Propulsive performance of a heaving and pitching foil with large amplitudes in unsteady ground effect

Abstract

To reveal the effect of ground on the force behavior, propulsion performance, and vortex dynamics of a flapping foil, we numerically study a flapping foil actuated by combined heaving and pitching motions with large amplitudes near a solid ground surface. The instantaneous forces in both streamwise and cross-stream directions undergo a sudden drop during upstroke in close ground effect. The time-averaged thrust is enhanced by the ground but varies non-monotonically with ground distance at high foil oscillating frequencies. Three force regimes are identified in lift production, giving rise to two equilibrium altitudes of zero lift, one stable and another unstable. Moreover, we propose a simple scaling law model by a path-length-based Strouhal number and ground effect for thrust and power performance of a large-amplitude flapping foil. The results of the model are consistent with numerical results and previous experimental studies. The vortex dynamics in the wake structure are largely affected by ground proximity; in particular, the formed vortex pairs and their orientations are sensitive to their initial relative positions. Different sources and mechanisms of satellite vortex formation are then discussed. The ground exerts little effect on the phase angles that optimize the propulsive efficiency. This study is expected to provide new insights into the development and maneuvering of flapping foil-based propulsive systems.