Viscous-Flow Simulation of an Open-Wheel Race Car

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SAE TECHNICALPAPER SERIES 983041

Viscous-Flow Simulation of an Open-WheelRace Car

Joseph KatzSDSU

Hong Luo, Eric Mestreau and Joseph BaumSAIC

Reinald LhnerGeorge Mason Univ.

Reprinted From: 1998 Motorsports Engineering Conference ProceedingsVolume 1: Vehicle Design and Safety

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Motorsports EngineeringConference and Exposition

Dearborn, MichiganNovember 16-19, 1998

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1983041

Viscous-Flow Simulation of an Open-Wheel Race Car

Joseph KatzSDSU

Hong Luo, Eric Mestreau and Joseph BaumSAIC

Reinald LhnerGeorge Mason Univ.

Copyright 1998 Society of Automotive Engineers, Inc.

ABSTRACT

A numerical solution based on the Navier-Stokes equa-tion, combined with unstructured grid mesh, was used tomodel an open wheel race car. The solution is based ona fast, matrix-free, implicit method, with relatively lowstorage requirements, resulting in solution times up to anorder of magnitude smaller than other numerical solu-tions. The computations provide details on the flow fieldaround the car and a complete pressure distribution onthe vehicles surface. The calculated results may be usedas a supplementary tool for wind tunnel or road testingand can provide information, such as the underbody flow,which is difficult to evaluate experimentally. One of theprimary advantages of such a viscous flow simulation isthe ability to model wheel rotation and to detect regionsof flow separation, particularly on the suction side of thefront and rear wings.

INTRODUCTION

The complex nature of the flowfield over open-wheel racecar configuration often results in numerous non-lineareffects which complicate the estimation of expected per-formance-gains due to proposed design modifications.Traditionally, both wind-tunnel and road tests are usedextensively during the aerodynamic development of sucha vehicle. Those methods have matured to providedependable integral results such as the lift and drag butquite often cannot provide sufficient details on the flow-field to explain why certain trends are observed. There-fore, a design tool that can provide detailed flow-information on and off the surface of the vehicle, can helpexplain some of those nonlinear effects and shorten thedesign cycle. To fill this void, recently, the use of comple-mentary computational methods has increased [1-3] andtheir significance as an additional independent designtool has been gradually established. Earlier computa-tional tools were limited by computer performance and

initially inviscid methods were used, with some success[4], for various race cars and road vehicles with largeregions of attached flows. Because of the massive flowseparations, particularly those created by the largewheels, viscous flow simulation is necessary for openwheel race cars. Consequently, the solution of the fullNavier-Stokes (N.S.) equations is required for the flow-field surrounding the complex geometry of an INDY-typerace car, such as the one shown in Fig. 1.

Figure 1. Solid body model of a generic INDY race car.

The objective of the present work is to demonstrate theapplicability of the approach as a complementary tool,particularly in areas where the experimental approachhas limited capabilities. For example, flow-visualizationinside the diffusers under the car, as well as tracing thefront wing wake in a high-Reynolds number flow, is closeto impossible in a wind tunnel experiment. Similarly, eval-uating the pressure distribution over a large number ofproposed wing configurations, in a small-scale test, maybecome an endless chore. In all these cases, the use of




2computational methods can easily fill the required infor-mation gap.

