Force and power of flapping plates in a fluid

The force and power of flapping plates are studied by vortex dynamic analysis. Based on the dynamic analysis of the numerical results of viscous flow past three-dimensional flapping plates, it is found that the force and power are strongly dominated by the vortical structures close to the body. Further, the dynamics of the flapping plate is investigated in terms of viscous vortex-ring model. It is revealed that the model can reasonably reflect the essential properties of the ring-like vortical structure in the wake, and the energy of the plate transferred to the flow for the formation of each vortical structure possesses a certain relation. Moreover, simplified formulae for the thrust and efficiency are proposed and verified to be reliable by the numerical solutions and experimental measurements of animal locomotion. The results obtained in this study provide physical insight into the understanding of the dynamic mechanisms relevant to flapping locomotion.