Characterization of the Near-Wake of an Ahmed Body Profile St´ ephanie Pellerin, B´ ereng` ere Podvin, Luc Pastur Abstract—In aerovehicles context, the flow around an Ahmed body profile is simulated using the velocity-vorticity formulation of the Navier-Stokes equations, associated to a penalization method for solids and Large Eddy Simulation for turbulence. The study focuses both on the ground influence on the flow and on the dissymetry of the wake, observed for a ground clearance greater than 10% of the body height H. Unsteady and mean flows are presented and analyzed. POD study completes the analysis and gives information on the most energetic structures of the flow. Keywords—Ahmed body, bi-stability, LES, near wake. I. I NTRODUCTION D RAG reduction of separated flows are current topics of automobile industry applications. A thorough understanding of the physics of unsteady separation in the absence of control is therefore required in order to define and evaluate the action of upstream wall actuators. More than 30% of the drag of automobile vehicles is due to phenomena that occur in the vicinity of the rear window, which emphasizes the necessity to modify the vortex dynamics in the recirculation region and in the near wake. II. NUMERICAL APPROACH A. Large Eddy Simulation Using the (v − ω) Formulation The numerical method is based on the (v − ω) velocity-vorticity formulation for incompressible flows, allowing an accurate simulation of a given configuration and a direct manipulation of the flow through modification of the vorticity at the boundary. The turbulent behavior is modeled with Large Eddy Simulation using the filtered Navier-Stokes equations obtained by means of the subgrid decomposition. The exact field is split into filtered variables and subgrid variables. The filtered Navier-Stokes equations using the (v − ω) formulation are given as: ∂ω ∂t −∇× (v × ω)= −Re −1 ∇×∇× ω + ∇× τ (1) ω = ∇× v ∇· v =0 (2) where Re is the Reynolds number, v the filtered velocity vector and ω its curl, resolved on the grid. The vector τ representing the subgrid scale contributions is function of the St´ ephanie Pellerin is with the LIMSI-CNRS, Univ. Paris-Sud, Universit´ e Paris Saclay, Bˆ at 508, Rue John Von Neumann, 91403 Orsay Cedex, France (e-mail: pellerin@limsi.fr). B´ ereng` ere Podvin is with the LIMSI-CNRS, Universit´ e Paris-Saclay, Bˆ at 508, Rue John Von Neumann, 91403 Orsay Cedex, France. Luc Pastur is with the LIMSI-CNRS, Univ. Paris-Sud, Universit´ e Paris Saclay, Bˆ at 508, Rue John Von Neumann, 91403 Orsay Cedex, France. subgrid viscosity ν sgs , as follows, τ = − νsg Re ∇×ω. The mixed scale subgrid model, developed in LIMSI [1], is chosen is this study: ν sg = ( C 2 S Δ 2 ‖ω‖ ) α (C B Δ‖u ′ ‖) (1−α) (3) where k corresponds to a kinetic energy associated with the subgrid cell. Classical vorticity and TKE models are respectively obtained for values 0 or 1 of the exponent α, taken equal to 0.5 in this study. C S and C B correspond respectively to the Smagorinsky and Bardina constants. Δ is a characteristic length of the local cell. This model has the advantage to damp smoothly the eddy viscosity in the regions where all the scales are well resolved. B. Penalization Method Solid are modelled through a penalization method, adapted to the (v − ω) formulation of the Navier-Stokes equations. The velocity and vorticity fields are imposed equal to zero inside the solids. The vorticity vector needs to be zero inside the solid at each time step, which is enforced by setting ∂ω dt =0. The diffusive terms of (1) are cancelled, at each time step, using a penalization matrix. On a given solid surface, the tangential velocity is zero. The vorticity field at the wall (tangential components) is then calculated from velocity derivatives. C. Resolution A M.A.C. staggered grid is used for the spatial discretization. Time and spatial discretizations use 2nd order schemes. The coupled Helmholtz problem of the vorticity transport equation is solved with a block Jacobi iterative algorithm. The velocity field is then obtained through a projection method [2]. An infinite upstream velocity U ∞ is imposed at the inlet of the domain from which the tangential components of the vorticity are deduced. Perturbations (white noise) are superimposed on them to obtain the correct development of the turbulent flow. At the outlet surface, a convective transport hypothesis is applied (viscous effects (v − ω) neglegted). The vorticity tangential components are calculated using an extrapolation along the characteristics. In the vertical direction y, slip conditions are imposed at the lower and upper surfaces. A periodicity condition is used for the transverse direction z. III. MODELIZATION The chosen configuration is an Ahmed body [3] which has a sharp rear corner, above a flat surface. It models a ground vehicle on the road. The characteristic length of the problem World Academy of Science, Engineering and Technology International Journal of Aerospace and Mechanical Engineering Vol:10, No:5, 2016 926 International Scholarly and Scientific Research & Innovation 10(5) 2016 ISNI:0000000091950263 Open Science Index, Aerospace and Mechanical Engineering Vol:10, No:5, 2016 publications.waset.org/10004460/pdf