Vortex-induced vibration of a circular cylinder of finite length

Abstract

Vortex-induced vibration (VIV) of a rigid circular cylinder of finite length subject to uniform steady flow is investigated numerically. The study is focused on the effect of the free end on the response of the cylinder. The vibration of the cylinder is confined only in the cross-flow direction. Three-dimensional Navier-Stokes equations are solved by the Petrov-Galerkin finite element method and the equation of the motion is solved for the cylinder displacement. Simulations are conducted for a constant mass ratio of 2, a constant Reynolds number of 300 and cylinder length to diameter ratios of L/D = 1, 2, 5 10, and 20. It is found that the vortex shedding in the wake of a fixed cylinder is suppressed if the cylinder length is less than 2 cylinder diameters. However, if the cylinder is allowed to vibrate, VIV happens at L/D = 1 and 2 and the response amplitudes at these two cylinder lengths are comparable with that of a 2D-cylinder. The vortices that are shed from a short cylinder of L/D = 1 and 2 are found to be generated from the free-end of the cylinder and convected toward the top end of the cylinder by the upwash velocity. They are found to be nearly perpendicular to the cylinder span. The wake flow in a vibrating cylinder with L/D greater than 5 includes the vortex shedding flow at the top part of the cylinder and the end-induced vortex shedding near the free-end of the cylinder. The phase difference between the sectional lift coefficient and the vibration displacement near the free-end of the cylinder changes from 0° to 180° at higher reduced velocity than that near the top end. Strong variation of the flow along the cylinder span occurs at reduced velocities where the lift coefficient near the free-end and that near the top end are in anti-phase with each other.