Efficient Swimming with Flexible Caudal Fins: Insights from Coupled Fluid-Membrane Interaction Modeling*

The fluid dynamics of marine animals' propulsion, particularly fish, can inspire the development of efficient underwater autonomous systems. Various fish species employ highly deformable fins reinforced with relatively stiffer rays. Numerical modeling can provide insights into the hydrodynamics of deformable fin propulsors but can be challenging due to the extremely low mass ratio of the fin material, leading to high added-mass effects. In this study, we utilize the sharp interface immersed boundary method coupled with a membrane deformation model to perform a fully coupled hydroelastic simulation of the flexible caudal fin. The detrimental numerical instability associated with strong added-mass effects typically requires computationally expensive implicit coupling for stabilization. However, we employ an added mass stabilization scheme (AMaSS), which allows for the use of explicit coupling between the fluid and membrane solvers, thereby reducing computational costs. The developed numerical model is then used to systematically study the effect of material properties and fin kinematics on the fin's performance. Our findings reveal that flexible fins exhibit superior efficiency in propulsion compared to their rigid counterparts. To further understand the mechanics contributing to hydrodynamic force generation, we utilize the force partitioning method to decompose the hydrodynamic forces into distinct components, providing a detailed analysis of the contributions from different flow structures and membrane kinematics. The insights gained from this study can inform the design of bio-inspired underwater vehicles and robotic systems, enhancing their propulsion efficiency and maneuverability.