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A Best-Practice for High Resolution Aerodynamic Simulation
around a Production Car Shape
Werner Seibert and Marco Lanfrit, Fluent Deutschland GmbH,
Darmstadt, Germany Burkhard Hupertz and Lothar Krger, Ford AG,
TASE, Cologne, Germany
SYNOPSIS
During the year 2001 the CFD-Subcommittee of the European
Automotive Data Exchange organisation conducted a benchmark study
to get a better understanding of CFD and its application within the
automotive industry, especially for the prediction of external
aerodynamics. Many suppliers of commercial codes participated and
contributed. Five different car shapes plus a modification of each,
either in geometry or in the boundary conditions were provided,
summing up to a total of ten cases. All of these cases had to be
prepared by the vendors free-of-charge and within a tight time
schedule. As a consequence the pure amount of work coming along
with limited resources did not allow to set-up and run all of the
simulations as thoroughly as desirable. Following the idea of the
EADE subcommittee to find out whether CFD can be used today for an
aerodynamic optimisation, and getting an assessment of its
capabilities and accuracy, one of the above car shapes was
investigated again and in more detail as a continuation of the
first benchmark loop.
The Ford Ka model was reviewed with the goal to create a more
elaborate, best-practice aerodynamics prediction using the
Navier-Stokes solver of the commercial code FLUENT 6. Based on the
identical CAD-files as used during the first loop of the benchmark,
new high-resolution hybrid meshes have been created for the base
geometry. The improvement in the accuracy of predicting drag
coefficients is shown, the influence of various turbulence models
(realisable k- and Reynolds Stress Model) is discussed as well. A
time-accurate simulation representing 2.5 seconds in physical time
was also performed and is documented. Recommendations for setting
up, for the necessary hardware environment and the handling of such
simulations are given. All results of the computations are
validated using the appropriate wind-tunnel data.
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1. SUMMARY OF CASES INVESTIGATED
A total number of 4 simulation runs have been performed for the
Ford Ka configuration, based on 2 mesh arrangements with different
resolutions. The geometry used for all cases is identical and is
taken from the data released for the initial EADE Aerodynamics
Benchmark in 2001, and its detailing is fairly close to the car
which can be seen out on the road. The description of the surfaces
was transferred using IGES format in a scale of 1:1. Exactly the
same CAD data has been used for the manufacturing of the 1:1
wind-tunnel model.
The model features a detailed, asymmetric underbody, wheels and
wheel wells, side mirrors, off-sets at the windshield and the side
windows. The intake areas for brakes and cooling air are
closed.
Common to all simulation runs are the boundary conditions,
prescribed in accordance with the wind-tunnel test arrangement. The
wheels are fixed and there is neither a moving ground nor boundary
layer suction. The velocity of the free stream is 140 km/h
approaching the car body at 0 degrees of yaw.
Mesh Resolution and Cell Count With regard to the meshes, two
different cases were used for the computations. The first or
initial mesh was created during the first loop of the benchmark and
will be referred to as the coarse mesh. A second one with higher
resolution both in surface and volume mesh was prepared for the
present follow-up investigation. It will be referred here as the
fine mesh. In both cases the available hardware to run subsequent
computing jobs actually set the limitations.
The coarse mesh should be regarded as a minimum or entry-level
in resolution, suitable to get iterated to convergence with 2-4
processors of ordinary workstations. The fine mesh needs several
clustered workstations or some shared memory platform, a total
number of 8-16 processors is recommended to achieve solutions
within timeframes acceptable for engineers in the automotive
industry. Both numbers given are valid for steady-state solutions.
The hardware prerequisites for time-accurate computations are
discussed within a separate chapter, although the mesh used is
identical to the fine case.
It should be mentioned in this context, that the fine mesh shown
under no circumstances means an upper limit to the present
approach, instead it reaches just
Fig. 2: Underbody of the present configuration
Fig. 1: Surface geometry of the present configuration
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about one half of the total cell count which is typically used
today for leading-edge, high-tech simulations, e.g. for the
development of racing cars.
The following table lists some characteristics of the two mesh
set-ups used for all the computations which are discussed here.
Mesh adaption was applied only in the coarse mesh case, the fine
mesh case did not need any further modification.
coarse mesh fine mesh typical element length at car body 10 - 20
mm 2 - 10 mm # of surface elements at car (triangles) 326 K 760 K #
of near wall prismatic layers 5 5 initial # of volume cells (prisms
+ tetrahedra) 3.5 M 11.0 M final # of volume cells after adaption
5.5 M 11.0 M
The implication of lowering the typical element length at the
cars surface becomes obvious, if two snapshots of the resulting
surface mesh at the rear-view mirror and the surrounding area are
compared.
