Global modes and nonlinear simulations of inverted flag flapping

Inverted flag flapping, in which the flag is clamped at its trailing edge with respect to the oncoming flow, is capable of undergoing substantially larger-amplitude flapping than in the conventional configuration, where the flag is pinned or clamped at its leading edge. The associated increase in bending makes the inverted flag system a promising candidate for energy harvesting technologies that convert strain energy to electricity using, \emph{e.g.} piezoelectric materials. Because of this potential, recent studies have sought to investigate the response of the inverted flag system for a range of physical parameters. Of particular interest for this study, vortex shedding has been associated with large-amplitude flapping, and Sader \emph{et al.} (2016) showed that flapping possesses many features of a vortex-induced vibration (VIV) for a range of physical parameters. In this talk, we use a global mode analysis and nonlinear simulations to identify the mechanisms that initiate flapping. VIV is confirmed for a range of flow/flag parameters, and is shown to be initiated by an inherent instability in the deflected flag's equilibrium. Moreover, it is shown that non-VIV flapping is possible under a certain parameter space. This is yet to be observed experimentally.