Principles of Wake Energy Recovery and Flow Structure in Bodies Undergoing Rapid Shape Change

Abstract

For a body moving within a fluid, its shape and the manner in which it morphs greatly impact the energy transfer between it and the flow. In vanishing bodies, vorticity is globally shed, while added mass-related energy is released into the fluid. We investigate square-tipped, streamlined-tipped, and hollow foils towed at $10^{\circ }$ angle of attack and quickly retracted in the span-wise direction, as generic models of bodies of different form undergoing rapid shape and volume change. Particle image velocimetry shows that large differences exist in their globally shed wakes. The retracting square-tipped foil forms a wake with energy in excess of the potential flow estimate before retraction starts; the extra energy results in the formation of an additional vortex ring that adds unsteadiness and complexity to the form of the wake. The streamlined-tipped foil avoids creating such ring vortices, but sheds a much less energetic wake: numerical simulation shows that energy is transferred back to the foil during the retraction phase through a thrust force. Circulation calculations show that energy transfer is enabled by the gradual shape change in this foil and is associated with simultaneous pressure gradient-induced and vorticity tilting-induced vorticity annihilation. Finally, the hollow foil combines the advantages of near-complete transfer of the original added mass-related energy to the wake and absence of a vortex ring formation, resulting in an energetic and also cleanly-evolving, stable wake. Hence, modest differences in morphing body shape are shown to result in significantly different flow patterns.