Energy harvesting by flow-induced flutter in a simple model of an inverted piezoelectric flag

Abstract

Two-dimensional numerical simulations are used to study the coupled fluid–structure–electric interaction of a simple model of an inverted piezoelectric flag, and to investigate the dynamics of the flow–structure interaction of this configuration as well as its energy harvesting performance. In particular, the dynamic response of the inverted flag as well as the associated flow patterns are examined for a range of inertia, bending stiffness and Reynolds numbers, and categorized into distinct vibrational states based on the symmetry of the motion as well as the amplitude. Simulations indicate that large-amplitude vibrations can be achieved over a large range of parameters and there is also evidence of lock-on between the flag flutter and the intrinsic wake shedding phenomenon. The initial inclination of the flag to the prevailing flow is found to significantly affect the flutter performance for inclination angles exceeding $15^{\circ }$. The state with large symmetric flutter is identified as being most promising for energy harvesting, and the effect of piezoelectric material parameters on the energy harvesting performance of this flutter state is examined in detail. The maximum energy efficiency of the flags is found to be approximately $7\,\%$, and the maximum occurs when there is a match between the time scales of flutter and the intrinsic time scale of the piezoelectric circuit. The simulations are used to examine a simple scaling law that could be used to predict the energy harvesting performance of such devices.