Flow-induced vibrations of square and rectangular cylinders at low Reynolds number

Abstract

One-degree-of-freedom (1-dof) and two-degrees-of-freedom (2-dof) flow-induced vibrations (FIVs) of square and rectangular cylinders at a mass ratio of 10 and a low Reynolds number of 200 are studied numerically by solving the two-dimensional incompressible Navier–Stokes equations. The aim of the study is to identify the effects of the aspect ratio α, defined to be the ratio of the cylinder dimension in the cross-flow direction to that in the inline direction, on the vortex-induced vibration (VIV) and galloping responses. Simulations are conducted for aspect ratios of 0.3, 0.5, 0.7, 1 and 1.25 and reduced velocities ranging from 1 to 30. Distinct VIV lock-in and galloping regimes are found for all the aspect ratios except α = 0.3, for which only VIV lock-in is found. The VIV lock-in regime and the galloping regime are separated by a reduced velocity range, where the response amplitude is very small and the response frequency is a linear function of the reduced velocity. It is found that the maximum amplitude in the VIV lock-in regime decreases with increasing aspect ratio. Galloping does not start until the reduced velocity exceeds a critical value. The critical reduced velocity for galloping increases with increasing aspect ratio. For α = 0.5, galloping starts at Vr = 7 and 6 for 1-dof and 2-dof vibrations, respectively. The critical reduced velocity for galloping is increased to 17 at α = 1.25 for both 1-dof and 2-dof vibrations. Because the response amplitude in the inline direction is much smaller than that in the cross-flow direction, the response amplitude and frequency in 2-dof vibration are very similar to their counterparts in 1-dof vibration. However, the response amplitude in 2-dof galloping is greater than that in 1-dof galloping. A 2T vortex shedding mode is observed in the VIV lock-in regime for α = 0.3 and 0.5.