Application of Detached–Eddy Simulation for Automotive ... · PDF fileSAE 2009-01-0333...

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SAE 2009-01-0333 Application of Detached–Eddy Simulation for Automotive Aerodynamics Development M. Islam, F. Decker Audi AG, Wind–Tunnel Centre, 85045 Ingolstadt, Germany E. de Villiers, A. Jackson, J. Gines ICON Ltd., Rofel House, Colet Gardens, London, W14 9DH, United Kingdom / www.iconCFD.com T. Grahs, A. Gitt–Gehrke 1 Volkswagen AG, Letterbox 1697, 38436 Wolfsburg, Germany 1 Volkswagen AG, Letterbox 7359, 38231 Salzgitter, Germany J. Comas i Font SEAT S.A., Centro Tecnico, Dept. EK-41, 08760 Martorell, Spain Copyright c 2009 SAE International ABSTRACT This paper presents a complete methodology for performing finite–volume–based detached–eddy sim- ulation for the prediction of aerodynamic forces and detailed flow structures of passenger vehi- cles developed using the open–source CFD toolbox OpenFOAM R . The main components of the method- ology consist of an automatic mesh generator, a setup and initialisation utility, a DES flow solver and analysis and post–processing routines. Validation of the predictions is done on the basis of detailed comparisons to experimental wind–tunnel data. Results for lift and drag are found to compare favourably to the experiments, with some moderate discrepancies in predicted rear lift. Point surface– pressure measurements, oil–streak images and maps of total pressure in the flow field demonstrate the ap- proach’s capabilities to predict the fine detail of com- plex flow regimes found in automotive aerodynamics. Standard DES methods can cost an order of magni- tude more than traditional methods, but optimisation and automation of mesh generation, setup and solu- tion algorithms ensure quick turn–around times. Due to the fully parallel nature of these components, the entire process can be executed in a distributed fash- ion. Efficient solution algorithms provide exceptional accuracy when compared to Reynolds–averaged ap- proaches without sacrificing stability, even when the flow exhibits high Courant numbers. The proposed methodology is highly customisable, which allows for targeted developments to suit the in- dividual needs of aerodynamics CFD. On the basis of the results presented here, the methodology is found to be appropriate and suitable for use in the industrial development process. INTRODUCTION The use of numerical simulations to predict the aerodynamic characteristics of road vehicles is now a standard practice in automotive development [1]. The current state–of–the–art makes use of ei- ther finite–volume solvers based on the Reynolds– averaged Navier–Stokes (RANS) equations or lattice– Boltzmann solvers, both in the context of commercial, proprietary computational fluid dynamics (CFD) soft- ware packages. Recent developments in the field of automotive aerodynamics have generated the need for accelerated development of the application of CFD therein. First, the steady increase in the number of different vehicle models brought to market has not been matched by a commensurate increase in wind– tunnel capacity, necessitating the use of alternatives to experimental testing, preferrably CFD. Second, the continual improvement of vehicle aerodynamics, both in terms of drag coefficient as well as lift, requires the tools of aerodynamics development to perform at ever–increasing levels of accuracy; this applies to both wind–tunnel technology and CFD. Third, CFD methods must be able to keep pace with continu- ally shortening development cycles, placing continu- ally increasing demands on computational efficiency and robustness. Fourth, these increasing demands require the CFD software to be specifically tailored to the needs of the application, and therefore to contain considerable know–how derived from the application, as well as to be usable flexibly on a large scale. In the present paper, we present a complete method- ology for carrying out automotive aerodynamics CFD that addresses precisely these issues. The method- ology is based on the open–source CFD toolbox OpenFOAM R [2] and is applied in an industrial con- text to a wide range of vehicles from the brands of the Volkswagen Group Audi, Volkswagen and SEAT. 1

Transcript of Application of Detached–Eddy Simulation for Automotive ... · PDF fileSAE 2009-01-0333...

SAE 2009-01-0333

Application of Detached–Eddy Simulation for AutomotiveAerodynamics Development

M. Islam, F. DeckerAudi AG, Wind–Tunnel Centre, 85045 Ingolstadt, Germany

E. de Villiers, A. Jackson, J. GinesICON Ltd., Rofel House, Colet Gardens, London, W14 9DH, United Kingdom / www.iconCFD.com

T. Grahs, A. Gitt–Gehrke1

Volkswagen AG, Letterbox 1697, 38436 Wolfsburg, Germany1Volkswagen AG, Letterbox 7359, 38231 Salzgitter, Germany

J. Comas i FontSEAT S.A., Centro Tecnico, Dept. EK-41, 08760 Martorell, Spain

Copyright c© 2009 SAE International

ABSTRACT

This paper presents a complete methodology forperforming finite–volume–based detached–eddy sim-ulation for the prediction of aerodynamic forcesand detailed flow structures of passenger vehi-cles developed using the open–source CFD toolboxOpenFOAM R©. The main components of the method-ology consist of an automatic mesh generator, a setupand initialisation utility, a DES flow solver and analysisand post–processing routines.

Validation of the predictions is done on the basisof detailed comparisons to experimental wind–tunneldata. Results for lift and drag are found to comparefavourably to the experiments, with some moderatediscrepancies in predicted rear lift. Point surface–pressure measurements, oil–streak images and mapsof total pressure in the flow field demonstrate the ap-proach’s capabilities to predict the fine detail of com-plex flow regimes found in automotive aerodynamics.