METHODOLOGY

The present work is based on solving the finite elementequivalent of the N.S. equations with the flux-correctedtransport concept (Ref. 5). An unstructured mesh is usedwhich makes the grid generation around complex config-uration much simpler than with other structured gridmeshes. The process usually begins with the preproces-sor FECAD that prepares the CAD surface for the gridgenerator, FRGEN3D. The grid generator then createsthe computational mesh, which is used by the solver,FEFLOW97/8, that solves the finite-element equivalent ofthe N.S. equations. A post processor (FEPOST3D) isthen used to graphically display and analyze the compu-tational results. These utilities are briefly described in thefollowing paragraphs.Generation of the vehicle surface model is still one of thelargest tasks in the process of obtaining a numerical solu-tion. The experience gained over several years in thegeneration of surface and volume meshes for the simula-tion of flows about such complex geometric structures asairplanes, tanks, trains, cars and trucks [6-8], has shownthat once the surface and volume mesh generation hasbeen automated, the surface description (i.e., point, lineand patch definition), as well as the correct definition ofboundary conditions, become the dominant time con-suming task. This information led to the development ofthe preprocessor FECAD, a suite of efficient, user-friendly utilities that allows the quick production ofFRGEN3D-compatible, error-free input. In addition tobasic CAD-CAM operations (shrinking, translating, rotat-ing, surface lofting, etc.), FECAD also eases the mergingof several surface parts into one cohesive, well-definedinput-file. This allows the merging of files produced by dif-ferent users and/or different surface generators. Mostimportantly, FECAD allows graphical interrogation of thesurface data, and has many built-in diagnostics to avoidundesirable features such as doubly defined points, iso-lated points or lines, badly defined lines or surfaces, andlines or surfaces that are directed incorrectly. FECADalso allows the specification and visualization of bound-ary conditions, saving the user many error-prone hoursduring the later stages of a run. FECAD has proven to bean invaluable aid when trying to construct an error-freeFRGEN3D-compatible input file in a matter of days oreven hours. In order to specify the desired element sizeand shape distribution in space, a combination of back-ground grids [9] and sources is employed. This task isagain performed within the point-and-click environment ofFECAD.The solid body model of a generic INDY car, created bythe FECAD preprocessor is shown in Fig. 1. The modelincludes simulation of the internal flow across the radiatorducts and the proper boundary conditions to simulatewheel rotation and moving ground. More details on thegeometry and specific dimensions of this vehicle can be

found in the 1996 rulebook [10] of the sanctioning organi-zation (CART).The grid generator used is FRGEN3D [9]. This unstruc-tured grid generator is based on the advancing frontmethod. After defining the surface of the domain to begridded, the surfaces are triangulated. Thereafter, theface that forms the smallest new element is deleted fromthe front, and a new element is added. This process isrepeated recursively until no more faces are left in thefront. Results of the grid generation are presented in Fig.2. and the triangular surface elements density can beeasily adjusted in areas where larger resolution isrequired, without dramatically increasing the total numberof grid points. The mesh used in this computationassumes a symmetrical model and contains 8,314,454tetrahedral elements, 1,459,199 grid points, and uses174,134 boundary points on the car surface and the farfield (per one half of the model).

Figure 2. Unstructured grid around the open-wheel race car model. To simulate a moving ground, the wheels rotate in coordination with the speed of the floor grid.

The flow solver employed was FEFLO97, a new 3-D ALEedge-based [11] hydro-solver based on the Finite-Ele-ment Method Flux-Corrected Transport (FEM-FCT) con-cept [5], which solves the Euler and Reynolds-averagedturbulent, Navier-Stokes equations. H-refinement is thepreferred approach for grid adaptation [12]. The high-order scheme used is the consistent-mass Taylor-Galer-kin algorithm. Combined with a modified second-orderLapidus artificial viscosity scheme, the resulting schemeis second-order accurate in space, and fourth-orderaccurate in phase. The spatio-temporal adaptation isbased on local H-refinement, where the refinement/dele-tion criterion is a modified H2-seminorm [12]. The criticalparameter for the refinement/deletion criteria is density.Various turbulent models can be used, and the model was tested successfully with this approach. Forthe calculations presented here a full-size vehicle at 100mph was simulated; however, no turbulence model was




3used and the data represents a virtual high-Reynoldsnumber laminar flow case. When compared with experi-mental data, this temporary simplification typically resultsin earlier flow separation on highly curved surfaces.The FEFLO98 solver has recently been improved with anew, fast, matrix-free implicit algorithm. This algorithmsolves an approximate system of linear equations whicharise from the Newton linearization by the GMRES (Gen-eralized Minimum RESidual) algorithm with a LU-SGS(Lower-Upper Symmetric Gauss-Seidel) preconditioner.This preconditioner has been further modified to allowthe accurate solution of virtually incompressible flows(i.e., down to Mach numbers of 0.00001). The mostremarkable feature of the new GMRES+LU-SGS methodis that the storage of the Jacobian matrix can be com-pletely eliminated by approximating the Jacobian withnumerical fluxes, resulting in a matrix-free implicitmethod. Numerical tests demonstrate a factor of 10-15increase in performance over the best current implicitmethods, without increasing memory requirements. Inthis particular case, the residual is reduced by threeorders of magnitude within 200 time steps and the wholecomputation requires about 5 hours of CPU time (on aCray C-70 computer).Post-processing was performed with the FEPOST3D andFEMOVIE packages [13]. FEPOST3D performs all CPU-intensive filtering operations on the Supercomputer. Onlythe plane or surface data are sent back to the graphicsworkstation for plotting.

