Geometric Characteristics of Flapping Foils for Enhanced Propulsive Efficiency

The shape of a foil undergoing a combined pitching heaving motion is critical to its design in applications that demand high efficiency and thrust. This study focuses on understanding of how the shape of a foil affects its propulsive performance. We perform two-dimensional numerical simulations of fluid flows around a flapping foil for different governing parameters in the range of biological swimmers and bio-inspired underwater vehicles. By varying the foil shape using a class-shape transformation method, we investigate a broad range of foil-like shapes. In the study, we also show consistent results with previous studies that a thicker leading-edge and sharper trailing-edge makes for a more efficient foil shape undergoing a flapping motion. In addition, we explain that the performance of the foil is highly sensitive to its shape, specifically the thickness of the foil between the 18th and 50th percent along the chord of the foil. Moreover, we elucidate the flow mechanisms behind variations in performance metrics, particularly focused on constructive interference between the vortices generated at the leading-edge with the trailing-edge vortex, as well as the pressure field differences that lead to higher power consumption in less efficient foil shapes.