Hydroelastic response and energy harvesting potential of flexible piezoelectric beams in viscous flow

Abstract

Electroactive polymers such as piezoelectric elements are able to generate electric potential differences from induced mechanical deformations. They can be used to build devices to harvest ambient energy from natural flow-induced deformations, e.g., as flapping flags subject to flowing wind or artificial seaweed subject to waves or underwater currents. The objectives of this study are to (1) investigate the transient hydroelastic response and energy harvesting potential of flexible piezoelectric beams fluttering in incompressible, viscous flow, and (2) identify critical non-dimensional parameters that govern the response of piezoelectric beams fluttering in viscous flow. The fluid-structure interaction response is simulated using an immersed boundary approach coupled with a finite volume solver for incompressible, viscous flow. The effects of large beam deformation, membrane tension, and coupled electromechanical responses are all considered. Validation studies are shown for the motion of a flexible filament in uniform flow, and for a piezoelectric beam subject to base vibration. The predicted flutter velocities and frequencies also compared well with published experimental and numerical data over a range of Reynolds numbers for varying fluid and solid combinations. The results showed that for a heavy beam in a light fluid (i.e., high βρ regime), flutter incepts at a lower critical speed with a lower reduced frequency than for a light beam in a heavy fluid (i.e., low βρ regime). In the high βρ regime, flutter develops at the second mode and is only realized when the fluid inertial forces are in balance with the solid elastic restoring forces, which leads to large amplitude oscillations and complex wake patterns; the flutter speed is practically independent of the Reynolds number (Re) and solid to fluid mass ratio (βρ), because the response is dominated by the solid inertial forces. In the low βρ regime, fluid inertial forces dominate, flutter develops at higher modes and is only realized when the solid inertial forces are proportioned to the solid elastic restoring forces; the flutter speed depends on both Re and βρ, and viscous force and beam tension effects tend to delay flutter and reduce vibration amplitudes, leading to thinner, more simplified wake patterns. The results demonstrate that energy extraction via fluttering piezoelectric beams is possible. The overall efficiency was observed to be influenced by the piezoelectric circuit resistance, which is known to be directly related to the square of the piezoelectric coupling factor. The results show that the maximum strain limit of piezoelectrics may be exceeded, and hence careful optimization of the material and geometry is recommended to maximize the energy capture for a given range of expected flow conditions while satisfying safety and reliability requirements.