Abstract
Vortex interactions behind step cylinders with diameter ratio 2 ≤ D/d ≤ 3 at Reynolds number (ReD) 150 were investigated by directly solving the three-dimensional Navier–Stokes equations. In accordance with the previous paper [C. Tian et al., “Vortex dislocation mechanisms in the near wake of a step cylinder,” J. Fluid Mech. 891, A24 (2020)], some interesting characteristics of vortex dislocations, e.g., two phase difference accumulation mechanisms, the trigger and threshold values of vortex dislocations, antisymmetric vortex interactions, and long N-cell cycles, were observed. By performing a detailed investigation of diameter ratio effects, more features of vortex dynamics were discovered. In addition to the known antisymmetric vortex interactions, a symmetric vortex interaction between neighboring N-cell cycles was observed. The long-time observations revealed an interruption of these two types of vortex interactions. By using a well-validated phase tracking method, we monitored the time trace of the phase difference accumulation process in different D/d cases from which decreasing (known) and increasing (new) phase difference tendencies were identified. Both caused the interruption of continuous symmetric or antisymmetric phenomena but through two distinct mechanisms. Meanwhile, the diameter ratio effects on the trigger and threshold values were discussed. Additionally, the likelihood of antisymmetric or symmetric vortex interactions and increasing or decreasing phase difference tendencies was analyzed. Moreover, diameter ratio effects on shedding frequencies and the extensions of three main vortex cells, i.e., S-, N-, and L-cell vortices, were described.