Numerical study on hydrodynamic behavior of flexible multi-stage propulsion foil

To examine mechanisms of the high speed and efficiency of propulsion of aquatic animals and to apply the findings to the design of underwater vehicles, this study uses dolphins as an example. The motion of aquatic animals is divided into three stages for the convenience of analysis of bio-propulsion: the oscillation of one-third of the rear body, the oscillation of the caudal fin, and the deformation of the caudal fin. We call the case multi-stage propulsion when all the stages are contained in a bio-propulsion. We investigate the effects of the phase difference between oscillations of the first and second stages φ on hydrodynamic performance and the chordwise deformation factor δc0 on hydrodynamic performance. The results show that when the phase difference was 90°, the propulsion efficiency was the highest and an appropriate caudal chordwise deformation could increase the propulsion efficiency, which was consistent with the result of previous studies. The key part of this paper is the comparative study between different propulsion modes in terms of fluid mechanism from multiple perspectives, such as the force generated by the oscillating motion, the shedding frequency of the wake vortex, and the spacings of vortices induced by different propulsion modes. The aim of this paper is to understand the mechanism supporting a larger thrust and higher efficiency of multi-stage propulsion and provide reference for the improvement and optimization of bionic propulsion in the future.