Investigating the Effect of Chord-wise Flexibility to Control Aperiodicity in the Flow-field around a Flapping Foil

Bio-inspired Flapping-wing Micro Air Vehicle (FMAV) has received significant attention in recent times due to its multi-fold applications. The present work investigates the nonlinear Fluid-Structure Interaction (FSI) of a chord-wise flexible flapping foil with surrounding unsteady flow-field at a low Reynolds number (Re = 300). The foil is modeled as an inextensible flexible filament, and heaving motion is prescribed at the leading edge. The aerodynamic loads on the foil are computed using a discrete forcing Immersed Boundary Method (IBM) based in-house FSI solver. Numerical simulations have been performed at different heave amplitudes for various flexibility values $(\gamma)$ of the foil. It is observed that the system transitions from periodicity to chaos at the heaving amplitude of $0.475$ for the rigid foil. However, when flexibility is introduced, the foil with bending rigidity, $\gamma=1.0$  shows periodic dynamics up to the heaving amplitude of $0.575$. Surprisingly, higher flexibility ($\gamma < 1.0$) advances the onset to a chaotic regime. Therefore, the proper choice of flexibility can be effective in delaying aperiodicity in the flow field. Time series analysis tools have been employed to characterize various dynamical states of the coupled FSI system.