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Effect of leading-edge curvature actuation on flapping fin performance

Published online by Cambridge University Press:  01 July 2021

David Fernández-Gutiérrez Open the ORCID record for David Fernández-Gutiérrez [Opens in a new window]  and
Wim M. van Rees Open the ORCID record for Wim M. van Rees [Opens in a new window]
David Fernández-Gutiérrez
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Wim M. van Rees*
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
*
†Email address for correspondence: wvanrees@mit.edu
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Abstract

Ray-finned fish are able to adapt the curvature of their fins through musculature at the base of the fin. In this work we numerically investigate the effects of such leading-edge curvature actuation on the hydrodynamic performance of a heaving and pitching fin. We present a geometric and numerical framework for constructing the shape of ray-membrane-type fins with imposed leading-edge curvatures, under the constraint of membrane inextensibility. This algorithm is coupled with a three-dimensional Navier–Stokes solver, enabling us to assess the hydrodynamic performance of such fins. To determine the space of possible shapes, we present a simple model for leading-edge curvature actuation through two coefficients that determine chordwise and spanwise curvature, respectively. We systematically vary these two parameters through regimes that mimic both passive elastic deformations and active actuation against the hydrodynamic loading, and compute thrust and power coefficients, as well as hydrodynamic efficiency. Our results demonstrate that both thrust and efficiency are predominantly affected by chordwise curvature, with some small additional benefits of spanwise curvature on efficiency. The main improvements in performance are explained by the altered trailing-edge kinematics arising from leading-edge curvature actuation, which can largely be reproduced by a rigid fin whose trailing-edge kinematics follow that of the curving fin. Changes in fin camber, for fixed trailing-edge kinematics, mostly benefit efficiency. Based on our results, we discuss the use of leading-edge curvature actuation as a robust and versatile way to improve flapping fin performance.

JFM classification

Biological Fluid Dynamics: Swimming/flying Biological Fluid Dynamics: Propulsion Wakes/Jets: Wakes

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Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 921 , 25 August 2021 , A22
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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Fernández-Gutiérrez et al Supplementary Movie 1

Perspective views of the fin geometry during a flapping cycle for different combinations of chordwise and spanwise curvature parameters.

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Video 2.1 MB

Fernández-Gutiérrez et al Supplementary Movie 2

Vorticity field generated by the reference rigid fin during the first two cycles, viewed from different perspectives

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Video 1.7 MB

Fernández-Gutiérrez et al Supplementary Movie 3

Vorticity field generated by the curving fin in the maximum thrust configuration during the first two cycles, viewed from different perspectives.

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Video 2.1 MB

Fernández-Gutiérrez et al Supplementary Movie 4

Vorticity field generated by the curving fin in the maximum efficiency configuration during the first two cycles, viewed from different perspectives.

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Video 1.2 MB
Supplementary material: PDF

Fernández-Gutiérrez et al Supplementary Material

Fernández-Gutiérrez et al Supplementary Material

Download Fernández-Gutiérrez et al Supplementary Material(PDF)
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