Experimental and Numerical Investigations of the Flow Development over Circular Cylinders with Stepwise Discontinuities in Diameter

Abstract

Flow past circular cylinders with stepwise discontinuities in diameter was investigated experimentally and numerically for the diameter ratio D/d = 2 and three Reynolds numbers, Re = 150, 300, and 1050. The investigation was focused on the vortex shedding phenomena occurring in the wake of the cylinders. In the first series of experimental and numerical studies, the flow development past a single step cylinder was investigated. The single step cylinder model is comprised of a small diameter cylinder (d) attached coaxially to a large diameter cylinder (D). The results show that three distinct spanwise vortex cells form 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 between the three cells, complex vortex connections occur in two vortex-interaction regions located between the adjacent cells. The region at the boundary between the S-cell and the N-cell is relatively narrow and its spanwise extent does 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 exhibits a transient behavior, with large scale vortex dislocations causing cyclic variation in the extent of N-cell vortices. For Re = 300 and 1050, small scale streamwise vortices forming in the wake complicate the vortex dynamics within the adjacent S-cell and L-cell. There is no significant Reynolds number effect on the average spanwise extent of the vortex cells and the two transition regions between neighboring cells. Finally, formation of N-cell vortices is linked to downwash fluctuations near the step. The flow development past a dual step cylinder was studied experimentally for Re = 1050. The dual step cylinder model is comprised of a small diameter cylinder (d) and a large diameter cylinder (D) mounted at the mid-span of the small cylinder. The experiments were completed for a range of large cylinder aspect ratios 0.2 ≤ L/D ≤ 17. The flow development is highly dependent on the aspect ratio of the large cylinder, L/D. The results identify four distinct flow regimes: (i) for L/D = 17, three vortex shedding cells form in the wake of the large cylinder, one central cell and two cells of lower frequency extending over about 4.5D from the large cylinder ends, (ii) for 7 < L/D ≤ 14, a single vortex shedding cell forms in the wake of the large cylinder, whose shedding frequency decreases with decreasing L/D, (iii) for 2 ≤ L/D ≤ 7, vortex shedding in the wake of the large cylinder is highly three-dimensional, with vortices deforming in the near wake, (iv) for 0.2 ≤ L/D ≤ 1, only small cylinder vortices are shed in the wake and can form vortex connections across the wake of the large cylinder.