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Modes of synchronisation in the wake of a streamwise oscillatory cylinder

Published online by Cambridge University Press:  26 October 2017

Guoqiang Tang ,
Liang Cheng ,
Feifei Tong Open the ORCID record for Feifei Tong [Opens in a new window] ,
Lin Lu  and
Ming Zhao Open the ORCID record for Ming Zhao [Opens in a new window]
Guoqiang Tang
Affiliation:
DUT-UWA Joint Research Centre, State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, No. 2 Linggong Road, Dalian 116024, China
Liang Cheng*
Affiliation:
DUT-UWA Joint Research Centre, State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, No. 2 Linggong Road, Dalian 116024, China School of Civil, Environmental and Mining Engineering, The University of Western Australia, 35 Stirling Highway, Perth, WA 6009, Australia
Feifei Tong*
Affiliation:
School of Civil, Environmental and Mining Engineering, The University of Western Australia, 35 Stirling Highway, Perth, WA 6009, Australia
Lin Lu
Affiliation:
DUT-UWA Joint Research Centre, State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, No. 2 Linggong Road, Dalian 116024, China
Ming Zhao
Affiliation:
School of Computing, Engineering and Mathematics, Western Sydney University, Locked Bay 1797, Penrith, NSW 2751, Australia
*
†Email addresses for correspondence: liang.cheng@uwa.edu.au, feifei.tong@uwa.edu.au
†Email addresses for correspondence: liang.cheng@uwa.edu.au, feifei.tong@uwa.edu.au
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Abstract

A numerical analysis of flow around a circular cylinder oscillating in-line with a steady flow is carried out over a range of driving frequencies $(f_{d})$ at relatively low amplitudes $(A)$ and a constant Reynolds number of 175 (based on the free-stream velocity). The vortex shedding is investigated, especially when the shedding frequency $(f_{s})$ synchronises with the driving frequency. A series of modes of synchronisation are presented, which are referred to as the $p/q$ modes, where $p$ and $q$ are natural numbers. When a $p/q$ mode occurs, $f_{s}$ is detuned to $(p/q)f_{d}$ , representing the shedding of $p$ pairs of vortices over $q$ cycles of cylinder oscillation. The $p/q$ modes are further characterised by the periodicity of the transverse force over every $q$ cycles of oscillation and a spatial–temporal symmetry possessed by the global wake. The synchronisation modes $(p/q)$ with relatively small natural numbers are less sensitive to the change of external control parameters than those with large natural numbers, while the latter is featured with a narrow space of occurrence. Although the mode of synchronisation can be almost any rational ratio (as shown for $p$ and $q$ smaller than 10), the probability of occurrence of synchronisation modes with $q$ being an even number is much higher than $q$ being an odd number, which is believed to be influenced by the natural even distribution of vortices in the wake of a stationary cylinder.

JFM classification

Vortex Flows: Vortex dynamics Wakes/Jets: Vortex streets

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Papers
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Journal of Fluid Mechanics , Volume 832 , 10 December 2017 , pp. 146 - 169
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© 2017 Cambridge University Press 

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