Large amplitude flapping of an inverted elastic foil in uniform flow with spanwise periodicity

Abstract

An elastic foil interacting with a uniform flow with its trailing edge clamped, also known as the inverted foil, exhibits a wide range of complex self-induced flapping regimes such as large amplitude flapping (LAF), deformed and flipped flapping. In particular, the LAF is of interest for its applications in the development of energy harvesting devices. Here, we perform three-dimensional numerical experiments assuming spanwise periodicity on the LAF response of an inverted foil at Reynolds number Re=30,000 for a relatively low mass-ratio m∗=1.0 using a variational fluid–structure formulation and large-eddy simulation (LES). We examine the role of the vortex structures particularly the counter-rotating periodic vortices generated from the leading and trailing edges of the inverted foil, and the interaction between them on the LAF. For that purpose, we investigate the dynamics of the inverted foil for a novel configuration wherein we introduce a fixed splitter plate at the trailing edge to suppress the vortex shedding from the trailing edge and thereby inhibit the interaction between the counter-rotating vortices. Unlike the vortex-induced vibration of an elastically-mounted circular cylinder, we find that the inhibition of the interaction has an insignificant effect on the transverse flapping amplitudes, due to a relatively weaker coupling between the counter-rotating vortices emanating from the leading edge and trailing edge. The inhibition of the trailing edge vortex generally reduces the streamwise flapping amplitude, the flapping frequency and the net strain energy of foil. To further generalize our understanding of the LAF, we next perform low-Reynolds number (Re∈[0.1,50]) simulations for the identical foil properties to realize the impact of vortex shedding on the large amplitude flapping. Due to the absence of vortex shedding process in the low-Re regime, the inverted foil no longer exhibits the periodic flapping. Nevertheless, the flexible foil still loses its stability through divergence instability to undergo a large static deformation. This study has implications on the development of novel control mechanisms for energy harvesting and propulsive devices.