Thrust enhancement of a flexible foil oscillating near an air-water interface

Fish swimming near water surfaces is widely observed in nature. In this study, two-dimensional (2D) simulation was performed to analyze the hydrodynamic effects of the air-water interface on the propulsive performance of a heaving flexible foil. A sharp immersed boundary method was used to solve the fluid-flexible-body interaction problem, and a coupled level-set and volume-of-fluid (CLSVOF) method was adopted to capture the air-water interface. The flexible foil was modeled as a thin shell based on the nonlinear Kirchhoff thin-shell theory, and a plunging motion was prescribed on its leading edge. The effects of the submergence depth and the free-stream velocity were examined. The thrust produced by the foil was reduced near the air-water interface when the free-stream velocity was relatively low. The foil moving in a high-velocity stream, on the other hand, produced more thrust near the air-water interface than that far from the interface. The thrust enhancement or reduction due to the free-surface effect was found to be associated with the propagation of the leading-edge-induced wave, the phase velocity of which was estimated using the nonlinear dispersion relation. It was found that the thrust enhancement can  be amplified for up to 49% due to the free-surface effect.