Shape of retracting foils that model morphing bodies controls shed energy and wake structure

Abstract

The flow mechanisms of shape-changing moving bodies are investigated through the simple model of a foil that is rapidly retracted over a spanwise distance as it is towed at constant angle of attack. It is shown experimentally and through simulation that by altering the shape of the tip of the retracting foil, different shape-changing conditions may be reproduced, corresponding to: (a) a vanishing body, (b) a deflating body, and (c) a melting body. A sharp-edge, 'vanishing-like' foil manifests strong energy release to the fluid; however it is accompanied by an additional release of energy, resulting in the formation of a strong ring vortex at the sharp tip edges of the foil during the retracting motion. This additional energy release introduces complex and quickly-evolving vortex structures. By contrast, a streamlined, 'shrinking-like' foil avoids generating the ring vortex, leaving a structurally simpler wake. The 'shrinking' foil also recovers a large part of the initial energy from the fluid, resulting in much weaker wake structures. Finally, a sharp-edged but hollow, 'melting-like' foil provides an energetic wake while avoiding the generation of a vortex ring. As a result, a melting-like body forms a simple and highly energetic and stable wake, that entrains all of the original added mass fluid energy. The three conditions studied correspond to different modes of flow control employed by aquatic animals and birds, and encountered in disappearing bodies, such as rising bubbles undergoing phase change to fluid.

Optimal dynamic soaring consists of successive shallow arcs

“…By Kelvin's circulation theorem, a vortex of equal intensity and opposite sign (anticlockwise in figure 2c) must have been shed where the glider entered the layer. After the glide phase, the glider leaving the wind layer is a 'vanishing foil' [36], and its bound vorticity is shed into the flow.…”