Vortex formation in lid-driven arc-shape cavity flows at high Reynolds numbers

High-Reynolds number lid-driven flow in arc-shape cavities with different cross sections is considered up to Re=8000. The unsteady streamfunction-vorticity transport formulation is adopted and a second order finite difference numerical method is applied to computational grids generated by body-fitted coordinate transformation. The effects of aspect or arc angle ratio r, on the formation and growth of vortical structures, as well as on the existence and development of periodic solutions are discussed. It is found that for the case where r>1/2, only a secondary vortex appears in addition to a primary core vortex, for stationary solutions, whereas tertiary and quaternary vortices appear for the cases where r<1/2, near the curved wall. Periodic solutions at high Reynolds numbers are observed when r⩾1/2; while transient oscillations decay in time for r<1/2.