Vortex-induced vibrations of a flexible cylinder at subcritical Reynolds number

The flow past a fixed rigid cylinder becomes unsteady beyond a critical Reynolds number close to 47, based on the body diameter and inflow velocity. The present paper explores numerically the vortex-induced vibrations (VIV) that may develop for a flexible cylinder at subcritical Reynolds number (Re), i.e. for Re < 47. Flexible-cylinder VIV are found to occur down to Re approximate to 20, as previously reported for elastically mounted rigid cylinders. A detailed analysis is carried out for Re = 25, in two steps: the system behaviour is examined from the emergence of VIV to the excitation of the first structural modes; and then focus is placed on higher-mode responses. In all cases, a single vibration frequency is excited in each direction. The cross-flow and in-line responses exhibit contrasting magnitudes (peak amplitudes of 0.35 versus 0.01 diameters), as well as distinct symmetry properties and evolutions (e.g. standing/travelling waves). The flow, unsteady once the cylinder vibrates, is found to be temporally and spatially locked with body motion. The synchronization with the cross-flow standing-wave responses is accompanied by the formation of cellular wake patterns, regardless of the modes involved in the vibrations. Body trajectory varies along the span, but dominant orbits can be identified. Despite the low amplitudes of the in-line responses, connections are uncovered between orbit orientation and flow-structure energy transfer, with different trends in each direction.