Numerical investigations on a tethered undulating foil near free surface using a smoothed-particle hydrodynamics method

Research on biomimetic propulsion near the free surface offers valuable insights into the design and control of underwater biomimetic vehicles. This study employs the smoothed-particle hydrodynamics method to examine the propulsion of an undulating hydrofoil near the free surface, focusing on the effects of the Froude number (Fr) and the dimensionless submergence depth (H/L) on hydrodynamic performance, and analyzing results alongside vortex structures and free surface deformation. The main results indicate that the time-averaged thrust generated by the undulating hydrofoil tends to decrease with decreasing H/L and increasing Fr. At Re=4000, when H/L<1.5, the hydrofoil achieves the locally optimal propulsion efficiency at Fr=0.2, while for 1.5<H/L<2.5, it reaches its optimal efficiency at Fr=0.4. The hydrofoil is attracted to the free surface when Fr=0.2 and 0.4, whereas it experiences a repulsive force away from the surface when Fr=0.6. Additionally, a “P + S” type vortex street forms in the wake when the hydrofoil travels near the free surface. As Re increases, the variation trend of the hydrofoil's hydrodynamic characteristics with respect to H/L remains nearly consistent, while the number of small vortices in the wake gradually increases. The present method provides an effective approach for simulating bionic hydrodynamic problems near the free surface.