Best-Practice Meshing for Simulation of Vehicle Aerodynamics A
high-quality, non-uniform surface mesh resolving all radii well
built the basis for the fine mesh case. A reasonable resolution of
the boundary layers was ensured by the extrusion of 5 prismatic
near wall layers from the upper parts of the car bodys surface
mesh. The aspect ratio (element length to element height) is
typically 5, a growth rate of 1.2 is recommended and was matched
during the creation of the subsequent layers, located on top of
each other. These rules lead to a smooth transition in the growing
volume size not just for the prismatic layers, but also for the
adjoining tetrahedral elements, surrounding the near wall mesh.
Checks of the y+ values during the following computations showed,
that for both the coarse and the fine mesh the appropriate values
are well within the recommended and valid range, below 300 for the
coarse mesh and below 160 for the fine mesh. The prism layers are
extruded on the upper side of the car, comprising: roof, side,
back, engine hood and windscreen, thus covering all of the upper
car.
Fig. 3: Table of meshing characteristics
Fig. 4 Typical resolution of the surface by coarse and fine mesh
case Fig. 5
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Another set of prism layers is located on the floor of the
wind-tunnel. The complex geometry of the underbody with all its
cavities and a small region close to the foot-print of the wheels
(surfaces are intersecting at very small angles) are meshed with
tetrahedra only. As a consequence there are some exposed
rectangular side faces of the layers, where a transition to
triangular elements filling the remaining parts of the
computational domain has to be done. Best practice is to duplicate
these side faces and re-mesh the copy with tri-elements before the
final filling with tets. Handling of the two different mesh types
adjacent to each other is done by the solvers arbitrary interface
feature.
For a better local control of the volumetric mesh density within
the cuboid representing the walls of the wind-tunnel another box
was defined. This artifice allows one to concentrate most of the
volume cells within the near-body and wake area, where high
gradients of the flow velocities are expected. No cells must be
wasted within the far-field towards the outer boundaries of the
domain.
Fig. 6: Exposed rectangular side faces at an edge of the
prismatic layers
Fig. 7: Re-triangulated mesh for transition to tetrahedral
volume cells
Fig. 8: Centre plane cut through coarse volume mesh
Fig. 9: Centre plane cut through fine volume mesh
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2. SUMMARY OF THE STEADY-STATE RESULTS
With respect to the aerodynamic coefficients, the integral
results of the steady-state computations are listed in a table and
compared to the values received from a wind-tunnel experiment. Case
1 was computed on a simple workstation cluster, comprising 4
processors, so some overhead time caused by the network is included
in the shown total time. Cases 2 and 3 ran on shared memory
machines, where 16 and 32 processors were used respectively.
Nevertheless for giving just an idea of what hardware resources are
needed, the computing hours were simply multiplied with the number
of used processors and are shown here as CPU hrs.
case mesh size & turbulence model cD cD CPU hrs 0
wind-tunnel experiment 0.321 - - 1 coarse mesh (5.5 M cells)
realizable k- 0.336 4.7 % 450 2 fine mesh (11 M cells) realizable
k- 0.328 2.1 % 750 3 fine mesh (11 M cells) RSM 0.322 0.3 %
1200
Now its clearly visible, that the initial, coarse mesh case
which was supplied to the EADE benchmark does not fulfil the
accuracy standard that typically is expected by a thorough
simulation setup. Although in cases where classical three-box-type
cars (sedan shape) are investigated, mesh sizes of 5 -6 M cells are
sufficient to deliver a drag prediction of about 3% accuracy. This
corresponds to the results achieved during the Benchmark when
looking at the other cases investigated [1].
But running a simulation for a compact hatchback car as the Ford
Ka, featuring a characteristic separation area which is typically
greater than one half of the reference area, a standard approach no
longer leads to satisfying results. Raising the total cell count
(by a factor of 2 for the present case) and making sure that the
higher resolution is not only concentrated close to the body, but
covers the wake and all other potential separation regions (aft of
the tyres and rear-view mirrors) as well, will again lead to an
acceptable accuracy. With such a high-resolution mesh there is only
one question left: how much CPU-time can be afforded. Choosing the
realisable k- turbulence model, is the fastest, straightforward
approach, usually is leading to an accuracy in drag-prediction
better than 3%. A solution with RSM typically needs a somewhat
longer computing time (factor is approx. 1.6), it is more demanding
with respect to the quality of the mesh (low skewness), but is able
to deliver a prediction in drag which is well within the tolerance
of an experiment (0.3% difference in the present case). The basic
approach of creating a hybrid mesh with near wall prismatic layers
and tetrahedra for all other parts of the computational domain,
remains the same when such a high-accuracy solution is
targeted.
