Vortex-induced vibrations of cylinders bent by the flow

Flexible cylinders exposed to transverse flows may undergo transverse vortex-induced vibrations due to the oscillating lift force imposed by their wake. But the drag on such structures often leads to large in-line deflections that may significantly affect the dynamics through the combined effects of the curvature-induced tension, the local inclination of the cylinder, the non-uniformity of the normal flow profile, and the large axial flow component. In this paper, we investigate the consequences of flow-induced bending on the vortex-induced dynamics of slender cantilever cylinders, by means of numerical simulations. We combine a distributed wake oscillator approach to model the dynamics of the wake with Lighthill's large-amplitude elongated body theory to account for the effect of the axial flow in the reactive (added mass) force. The use of such reduced order models facilitates the identification of the physical mechanisms at play, including through the linear analysis of the coupled fluid–structure system. We find that the primary consequence of flow-induced bending is the inhibition of single mode lock-in, replaced by a multi-frequency response of the structure, and the reduction of the vibration amplitude, as a result of the broadening of the wake excitation spectrum and of the localization of the energy transfer due to the variations induced in the normal flow profile. We also find that the curvature-induced tension is of negligible influence, but that the axial flow component may on the other hand significantly alter the dynamics owing to the destabilizing effect of the reactive force on the structural modes.