Figure 3. Streamline traces in the flow under the car.

RESULTS

Results of the computations are divided into two sections.The first is the off-body flow visualization and the sec-ond is the surface pressure distribution. Flow visualiza-tions are widely used during wind-tunnels experiments;however, in some areas conventional methods are notalways effective. Similarly, surface pressure measure-ments may be measured in a wind tunnel but are notwidely used in race-car wind tunnels because of the shortdevelopment time requirement.

Typical streamline traces in the flowfield nearby the carmodel are presented in the following six figures. Thesefigures, as viewed in the post-processor, are far moredetailed and use colors to identify the local velocity on thestreamline. Unfortunately, most of the resolution and theaerodynamic information is lost while converting thoseflow visualizations into the gray-scale images in this arti-cle. An example of such streamline traces is shown inFig. 3. The tracing begins behind the front wheels andthe fluid particles are partially captured by the large sepa-ration zone behind the wheel. Some slow moving parti-cles may rise in the flow behind the wheel and join thehigh speed stream above it. To simulate actual road con-dition the tire had a flat contact patch with the road whichwas further modified by two small wedges insertedunderneath. This was done to improve local numericalstability and was plotted by the postprocessor as an ele-vated block (see Figs 3 and 4). Also, the effect of thesmall turning vane in front of the side pod is clearly visibleI this figure. The flow is kept attached to the bodyworkand is less affected by the wheel-base separation. Thestreamlines above the wheel seem to head inward andeventually will end up flowing beneath the rear wing.

Figure 4. Streamline traces released in the vehicle symmetry plane.

The streamline traces shown in Fig. 4 provide a generalindication about the flow direction in the symmetry plane.The raised nose design clearly allows sufficient flowunder the vehicle, but most of the flow moving above thenose will end up near the drivers helmet. The rear wingclearly changes the streamline curvature, indicating thelarge level of downforce created. However, the stream-lines leaving the trailing edge flap are not parallel to theflap due to local flow separation there. This separationmay be exaggerated by the current computation butsome partial flow separation was observed during roadtesting with the higher downforce settings. The lack ofstreamlines behind the lower portion of the vehicle mayindicate the high bluff body drag created.The information about the orientation of the flow ahead ofthe vehicle is relevant to both downforce and cooling con-siderations. Fig. 5 and Fig. 6 demonstrate how some ofthis information can be obtained by using numerical flow




4visualizations. For example, the raised central portion ofthe front wing allows more flow to move under the car,which eventually contributes to more airspeed there andmore downforce. But, more importantly, this portion of theflow seems to reach the cooling inlets, directly affectingthe side pod design. The streamlines in Fig. 6 show thatsome of the flow at the wing root still reaches the coolingducts, but most of the streamlines travel above the vehi-cle side pod. Once the airflow moves past the side pods(Figs. 5 and 6), it is channeled below the rear wing. Acareful examination of the streamlines near the front wingtip, in both figures, indicates that the tip-vortex stretchesinside the front wheels and then moves outside andupward, missing the rear wing.

Figure 5. Streamline traces released at the front wing leading edge level.

Figure 6. Streamline traces released above the front wing leading edge plane.

The high suction of the rear wing is evident in Fig. 7 aswell. Here the streamlines were released in a plane out-side the front wheels. The flow initially is displaced out-ward by the large rotating wheels; however, the suctionbehind the front wheels turns some of the streamlinesinward. A large portion of the streamlines eventually rises

above the rear bodywork and travels under the large rearwing. The effect of the small flow turning device abovethe rear wing may be clarified by observing the stream-lines in this area. Because of the locally horizontal flow ithas the potential to create some downforce, and at thesame time reduce the rear wheel drag by diverting theflow away from it.

