Hydrodynamic performance of an unconstrained flapping swimmer with flexible fin: A numerical study

Flexible tail fins are commonly found in undulatory swimmers which can propel freely in omni-direction with flapping-wing-based propulsion. In this work, the hydrodynamic performance of an unconstrained flapping foil equipped with a flexible tail fin at different length is investigated numerically. As the fin length L-fin changes from 0.2c to c with c being the cord length, the propelling speed of the system first increases and then decreases after maximum propelling speed is achieved when the fin length is 0.8c. There are two kinds of wake vortical structures observed with bending stiffness k(b) = 2.0: (i) the regular reverse Benard-von Karman vortex configuration for foil with short fin and (ii) the aligned vortices with two-layered street at downstream for foil with long fin ( L-fin & GE; 0.6c). Control volume analysis reveals that for both types of vortical structures, the time-averaged thrust force is mainly related to the momentum flux contribution from the downstream face. Besides, the wake symmetry of a pitching foil with flexible tail fin is sensitive to the vertical phase velocity of vortices, where it can be used to predict whether the wake symmetry of the unconstrained system is preserved. Moreover, the bending stiffness effectively affects the hydrodynamic performance, and the breaking of wake symmetry greatly reduces the propulsive efficiency. The results obtained shed some new light on the role of flexible structures in the self-propulsive biological system and furthered our understanding of flexible self-propulsion system.