Optimizing energy production from vortex-induced vibrations using control strategy deduced from an exact nonlinear asymptotic model

We investigate the onset of vortex-induced vibrations (VIVs) in the wake of a spring-mounted, damped, rigid circular cylinder immersed in a viscous flow. We undertake an asymptotic expansion to compute analytically the leading-order equations describing the nonlinear interaction of the fluid and structural modes close to the threshold of instability of the fluid-only system. By doing so, it is possible to derive a simple model rigorously valid for small departures from the instability threshold and small cylinder displacements, for which the wake dynamics is governed by the exact Navier-Stokes equations. The ability of the model to reproduce the physics of VIVs can be assessed from the analysis of the nonlinear limit cycles reached naturally by the system at large time. VIVs are thought here to be used for energy production. Consequently, we address the question of the forced dynamics, and shown that it is possible to optimize the magnitude of energy dissipated by structural damping (at disposal to be harnessed) provided a convenient control velocity is applied at the cylinder wall, whose amplitude is determined in the framework of feedback control.