Passive locomotion of freely movable flexible fins near the ground

Abstract

We numerically examine the hydrodynamic interaction between a flexible fin and surrounding fluid near the ground when four relevant parameters of initial position, bending rigidity, mass ratio and Reynolds number are varied. The leading edge of the fin is fixed in the streamwise direction, whereas the lateral motion is freely movable by the fluid-flexible body interaction near the ground. When the fin is initially positioned far from the ground, the fin passively migrates toward another wall-normal position near the ground for an equilibrium state due to larger positive deflection angle for the fin than the negative angle by the effects of vorticity generated by the lateral velocity gradient near the ground. In addition, as the flapping amplitude of the fin is small for large bending rigidity and small mass ratio, the great asymmetry between the positive and negative deflection angles reduces the transient time of the fin to reach the equilibrium position near the ground, and thus the fins can quickly take the hydrodynamic benefits with low drag at an equilibrium state without any energy consumption for lift force due to local balance between the flapping motion and the ground. The most important observation is that the equilibrium position of the fin is invariant to the initial position, bending rigidity and mass ratio of the fin. However, the equilibrium position of the fin is dramatically affected by the Reynolds number. The present results provide new insights into the functional role of the relevant parameters in passively flapping-based locomotion near the ground.