Title: On the Mechanism of Large Amplitude Flapping of Inverted Foil in a Uniform Flow,
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. Here, we perform three-dimensional numerical experiments
to examine the role of vortex shedding and the vortex-vortex interaction on the
LAF response at Reynolds number Re=30,000. Here 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
trailing edge and inhibit the interaction between the counter-rotating
vortices. 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. However, the inhibition of the trailing edge vortex 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$\in[0.1,50]$) 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. However, the
flexible foil still loses its stability through divergence instability to
undergo a large static deformation. 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.