Hydrodynamics of an actively heaving flexible foil under an incident surface wave

We numerically investigate the hydrodynamics of an actively heaving flexible foil flapping under a wave surface. The coupled level set and volume-of-fluid method is used to capture the air-water interface, and the immersed-boundary method is used to capture the fluid-structure interaction. A sinusoidal heaving motion is imposed at the foil's leading edge, and its posterior parts oscillate passively according to its flexible characteristics, allowing dynamic interactions with the wave-induced flow. The propulsive performance of the foil is examined for the influence of three main factors: the ratio of the heaving frequency to the wave frequency , the phase difference between the heaving motion and the incident wave and the submergence depth of the foil . At, the results reveal that the propulsion of the flexible foil benefits from flapping near the wave surface when, and the propulsive efficiency is optimised at, where is the foil's length. However, when = 1.0 and 2.0, the propulsion of the flexible foil is hindered near the wave surface. This hydrodynamic hindrance is closely related to vortex splitting and roll-up phenomena, which induce the formation of a drag wake. By adjusting the phase difference, the hindrance in the flexible foil propulsion can be mitigated to enhance propulsive performance. To further understand the relationship between the flapping kinematics and propulsive dynamics, we perform a scaling analysis based on lift force and added mass force, offering good quantification of propulsive performance.