De Bortoli, Álvaro Luiz

Ferreira, Davi E. T. I.

Universidade Federal do Rio Grande do Sul

Vehicle aerodynamics based on virtual boundary method

Lume 5.8

Vehicle Aerodynamics based on Virtual Boundary MethodDavi E.T.I. Ferreira, Álvaro L. De BortoliUFRGS/IM-DMPA - Programa de Pós-Graduação em Matemática AplicadaAv. Bento Gonçalves 9500, 91509-900, Porto Alegre, RSE-mail: daviferreira@mat.ufrgs.br, dbortoli@mat.ufrgs.br,ABSTRACTThis work develops a numerical method for thesolution of incompressible bidimensional flow forvehicle geometries based on the Finite Differencemethod. The computational code solves the Navier-Stokes equations for an adequate distribution ofthe discrete points in the mesh. The integra-tion is based on the three-stages Runge-Kutta ex-plicit sheme for momentum equations and sucessiveunder-relaxation for pressure.The virtual boundary technique based on Gaus-sian approximation is employed to indicate thesolid body in the flow field, with the surface notcoinciding with the computational grid. This tech-nique allows the transference of information be-tween the points of the immersed contour and itsneigbouring points.We opt to use cartesian coordinates, insteadboundary fitted, because the application of finitedifferences turn simple. However, this option implyin difficulties to apply the boundary conditions.Figure 1 indicates the vector field for a simpli-fied vehicle geometry, and figure 2 shows the sur-face pressure distribution on the model, for Eu-ler, potencial and Bernoulli equations. Preliminaryresults indicate difficulties when comparing ana-lytical/potencial (Laplace) with numerical results.Such occurs because of an increase of the velocity inthe geometry corner and because of a vortex forma-tion behind the corner, which influences the pres-sure coefficient on the horizontal surface.We intend to obtain an efficient code to easilyimprove vehicle geometry of competition automo-biles. Therefore, we stress the fact that there arestill few information about vehicle aerodynamics inthe available literature; the contribution of our workgoes in this direction.References[1] A. Jameson and L. Martinelli, Mesh Refine-ment and Modeling Errors in Flow Simulation,AIAA Journal, 36 (1998) 676-685.Figure 1: Vector field for a simplified vehiclegeometry (model)Figure 2: Pressure coefficient comparison for vehiclemodel[2] B. Basara, Numerical Simulation of TurbulentWakes Around a Vehicle, ASME FEDSM99-7324, (1999)[3] C.A.S. Moser, J.H. Silvestrini and A.L. DeBortoli, Numerical simulation on the transi-tion of the cylinder wake based on the virtualboundary method, XXII CILAMCE,(2001).[4] W. H. Hucho and G. Sovran, Aerodynamicsof Road Vehicles, Fluid Mechanics to VehicleEngineering, 25 (1993) 485-537.

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Vehicle aerodynamics based on virtual boundary method

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Universidade Federal do Rio Grande do Sul

Lume 5.8