Two degrees of freedom vortex-induced vibration responses with zero mass and damping at low Reynolds number

This work aims to characterize the two degrees of freedom (transverse and streamwise) responses of vortex-induced vibrations (VIV) of a cylinder at low Reynolds number for the limiting case of zero mass ratio and zero damping. The main focus is on determining the maximum peak amplitude value as a function of the Reynolds number. We believe it occurs for zero mass ratio and damping. We numerically investigate the responses in the following parameter space: Reynolds number (75⩽Re⩽175), reduced velocity (5.0⩽Ur⩽11.0) and mass ratio (m∗=0). For comparison, we also investigate one and two degrees of freedom VIV for m∗=1. The effect of Re and m∗ onto the oscillation responses are examined. Overall maximum transverse peak amplitude (AY) of 0.9D is obtained for the two dof VIV with m∗=0 at Re=175, a significant 50% increase from 0.6D for single dof VIV. The peak AY occurs at different Ur with respect to the Reynolds number. Furthermore, the maximum AY continuously increases with Re in contrast with the plateau observed for single dof VIV. This is most evident for the XY oscillation for m∗=0. Critical mass ratios of 0.106 for XY oscillation and 0.117 for transverse only oscillation have been obtained at Re=100.