Hydrodynamics of Cylinders Oscillating with Small Amplitude in Still Fluid or Free Stream

Abstract

In the present study, we conducted numerical simulations of the two-dimensional viscous flow around a harmonically oscillating cylinder in a still fluid or transverse to a free stream at a Keulegan–Carpenter number of 0.5, a Stokes number of 200 and varying ratios of the free-stream velocity to the maximum oscillation velocity. The unsteady force in the direction of motion obtained from the simulations in still fluid is in excellent agreement with the analytical solutions of Stokes and Wang that are pertinent to attached flow around the cylinder. We demonstrate that the analytical solutions are valid also in separated flows occurring for corresponding cylinder oscillations transverse to a free stream for velocity ratios up to 2.0. At a velocity ratio of 5.0, the hydrodynamic force exhibits substantial deviations from the theoretical force due to the increased level of the fluctuations induced by the vortex shedding in the wake. These findings indicate that the ‘inviscid potential force’ due to the irrotational flow is embedded in the general viscous flow. However, we find that the hydrodynamic force in the streamwise direction exhibits fluctuations at twice the frequency of oscillation; interaction between the no-slip boundary condition and the potential of the irrotational flow around the cylinder seems likely to be the reason behind this phenomenon.