Impact of transverse shear on vortex induced vibrations of a circular cylinder at low Reynolds numbers

Abstract

This paper presents a numerical investigation on the vortex induced vibrations (VIV) of an elastically mounted circular cylinder in linear shear flows at low Reynolds numbers with an aim to shed light on a novel aspect of the VIV phenomena, i.e., the impact of transverse shear. In this regard, two-dimensional numerical computations are carried out by deploying a stabilized space–time finite-element formulation. The Reynolds number and the shear parameter are considered in the ranges 70⩽Re⩽500 (for a fixed reduced velocity of U∗=4.92) and 0%⩽β⩽40%, respectively. The cylinder of low dimensionless mass (m∗=10) is allowed to vibrate along both the transverse and in-line directions. The structural damping coefficient is kept zero to maximize the displacement response. Phenomena of hysteresis are observed around Re∼84 and 325. Modes of vortex shedding are 2S, C(2S) and S+P for various values of Re and β. However, only one hysteresis is observed for β=40% at Re∼84. It is further observed that the maximum displacement along the transverse direction does not get affected by the shear introduced at the inlet, however, the maximum in-line displacement depends on the shear parameter. The maximum displacement along the in-line direction increases as the shear parameter increases. For the first hysteresis (Re∼84), the extent of Re (for maximum in-line displacement) varies as the shear parameter is changed. The range of Re for the second hysteresis (for all response parameters) depends on the shear parameter such as for β=0–10% the range is 300–325, for β=20% and 30% it is 325–340 and 225–325, respectively. Strouhal number variation with Re is similar to that for other variables. Plots of pressure coefficient distribution for all shear parameters for instantaneous flow field indicate that the difference between the maximum and the minimum values of the pressure coefficient can vary significantly depending on the Reynolds number and the shear parameter.