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Clarifying the relationship between efficiency and resonance for flexible inertial swimmers

Published online by Cambridge University Press:  23 August 2018

Daniel Floryan Open the ORCID record for Daniel Floryan [Opens in a new window]  and
Clarence W. Rowley
Daniel Floryan*
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
Clarence W. Rowley
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
*
†Email address for correspondence: dfloryan@princeton.edu
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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).

JFM classification

Biological Fluid Dynamics: Propulsion Biological Fluid Dynamics: Swimming/flying
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 853 , 25 October 2018 , pp. 271 - 300
Copyright
© 2018 Cambridge University Press 

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Floryan et al. supplementary movie

Comparison between Euler-Bernoulli mode P2 and flutter mode S1 for $S = 0.1$. The modes have been normalized so that their second derivatives at the leading edge are real and equal to 1.

Download Floryan et al. supplementary movie(Video)
Video 1.1 MB