Numerical analysis of a heaving flexible foil under an incident surface wave

The hydrodynamics of an actively heaving flexible foil beneath an incident surface wave is numerically investigated. An immersed boundary method (IBM) is employed to consider the fluid-structure interaction, and a coupled level-set and volume-of-fluid (CLSVOF) method is used to accurately resolve the air–water interface. A sinusoidal heaving motion with amplitude (A_f) and frequency (f_f) is imposed at the foil’s leading edge, while the posterior parts flutter passively due to the dynamic interaction with the wave-induced flow superimposed on a uniform flow. The propulsive performance of the foil is examined by varying three key parameters: the frequency ratio between the heaving and wave frequencies (f_f /f_w), the phase difference between the heaving motion and the incident wave (Φ), and the submergence depth of the foil (D). At Φ = 0, the foil demonstrates enhanced propulsive performance near the surface wave at f_f /f_w = 0.5, whereas propulsion is hindered at f_f / f_w = 1.0 and 2.0. By modulating the phase difference Φ, the adverse effects on propulsion can be mitigated, leading to improved performance near the wave surface.