Resonance in vortex-induced in-line vibration at low Reynolds numbers

TL;DR

This paper combines simulations and a new theoretical model to analyze vortex-induced in-line vibrations of a cylinder at low Reynolds numbers, revealing resonance phenomena and the effects of vortex shedding on response amplitude.

Contribution

It introduces a novel fluid force model that captures vortex shedding effects and explains resonance behavior in low Reynolds number vortex-induced vibrations.

Findings

Response amplitude increases significantly with Reynolds number.

Vibration is driven by alternating vortex shedding, with a single excitation region.

Peak amplitudes are independent of mass ratio, consistent with previous experiments.

Abstract

We present simulations of a circular cylinder undergoing vortex-induced vibration in-line with a free stream in conjunction with a theory for the fluid dynamics. Initially, it is shown that increasing the Reynolds number from 100 to 250 results in a 12-fold increase of the peak response amplitude at a fixed mass ratio of $m^*=5$. Subsequently, $m^*$ is varied from 2 up to 20 at a fixed Reynolds number of 180. The response amplitude as a function of the reduced velocity $U^*$ displays a single excitation region with peak amplitudes of approximately 1\% of the cylinder diameter, irrespectively of the $m^*$ value. The vibration is always excited by the alternating shedding of single vortices. We develop a new model for the in-line fluid force, which comprises an inviscid inertial force, a quasi-steady drag, and a wake drag induced by vortex shedding. Our analysis shows that the wake drag appropriately captures a gradual shift in the timing of vortex shedding in its phase variation as a function of $U^*$ while the magnitude of the wake drag displays a resonant amplification within the excitation region. We use the theory to illustrate why peak amplitudes, which occur when the vibration frequency is equal to the structural frequency in still fluid, do not depend on $m^*$, in agreement with our simulations as well as previous experiments at Reynolds numbers higher than considered here. This new theory provides physical insight which could not be attained heretofore by employing semi-empirical approaches in the literature.