Vortex-induced vibration at low Reynolds numbers: Vortex shedding modes transitions

Abstract

A numerical model based on the finite difference method is presented to investigate the vortex-induced vibration of a circular cylinder with two degrees of freedom. The immersed boundary method is used to deal with boundary conditions at fluid–solid interfaces. Systematic studies are conducted for Ur = 3–8 (reduced velocity), Re = 170–210 (Reynolds number), m* = 3–10 (mass ratio) and ζ = 0–0.01 (damping ratio). The numerical results indicate that the “P + S” vortex shedding mode and the raindrop-shaped trajectory are more likely to appear in the range of Ur = 4.7–5.1, Re > 180, m*>5, and ζ < 0.007, which correspond to the streamwise resonance. The streamwise displacement exhibits two frequencies fx/fn = 1 and fx/fn = 2, and their amplitude ratios RA = Afx/fn = 1/Afx/fn = 2 can be applied to identify the motion trajectory of the structure and the vortex shedding mode. The trajectory is a raindrop shape and the vortex shedding mode is asymmetric “P + S” for RA > 1.6; the trajectory is an asymmetric “8” shape and the vortex shedding mode is asymmetric “2P” for RA < 1.6; and the trajectory is a symmetric “8” shape and the vortex shedding mode is “2S” or “2P” for RA = 0. These findings contribute to a better understanding of the formation conditions of the “P + S” vortex shedding mode and its transitions with the other vortex shedding modes.