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Vibrations of a square cylinder submerged in a wake

Published online by Cambridge University Press:  23 August 2018

Rajesh Bhatt  and
Md. Mahbub Alam Open the ORCID record for Md. Mahbub Alam [Opens in a new window]
Rajesh Bhatt
Affiliation:
Institute for Turbulence-Noise-Vibration Interactions and Control, Shenzhen Graduate School, Harbin Institute of Technology, 518055 Shenzhen, PR China Digital Engineering Laboratory of Offshore Equipment, Harbin Institute of Technology, 518055 Shenzhen, PR China
Md. Mahbub Alam*
Affiliation:
Institute for Turbulence-Noise-Vibration Interactions and Control, Shenzhen Graduate School, Harbin Institute of Technology, 518055 Shenzhen, PR China Digital Engineering Laboratory of Offshore Equipment, Harbin Institute of Technology, 518055 Shenzhen, PR China
*
†Email addresses for correspondence: alam@hit.edu.cn, alamm28@yahoo.com
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Abstract

A numerical investigation is conducted on the flow around and vibration response of an elastic square cylinder (side width $D$) in the wake of a stationary cylinder at Reynolds numbers of $Re=100$ and 200 based on $D$ and the free-stream velocity. The downstream cylinder, referred to as the wake cylinder, is allowed to vibrate in the transverse direction only. The reduced velocity $U_{r}$ is varied from 1 to 30. Cylinder centre-to-centre spacing ratios of $L^{\ast }(=L/D)=2$ and 6 are considered. Simulations are also conducted for a single isolated cylinder, and the results are compared with those for the wake cylinder. The focus is given to vibration response, frequency response, fluctuating lift force, phase relationship between the lift and displacement, work done and the flow structure modification during the cylinder vibration. The results reveal that the dependence of the Strouhal number $St$ on $U_{r}$ can distinguish different branches more appropriately than that of the vibration amplitude on $U_{r}$. The vibration response of the single cylinder at $Re=100$ is characterized by the initial, lower and desynchronization branches. On the other hand, that at $Re=200$ undergoes initial, lower and galloping branches. The galloping involves the characteristics of both the initial and the lower branches or the initial and the desynchronization branches depending on $U_{r}$. For the wake cylinder, the gap flow has a significant impact on the vibration response, leading to (i) the absence of galloping at either $Re$ and $L^{\ast }$, (ii) the presence of an upper branch at $Re=200$, $L^{\ast }=6$ and (iii) an initial branch of different characteristics at $Re=100$, $L^{\ast }=6$. The different facets are discussed in terms of wake structures, work done and phase lag between lift and displacement.

JFM classification

Vortex Flows: Vortex shedding Wakes/Jets: Wakes
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 853 , 25 October 2018 , pp. 301 - 332
Copyright
© 2018 Cambridge University Press 

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