Flapping dynamics of an inverted flag

Abstract

The dynamics of an inverted flag are investigated experimentally in order to find the conditions under which self-excited flapping can occur. In contrast to a typical flag with a fixed leading edge and a free trailing edge, the inverted flag of our study has a free leading edge and a fixed trailing edge. The behaviour of the inverted flag can be classified into three regimes based on its non-dimensional bending stiffness scaled by flow velocity and flag length. Two quasi-steady regimes, straight mode and fully deflected mode, are observed, and a limit-cycle flapping mode with large amplitude appears between the two quasi-steady regimes. Bistable states are found in both straight to flapping mode transition and flapping to deflected mode transition. The effect of mass ratio, relative magnitude of flag inertia and fluid inertia, on the non-dimensional bending stiffness range for flapping is negligible, unlike the instability of the typical flag. Because of the unsteady fluid force, a flapping sheet can produce elastic strain energy several times larger than a sheet of the deformed mode, improving the conversion of fluid kinetic energy to elastic strain energy. According to the analysis of the leading-edge vortex formation process, the time scale of optimal vortex formation correlates with efficient conversion to elastic strain energy during bending.

Large amplitude flow-induced oscillations and energy harvesting using a cyber-physical pitching plate

“…6, large amplitude LCOs will persist until the system encounters a saddle-node bifurcation at 1=k n % 0:3, where the stable and unstable LCOs coalesce. A similar hysteretic behavior has been also observed by a number of investigators (e.g., Razak et al, 2011;Amandolese et al, 2013;Kim et al, 2013), although the ranges of the hysteresis reported in these studies are generally smaller than what we observed in the present study. In Region III, the oscillations are symmetric about α ¼ 0 and have a nearly sinusoidal character with a welldefined frequency.…”

“…6 or 7). Similar dynamical regimes have been reported by Dimitriadis and Li (2009), who studied the stall flutter behaviors of a symmetric airfoil with pitch-plunge degrees of freedom and also by Kim et al (2013) who examined a self-excited flapping behavior of the inverted flexible flag model with a free leading edge and a clamped trailing edge. We discuss each of these regimes in more detail in the next few paragraphs.…”

Dynamics of fluid flow over a circular flexible plate

“…This behaviour is also consistent with the experimental finding that the mass ratio has negligible effect on the flapping dynamics of an inverted flag, i.e. a free leading edge and a fixed trailing edge of a flexible plate (Kim et al 2013).…”

“…On the other hand, fluid flow over flexible structures is also commonly observed and some problems have been studied, such as the flutter of a flag in wind (e.g. Connell & Yue 2007;Huang & Sung 2010;Kim et al 2013), the reconfiguration of plants subject to external load (e.g . Vogel 1996;Schouveiler & Boudaoud 2006;Gosselin, de Langre & Machado-Almeida 2010), and the locomotion of swimming and flying animals by flapping wings or fins (e.g.…”

Coupling Motion and Energy Harvesting of Two Side-by-Side Flexible Plates in a 3D Uniform Flow

“…The conversion efficiency from the fluid kinetic energy to the plate's bending energy can be defined as [51]:…”