Numerical simulation of flows past flat plates using volume penalization

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 30o degrees or a round shape. We study the shear layer instability of the flow considering different scenarios, either an impulsively started plate, or an uniformely accelerated plate, for Reynolds number Re = 9500. The volume penalization method 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