Vortex-induced vibrations of dual-step cylinders with different diameter ratios in laminar flows

Vortex-induced vibrations of dual-step cylinders in laminar flows at the Reynolds number of 200 based on a larger diameter are investigated through three-dimensional direct numerical simulations. Four larger-to-smaller diameter ratios (D/d) of 4.0, 2.0, 1.43, and 1.19 are considered for the cylinder with a low mass ratio of 2. Numerical results reveal that D/d significantly influences vibration responses and the vortex shedding process. The case with D/d = 1.43 can effectively reduce vibration amplitudes. The wake vortices are shed in cellular patterns along the cylinder span, with a distinct frequency for each cell. A direct and “X-shaped” connection of wake vortex-shedding modes occurs between different vortex cells, and a loop connection appears between the same cell vortices. A new wake pattern entitled the “out-of-phase vortex shedding” is found downstream of the smaller cylinder at D/d = 2.0. This is manifested by the wake vortices not being shed at a fixed frequency and intensity. The essential reason for this phenomenon lies in a non-lock-in condition between the structural vibration and vortex shedding frequencies of the smaller cylinder. As D/d decreases, a coherence between vortex cells is enhanced, leading to a disappearance of the “out-of-phase vortex shedding.”