Resonance and propulsion performance of a heaving flexible wing

TL;DR

This study investigates how the bending rigidity of a flexible heaving wing affects its propulsion, revealing resonance phenomena that maximize thrust and efficiency in an inviscid flow model.

Contribution

It introduces a detailed analysis of resonance effects in flexible wings and links these to propulsion performance using potential flow theory.

Findings

Resonance occurs at specific rigidity values, maximizing thrust.

Flexibility significantly enhances flapping efficiency.

Resonance positions align with linear stability analysis predictions.

Abstract

The influence of the bending rigidity of a flexible heaving wing on its propulsive performance in a two-dimensional imposed parallel flow is investigated in the inviscid limit. Potential flow theory is used to describe the flow over the flapping wing. The vortical wake of the wing is accounted for by the shedding of point vortices with unsteady intensity from the wing's trailing edge. The trailing-edge flapping amplitude is shown to be maximal for a discrete set of values of the rigidity, at which a resonance occurs between the forcing frequency and a natural frequency of the system. A quantitative comparison of the position of these resonances with linear stability analysis results is presented. Such resonances induce maximum values of the mean developed thrust and power input. The flapping efficiency is also shown to be greatly enhanced by flexibility.