Propulsion performance of flapping hydrofoil by using discrete vortex method

The insight to the hydrodynamics of the flapping hydrofoils can be utilized to comprehend the fluid-mechanical mechanisms for the variation of the hydrofoil's propulsion performance, and optimize the design of the bio-inspired underwater robots. This paper numerically investigates the hydrodynamic performance of a two-dimensional NACA 0012 (defined by National Advisory Committee for Aeronautics) hydrofoil undergoing combined pitching and heaving motions, based on the discrete vortex method. A novel boundary method which couples the Joukowsky transformation and the circle theorem is used to deal with the vortex elements inside the hydrofoil surface. The numerical method is validated by the experiments from the available relative cases by comparing the hydrodynamic forces and the wake patterns with the pure pitching and pure heaving hydrofoil. Via the vortex dynamics, the discussion is carried out to explain the thrust deterioration within the large Strouhal number and large pitching amplitude in the combined motion. Further, a parameter optimization study is conducted under different heaving amplitudes and pivot locations. When the heaving amplitude is 1.25c and the pivot location is at 0.45c, the propulsion efficiency of the flapping hydrofoil is found maximized. Finally, by combining the time history of hydrodynamic forces and the formation and release of the leading-edge vortex and trailing-edge vortex in the vorticity field, this paper explains the reason why the optimal efficiency is obtained.