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Numerical simulation of flows past flat plates using volume penalization

Abstract : We present numerical simulations of two-dimensional viscous incompressible flows past flat plates having different kind of wedges: one tip of the plate is rectangular, while the other tip is either a wedge with an angle of 30∘30∘ or a round shape. We study the shear layer instability of the flow considering different scenarios, either an impulsively started plate or an uniformly accelerated plate, for Reynolds number Re=9500Re=9500 . The volume penalization method, with either a Fourier spectral or a wavelet discretization, is used to model the plate geometry with no-slip boundary conditions, where the geometry of the plate is simply described by a mask function. On both tips, we observe the formation of thin shear layers which are rolling up into spirals and form two primary vortices. The self-similar scaling of the spirals corresponds to the theoretical predictions of Saffman for the inviscid case. At later times, these vortices are advected downstream and the free shear layers undergo a secondary instability. We show that their formation and subsequent dynamics is highly sensitive to the shape of the tips. Finally, we also check the influence of a small riblet, added on the back of the plate on the flow evolution.
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Kai Schneider, Mickaël Paget-Goy, Alberto Verga, Marie Farge. Numerical simulation of flows past flat plates using volume penalization. Computational and Applied Mathematics, Springer Verlag, 2014, 33 (2), pp.481-495. ⟨10.1007/s40314-013-0076-9⟩. ⟨hal-01500522⟩

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