Passive Propulsion of Flexible Foils under Water Waves

A fluid-structure interaction problem of a flexible foil with a fixed leading edge in an incident wave was simulated to understand passive propulsion mechanisms of fish swimming underneath wave surfaces. The interaction between the fluid flow and foil motion was simulated in the framework of a diffused immersed boundary (IB) method, with the wave surface captured by the coupled level-set and volume-of-fluid (CLSVOF) method. A detailed kinematics study shows that the passive flapping is asymmetric, with an increased trailing edge amplitude and a higher maximum vertical speed during the upstroke when the foil approaches the wave surface. For the various reduced frequency values considered, there is a peak trailing edge amplitude, which indicates a resonance. The resonance phenomenon occurs for all the Reynolds numbers considered in our simulations. Passive propulsion can be achieved in incident waves with a cruising speed as high as ten body lengths per unit time. A peak propulsive efficiency is obtained when Strouhal number (St) is between 0.2 and 0.4, similar to the actively flapping foils in free streams. The thrust force coefficient (C_T) is observed to be scaled by C_T ~ St² within the range of St < 0.2. Passing-over leading-edge vortex occurs when St is higher than a threshold value between 0.2 and 0.27, and possibly contributes to the scaling of C_T ~ St³ and enhanced thrust force generation at higher St.