Scaling Laws for Three-Dimensional Combined Heaving and Pitching Propulsors

TL;DR

This paper develops and validates new scaling laws for thrust and power of 3D combined heaving and pitching hydrofoils, aiding the design of efficient bio-inspired propulsion systems.

Contribution

It extends existing 3D pitching scaling laws to combined heaving and pitching hydrofoils, validated with simulations and experiments, and provides design insights for high-efficiency propulsion.

Findings

Scaling laws predict thrust and power within ±25% and ±16%.

Peak efficiency occurs at large amplitudes with optimal heave ratio.

Increasing aspect ratio and amplitude, decreasing drag, and adjusting pitch axis improve efficiency.

Abstract

We present new scaling laws for the thrust production and power consumption of three-dimensional combined heaving and pitching hydrofoils by extending the three-dimensional pitching scaling laws introduced by Ayancik et al. (2019). New 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 pitching axis locations. The developed scaling laws are shown to predict inviscid numerical data and experimental data well, within $\pm$ 25% and $\pm$ 16% of the thrust and power data, respectively. The scaling laws reveal 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 performance across this wide amplitude range. By using the scaling laws as a guide, it is determined that peak efficiencies occur when $A^*$ > 1 and for these large-amplitude motions, there is an optimal $h^*$ that maximizes the efficiency in the narrow range of 0.75 < $h^*$ < 0.94. Finally, the scaling laws show that to further improve efficiency in this high-efficiency regime, the aspect ratio, and dimensionless amplitude should be increased, while 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.