Propulsion performance of a flapping foil near free surfaces: Effects of submergence depth, Strouhal number, and pitching amplitude

We numerically investigate the propulsion performance of a flapping foil operating near a free surface, focusing on the effects of submergence depth, Strouhal number, pitching amplitude, and surface features. A two-dimensional flapping foil of a National Advisory Committee for Aeronautics (NACA) section 0015, subjected to coupled pitching and heaving motions, is simulated using the Volume of Fluid (VOF) method and overset grid techniques at a Reynolds number of 1 × 105. Results show that submergence depth critically affects the hydrodynamic performance of the flapping foil by modulating the ground effect. At small submergence depths, interactions between the free surface and flapping foil induce energy dissipation and reduce thrust generation, particularly on the upper surface of the foil during its ascending phase. However, as submergence depth increases beyond a threshold, i.e., more than five times the flapping chord length, the ground effect diminishes rapidly. Further, the Strouhal number exhibits a positive correlation with the thrust generation of the flapping foil, enhancing propulsion through intensified dipole structures and jet-like wake effects. In contrast, pitching amplitude shows a negative correlation, as excessive amplitudes decrease propulsion performance. Moreover, the comparative analysis of free and rigid surfaces highlighted that the free surface introduces energy dissipation and slightly degrades propulsion performance at small submergence depths.