Controlling the chaotic wake of a flapping foil by tuning its chordwise flexibility

Effects of chord-wise flexibility as an instrument to control chaotic transitions in the wake of a flexible flapping foil have been studied here using an immersed boundary method-based in-house fluid-structure-interaction solver. The ability of the flapping foil at an optimum level of flexibility to inhibit chaotic transition, otherwise encountered in a similar but rigid configuration, has been highlighted. The rigid foil manifests chaotic transition through a quasi-periodic-intermittency route at high dynamic plunge velocities; whereas, increasing the level of flexibility gradually regularises the aperiodic behaviour through a variety of interesting wake patterns. If flexibility is increased beyond an optimum level, aperiodicity sets in again and robust chaos is restored at very high flexibility levels. The mechanisms of triggering the order-to-chaos transition are different between the rigid and the high flexibility cases. Along the route to order and back to chaos, the flexible foil exhibits different flow-field behaviours, including far-wake switching, primary \& secondary vortex streets, bifurcated wakes and interactive vortices between the bifurcated wakes. The underlying interaction mechanisms of the flow-field vortices responsible for the associated dynamical signatures of the wake have been closely tracked. This study further examines the optimum propulsive performance range of the flexible flapper and investigates its connection with the periodicity/regularity of the system.