The effect of Reynolds number on the critical mass phenomenon in vortex-induced vibration

Abstract

In this study, we investigate the critical mass phenomenon in vortex-induced vibration over a wide range of Reynolds numbers (Re=4000–30 000). We consider an elastically mounted cylinder that is able to vibrate transverse to a fluid flow. If we remove the restoring spring (k=0), then above a certain critical mass ratio (m∗ is oscillating body mass/displaced fluid mass), the cylinder will experience almost no motion, despite its unrestrained freedom to move transverse to the flow. However, when the mass ratio is decreased below a special critical value, without altering anything else in the system, we see a catastrophic increase in amplitude, and the body settles into a large amplitude periodic vibration. This corresponds to a change from a desynchronized wake to a 2P mode of vortex formation, where two pairs of vortices are formed per cycle of motion. Since a system with no restoring force represents a case of infinite normalized velocity (U∗→∞), the observation of high amplitude motion indicates that the regime of U∗ giving resonant vibration extends to infinity, for sufficiently small mass ratio. In this work, we measure the critical mass directly from experiments with no spring stiffness, and we show also how the critical mass may be accurately predicted from force measurements from controlled vibration experiments, or from free vibration measurements of elastically mounted cylinders. Critical mass gradually increases with Reynolds number from a value of 0.36 to 0.54, over the regime Re=4000–30 000. The fact that the critical mass is a function of Reynolds numbers should be expected because it depends on the vortex-induced forces, which are influenced by gradual changes in vortex formation as Re increases. The evaluation of critical mass in this configuration, and indeed in other diverse vortex-induced vibration (VIV) systems, is important because it can predict the regime of normalized velocities that will yield large amplitude vibration, and which one may wish to avoid in practice. The fact that critical mass, at moderate Reynolds numbers, in several diverse VIV systems, including cylinders in one or two degrees of freedom, pivoted bodies, cantilevers, and tethered spheres, are all within a small range 0.36–0.6, remains an interesting question.