Standard DES methods can cost an order of magni-tude more than traditional methods, but optimisationand automation of mesh generation, setup and solu-tion algorithms ensure quick turn–around times. Dueto the fully parallel nature of these components, theentire process can be executed in a distributed fash-ion. Efficient solution algorithms provide exceptionalaccuracy when compared to Reynolds–averaged ap-proaches without sacrificing stability, even when theflow exhibits high Courant numbers.

The proposed methodology is highly customisable,which allows for targeted developments to suit the in-dividual needs of aerodynamics CFD. On the basis ofthe results presented here, the methodology is foundto be appropriate and suitable for use in the industrialdevelopment process.

INTRODUCTION

The use of numerical simulations to predict theaerodynamic characteristics of road vehicles is nowa standard practice in automotive development [1].The current state–of–the–art makes use of ei-ther finite–volume solvers based on the Reynolds–averaged Navier–Stokes (RANS) equations or lattice–Boltzmann solvers, both in the context of commercial,proprietary computational fluid dynamics (CFD) soft-ware packages. Recent developments in the field ofautomotive aerodynamics have generated the needfor accelerated development of the application of CFDtherein. First, the steady increase in the number ofdifferent vehicle models brought to market has notbeen matched by a commensurate increase in wind–tunnel capacity, necessitating the use of alternativesto experimental testing, preferrably CFD. Second, thecontinual improvement of vehicle aerodynamics, bothin terms of drag coefficient as well as lift, requiresthe tools of aerodynamics development to performat ever–increasing levels of accuracy; this applies toboth wind–tunnel technology and CFD. Third, CFDmethods must be able to keep pace with continu-ally shortening development cycles, placing continu-ally increasing demands on computational efficiencyand robustness. Fourth, these increasing demandsrequire the CFD software to be specifically tailored tothe needs of the application, and therefore to containconsiderable know–how derived from the application,as well as to be usable flexibly on a large scale.

In the present paper, we present a complete method-ology for carrying out automotive aerodynamics CFDthat addresses precisely these issues. The method-ology is based on the open–source CFD toolboxOpenFOAM R© [2] and is applied in an industrial con-text to a wide range of vehicles from the brands ofthe Volkswagen Group Audi, Volkswagen and SEAT.

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High numerical accuracy is achieved by applyingdetached–eddy simulations, as opposed to simula-tions based on the RANS or lattice–Boltzmann equa-tions, which, in an industrial context, use k-ε or simi-lar models for the integral length scales of turbulence.DES produces a much more accurate and detailedrepresentation of the flow when compared to tradi-tional simulation methods. Calculation costs are how-ever significantly higher, such that the principal chal-lenge in making such an approach viable is enhancingthe efficiency of the solution process. Evidence indi-cates that simulations using RANS equations with k-εturbulence modelling and steady–state solution algo-rithms can fail to capture all time and length scalesimportant to vehicle aerodynamics [3]. Rapid turn–around times are achieved by full parallelisation of thecomplete simulation process, including mesh genera-tion.

The method and results presented here form a sum-mary of a focused, multi–year effort to develop andvalidate this particular technology, in which over 150CFD simulations of vehicle aerodynamics were car-ried out on a palette of more than 20 different vehi-cles in order to optimise accuracy, performance androbustness.

The paper is structured as follows: In the next section,we present the numerical method used here, which isbased on the finite–volume method for CFD. Subse-quently, the method by which the computational meshis generated is presented and discussed. The follow-ing section comprises an extensive validation study,in which the numerical simulations are compared toexperimental data obtained in automotive wind tun-nels used by the group. On the basis of these results,an assessment of the methodology presented hereis made, followed by a discussion of intended futurework, a summary and some general conclusions.

NUMERICAL METHOD

The basis of large–eddy simulation (LES) is that thelarge scales of motion, which contain most of the en-ergy, do most of the transporting and are affected thestrongest by the boundary conditions are calculateddirectly, while the small scales are represented by amodel. In finite–volume practice, this separation ofscales is achieved by applying a spatial averaging fil-ter to the Navier–Stokes equations [4],

∇·u = 0 (1)∂u

∂t+∇·uu = −

1

ρ∇p+∇·ν(∇u+∇u

T ) + τ (2)

where u and p represent the filtered velocity and pres-sure, respectively, and τ is the sub–grid scale (SGS)stress that results from the filtering of non-linear termsand has to be modelled. The SGS stresses representa much smaller part of the turbulent energy spectrumthan the RANS turbulent energy, so that the accuracyof the stress model may be less critical to the accu-

racy of the overall solution than in RANS computa-tions.

For LES to be considered accurate, some higly lim-iting restrictions have to be adhered to with respectto the resolution of the mesh near solid boundaries.Specifically, the near–wall resolution must be of theorder of y+ = 1 with other dimensions similarly small.These restrictions make LES impractical on aero-dynamic geometries due to excessively large meshsizes required. The detached–eddy simulation (DES)approach largely circumvents this problem by sacri-ficing some of LES’ inherent accuracy in the near–wall region. DES refers to an approach whereby un-steady RANS turbulence modelling and mesh spac-ing is used in the boundary layer, while LES is em-ployed in the core and separated regions of the flow.In the near–wall regions, the RANS turbulence model,which has been calibrated in thin shear–layer flows,has complete control over the solution. In the LES re-gion, the turbulence model changes to an SGS formu-lation. DES can be considered a good aproximation,as long as the scale of the eddies in the boundarylayer is much smaller than the eddies in the bulk flow.This situation is almost always the case for externalaerodynamic flows.

