Underlying principle of efficient propulsion in flexible plunging foils

Passive flexibility was found to enhance propulsive efficiency in swimming animals. In this study, we numerically investigate the roles of structural resonance and hydrodynamic wake resonance in optimizing efficiency of a flexible plunging foil. The results indicates that (1) optimal efficiency is not necessarily achieved when the driving frequency matches the structural eigenfrequency; (2) optimal efficiency always occurs when the driving frequency matches the wake resonant frequency of the time averaged velocity profile. Thus, the underlying principle of efficient propulsion in flexible plunging foil is the hydrodynamic wake resonance, rather than the structural resonance. In addition, we also found that whether the efficiency can be optimized at the structural resonant point depends on the strength of the leading edge vortex relative to that of the trailing edge vortex. The result of this work provides new insights into the role of passive flexibility in flapping-based propulsion.