). Measurements were made for two rear vehicle body slant angles (25° and 35°) at a bulk air velocity of 40 m/s. This paper serves as a synopsis of the major results of this experimental investigation.
Full-text available
An adaptive low-pass filtering procedure for the modeled turbulent length and time scales is derived and applied to Wilcox' original low reynolds number k-ω turbulence model. It is shown that the method is suitable for complex industrial unsteady flows in cases where full large eddy simulations (LESs) are unfeasible. During the simulation, the modeled length and time scales are compared to what can potentially be resolved by the computational grid and time step. If the modeled scales are larger than the resolvable scales, the resolvable scales will replace the modeled scales in the formulation of the eddy viscosity. The filtered k-ω; model is implemented in an in-house computational fluid dynamics (CFD) code, and numerical simulations have been made of strongly swirling flow through a sudden expansion. The new model surpasses the original model in predicting unsteady effects and producing accurate time-averaged results. It is shown to be superior to the wall-adpating local eddy-viscosity (WALE) model on the computational grids considered here, since the turbulence may not be sufficiently resolved for an accurate LES. Because of the adaptive formulation, the filtered k-ω model has the potential to be successfully used in any engineering case where an LES is unfeasible and a Reynolds (ensemble) averaged Navier-Stokes simulation is insufficient.
The features of the 29th Shell Eco-Marathon UK that was held at Rockingham Motor Racing Circuit, Northamptonshire, in early July 2005, are discussed. Over 50 teams from seven different countries took part to claim the title of the 'world's most fuel-efficient vehicle' and gain energy in the Guinness Book of World Records. Two hydrogen-powered vehicles took part in the event but due the complexities in comparing the fuel efficiency, their results were not included in the overall leader board. The record was set by one of the contestants from japan who achieved a fuel consumption figure of 11,195 miles per gallon using a special shell fuel.
This study presents a new near-wall treatment for low-Reynolds number (LRN) turbulence models that maintains accuracy in 'coarse' mesh predictions. The method is based on a thorough examination of approximations made when integrating the discretized equations in the near-wall region. A number of modifications are proposed that counteract errors introduced when an LRN-model is used on meshes for which the first interior node is located at y (+) approximate to 5. Here the methodology is applied to the k - omega turbulence model by Bredberg et al. [1], although similar corrections are relevant for all LRN models. The modified model gives asymptotically, in the sense of mesh refinement, identical results to the baseline model. For coarser meshes (y (+) less than or equal to 10), the present method improves numerical stability with less mesh-dependency than the non-modified model. Results are included for fully developed channel flow, a backward-facing step flow and heat transfer in a periodic rib-roughened channel.
Some salient features of the time averaged ground vehicle wake
  • S R Ahmed
  • G Ramm
  • G Faltin
S. R. Ahmed, G. Ramm, and G. Faltin. Some salient features of the time averaged ground vehicle wake. Technical Report TP840300, Society of Automotive Engineers, Warrendale, Pa., 1984.
Calcul de la résistance aérodynamique d'un véhicule muni de pièces en mouvement
  • L Gagnon
L. Gagnon. Calcul de la résistance aérodynamique d'un véhicule muni de pièces en mouvement. M.Sc. Thesis, Laval University, 2010.
Supermileage design report, SAE Collegiate Design Series. Unpublished Report
  • Alérion Supermileage
Alérion Supermileage. Supermileage design report, SAE Collegiate Design Series. Unpublished Report. 2008.