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Influence of plane boundary proximity on the Honji instability

Published online by Cambridge University Press:  03 August 2018

Chengwang Xiong Open the ORCID record for Chengwang Xiong [Opens in a new window] ,
Liang Cheng ,
Feifei Tong Open the ORCID record for Feifei Tong [Opens in a new window]  and
Hongwei An Open the ORCID record for Hongwei An [Opens in a new window]
Chengwang Xiong
Affiliation:
School of Civil Engineering, Hebei University of Technology, Tianjin 300401, China School of Civil, Environmental and Mining Engineering, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia
Liang Cheng*
Affiliation:
School of Civil, Environmental and Mining Engineering, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia DUT-UWA Joint Research Centre, State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, No. 2 Linggong Road, Dalian 116024, China
Feifei Tong
Affiliation:
School of Civil, Environmental and Mining Engineering, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia
Hongwei An
Affiliation:
School of Civil, Environmental and Mining Engineering, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia
*
†Email address for correspondence: liang.cheng@uwa.edu.au
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Abstract

This paper presents a numerical investigation of oscillatory flow around a circular cylinder that is placed in proximity to a plane boundary that is parallel to the cylinder axis. The onset and development of the Honji instability are studied over a range of Stokes numbers ($\unicode[STIX]{x1D6FD}$) and gap-to-diameter ratios ($e/D$) at a fixed Keulegan–Carpenter number ($KC=2$). Four flow regimes are identified in the ($e/D,\unicode[STIX]{x1D6FD}$)-plane: (I) featureless two-dimensional flow, (II) stable Honji vortex, (III) unstable Honji vortex and (IV) chaotic flow. As $e/D$ increases from $-0.5$ (embedment) to $1$, the critical Stokes number $\unicode[STIX]{x1D6FD}_{cr}$ for the onset of the Honji instability follows two side-by-side convex functions, peaking at the connection point of $e/D=0.125$ and reaching troughs at $e/D=0$ and 0.375. The Honji instability is always initiated on the gap side of the cylinder surface for $0.375\leqslant e/D\leqslant 2$ and occurs only on the top side for $-0.5\leqslant e/D<0.125$. The location for the initiation of the Honji instability switches from the gap side to the top side of the cylinder surface for $0.125<e/D<0.375$. No Honji instability is observed at $e/D=0.125$, where the flow three-dimensionality is developed through a different flow mechanism. Consistently, the three-dimensional kinetic energy of the flow, which represents a measure of the strength of flow three-dimensionality, varies with $e/D$ in a trend opposite to that of $\unicode[STIX]{x1D6FD}_{cr}$. Three physical mechanisms are identified as being responsible for the observed variation trend of $\unicode[STIX]{x1D6FD}_{cr}$ with $e/D$ and for various flow phenomena, which are the blockage effect induced by the geometry setting, the existence of the Stokes layer on the plane boundary and the favourable pressure gradient in the flow direction over the gap between the cylinder and the plane surface.

JFM classification

Instability: Absolute/convective instability Boundary Layers: Boundary layer structure
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 852 , 10 October 2018 , pp. 226 - 256
Copyright
© 2018 Cambridge University Press 

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