Influence of plane boundary proximity on the Honji instability

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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 (β) and gap-to-diameter ratios (e/D) at a fixed Keulegan-Carpenter number (KC = 2). Four flow regimes are identified in the (e/D, β)-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 βcr 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 ≤ e/D ≤ 2 and occurs only on the top side for -0.5 ≤ 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 βcr. Three physical mechanisms are identified as being responsible for the observed variation trend of βcr 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.

Original languageEnglish
Pages (from-to)226-256
Number of pages31
JournalJournal of Fluid Mechanics
Volume852
DOIs
Publication statusPublished - 10 Oct 2018

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