Two Degrees of Freedom Vortex-Induced Vibration Responses With Zero Mass and Damping at Low Reynolds Number

Abstract

Vortex-induced vibration is an important phenomenon for offshore engineering. For applications like the piping in the deep water oil exploration projects, the mass ratios can be of order of one [1]. Hence, there is a practical need to understand the effects of low mass ratio on vortex-induced vibrations to enhance design safety. The main purpose of this study is to numerically explore the two degrees of freedom (transverse and streamwise) responses of vortex-induced vibrations of a cylinder at low Reynolds number for the limiting case of zero mass ratio and zero damping. We aim to characterize the responses. In particular, we focus on determining the maximum amplitude values. It is a continuation from the work of Etienne and Pelletier who studied such behaviors at very low Reynolds number (Re < 50) [2]. We 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, 0.1, 1}) with a fully coupled fluid-structure interaction numerical model based on the finite element method. Our results are generally in accordance with those from previous works for the displacement trajectories, force phase diagram, and the trends in frequency response and oscillation amplitude. The maximum transverse amplitude is found to be around 0.9 in the studied parameter space. In particular, with zero mass ratio, the maximum transverse amplitude starts to occur at values of reduced velocity higher than 6.5 for Reynolds number larger than 150. This is in contrast to the results of Etienne and Pelletier [2] who found that the maximum transverse amplitude always occurs at the reduced velocity of 6.5 for Reynolds number less than 50. Furthermore, with zero mass ratio, the maximum transverse amplitude increases when the Reynolds number increases. This behavior differs from what was suggested by Williamson and Govardhan [3] for a cylinder oscillating only in the transverse direction at Reynolds numbers in the range of 85 to 200. They found that the Reynolds number has no influence on the maximum transverse amplitude. We do not notice any response branching in this parameter space. However, the results in the present work clearly consist of two distinct characteristics. This indicates that the investigated mass ratio values encompass the critical mass ratio; whose value is estimated to be around 0.1 to 0.2.