For the the current investigation, the DES formula-tion proposed by Spalart is used [5]. The model isbased on the Spalart–Allmaras (S–A) one–equationeddy–viscosity model [6] normally used in RANS cal-culations. To accomplish the transition from near–wallRANS–based simulation to LES treatment of the inte-rior flow in one formulation, the near–wall distance yw

is replaced by d, defined as

d = min (yw, CDES∆) , (3)

which acts as the S–A RANS model for yw ¿ ∆and a SGS model for ∆ ¿ yw. CDES is an empir-ical constant calibrated to a value of 0.65 using theknown decay rate of isotropic turbulence [7]. The cur-rent investigation uses a version of the standard S–A DES model that has been modified to allow for itsuse in conjunction with wall functions and polyhedralmeshes [8]. Here, ∆ is defined as the cube root of thecell volume, not the maximum cell dimension moretraditionally used.

To minimise numerical dissipation, which can easilybe more diffusive than the SGS model, second–orderaccurate energy–conserving numerical schemes areused [9, 10]:

• fully implicit backward differencing in time (Gear’smethod);

• non–oscillatory minimally blended central–differencing scheme for momentum convection;

• a second–order TVD/NVD scheme for SGS vis-cosity convection;

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• explicit non–orthgonality correction.

To maintain overall stability and efficiency, an addi-tion provision has been added to reduce the order ofaccuracy locally in regions of high Courant number.The local blending mechanism blends first–order up-wind differencing with the central schemes used forthe momentum convection to increase stability in re-gions where small cell size or poor grid quality mightnormally lead to instability. In this way, stability of thesolution is significantly increased without an apprecia-ble reduction in overall accuracy.

MESH GENERATION

With the requirement for fast prototyping of complexgeometries, the automatic generation of high–qualitymeshes has become a critical factor in the CFD de-sign process. Traditional manual/sequential meshgeneration can create severe bottlenecks in the CFDsimulation process. For this reason, a new automaticparallel mesh generation capability has been devel-oped using the functionality available in the Open-FOAM toolbox. The key features of the new mesh–generation tool are:

• mesh generation in parallel;

• fully automatic operation;

• generation of hexahedral and split–hexahedralelements with an overall body–fitted structure;

• local patch–wise surface (including curvature) re-finement and volume refinement away from thesurface;

• surface–layer mesh generation on a patch–wisebasis;

• surface features in the geometry automaticallypreserved in the mesh;

• a guarantee that the generated mesh satisfiesuser–defined mesh quality checks;

• no principal requirement to perform any cleaningup of CAD surface data;

• developed using the open–source toolbox Open-FOAM.

The mesh–generation algorithm has been designedto keep any user interaction in the CFD process to aminimum through the use of intelligent algorithms andoptimised parameter defaults. It is possible with thesenewly developed tools to go directly from CAD to amesh with tens of millions of cells in hours rather thandays (a typical 30 million cell mesh can be generatedin under 1 hour on 64 processors).

In order to achieve accurate and robust flow solutions,it is essential that the mesh being generated can sat-isfy a set of mesh quality checks. At all stages inthe mesh–generation process, face– and cell–basedmesh quality is monitored to ensure that the finalmesh that is generated satisfies a set of user–definedcell– and face–based quality criteria. Currently, themesh–quality checks that are monitored during thegeneration phase are orthogonality, face pyramid vol-umes, face areas, face skewness, face interpolationweights, cell volume ratio, face twist and cell deter-minant. If at any stage in the process mesh qualitycannot be guaranteed, the mesh reverts back locallyto a previously valid error–free mesh. In the follow-ing sub–sections, a more detailed description of themesh–generation procedure is presented.

STAGE 1: CASTELLATED MESH GENERATIONInitially, a Cartesian base mesh with cells of near unitaspect ratio is generated. The mesh extends through-out the entire solution domain. This base mesh is nowrefined based on user defined patch–wise surface–refinement levels. The refinement engine that is usedis based on a fast octree surface intersection check-ing routine. Figure 1 shows details of how an initial

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Figure 1: Initial surface refinement stage

base mesh (with a refinement level of 0 everywhere)is refined in the neighbourhood of a surface which re-quires a user defined refinement level of 2. Additionalsurface refinement can also be performed based onthe local surface curvature.

As well as surface refinement, volume–refinementstrategies are used to refine the mesh away from thesurface, where mesh resolution is required e.g. wakeregions.

Once the refinement phase is complete, an intersec-tion check is done to determine which parts of themesh should be discarded. This is accomplished byfirst determining if there is a surface between neigh-bouring cell centres using an octree–based search. Ifa surface is detected, the mesh between the neigh-bouring cells is locally decoupled. As a final stagea topological walk is performed to agglomerate allconnected elements with the remainder being deletedfrom the mesh.

An example of the type of intermediate castellatedsurface mesh is shown in Figure 2, using an Audi A6

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as a test case, which will be the focus of extensive re-sults presented in this paper. The different coloursshow the parallel surface mesh deomposition for amesh generated on 8 processors.

