3D wake dynamics and large-amplitude flapping of an inverted elastic flag

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. To examine the 3D wake-vortex structures and the LAF response, we present 3D numerical experiments at Reynolds number Re=30,000 by assuming spanwise periodicity. We further investigate the dynamics of a novel inverted foil configuration wherein we introduce a fixed splitter plate at the trailing edge to suppress the vortex shedding from trailing edge and 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 vortex interaction has an insignificant effect on the transverse flapping amplitudes. Finally, we introduce an analogous analytical model for the LAF based on the dynamics of an elastically mounted flat plate undergoing flow-induced pitching oscillations in a uniform stream.