Figure 7. Streamline traces released outside of the front wing side fin.

The top view of the flow approaching the rear wing isshown in Fig. 8. The boat-tail shape of the body and thelarge suction under the rear wing is forcing the flow tomove inward between the rear wheels and the body. This,in effect, creates an angularity in the direction of the flowreaching the rear wheel and the rear separation bubblefaces inward. Further behind the car, after passing therear wing, the streamlines are closing inward quickly. Thisis most likely a reaction to the low pressure base flow (orbluff body effect) of the not so streamlined vehicle andits wheels and due to the flow induced by the rear wingvortices.

In the second part of this article, calculated surface pres-sure data is presented. The surface pressure distributionis a direct outcome of the copmputations and readilyavailable on all surfaces. By integration, it can be used todetermine aerodynamic loads on various body panelsand can be used to redesign a particular surface shape(e.g. to reduce flow separation). As an example, the pres-sure distribution along the ground-plane symmetry line ispresented in Fig. 9. The front suction peak is created bythe front wing, while the second one is a result of the flowaccelerating between the front wheels. The largest suc-tion peak is at the entrance to the underbody tunnels(which still exist in INDY cars), and the pressure coeffi-cient then gradually increases to values near zero behindthe vehicle. The experimental data shown by the (*) sym-bols was collected by a static pressure rake behind thecar, and it agrees reasonably well with the computed val-ues.




5Figure 8. Top view of the streamline traces approaching the rear wing.

Figure 9. Pressure distribution on the moving ground plane centerline.

Experimental evaluation of the pressure distribution onmoving surfaces, such as shown in Fig. 9, is quite diffi-cult, particularly when it comes to rotating wheels. Fig. 10demonstrates such results when using the computationswith a rotating surface. Here the pressure distributionalong the wheel centerline is presented in a polar dia-gram (note that the Cartesian ordinates serve to indicatethe Cp magnitude only, but the pressure distributionshown is wrapped around the circular tire outline). In frontof the tire, at the lower part of the wheel, a high pressurearea exists (positive is inside the circle, on which Cp =0),and the loop in the data shows the pressures on theground as well. As the flow accelerates over the wheel,the pressure coefficient drops and reaches negative val-

ues above the wheel. The small dip near the top of thetire is probably due to the flow separation line there. Thissuction region inside the separated region, extends witha fairly constant pressure coefficient behind the wheel,clearly contributing to the drag force on this wheel.The pressure distribution (or velocity distribution) on awing can serve to evaluate its performance and indicate ifits lift or drag can be altered according to a particulardesign need. For example, the pressure distributionalong longitudinal sections of the race cars front and rearwings is provided in the following three figures. The pres-sure distribution near the mid-line of the inner section(with the shorter flap, see Fig. 1) is shown in Fig. 11.

Figure 10. Polar description (with Cp=0 on the circular tire outline) of the pressure coefficient along the rear wheel centerline.

Figure 11. Pressure distribution along an inner section (with the shorter flap) of the front wing.




6The shape of the pressure distribution in Fig. 11 followscurrent design trends with a large laminar portion on thewings suction (lower) side. In this particular computation(without the turbulence model) a laminar bubble seems toform behind the leading edge, creating the wavy shape inthe Cp curve near the leading edge. The rear flap showssimilar trends and some visible trailing edge separationas well. It is believed that in the high-speed (over 100mph) and turbulent flow case, those laminar bubbles nearthe leading edge will disappear.

Figure 12. Pressure distribution along an outer section (with the longer flap) of the front wing.

Figure 13. Pressure distribution along the centerline of the rear wing.

