Flow energy harvesting by fluttering slender bodies in axial currents

Coupled fluid-solid instabilities offer promising perspectives for the development of new technologies to harvest energy from water currents. A fundamental study of these instabilities and of the impact of the damping induced by the energy harvesting on the fluid-solid system is essential to identify promising configurations, quantify energy harvesting potential and characterize possible design optimization. In this work, we focus on the dynamics of long flexible cylinders placed in axial currents. It is well established that above a critical velocity threshold the flexible cylinder's rest position becomes unstable to flutter and self-sustained limit-cycle oscillations can develop. A fraction of the solid kinetic energy can then be converted into electrical form, acting as a dissipative mechanism on the fluid-solid system. The non-linear dynamics of the dissipative system are studied in this paper using a reduced-order model of the deformable cylinder in the form of a bi-articulated system of two rigid cylinders with energy harvesting at each articulation. The impact of energy extraction on the system's properties and the optimal placement of energy harvesters are then analyzed and discussed. It is shown that optimal energy harvesting only involves a single harvester at the upstream end, away from the region of useful curvature that drives the instability mechanism at the origin of the self-sustained oscillations.