Clarifying the relationship between efficiency and resonance for flexible inertial swimmers

TL;DR

This study analyzes a passive flexible swimmer model to understand how efficiency relates to resonance, revealing that efficiency does not resonate but is influenced by flutter modes and drag effects.

Contribution

It clarifies the relationship between efficiency and resonance in flexible swimmers using a linear inviscid model, including effects of drag and flutter modes.

Findings

Resonant peaks in thrust and power coefficients occur at specific frequencies and stiffnesses.

Efficiency does not exhibit resonant behavior across the studied parameter range.

Drag introduces resonant peaks in efficiency, aligning with experimental observations.

Abstract

We study a linear inviscid model of a passively flexible swimmer, calculating its propulsive performance, eigenvalues, and eigenfunctions with an eye towards clarifying the relationship between efficiency and resonance. The frequencies of actuation and stiffness ratios we consider span a large range, while the mass ratio is mostly fixed to a low value representative of swimmers. We present results showing how the trailing edge deflection, thrust coefficient, power coefficient, and efficiency vary in the stiffness-frequency plane. The trailing edge deflection, thrust coefficient, and power coefficient show sharp ridges of resonant behaviour for mid-to-high frequencies and stiffnesses, whereas the efficiency does not show resonant behaviour anywhere. For low frequencies and stiffnesses, the resonant peaks smear together and the efficiency is high. In this region, flutter modes emerge, inducing travelling wave kinematics which make the swimmer more efficient. We also consider the effects of a finite Reynolds number in the form of streamwise drag. The drag adds an offset to the net thrust produced by the swimmer, causing resonant peaks to appear in the efficiency (as observed in experiments in the literature).