Figure 2: Visualisation of castellated surface meshfor Audi A6 test case

STAGE 2: BOUNDARY–RECOVERED MESH Inthe second stage of the mesh–generation process,the surface geometry is recovered in the CFD mesh.The surface faces of the castellated mesh, generatedat the end of stage 1, are moved (snapped) to the sur-face. This is achieved by constraining the faces to beplanar and iteratively projecting them onto the surfaceusing a technique to preserve the underlying surfacefeature edges in the reconstructed surface mesh. Fig-ure 3 shows a basic schematic of how the boundaryfaces are projected onto the underlying surface.

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Figure 3: Schematic illustration of projecting facesto surface during boundary recovery

As an additional step, at the end of this boundary–recovery stage, co–planar boundary faces from thesame cell are merged, provided this leads to an im-provement in the overall mesh quality. The result-ing surface mesh generated after these snapping andmerging operations is shown in Figures 4 and 5 on theAudi A6 test case. At every stage during the mesh–generation process cell– and face–based mesh qual-ity are monitored; if a step leads to mesh elementsthat do not satisfy some user–defined quality criteria,

the mesh is locally moved back to a previously gener-ated valid state.

Figure 4: Original CAD surface and resulting sur-face mesh for Audi A6 test case

Figure 5: Original CAD surface and resulting sur-face mesh of vehicle underbody for AudiA6 test case

STAGE 3: BOUNDARY–LAYER ADDITION Withthe need for improved viscous–flow modelling, an op-tional final stage in the mesh generation process is toadd layers of cells next to the surface. This can beperformed on a patch–wise basis. The base mesh,generated after stage 2, is projected off the surfaceand a layer of cells is generated in the void that iscreated. As in the previous stages of the mesh–generation process, if layer addition results in viola-tion of any of the mesh quality criteria, surface layersare not generated in this region.

Figure 6 shows the mesh on processor boundariesat the rear of the Audi A6 test case. This shows thesurface layers that have been generated in this region.The layer mesh is terminated at concave and convex

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Figure 6: Finite–volume mesh on processor bound-aries, showing surface layers generatedon rear of an Audi A6

edges if the resulting mesh quality in the layer meshcannot be maintained around these edges.

An overview of the final finite–volume mesh that hasbeen generated on the Audi A6 case is shown in Fig-ure 7. This shows the refinement of the mesh in theinterior cells away from surface which is the resultof the volume–refinement strategy employed duringstage 1.

Figure 7: Visualisation of finite–volume mesh of anAudi A6

VALIDATION

The validation of the simulation methodology is basedon data obtained from wind–tunnel experiments of theaerodynamics of a wide range of vehicles producedby the Volkswagen Group. The data are obtainedfrom measurements carried out in the Audi aeroa-coustic wind–tunnel and the Volkswagen climatic windtunnel. Here, we present detailed validation resultsfor a generic vehicle model and a production vehicle,followed by an overview of some of the results ob-tained for a number of other vehicles with widely dif-fering shapes, including compact hatchbacks, sportscoupes, saloons and super–sports cars. This verywide range of validation cases is chosen as a testof the general applicability and robustness of themethodology, an essential feature for use in the ac-

tual vehicle–development process.

The computational meshes are generated using trian-gulated CAD geometries prepared to yield water–tightclosed surfaces. The computational domain is sim-ply a large rectangular box of sufficient dimensions toavoid any blockage effects or interference of the walls.The floor of the domain is treated with a combinationof slip and no–slip wall boundary conditions: The no–slip wall begins at a position upstream of the vehiclecorresponding to the distance required to generatethe experimentally determined boundary–layer thick-ness on the basis of the 1/7th–power law. The roofand sides of the domain are given symmetry–planeboundary conditions, the inlet a fixed–value bound-ary condition for velocity and SGS viscosity, and theoutlet a standard fixed–pressure boundary condition.In the work reported here, the CFD simulations aretypically run for a total physical time of around 2.5seconds in order to flush any start–up transients outof the domain and to allow the flow field to reach aquasi–steady state. The flow field is initialised with apotential–flow solution.

VOLKSWAGEN RED–MODEL VALIDATION CASEA wealth of experimental data have been collectedfor a generic vehicle model — referred to as the“Red” model due to its colour — used at Volkswagenfor wind–tunnel calibration and CFD validiation, andshown in Fig. 8. Due to its geometric simplicity but

Figure 8: Volkswagen Red model

the simultaneous complexity of its aerodynamics, thismodel lends itself well to the validiation study under-taken here. In particular, the rounded tail end of thevehicle presents a significant challenge to CFD due tothe pressure–gradient induced separation and vortexgeneration that occurs there. The experimental dataare obtained from measurements carried out in theVolkswagen climatic wind tunnel. The CFD data areobtained from a simulation done on a mesh with ap-proximately 26 million cells and run for a total of 2.5seconds physical time; the flow–field data reportedbelow are obtained from a time–average of the so-lution over the last 0.25 seconds of the run.

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cD [-] cLf [-] cLr [-]Experiment 0.249 -0.052 0.128Simulation 0.265 -0.048 0.118

Table 1: Comparison of predicted and measuredaerodynamic coefficients for VolkswagenRed–model test case

The most fundamental set of data for the validationexercise is the aerodynamic coefficients, shown forthe simulation and experiment in Table 1. On thewhole, the accuracy of the predicted force coefficientscan be seen to be very good. The predicted drag co-efficient cD deviates from the experimental value byan overprediction of 6.4% or 16 counts. Prediction offront–lift coefficient cLf

is excellent, with an error ofonly 2 counts. Considering the difficulty of accuratelypredicting the flow over the rear upper surface of thevehicle, the underprediction of rear–lift coefficient cLr

by 10 counts or 7.8% is also a very good result.

