Scaling laws for 3D pitching hydrofoils

Building on our previous work on 2-D pitching airfoils, we explored how forces and torques scale for 3-D pitching airfoils. The terms we added to existing theories were inspired by the 3-D elliptical ring shapes of wake vortices. We validated the new terms by comparing our predictions with water channel experiments over a range of frequencies, amplitudes, and aspect ratios. The modified scalings offer guidance for theories about fish morphology and design strategies for bio-inspired robots. (This work was done in collaboration with the Biofluids Research Lab at Lehigh University.)


Authors: Fatma Ayancik, Qiang Zhong, Daniel Quinn, Aaron Brandes, Hilary Bart-Smith, Keith Moored

Abstract: Scaling laws for the thrust production and energetics of self-propelled or fixed-velocity three-dimensional rigid propulsors undergoing pitching motions are presented. The scaling relations extend the two-dimensional scaling laws presented in Moored & Quinn (AIAA J., 2018, pp. 1–15) by accounting for the added mass of a finite-span propulsor, the downwash/upwash effects from the trailing vortex system of a propulsor and the elliptical topology of shedding trailing-edge vortices. The novel three-dimensional scaling laws are validated with self-propelled inviscid simulations and fixed-velocity experiments over a range of reduced frequencies, Strouhal numbers and aspect ratios relevant to bio-inspired propulsion. The scaling laws elucidate the dominant flow physics behind the thrust production and energetics of pitching bio-propulsors, and they provide guidance for the design of bio-inspired propulsive systems.

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