Theoretical and numerical studies on a five-ray flexible pectoral fin during labriform swimming

Natural fish have evolved with an excellent swimming performance after millions of years. Based on the flexible features of the pectoral fin, this paper focuses on the kinematics and hydrodynamics of the fin when fish are swimming stably in still water in labriform mode. The locomotion mechanism based on the morphology of the pectoral fin is applied to establish a kinematic model composed of five rays and membranes, which is adopted to control the pectoral fin to reach deformation in approximately the same way as the labriform mode. A semi-empirical theoretical model based on the kinematics is proposed to calculate the hydrodynamic force. In order to study the flow field, the numerical simulation of fluid-structure interaction is carried out and the results are validated by the present semi-empirical model, which also verifies the feasibility of the semi-empirical theoretical model for describing the dynamics of the pectoral fin under a complex water environment. In addition, the relationship between propulsion performance and locomotion parameters (e.g. frequency of motion, amplitude of flapping and rowing angle, and phase lag between flapping and rowing) of the multi-degree of freedom flexible pectoral fin is also revealed. It is found that the frequency and amplitude of the flapping angle have a significant influence on the hydrodynamic thrust, while the rowing angle and phase lag have little effect. The established models and the results provide effective tools and significant reference for the design of bionic pectoral fins.