Integral values of the aerodynamic force coefficientsare important overall measures of the accuracy of theflow predictions, but can in practice be misleading dueto cancellation of errors. For this reason, it is im-portant to consider also the flow structures predictedby the simulation. First, a comparison of the static–pressure coefficients, cp, on the vehicle surface is in-formative. cp is defined by

cp =p− p∞1

2ρ∞U∞

, (4)

where p is the static pressure, p∞ is the free–streamstatic pressure, ρ∞ is the free–stream density and U∞is the free–stream velocity. This comparison is shown

Figure 9: Comparison of experimental and pre-dicted static–pressure coefficients cp forVolkswagen Red model — rear view

in Fig. 9, where the difference between the predictedand measured values of cp is visualised at the dis-crete points shown with the given colour scale. Thesepoints correspond to the numerous pressure taps em-bedded in the surface of the wind–tunnel model. Thefigure indicates that a discrepancy exists between thepredicted and measured static–pressure distribution

on the rear upper surface of the vehicle, in particu-lar in the area of maximum curvature, at the transi-tion from the side walls to the rear surface. As willbe seen shortly, in this region the flow is partially at-tached, partially separated; clearly there are somedifferences in the predicted flow structures there thatresult in the deviation from the experimentally deter-mined pressure. As the base pressure of the vehicleis well–matched, it is likely that the x–component ofthe underpredicted pressure on the upper surface is asignificant cause of the overpredicted drag coefficient.Underprediction of the pressure is also observed atthe lower edge of the bumper in the transition to theunderbody. Note that the apparent high overpredic-tion of cp at the A–pillar is due to erroneous position-ing of the probe locations in the simulation and shouldtherefore not be taken into consideration.

Figure 10: Comparison of experimental and pre-dicted static–pressure coefficients cp forVolkswagen Red model — underbodyview

Examination of the pressure distribution on the un-derbody, shown in Fig. 10, also provides further in-formation. It appears that the largest discrepan-cies in the simulation are found in the vicinity of thewheels, where complex vortical structures and re-gions of separated flow are found. Particularly be-tween and around the front wheels, the pressure isunderpredicted. With the front–lift coefficient is pre-dicted very well, it can be found that this underpredic-tion in local pressure is compensated by a slight un-derprediction on the vehicle’s bonnet, not shown here.Moderate underprediction of pressure is also seen onthe portion of the underbody behind the wheels, par-tially compensating in rear lift for the underpredictionof pressure on the upper surface.

The ability of a CFD method to capture the three–dimensionality of the flow is also of paramount im-portance. Further insight into the aerodynamics ofthe model and the accuracy of the CFD solution istherefore gained by examining the surface–flow topol-ogy, obtained by generating oil–streak patterns onthe model’s surface. Figure 11 shows a comparisonof experimental and predicted surface–flow topologyon the rear upper surface of the model. As men-tioned, this region of flow is particulary interesting dueto the pressure–gradient induced separation arisingfrom the strong curvature of the surface. Evidence of

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Figure 11: Comparison of experimental and pre-dicted surface–flow topology in rear re-gion of Volkswagen Red model

the flow’s complexity is immediately evident, as is theCFD method’s ability to predict its large–scale topol-ogy very well. Matched very well are the attached flowcoming off the top corner of the side and roof and ex-tending diagonally across the rear surface, the sepa-ration of the flow at the edge between the side and therear surface up to the point of transition to attachedflow, and the small zone of separated flow at the cen-tre of the rear surface. All the salient features of theflow structure are captured with high fidelity. This re-sult is somewhat in contrast with the discrepanciesobserved in the predicted static pressures in this re-gion and merits further investigation.

In general, it can be seen that the predictions madeby the DES methodology when applied to this caseare of very high quality, given its complexity. Both theintegral force coefficients and the flow structures arepredicted well, notwithstanding the discrepancies ob-served.

AUDI A6 VALIDATION CASE A further analysis ofthe simulation results is carried out using experimen-tal data for the Audi A6, for which particularly detaileddata are available. The data used for the validiationof this test case are obtained from experiments car-ried out in the Audi aeroacoustic wind tunnel [11, 12].Although this facility is equipped with technology forcarrying out aerodynamic testing with full ground sim-ulation (i.e. boundary–layer suction upstream of thevehicle, rotating wheels and a moving belt betweenthe wheels), test results reported on here are for themore conventional configuration of static ground andwheels. Furthermore, the vehicle is measured in its“mock–up” configuration, i.e. with all inlets for coolingair flow closed.

The simulation results reported on here are obtainedfrom a DES run on a finite–volume mesh of approxi-mately 18 million cells, where the flow field and aero-dynamic forces are time–averaged over the last 0.25seconds of the simulation.

