Energy Production Characteristics of a Spring-Mounted Cantilevered-Free Flexible Plate in a Uniform Flow

Abstract

We study a new fundamental system that comprises a cantilevered thin flexible plate exactly aligned with the direction of a uniform flow in which the upstream end of the flexible plate is not fixed. Instead, it is attached to a spring-damper system that allows the entire system to oscillate perpendicularly to the flow direction as a result of the mounting’s dynamic interaction with the flow-induced oscillations of the flexible plate. This models an energy-harvesting system whereby the rate of energy extraction by the damper represents power generation from the kinetic-energy flux of the mean flow transferred via fluttering motions of the flexible plate to the motion of the mounting system. The two-dimensional modelling presented is an extension of the methods in [1,2] that mixed numerical simulation with eigenvalue analysis to study a fixed cantilevered flexible plate. The present system also includes a rigid inlet surface upstream of and fixed to the spring-mounted cantilever. Ideal flow is assumed wherein the rotationality of the boundary-layers is modelled by vortex elements on the solid-fluid interface and the imposition of the Kutta condition at the plate’s trailing edge. The Euler-Bernoulli beam model is used for the structural dynamics.Results presented first show how the replacement of the fixed leading edge with an interactively oscillating mounting modify the well-known linear-stability characteristics of a fluttering plate. The overall effect is that the critical flow speed for flutter onset is reduced and this is desirable for the present energy-harvesting application. This entails some subtle but important changes to the destabilisation mechanisms. The power generating potential of the fluid-structure interaction system is then illustrated. The present model of the dynamics of the plate-support interaction has been simplified so as to demonstrate proof-of-concept; thus, a discussion of the way forward to a more complete model is presented to close the paper.