Vortex shedding in the wake of a step cylinder

Abstract

Flow past a circular cylinder with a single stepwise discontinuity in diameter was investigated numerically for the diameter ratio D/d=2 and two Reynolds numbers, ReD=150 and 300. The primary focus was on vortex shedding and vortex interactions occurring in the cylinder wake. In agreement with previous experimental findings, three distinct spanwise vortex cells were identified in the step-cylinder wake: a single vortex shedding cell in the wake of the small cylinder (the S-cell) and two vortex shedding cells in the wake of the large cylinder, one in the region downstream of the step (the N-cell) and the other away from the step (the L-cell). Due to the differences in vortex shedding frequencies, complex vortex connections occurred in two vortex interaction regions located between the adjacent cells. However, distinct differences in vortex splitting and vortex dislocations were identified in the two regions. The region at the boundary between the S-cell and the N-cell was relatively narrow and its spanwise extent did not fluctuate significantly. In this region, vortex dislocations manifested as half-loop connections between two S-cell vortices of opposite sign. In contrast, the region at the boundary between the N-cell and the L-cell exhibited transient behavior, with large scale vortex dislocations causing cyclic variation in the extent of N-cell vortices. Spectral analysis of velocity data showed that the presence of the N-cell was continuous through all simulations. For ReD=300, small scale streamwise vortices forming in the wake of the large cylinder weaken the primary spanwise vortices and vortex connections, complicating vortex dynamics in the step-cylinder wake. However, no significant Reynolds number effect on the average spanwise extent of the vortex cells and the two transition regions between neighboring cells was observed. Finally, formation of N-cell vortices was shown to be linked to downwash fluctuations near the step.