The aerodynamic coefficients for the simulation andexperiment are shown in Table 2. The predicted coef-

cD [-] cLf [-] cLr [-]Experiment 0.271 0.068 0.116Simulation 0.267 0.070 0.142

Table 2: Comparison of predicted and measuredaerodynamic coefficients for Audi A6 testcase

ficients can be seen to compare very favourably withthe experimental data. The drag coefficient cD is pre-dicted to within 4 counts, or less than 1.5% of the ex-perimental value, better than the level of accuracy typ-ically required of CFD simulations for external aero-dynamics of road vehicles. The relative error of thefront–lift prediction is also excellent, at less than 3%with 2 counts. However, the rear–lift coefficient, cLr,is overpredicted considerably, by 26 counts or 22%.

Some clues explaining this discrepancy can be foundby examining the distribution of the static–pressurecoefficient cp along the vehicle’s centreline, shown inFig. 12. The figure shows a comparison of cp mea-sured at discrete points on the centreline with the con-tinuous cp distribution there extracted from the CFDresults. Across the bonnet, the static pressure canbe seen to be slightly overpredicted, with a switch tounderprediction as the flow approaches the base ofthe windscreen. Along the windscreen and roof ofthe vehicle, the CFD results compare very well to theexperiments. At the end of the roof, a spike in thepredicted pressure is generated by the presence of arooftop antenna there. As the flow progresses alongthe rear window and boot lid, static pressure is re-covered. However, it can be seen that the predictedpressure recovery is lower than in the experiments,yielding a possible explanation for the overpredictionin rear lift for this case.

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Figure 13: Comparison of experimental and pre-dicted static–pressure coefficients alongcentreline of lower vehicle surface

For the underside of the vehicle, the comparison isshown in Fig. 13. Note that the erratic character ofthe cp distribution in the simulation is due to the geo-metric complexity of the underbody components andthe local maxima and minima in pressure that aregenerated by the small–scale flow structures there.In general, the predicted distribution is seen to fol-low the experimental one well, although between thetwo front measurement points and between x = 1 mand x = 2 m larger discrepancies are found. Withregard to the overprediction of rear lift, no obviousoverprediction of the pressure in the rear part of theunderbody is seen, providing further reinforcementof the hypothesis that this discrepancy might be at-tributable to insufficient pressure recovery on the rearwindow and boot lid. Further confirmation of this canbe found in the off–centre pressure distribution, notshown here.

Figure 14 shows a comparison of the experimental

Figure 14: Comparison of experimental and pre-dicted surface–flow topology in C–pillarregion of Audi A6

and predicted flow topology near the surface of thevehicle in the rear C–pillar region. The images gen-erated from the simulation results show the surfacestreaklines generated on the basis of the wall shearstress, while the colour scale represents the near–wall velocity, ranging from low (blue) to high (red).Particularly for saloon vehicles, the flow structures inthis region are known to be subtle and of considerableimportance for the overall aerodynamics of the vehi-cle. Here, the predictions made by the DES methodcan be seen to be quite close to the structures ob-served in the oil–streak visualisation of the experi-ments. In particular, the fact that the flow remainsattached in the transition from the base of the C–pillarto the boot lid and rear window, as well as the pre-dicted size of the separation bubble at the base of therear window, provides further evidence of the goodfidelity of the turbulence modelling of this method.

Figure 15: Comparison of experimental and pre-dicted surface–flow topology around rearend of Audi A6

A further detail of note is separation of the flow andthe vortex generation in the vicinity of the tail light.Figure 15 shows the comparison of simulation withexperiment in this region. Here also, attachment andseparation of the flow in the appropriate regions is ob-served to be predicted largely correctly, even if some

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minor differences in the directionality of the flow in thevicinity of the longitudinal vortex can be seen.

Figure 16: Comparison of experimental and pre-dicted surface–flow topology around A–pillar and side window of Audi A6

Another region of particular interest in the vehicle’saerodynamics is the A–pillar and wing mirror. In Fig-ure 16, a comparison of the surface–flow structures inthis region is shown. Predicted well is the wake of themirror at the vehicle’s surface, straddling downstreamof the mirror the lower region of the window and theupper door shoulder. The flow immediately across theA–pillar is also predicted well. Some discrepanciesare observed at the reattachment line generated onthe upper section of the side window by the A–pillarvortex, indicating that the vortex size is slightly under-predicted. Possibly related to this is the fact that thesimulation predicts a stronger upward orientation ofthe flow on the upper section of the window, whereasthe oil–streak images indicate flow more parallel tothe shoulder of the door. An investigation of the in-fluence of mesh resolution of the prediction of thesedetailed flow structures may lead to further insight.

Prediction of the size and strength of vortices gener-ated by the vehicle can be analysed well by means oftotal–pressure measurements. Figure 17 shows plots

Figure 17: Comparison of experimental and pre-dicted total–pressure coefficient in wakeplane of Audi A6

of the total–pressure coefficient, cpt, defined as

cpt=

(p+ 1

2ρU2

)− p∞

1

2ρ∞U∞

, (5)

in a plane at x = 3.9m in the vehicle’s coordinate sys-tem, roughly 10 cm downstream of the rear bumper.In the simulation result, two off–centre local minimain cpt

can be observed just above the large wake re-gion. These correspond to the A–pillar vortices, andcan be observed to be somewhat stronger than in theexperiment. The figure also indicates that the wakegenerated by the front wheels, the outer region closeto the floor, is underpredicted by the CFD simulation.Predicted well are the general structure of the wake,including the degree of blockage of the flow throughthe underbody. This lends further weight to the hy-pothesis that the overprediction in rear lift is primarilydue to insufficient pressure recovery on the rear win-dow and boot lid.

