Vortex-induced vibrations of a square cylinder under linear shear flow

Abstract

This paper investigates the numerical vortex-induced vibration (VIV) of a square cylinder which is connected to a 2-DOF mass-spring system and is immersed in the planar shear flow by employing a characteristic-based split (CBS) finite element method (FEM). The reduced mass of the square cylinder is Mr = 2, while the reduced velocity, Ur, is changed from 3 to 12 with an increment of ΔUr = 1. The effects of some key parameters on the cylinder dynamic responses, vibrating frequencies, the flow patterns as well as the energy transferred between the fluid and cylinder are revealed. In this study, the key parameters are selected as follows: shear ratio (k = 0, 0.05 and 0.1) and Reynolds numbers (Re = 80 and 160). Numerical results demonstrate that the X–Y trajectories of the cylinder mainly appear as a symmetrical figure ‘8’ in uniform flow (k = 0) and an unsymmetrical figure ‘8’ and ‘O’ in shear flows (k = 0.05 and 0.1). The maximum oscillation amplitudes of the square cylinder in both the inline and transverse directions have distinct characteristics compared to that of a circular cylinder. Two kinds of flow patterns, ‘2S’ and ‘P + S’, are mainly observed under the shear flow. Also, the mean values of the energy of the cylinder system increase with the reduced velocity, while the root mean square (rms) of the energy reaches its peak value at reduced velocity Ur = 5.