Scaling and Performance of Simultaneously Heaving and Pitching Foils

The propulsive performance of an unsteady heaving and pitching foil is considered, and an extensive experimental parameter space of motion amplitudes, frequencies, and phase offsets between the heave and pitch motions is studied. The phase offset proves to be a critical parameter in determining the foil propulsive performance. To maximize thrust, the pitch motion needs to lag the heave motion by about 30 deg; but, to maximize efficiency, the lag needs to increase to about 90 deg, corresponding to a slicing motion where the angle of attack is minimized. Scaling relations are also presented, and they are developed from lift-based and added mass forces, which describe the experimental data closely. Using the scaling relations as a guide, increases in performance are found when foil amplitudes (specifically pitch) increase while maintaining a modest angle of attack.