Oscillatory flow regimes for a circular cylinder near a plane boundary

Abstract

Oscillatory flow around a circular cylinder close to a plane boundary is numerically investigated at low-to-intermediate Keulegan–Carpenter ($KC$) and Stokes numbers ($\unicode[STIX]{x1D6FD}$) for different gap-to-diameter ratios ($e/D$). A set of unique flow regimes is observed and classified based on the established nomenclature in the ($KC,\unicode[STIX]{x1D6FD}$)-space. It is found that the flow is not only influenced by $e/D$ but also by the ratio of the thickness of the Stokes boundary layer ($\unicode[STIX]{x1D6FF}$) to the gap size (e). At relatively large $\unicode[STIX]{x1D6FF}/e$ values, vortex shedding through the gap is suppressed and vortices are only shed from the top of the cylinder. At intermediate values of $\unicode[STIX]{x1D6FF}/e$, flow through the gap is enhanced, resulting in horizontal gap vortex shedding. As $\unicode[STIX]{x1D6FF}/e$ is further reduced below a critical value, the influence of $\unicode[STIX]{x1D6FF}/e$ becomes negligible and the flow is largely dependent on $e/D$. A hysteresis phenomenon is observed for the transitions in the flow regime. The physical mechanisms responsible for the hysteresis and the variation of marginal stability curves with $e/D$ are explored at $KC=6$ through specifically designed numerical simulations. The Stokes boundary layer over the plane boundary is found to be responsible for the relatively large hysteresis range over $0.25<e/D<1.0$. Three mechanisms have been identified to the change of the marginal stability curve over $e/D$, which are the blockage effect due to the geometry setting, the favourable pressure gradient over the gap and the location of the leading eigenmode relative to the cylinder.

Oscillatory flow regimes around four cylinders in a diamond arrangement

“…2015; Xiong et al. 2018 a ). Although 3-D flow features develop in most of the regimes other than and A, Nehari et al.…”

“…(1998) and Xiong et al. (2018 a ). The results mentioned above demonstrate that the numerical scheme based on Nektar++ is valid and the mesh quality is adequate.…”

“…(2015) and Xiong et al. (2018 a ), respectively. The two-dimensional (2-D) states of symmetry of the cross-sectional flows, as summarized by Elston, Sheridan & Blackburn (2004), are listed below.…”

“…(2015) and ( b ) flow features presented by streaklines by Xiong et al. (2018 a ) for regime at ; regime A at (11, 81.4); regime C at (5, 180); regime D at (6.28, 138.8); regime E at (6.28, 160.8); and regime F at (8.16, 220.3). The particles released from the upper and lower surfaces of the cylinder are dyed red and blue, respectively.…”

“…2017; Xiong et al. 2018 a ). At relatively low Re ( 1200) and KC ( 15), the flow exhibits a number of distinct features.…”