A similar pressure distribution diagram, but along anouter section (placed near the tip, at the center of thelarger flap) is shown in Fig. 12. In this case the flow onthe main element is attached, but partially separated onthe flap. The shape of the pressure distribution in thesetwo figures indicates a careful and well-balanced airfoil

design for the front wing. The trailing edge flap angle forthis particular condition, seems to be set at a too highvalue and the shown gap between the two elements isprobably too large. The interaction between the mainwing plane and its flap may be improved by closing thegap somewhat.The rear wing pressure distribution is presented in Fig.13. In this case, the INDY-car regulations force the use ofa very long airfoil chord, resulting in a non-airplane likepressure distribution. The suction peak at the front is typ-ical to most airfoils at larger angles of attack; however,the second suction peak at the aft section of the mainelement is less traditional. This is a result of the sharpturn of the streamlines near the gap region, causing alocal trailing edge separation. The flap, in this case, too,is partially separated. This is standard practice in searchof maximum rear downforce at the cost of increasingrear-wing drag. The streamline plot, presented in Fig. 14,visualizes the flow in the symmetry plane of the rearwing. The small trailing edge separation at the base ofthe main wing element is hardly visible in this gray-scaleimage, but the separation of the rear flap is more pro-nounced. These flow separations are amplified by theabsence of the turbulence model, but traces of it weredetected during full scale testing (by using tufts).

Figure 14. Streamlines released near the symmetry plane of the rear wing.

CONCLUSIONS

The numerical model used in this study demonstrates thefeasibility of solving the Navier-Stokes equations for acomplex race car configuration within practical time limits.Computed results clearly demonstrate the ability to simu-late viscous flow separation on the complex componentsof open-wheel race cars (e.g the flow over rotatingwheels). When properly used, this approach can providethe reasoning for planned model modifications. It can beused to propose and numerically test numerous wing




7shapes and to virtually investigate various ideas beforebuilding a test model. Numerical results may be used in acomplementary manner with other experimental tech-niques because of the easily available pressure distribu-tion and flow orientation information, particularly in areasnear the wings, under the car and near the rotatingwheels.

REFERENCES

1. Werner, F., Frik, S., and Schulze, J., Aerodynamic Optimi-zation of the Opel Calibra ITC Racing Car Using Experi-ments and Computational Fluid Dynamics, SAE 98-0040,Feb. 98, Detroit MI.

2. Axelsson, N., Ramnefors, M., and Gustafsson, R., Accu-racy in Computational Aerodynamics Part 1: StagnationPresure, SAE 980037, Feb. 98, Detroit MI.

3. Perzon, S., Sjogren, T., and Jonson, A., Accuracy in Com-putational Aerodynamics Part 2: Base Pressure, SAE980038, Feb. 98, Detroit MI.

4. Katz J., and Dykstra, L., "Application of ComputationalMethods to the Aerodynamic Development of a PrototypeRace-Car," SAE Paper 942498, Proceedings of the 1994Motor Sport Engineering Conf., P-287, pp. 161-169, , Dec.5-8, 1994, Detroit, MI.

5. Lhner, R., Morgan, K., Peraire, J., and Vahdati, M., FiniteElement Flux-Corrected Transport (FEM-FCT) for the Eulerand Navier-Stokes Equations, Int. J. Num. Meth. Fluids 7,1093-1109 (1987).

6. Baum, J.D. and Lhner, R., Numerical Simulation of ShockInteraction with a Modern Main Battlefield Tank, AIAA-91-1666 (1991).

7. Baum, J.D., Luo, H., and Lhner, R., Numerical Simulationof a Blast Inside a Boeing 747, AIAA--93-3091 (1993).

8. Baum, J.D., Luo, H., and Lhner, R., Numerical Simulationof Blast in the World Trade Center, AIAA-95-0085 (1995).

9. Lhner, R., and Parikh, P., Three-Dimensional Grid Gener-ation by the Advancing Front Method, Int. J. Num. Meth.Fluids 8, 1135-1149 (1988).

10. C.A.R.T., Aerodynamic and Body Work Specifications,Cart Rulebook 1996, Chapter 9.4.

11. Luo, H., Baum, J. D., and Lhner, R., Edge-Based FiniteElement Scheme for the Euler Equations, AIAA J. 32, 6,1183-1190 (1994).

12. Lhner R., and Baum, J. D., Adaptive H-Refinement on 3-D Unstructured Grids for Transient Problems, Int. J. Num.Meth. Fluids 14, 1407-1419 (1992).

13. Lhner, R., Parikh, P., and Gumbert, C., Some AlgorithmicProblems of Plotting Codes for Unstructured Grids, AIAA-89-1981-CP (1989).




Viscous-Flow Simulation of an Open-Wheel Race Car

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