Numerical simulation of vortex-induced vibration of a square cylinder at a low Reynolds number

Abstract

Vortex-induced vibrations (VIV) of a square cylinder at a Reynolds number of 100 and a low mass ratio of 3 are studied numerically by solving the Navier-Stokes equations using the finite element method. The equation of motion of the square cylinder is solved to simulate the vibration and the Arbitrary Lagrangian Eulerian scheme is employed to model the interaction between the vibrating cylinder and the fluid flow. The numerical model is validated against the published results of flow past a stationary square cylinder and the results of VIV of a circular cylinder at low Reynolds numbers. The effect of flow approaching angle (α) on the response of the square cylinder is investigated. It is found that α affects not only the vibration amplitude but also the lock-in regime. Among the three values of α (α = 0°, 45°, and 22.5°) that are studied, the smallest vibration amplitude and the narrowest lock-in regime occur at α = 0°. It is discovered that the vibration locks in with the natural frequency in two regimes of reduced velocity for α = 22.5°. Single loop vibration trajectories are observed in the lock-in regime at α = 22.5° and 45°, which is distinctively different from VIV of a circular cylinder. As a result, the vibration frequency in the in-line direction is the same as that in the cross-flow direction.