A comparison of the pressure coefficients plotted along the
centreline within the mid plane of the car (Fig.11) illustrates
some of the improvement when switching from the coarse to the fine
mesh and on the fine mesh, from the realisable k- to the RSM
turbulence model. Most notably, the peak pressure located at the
foot of the windshield is now captured much better by the
high-resolution simulations.
Fig. 10: Table of drag coefficients and computing time spent
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The comparison of the wake pictures created within a plane
x=const. at 100 mm behind the rear end of the car shows also some
remarkable changes. But before discussing these, the circumstances
under which such pictures are created, should be explored a bit.
The measured total pressure of the experiment is by nature
time-averaged and represents more or less the silhouette of the
car, although not being completely symmetric as would be expected,
at least within the upper part (Fig. 12). A comparable plot based
on the computed results of case 1 (Fig. 13) looks also roughly
symmetric. For a steady-state solution on a coarse mesh, the
numerical diffusion is relatively high, which leads to some
averaging effect in the computation as well. Unfortunately this is
not necessarily a time-averaging. Time-dependencies within a flow
field typically create a slightly unstable solution, this usually
may be observed by looking at the residuals. Although integral
values, such as the drag coefficient, may become stable and look
converged, local values within the flow-field might still be
subject to changes during any further iteration steps. The
steady-state approach is strictly speaking applicable only to
time-independent flows.
In cases, where there are transient effects maltreated by
running a steady-state solution procedure, the post-processing for
a specific iteration shows flow conditions belonging to some
non-physical time. It is simply a snapshot of the variables at an
instant. This effect, which might easily lead to misinterpretation
or at least become a matter of discussion during the validation of
computational results, becomes even more obvious, when a
high-resolution simulation is investigated in detail.
Fig. 12: Experiment Fig. 13: Case 1 Fig. 14: Case 3 Total
pressure in wake plane behind the car vs. simulation assuming
steady-state!
Fig. 11:Pressure coefficient
along centreline
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A plot of the total pressure wake contours delivered by the
high-resolution RSM case (Fig.14) shows an extremely asymmetric
shape. But being aware of the restrictions with respect to the
applicability of a quasi steady-state simulation to a highly
time-dependant flow field, should prevent one from spending time
finding reasons for all the details of such a picture. Indeed this
is nothing more than a snapshot of the wake contours at some point
of the solution process. It may look completely different when
investigated at another stage of the iteration process. What this
picture does show is, that the increased density of the mesh yields
a much better rendering of the vortices created by the A-pillar and
the rear-view mirror. But for a valid assessment of such wake
pictures and its details created by time-dependant flow, a
transient simulation providing time-accuracy seems to be
indispensable.
3. TRANSIENT SIMULATION
The above steady-state simulations were solved far beyond the
usually sufficient number of 2000-3000 iterations, but although the
residuals reduced quite well and led to the results listed, they
did not completely stabilise and showed some remaining random
oscillatory behaviour. By looking into the flow field and isolating
those volume cells having high mass imbalance values, the areas
where the flow is time-dependant can be located. Apparently it is
mainly in the wake region where there is a noticeable imbalance,
and to a lesser extent behind the rear-view mirrors and aft of the
front tyres.
Actually this is not surprising, as the flow around vehicles is
nearly always transient in nature. But with regard to the highly
compact shape of this vehicle, leading to a large and unstable
separation area in the rear, this car seemed to be an especially
interesting and challenging case for further investigations by a
time-dependent simulation. Such a computation should at least help
to understand the problem with the deformed wake-contours as
described above. It could also show a possible dependency between
the transient phenomena and the aerodynamic coefficients.
Furthermore it could also give some insight into the topology of
the detached flow and maybe help to understand its mechanisms. It
would become indispensable in cases where aeroacoustic effects are
the main subject of a simulation [2].
On checking the values of effective viscosity in the wake region
of the steady-state solutions (these are used to close the RANS
equations), we should not be surprised to see a fully turbulent
vortex street. When looking at the ideal shape of a 2D cylinder and
using this generic shape as a reference, we may expect a Strouhal
Number of roughly 0.25, which yields a frequency of approximately 7
Hz (period 0.14 sec).
Fig. 15: Marked cells with high mass imbalance (coarse mesh,
case 1)
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The recommended minimum approach is to perform at least 30
time-steps per period, assuming the above frequency this leads to a
resolution in time of 0.005 seconds. Furthermore a total number of
at least 10 periods should be treated. Thus a physical time frame
of roughly 1.5 seconds ought to be considered. Within each
time-step about 20 iterations will be necessary, this finally
yields to a total number of approximately 6000 iterations.
