Influence of plane boundary proximity on the Honji instability

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.

The upper-bound limit of Stokes-Wang solution for oscillatory flow around a circular cylinder

“…The spanwise averaged cross-sectional flow fields (not shown here) are similar to their counterparts obtained from 2-D DNS. This observation is consistent with previous findings in literature of oscillatory flow past cylinder(s)[14,[16][17][18]. Since the primary objective of this study is on CD and CM and 3-D simulations at high β constitute a daunting task computationally, the following discussions are based on the results from 2-D DNS.…”

The bypass transition mechanism of the Stokes boundary layer in the intermittently turbulent regime

“…The existence of inflection points in the velocity profiles of a laminar Stokes boundary layer at different phases shown in figure 4 is directly responsible for the destabilisation of the negative vortex layer, as indicated in figure 3(a,b) at t/T = 0.469. The boundary layer separation and vortex shedding are observed in figure 3(c), possibly due to the large size of roughness element h = 1 that acts like a bluff body attached to the wall (Xiong et al 2018a). The corrugation of the positive vortex layer and the further formation of a counter-rotating vortex pair after the flow reversal, which are observed at t/T = 0.562 in figure 3, resulted from the nonlinear evolution of the inflection-point instability, as suggested by Scandura (2013).…”

Hydrodynamic damping of an oscillating cylinder at small Keulegan–Carpenter numbers

“…The present blockage ratios are 2 % and 1 % respectively for K ≤ 3 and K > 3, which are judged to be adequate based on the experiences reported in the literature. For instance, previous investigations on Honji instabilities by An, Cheng & Zhao (2011), Suthon & Dalton (2011) and Xiong et al (2018a) employed domain sizes with blockage ratios of 6.67 %, 2.5 % and 1.67 % respectively. For studies associated with quantifying flow regimes on multiple cylinders, 1.67 % and 3.33 % were used for two circular cylinders (Zhao & Cheng 2014) and the range 2 %-2.91 % was selected for a cluster of four cylinders (Tong et al 2015;Ren et al 2019).…”

“…Previous studies (e.g. An et al 2011;Xiong et al 2018a) showed that good correlations exist between L z and the characteristic length of 3-D structures (λ), which can be estimated according to the empirical formula proposed by Sarpkaya (2002) as, λ/D = 22β −3/5 ( λ ∼ 0.34D at β = 1035). Xiong et al (2018a) suggested that a ratio of L z /λ ≈ 3 and N z = 18 are generally adequate in resolving spanwise structures of oscillatory flows.…”

“…2011; Xiong et al. 2018 a ) showed that good correlations exist between and the characteristic length of 3-D structures (), which can be estimated according to the empirical formula proposed by Sarpkaya (2002) as, ( at ). Xiong et al.…”