Scaling Laws for Three-Dimensional Combined Heaving and Pitching Propulsors

Abstract

We present three-dimensional scaling relations for the thrust production and power consumption of combined heaving and pitching hydrofoils by extending the three-dimensional pitching scaling laws introduced by Ayancik et al. (“Scaling Laws for the Propulsive Performance of Three-Dimensional Pitching Propulsors,” Journal of Fluid Mechanics, Vol. 871, July 2019, pp. 1117–1138). Self-propelled inviscid simulations and previously published experimental data are used to validate the scaling laws over a wide range of motion amplitudes, Strouhal numbers, heave ratios, aspect ratios, and pitch axis locations. The scaling laws are shown to predict inviscid numerical and experimental data well, within and of the thrust and power data, respectively. It reveals that both the circulatory and added mass forces are important when considering a wide range of motion amplitudes and that nonlinear corrections to the classic linear theory are essential to modeling the power performance across a wide amplitude and aspect ratio range. By using the scaling laws as a tool, it is obtained that peak efficiency occurs when dimensionless amplitude and for these large-amplitude motions there is an optimal nondimensional heave ratio , where the efficiency maximizes in the narrow range of . Finally, the scaling laws show that to further improve efficiency in this high-efficiency regime, the aspect ratio and dimensionless amplitude should be increased, whereas the Lighthill number should be decreased (lower drag and/or a larger propulsor planform area to wetted surface area ratio), and the pitch axis should be located behind the leading edge. This scaling model can be used to guide the design of the next generation of high-efficiency bio-inspired machines.