The flow past a circular cylinder translating at different heights above a wall

Abstract

The flow past a circular cylinder moving through a fluid at different heights above a plane no-slip boundary is investigated numerically for Reynolds numbers ≤200. The gap height is varied from large values, effectively corresponding to the freestream case (G/D=∞), down to a small value where the cylinder is just above the wall (G/D=0.005). The initial transition from steady two-dimensional flow can occur through either a Hopf bifurcation to unsteady flow or through a regular bifurcation to steady three-dimensional flow. The critical Reynolds numbers for each case are determined as a function of gap height. It is found that steady two- to three-dimensional transition occurs first at gap ratios G/D≲0.25, beyond which the initial transition is to unsteady flow. At G/D=0.3, a sharp increase in the critical Reynolds number is observed at which three-dimensionality occurs. On increasing gap height, the critical Reynolds number initially decreases before again increasing towards the value observed for an isolated cylinder. The force coefficients and Strouhal numbers are quantified. Finally, three-dimensional simulations are performed at Re=200 for the smallest gap ratio, effectively corresponding to a cylinder sliding along a wall, to examine how the wake evolves as it saturates.