Leading edge strengthening and the propulsion performance of flexible ray fins

Abstract A numerical model of a ray-reinforced fin is developed to investigate the relation between its structural characteristics and its force generation capacity during flapping motion. In this two-dimensional rendition, the underlying rays are modelled as springs, and the membrane is modelled as a flexible but inextensible plate. The fin kinematics is characterized by its oscillation frequency and the phase difference between different rays (which generates a pitching motion). An immersed boundary method (IBM) is applied to solve the fluid–structure interaction problem. The focus of the current paper is on the effects of ray flexibility, especially the detailed distribution of ray stiffness, upon the capacity of thrust generation. The correlation between thrust generation and features of the surrounding flow (especially the leading edge separation) is also examined. Comparisons are made between a fin with rigid rays, a fin with identical flexible rays, and a fin with flexible rays and strengthened leading edge. It is shown that with flexible rays, the thrust production can be significantly increased, especially in cases when the phase difference between different rays is not optimized. By strengthening the leading edge, a higher propulsion efficiency is observed. This is mostly attributed to the reduction of the effective angle of attack at the leading edge, accompanied by mitigation of leading edge separation and dramatic changes in characteristics of the wake. In addition, the flexibility of the rays causes reorientation of the fluid force so that it tilts more towards the swimming direction and the thrust is thus increased.