Orbital flow around a circular cylinder. Part 2. Attached flow at larger amplitudes

Abstract

A time-stepping numerical model of uniform circular orbital flow around a cylinder provides results which are compared with the steady-state predictions of a boundary-layer solution by Riley. At small amplitudes of motion excellent agreement is found in most respects, but in the numerical model the outer recirculating flow and related components of loading do not reach a steady state after any finite time. At a Stokes parameter β of 500, the boundary-layer approach remains reasonably accurate for amplitudes of motion up to about 8 % of the cylinder diameter; for amplitudes up to twice this at the same value of β the flow remains largely attached. The strength of the outer recirculating flow is enhanced by nonlinear interactions, but the computed nonlinear loading exceeds that observed in experiments. Flow visualization shows a three-dimensional structure in the flow, and it is argued that this has an important effect on the loading that cannot yet be predicted. A computed force component at a frequency of about 30 % of that of the ambient flow is related to the retrogressive motion of vortex structures around the cylinder.