On the propulsive performance of a pitching foil with chord-wise flexibility at the high Strouhal number

During the predatory behaviour, the aquatic animals rapidly oscillate their fins to attack the preys or escape from the predators. In the light of this situation above, we experimentally investigate a chord-wise flexible foil pitching at the high Strouhal number, which is significantly larger than the previous studies almost performed at St<1. In the present work, the chord-wise flexibility of the foil has been considered as two components: the flexible length represented by the c_f and the hardness of the flexible materials denoted by the Shore A hardness number. The experimental data indicates that the softer foil shows an overwhelming ability on generating efficient propulsion than the harder counterparts at smaller c_f. Along with the increase of c_f, the flexibility of foil shows the positive/negative influences on the foil's propulsive performance, which is closely related to the temporal evolution of the foil's shape and the effects of flexible materials on the wake structures produced by the foil. Synthetically, taking the c_f and Shore A hardness number of into account, we reveal that the propulsive force of a pitching foil is relied heavily on the St, and the foil can obtain optimal propulsive efficiency when the St and the inertia of flexible section are synchronously smaller. This work is helpful for well-understanding the predatory behaviour and designing the bio-inspired underwater robotics.