Scaling laws for the propulsive performance of three-dimensional pitching propulsors

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 (2018) 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.

Three-dimensional scaling laws of cetacean propulsion characterize the hydrodynamic interplay of flukes' shape and kinematics

“…Further details of the method and extensive validations of the solver can be found in [32]. Further validations and applications of the solver can be found in [21,23,33,37,48]. Figure 3a presents an isometric view and (b) a top view of the typical deforming wake elements shed from the selfpropelled flukes.…”

“…It can be clearly observed that the efficiency increases for higher aspect ratio flukes, however, it is also clear that the scaling law does not capture this trend when only circulatory forces are considered. This motivated us to reconsider the neglected added mass terms due to pitching, which have a different aspect ratio correction than circulatory terms of AR/(AR + 1) as determined in our previous work [37]. The new scaling relations will then be where: royalsocietypublishing.org/journal/rsif J. R. Soc.…”

“…To extend the scaling relations to three dimensions, we will only consider modifications that account for variations in aspect ratio and we will assume that the effects of variations in sweep and curvature are small. Following our previous work on scaling laws for three-dimensional pitching propulsors [37], we will apply circulatory corrections to capture the effects of upwash and downwash from the trailing vortex system. Based on classical finite wing theory [50], the circulatory forces should scale with the aspect ratio as AR/(AR + 2).…”

“…These new scaling laws were valid for two-dimensional fixed-velocity or self-propelled pitching hydrofoils. Later, Ayancik et al [37] extended Moored and Quinn's scaling laws to consider three-dimensional effects for varying aspect ratio hydrofoils. They accounted for the added mass of a finite-span propulsor, the downwash/upwash effects from the trailing vortex system, and the elliptical topology of shedding vortices.…”

“…They accounted for the added mass of a finite-span propulsor, the downwash/upwash effects from the trailing vortex system, and the elliptical topology of shedding vortices. In the current study, we consider the scaling laws for three-dimensional, combined heaving and pitching hydrofoils by following the framework of Moored & Quinn [22] to modify Garrick's theory for combined heaving and pitching motions with the three-dimensional corrections determined by Ayancik et al [37].…”