Oscillatory flow around a vertical circular cylinder placed in an open channel: coherent structures, sediment entrainment potential and drag forces

Abstract

Flow and turbulent structures generated by the interaction of forced incoming oscillatory flow with a circular, vertical cylinder placed in an open channel with a horizontal bed are investigated using eddy-resolving simulations. Validation simulations performed with a Keulegan–Carpenter (KC) number of 20 and multiple-mode forcing corresponding to the laboratory experiment of Sumeret al.(J. Fluid Mech., vol. 332, 1997, pp. 41–70) show that detached eddy simulation (DES) predicts more accurately the amplification of the bed shear stress beneath the horseshoe vortex system (upstream side of the cylinder) and the maximum magnitude of the bed shear stress at the downstream (wake) side of the cylinder compared with unsteady Reynolds-averaged Navier–Stokes simulations. High-Reynolds-number DES simulations are then conducted with 1.5 ≤ KC ≤ 30.8 and one-mode sinusoidal forcing of the streamwise velocity in the approaching flow to investigate the changes in the wake vortex-flow regimes, the coherence of the horseshoe vortices and the generation of other near-bed coherent structures in the wake during the oscillatory cycle. The flow is periodic, no horseshoe vortices form and no vortices are shed in the wake forKC = 1.5. By contrast, forKC ≥ 8 horseshoe vortices are present over part of the oscillatory cycle and up to three wake vortices are shed over each half-cycle asKCis increased to 30.8. For an intermediate range ofKCnumbers, one (KC = 15.4) or two (KC = 8) of the vortices forming at the back of the cylinder during each half-cycle are washed around it when the flow reverses. The main horseshoe vortex and other horizontal near-bed vortices have a large capacity to amplify the bed shear stresses when the incoming velocity magnitude is significantly less than its peak value. Assuming the depth-averaged velocity in the incoming (undisturbed) oscillatory flow is the same in simulations conducted with differentKCnumbers, the peak values of the sediment entrainment potential measured by the mean (cycle-averaged) volumetric flux of sediment entrained from the bed over one oscillatory cycle occur for 8 ≤ KC ≤ 15.4. For allKCnumbers, the in-line force variation over the oscillatory cycle is fairly well approximated by the Morison equation. ForKC = 1.5, the in-line force is only due to inertia effects. ForKC = 30.8, the maximum and minimum values of the phase-averaged in-line force are approximatively in phase with those of the incoming flow velocity. ForKC ≥ 15, the phase-averaged in-line force coefficients vary between 0.8 and 1.1 during most of the oscillatory cycle (e.g. when the incoming flow velocity is not close to zero). This is different from cases withKC ≤ 8 where the in-line force coefficient is equal to zero twice during the oscillatory cycle as the in-line force becomes equal to zero for non-zero values of the incoming velocity. The largest cycle-to-cycle variations of the in-line force coefficient and in-line force are observed aroundKC = 8. ForKC = 8 and 15.4, the cylinder is subject to relatively large phase-averaged spanwise drag forces that are comparable to the peak phase-averaged streamwise drag forces. AsKCis increased to 30.8, the phase-averaged spanwise drag force becomes zero over the whole oscillatory cycle but the cylinder is still subject to large instantaneous spanwise forces over part of the oscillatory cycle.