Semi-active flapping foil for marine propulsion

The present study deals with numerical investigation of a semi-active flapping foil of which the kinematics is characterized by an imposed heave motion and a free pitch motion. A torsion spring is attached to the foil and acts to restore the foil parallel to the advance velocity. The prescribed flapping foil has been simulated using a boundary element method in combination with a Newton-Euler solver in order to study the influence of flapping frequency and spring stiffness on the propulsive performance. The spring stiffness has strong influence on the induced pitch angle and the effective angle of attack which consequently determines the openwater characteristics. The stiff spring resists the foil from pitching resulting in high heave force, while the more elastic hinge leads to drag generation at the end of each stroke. The results demonstrate that the semi-active flapping foil attached to an appropriate torsion spring performs efficiently over a wide range of advance ratio like a controllable-pitch propeller. The best efficiency is found for a Strouhal number and a pitch amplitude as reported in biological researches. The numerical results also imply that the resonance seems to have less influence on the propulsive performance.