The flow–field images shown in the previous figuresare derived from the time–averaged flow field of thelast 0.25 seconds of the simulation. Figure 18 showsa plot of the instantaneous total–pressure coefficientat the end of the simulation. In comparison to theflow field shown in Fig. 17, the instantaneous field

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Figure 18: Instantaneous total–pressure coefficientcoefficient in wake plane of Audi A6

clearly exhibits the small–scale turbulent structuresresolved by an LES formulation, where only the struc-tures smaller than the filter (cell) size are modelled.All the essential macroscopic features of the flow fieldare present — the vortices generated by the A–pillarand wing mirror, the underbody flow, the wakes of thewheels — but the fine structures are not damped out.

VALIDATION OVER WIDE VEHICLE RANGE Theresults of the detailed comparison of flow structures,surface pressures and integral force coefficients forthe Volkswagen Red model and Audi A6 generallyshow very good agreement between simulation andexperiment for important characteristics of vehicleaerodynamics. In order to test the robustness andrange of applicability of the simulation method, a largetest suite of vehicles — spanning a wide range ofbasic vehicle shapes — was created on which themethod was used. Here, the objective was to ascer-tain to what degree the fundamentally different aero-dynamics of different vehicle shapes — such as sub–compact hatchbacks, sports coupes, squreback ve-hicles and super–sports cars — can be captured bya single, consistent simulation approach. Success-ful demonstration of this capability is essential if themethodology is to be applied reliably in a real vehicle–development process.

Table 3 presents an overview of the accuracy of thepredicted drag and lift coefficients for a selection ofvehicles from the test suite used in the validation ac-tivities. The table shows that, on the whole, good ac-curacy is obtained for the prediction of drag coefficientover the whole range of vehicles. A few notable ex-ceptions can be identified, however. Both SEAT ve-hicles suffer from a significant overprediction in dragthat is not observed in the other squareback vehiclesin the suite. Closer investigation of these particularcases is required to ascertain the source of the dis-crepancy, including a verification of the exact corre-spondence of all the details of the simulated geom-etry to that of the vehicle tested in the wind tunnel.

Figure 19: Visualisation of SEAT Ibiza, VolkswagenPassat and Audi R8 aerodynamics val-idation cases showing near–wall veloci-ties and wake turbulence structures

At 16 counts, the error in the prediction for the Volk-swagen New Beetle is also quite high. This result canlikely be attributed to the fact that the aerodynamicsof this particular vehicle are dominated by pressure–gradient driven separation at the round rear surfaceof the vehicle, always a particular challenge for anyCFD methods that employ wall modelling. Further-

∆cD [-] ∆cLf [-] ∆cLr [-]SEAT Ibiza 0.018 -0.017 0.045SEAT Leon 0.021 -0.005 0.030VW Golf 0.003 0.034 0.024VW Passat 0.011 -0.033 0.035VW New Beetle 0.016 0.001 0.030Audi A3 0.007 -0.018 0.034Audi A5 0.011 -0.036 0.031Audi A6 -0.004 0.002 0.026Audi Q5 -0.001 -0.006 0.047Audi TT -0.001 -0.006 0.051Audi R8 0.022 0.021 -0.012

Table 3: Comparison of predicted aerodynamic co-efficients with experiment for range of vehi-cles

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more, the size of the error is consistent with the re-sults obtained for the Volkswagen Red model, whichhas a similar fundamental flow structure in the rear.The overprediction of the drag coefficient of the AudiR8 by 22 counts is also too high to be considered ac-ceptable. Differentiating this vehicle from the othersis the particularly low ground clearance and the flowin the underbody diffusors. Investigations as to thesource of the discrepancies here are still underway.

With regard to front lift, a clear trend is difficult to iden-tify, except perhaps a general tendency for underpre-diction. Here also the Audi R8 does not fit this trend,with the 21–count overprediction likely related to theoverprediction observed in drag coefficient. The sig-nificant overprediction of the front lift for the Volkswa-gen Golf merits further investigation.

The clearest trend to be observed in the deviationfrom the experiments is found in the rear–lift coeffi-cient. Here, again with the notable exception of theAudi R8, the trend for overprediction is obvious. Gen-erally, an overprediction of around 30 counts is foundin most vehicles. Worst among these vehicles is theAudi TT, which, with its strongly curved rear surface, isa particularly challenging case for CFD with wall mod-elling. Although the overprediction of rear lift yields aresult that errs on the side of caution, greater accu-racy is required, and this necessitates a deeper anal-ysis of this issue.

ASSESSMENT OF OVERALL APPROACH

The validation of the simulation results demonstratesthat the methodology presented here is able — inspite of the discrepancies observed — to deliver pre-dictions with very good accuracy. Given the broadscope of the present investigation, the overall accu-racy is, in the experience of the present authors, con-sidered at least on par with that of other CFD codesand is sufficient to be useful for actual production–vehicle development. Further criteria, some of whichare mentioned in the introduction of the paper, can beconsidered to complete the assessment.

