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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: [email protected]
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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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References

An, H., Cheng, L. & Zhao, M. 2010 Steady streaming around a circular cylinder near a plane boundary due to oscillatory flow. J. Hydraul. Engng 137 (1), 23–33.Google Scholar
An, H., Cheng, L. & Zhao, M. 2011 Direct numerical simulation of oscillatory flow around a circular cylinder at low Keulegan–Carpenter number. J. Fluid Mech. 666, 77–103.Google Scholar
Barkley, D. & Henderson, R. D. 1996 Three-dimensional floquet stability analysis of the wake of a circular cylinder. J. Fluid Mech. 322, 215–241.Google Scholar
Bearman, P. W., Downie, M. J., Graham, J. M. R. & Obasaju, E. D. 1985 Forces on cylinders in viscous oscillatory flow at low Keulegan–Carpenter numbers. J. Fluid Mech. 154, 337–356.Google Scholar
Bearman, P. W. & Mackwood, P. R. 1992 Measurements of the hydrodynamic damping of circular cylinders. In Proceedings of 6th International Conference on the Behaviour of Offshore Structures (BOSS 92), vol. 1, pp. 405–414. BPP Tech Services Ltd.Google Scholar
Blackburn, H. M. & Henderson, R. D. 1999 A study of two-dimensional flow past an oscillating cylinder. J. Fluid Mech. 385, 255–286.Google Scholar
Bolis, A.2013 Fourier spectral/ $hp$ element method: investigation of time-stepping and parallelisation strategies. PhD thesis, Imperial College London.Google Scholar
Cantwell, C. D., Moxey, D., Comerford, A, Bolis, A., Rocco, G., Mengaldo, G., De Grazia, D., Yakovlev, S., Lombard, J.-E., Ekelschot, D. et al. 2015 Nektar++: An open-source spectral/hp element framework. Comp. Phys. Comm. 192, 205–219.Google Scholar
Carstensen, S., Sumer, B. M. & Fredsøe, J. 2010 Coherent structures in wave boundary layers. Part 1. Oscillatory motion. J. Fluid Mech. 646, 169–206.Google Scholar
Elston, J. R., Blackburn, H. M. & Sheridan, J. 2006 The primary and secondary instabilities of flow generated by an oscillating circular cylinder. J. Fluid Mech. 550, 359–389.Google Scholar
Hall, P. 1984 On the stability of the unsteady boundary layer on a cylinder oscillating transversely in a viscous fluid. J. Fluid Mech. 146, 347–367.Google Scholar
Honji, H. 1981 Streaked flow around an oscillating circular cylinder. J. Fluid Mech. 107, 509–520.Google Scholar
Hussain, A. F. 1986 Coherent structures and turbulence. J. Fluid Mech. 173, 303–356.Google Scholar
Justesen, P. 1991 A numerical study of oscillating flow around a circular cylinder. J. Fluid Mech. 222, 157–196.Google Scholar
Karniadakis, G. E. & Sherwin, S. 2013 Spectral/hp Element Methods for Computational Fluid Dynamics. Oxford University Press.Google Scholar
Reed, H. L., Saric, W. S. & Arnal, D. 1996 Linear stability theory applied to boundary layers. Annu. Rev. Fluid Mech. 28 (1), 389–428.Google Scholar
Rocco, G.2014 Advanced instability methods using spectral/ $hp$ discretisations and their applications to complex geometries. Thesis, Imperial College London.Google Scholar
Sarpkaya, T. 1976 Forces on cylinders near a plane boundary in a sinusoidally oscillating fluid. J. Fluids Engng 98 (3), 499–503.Google Scholar
Sarpkaya, T. 2002 Experiments on the stability of sinusoidal flow over a circular cylinder. J. Fluid Mech. 457, 157–180.Google Scholar
Sarpkaya, T. 2006 Structures of separation on a circular cylinder in periodic flow. J. Fluid Mech. 567, 281–297.Google Scholar
Scandura, P., Armenio, V. & Foti, E. 2009 Numerical investigation of the oscillatory flow around a circular cylinder close to a wall at moderate Keulegan–Carpenter and low Reynolds numbers. J. Fluid Mech. 627, 259–290.Google Scholar
Shen, L. & Chan, E. 2013 Numerical simulation of oscillatory flows over a rippled bed by immersed boundary method. Appl. Ocean Res. 43, 27–36.Google Scholar
Suthon, P. & Dalton, C. 2012 Observations on the Honji instability. J. Fluid Struct. 32 (3), 27–36.Google Scholar
Tatsuno, M. & Bearman, P. W. 1990 A visual study of the flow around an oscillating circular cylinder at low Keulegan–Carpenter numbers and low Stokes numbers. J. Fluid Mech. 211, 157–182.Google Scholar
Xiong, C., Cheng, L., Tong, F. & An, H. 2018 Oscillatory flow regimes for a circular cylinder near a plane boundary. J. Fluid Mech. 844, 127–161.Google Scholar
Yang, K., Cheng, L., An, H., Bassom, A. P & Zhao, M. 2014 Effects of an axial flow component on the Honji instability. J. Fluid Struct. 49, 614–639.Google Scholar