As a Case 4 a transient simulation was initiated, running the
same numerical model setup as the steady-state fine mesh cases, but
now using global time-stepping. Following the considerations above,
a total physical time of 2.5 seconds was treated, allowing the
flow-field to convert from the quasi steady-state, initial solution
to a fully time-dependent and -accurate state. Roughly 9 days have
been spent on 32 processors of an SGI Origin, which is about 7000
CPU hrs.
Fig. 16: Clipping of the drag history during transient
simulation
Monitoring the drag coefficient during the solution iteration,
does not show a proper periodicity as known from the regular vortex
street behind a cylinder. Instead it varies within a range of about
+/- 3% with respect to the steady-state value (Fig.16). But
processing the received data sequence by a Fourier analysis leads
to a frequency of 6.8 Hertz, which is veryclose to the assumption
made before starting the run.
Fig. 17:Sequence of transient velocity contours aft of
the car
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The size and the location of the rear separation area notably
vary in time. A more in-depth investigation shows, that there are
several effects contributing and superimposing to give the final,
observed behaviour.
The velocity contours in the rear shown as a sequence (Fig.17)
and the wake pictures (Fig.18 and Fig. 19) can convey only a weak
impression of the actual interaction of various flow phenomena.
Vortices created at the front wheels, the cowl, the rear-view
mirrors and the A-pillar are all travelling downstream, combining
and influencing the wake pulsation.
Looking at the time-dependant variation of the wake contours
(Fig.19) it becomes obvious, that its hard to compare such
snapshots with an averaged plot based on the wind-tunnel
measurements (Fig.12). The observable deviation actually becomes
even larger, when a more accurate CFD-solution is used for such a
comparison. Hence the creation of animations is strongly
recommended for the post-processing of transient simulations. They
are helpful to understand the interaction and the dependencies of
the participating flow phenomena. They may help as well to explore
the underlying mechanisms.
Fig. 18: Velocity contours within a horizontal plane located at
the mirror height
Fig. 19: Sequence of time-dependant wake contours within a plane
behind the car
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For a validation of transient results against time-averaged
wind-tunnel data it is necessary to take care of some sampling of
data during the simulation runs. Once the computation is done, such
a data-base can be processed to create time-averaged
post-processing.
And only at the end of such a process can, for example, contour
pictures of the wake be compared to those created from the
measured, averaged values. Although FLUENT 6 provides such
functionality [3], unfortunately it was not activated at the right
time in this case (lessons learned ).
4. CONCLUSIONS
During the EADE Benchmark in 2001 an aerodynamic simulation of
the Ford Ka was created by Fluent based on a 5.5M cell hybrid mesh.
Unfortunately the computed drag coefficient showed a deviation of
4.7% versus the windtunnel-measurement and did not fall within the
expected range of accuracy that typically is achieved when a
comparable approach is applied to a notchback car. By the
preparation of a high-resolution mesh with 11M cells now and
re-computing the case with the same turbulence model as before
(realisable k-), it was possible to increase the accuracy in
predicting the coefficient of drag to 2.1%. This deviation was
further reduced to 0.3% by switching to the Reynolds Stress Model.
Although the compact shape of the investigated Ford Ka production
car leads to a large separation area in the back, these measures
yield a substantial improvement in calculating the integral
coefficients without taking the time-dependencies into account.
Attention has to be paid during the validation of such results,
especially when comparing variables close to or within the wake.
The wind-tunnel data available for the present case is
time-averaged and must not be compared to post processing at one
instance of a simulation run. To investigate the behaviour of the
separation area in a more in-depth way, an additional transient
simulation has been run and documented, mainly by creating
animations. These may demonstrate the capabilities of the present
CFD-method and its potential to assist the aerodynamicist in
getting a better understanding of reasons for and mechanisms of
flow separation for given vehicle shapes.
(Special thanks go to Dale Eckart of Ford in Dearborn for
providing the hardware resources to run the transient simulation
and the assistance in creating the animation of the results.)
5. REFERENCES [1] Kerschbaum H., Bartelheimer W. (Editors) EADE
CFD Benchmark Report, Munich, September 2001 [2] Sovani S.,
Hendriana D.
Predicting Passenger Car Window Buffeting with Transient
External Aerodynamics Simulations 10th Conference of the CFD
Society of Canada, Windsor, June 2002
[3] FLUENT 6 Users Manual Fluent Inc., Lebanon NH, 2001