After accuracy, of utmost importance is the time–to–solution, as any simulation methodology not able tokeep pace with the rapid evolutionary steps withina modern vehicle design cycle cannot be success-fully integrated into the development process. Dueto the fully parallelised operation of each of the stepsin the overall simulation process and the good par-allel performance of the CFD solver, given sufficientcomputing resources, turn–around times of less than24 hours can be obtained, beginning from a triangu-lated surface mesh and ending with a quasi–steadyDES solution. For example, the Audi A6 case, whichcan be considered to be representative, required 0.5hours clock time for mesh generation, 5 minutes forcase initialisation and 28 hours for the flow simulationon 192 cores of a 3.3 GHz Xeon Linux cluster with an

Infiniband interconnect and 2 GB RAM per core.

Conformity with the CAD process is also an importantattribute of this methodology. In this study, water–tighttriangulated CAD surfaces were used to represent thevehicle geometry, a standard approach in current au-tomotive CFD application. However, this can easilybe extended to surface data with reduced topologi-cal and quality requirements, thereby enabling eventighter integration with vehicle body and componentdesign.

Other than the obvious advantage of the absence oflicense fees, the open–source software approach of-fers several advantages over conventional proprietarysoftware for this application. As discussed in the in-troductory section of this paper, the continually in-creasing demands on the performance of CFD soft-ware require higher and higher degrees of tailoringfor specialised applications. For the work reportedon here, the fundamental customisability of the Open-FOAM toolbox was found to be exceptionally advan-tageous and powerful.

Related to this is the flexibility with which alternativeand/or advanced modelling approaches or numericscan be implemented and applied. Practitioners of ad-vanced CFD will know the importance of investigat-ing the possibilities offered by modelling and numer-ics developed specifically for their flow phenomena.Furthermore, where details of modelling and numer-ics in proprietary CFD codes are usually hidden, in theopen–source code used here they are — by definition— fully transparent. To the extent that these detailsare important for determining accuracy and assessingsources of inaccuracy, the openness of the softwareis of considerable advantage to the user. Again here,the general open–source framework, and the object–oriented C++ design of the code in particular, enabledthe generation of the high–quality results reported inthis paper.

Based on these conclusions, we find the methodologypresented here to be appropriate and suitable for usein the industrial development process.

FUTURE WORK

As shown in the validation section, there currentlyappears to be a consistent tendency of the chosenmethodology to overpredict rear lift, likely due to in-sufficient pressure recovery on the rear upper sur-face of the vehicle. Moreover, super–sports cars withlow ground clearance and smooth underbodies sufferfrom a clear overprediction in drag. Both topics are tobe analysed in more detail through a combination ofadditional numerical and experimental investigations.

The work to date presented in this paper has focusedon external aerodynamics of vehicles in a mock–upconfiguration, i.e. without the flow of air into and out

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Figure 20: Visualisation of velocity magnitude fromunderhood simulation of Audi A6

of the engine bay for cooling purposes. The influ-ence of cooling–air flow on vehicle aerodynamics canbe very significant and very complex, and is there-fore of considerable interest in the development pro-cess. Work is therefore underway to validate the pre-diction of vehicle aerodynamics that includes coolingflow. Figure 20 shows a visualisation of an underhoodsimulation of the Audi A6 discussed in detail previ-ously in the aerodynamics validation section. As afirst basic step, the simulation is performed on the ba-sis of the steady–state RANS–based incompressibleisothermal solver in OpenFOAM using the S–A tur-bulence model, using the identical mesh–generationprocess described previously. Mass–flow rate of airacross the radiator components is used as a plau-sibility check of the results, with the accuracy of thepredicted value found to be within 3.6% of the exper-imental value. Given the excellent accuracy of thisprediction, the next steps include detailed analysisof the aerodynamic predictions with both RANS andDES solvers.

More generally, the scalability and flexibility of thisoverall approach makes optimisation–based design,incorporating genetic–evolution or DOE algorithms, amore reastic undertaking than up to now.

SUMMARY AND CONCLUSIONS

In this paper, a complete methodology was presentedwith which DES can be applied productively within thedevelopment process for vehicle aerodynamics. Theapproach is based on the open–source CFD toolboxOpenFOAM and comprises the automatic generationof a body–fitted computational mesh, the initialisationof the flow field and boundary conditions and a DESflow solver, all fully parallel.

The method is applied to a very wide range of test

cases for validation, from a generic vehicle model toproduction vehicles of various types. Both the de-tailed analyses of the simulation results, as well asthe general overview of the results, show that manyimportant aspects of vehicle aerodynamics are pre-dicted well, ranging from integral drag and lift coeffi-cients to details of the flow topology. Some moder-ate discrepancies in the simulations are found, mostnotably the consistent overprediction of rear lift, andthese merit further investigation, but they are notdeemed to be fundamental.

The degree of automation and parallelisation inherentin the methodology, combined with some of the keycharacteristics of open–source software, yield a pow-erful and flexible new approach to advanced industrialCFD for vehicle aerodynamics.

ACKNOWLEDGEMENTS

The authors wish to thank H.G. Weller, M. Janssens(OpenCFD Ltd), J. Betz, K. Gruber, B. Jacquet, S. Kol-patzik, N. Lindener, D. Patnaik, T. Schutz, K. Zens(Audi AG), F. Purschke, G. Rapin, H. Schmidt, R. Sun-dermeier (Volkswagen AG), X. Agustin, R. Mari (SEATS.A.), C. Frick (science + computing AG), M. Renner,M. Schroter (GNS Systems GmbH), F. Campos andS. Weston (Icon Ltd) for their valuable support of andcontributions to the work presented here.

OpenFOAM is a registered trademark of OpenCFDLtd.

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