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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