Hydrodynamic performance of manta rays swimming in staggered arranged group

Abstract

To investigate the hydrodynamic performance of manta rays swimming in staggered arranged group, a morphological and kinematic model of manta rays is developed based on biological observations, and then a numerical calculation method is established for group swimming of manta rays based on the Immersed Boundary Method and the Sphere function-based Gas Kinetic Scheme (IB-SGKS). The group swimming of two manta rays with a fixed vertical spacing of 0.1 times the body thickness, and a flow direction spacing of 0—1.5 times the body length is systematically investigated. The average thrust/efficiency of the group system and each individual in the group are analyzed by combining the global three-dimensional (3D) vortex structure and the characteristic cross-section two-dimensional (2D) vortex structure. The numerical results are shown below. When the streamwise spacing between individuals is small, the propulsive performance decreases sharply compared with swimming alone; as the streamwise spacing increases, the propulsive performance of the leader manta ray is consistently better than that of swimming alone, with the maximum thrust enhanced up to 11.24% when <i>D</i><sub><i>x</i></sub> = 0.4BL, and the maximum efficiency is enhanced up to 3.58% when <i>D</i><sub><i>x</i></sub> = 0.3BL; with the increase of the streamwise spacing, in the thrust/efficiency curves of the follower manta ray appears volatility, with the maximum thrust enhanced to 48.14% when <i>D</i><sub><i>x</i></sub> = 0.4BL and the maximum efficiency reached to 12.39% when <i>D</i><sub><i>x</i></sub> = 0.5BL; the system average thrust and efficiency enhancement both reach their corresponding maximum values, specifically, 29.69% and 6.77%, when <i>D</i><sub><i>x</i></sub> = 0.4BL, which is because the tail vortex of the leading manta ray just passes through the front edge of the follower manta ray and directly acts on the tip vortex that initially falls off from the follower manta rays, thus substantially increasing their vortex energy.