Hydrodynamic performance of two manta rays swimming in staggered groups with different vertical spacing

To investigate the hydrodynamic performance of double manta rays swimming in a staggered formation with different combinations of vertical and streamwise spacing, a high similarity three-dimensional computational model and kinematic equations of manta rays were firstly established based on biological observations. Subsequently, the numerical calculation method of manta ray group swimming was established with the help of the immersed boundary method and the sphere function-based gas kinetic scheme(IB-SGKS), and the numerical simulation of the staggered group swimming process of manta rays in the streamwise spacing of 0.4, 0.5BL(Body Length) and variable vertical spacing was carried out. The results show that the streamwise spacing is the main factor affecting the propulsive performance of manta rays in staggered groups, and the vertical spacing only plays a fine-tuning role. Under the appropriate streamwise spacing, increasing the vertical spacing can help to improve the propulsive efficiency of the follower, and the conclusions of this paper provide theoretical guidance for the setup of bionic underwater vehicle group formation.