Scaling Laws for the Propulsive Performance of a Purely Pitching Foil in Ground Effect

TL;DR

This paper develops and validates new physics-based scaling laws for the thrust and power of a pitching hydrofoil operating near ground effect, applicable across a range of biologically relevant parameters.

Contribution

It introduces ground effect-specific modifications to existing scaling laws, accounting for added mass increase and wake vortex influence reduction, validated by simulations and experiments.

Findings

Scaling laws accurately predict propulsive performance in ground effect.

Physics-driven modifications improve existing models for near-ground hydrofoil dynamics.

Validated scaling laws facilitate bio-inspired hydrofoil design near ground surfaces.

Abstract

Scaling laws for the thrust production and power consumption of a purely pitching hydrofoil in ground effect are presented. For the first time, ground effect scaling laws based on physical insights capture the propulsive performance over a wide range of biologically-relevant Strouhal numbers, dimensionless amplitudes, and dimensionless ground distances. This is achieved by advancing previous scaling laws (Moored & Quinn 2018) with physics-driven modifications to the added mass and circulatory forces to account for ground distance variations. The key physics introduced are the increase in the added mass of a foil near the ground and the reduction in the influence of a wake vortex system due to the influence of its image system. The scaling laws are found to be in good agreement with new inviscid simulations and viscous experiments, and can be used to accelerate the design of bio-inspired hydrofoils that oscillate near a ground plane or two out-of-phase foils in a side-by-side arrangement.