Hydrodynamic benefits of passive flexibility in a self-propelled oscillatory ray

In the present study, numerical simulations are conducted to investigate the hydrodynamic benefits of a self-propelled oscillatory ray with passive flexibility compared to those with active flexibility. For the active flexibility case, the prescribed motion is applied to the entire surface of the ray. On the other hand, for the passive flexibility case, the motion of the leading edges is only prescribed, whereas that of the rest parts is determined by the interaction with the surrounding fluid. The cruising speed and input power of the ray with passive flexibility increase as the horizontal bending rigidity decreases, and its propulsive efficiency is maximized at a specific horizontal bending rigidity. Compared to the active flexibility case, the propulsive performance of the oscillatory ray with passive flexibility is improved by not only enhanced circulation and added-mass effects but also by the favorable repartition of the resultant force caused by a large deflection angle. Strong vortical structures induced by a large deformation over the entire region of the fin generate strong negative pressure on the forward side of the overall surface, even near the central body (i.e., increased circulation effect). Furthermore, the positive pressure on the backward side increases in the passive flexibility case due to high fin acceleration caused by more intense oscillating motions (i.e., increased added-mass effect). When the oscillating frequency and the Reynolds number vary, the performance of the ray with passive flexibility is confirmed to be higher than that with active flexibility.