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Effect of trailing-edge shape on the self-propulsive performance of heaving flexible plates

Published online by Cambridge University Press:  21 January 2020

Chengyao Zhang ,
Haibo Huang Open the ORCID record for Haibo Huang [Opens in a new window]  and
Xi-Yun Lu Open the ORCID record for Xi-Yun Lu [Opens in a new window]
Chengyao Zhang
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, PR China
Haibo Huang
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, PR China
Xi-Yun Lu*
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, PR China
*
†Email address for correspondence: xlu@ustc.edu.cn
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Abstract

The effect of trailing-edge shape on the self-propulsive performance of three-dimensional flexible plates is studied numerically. In our study, the trailing edges of the plates are symmetric chevron shapes, and the trailing-edge angle $\unicode[STIX]{x1D719}$ varies from $30^{\circ }$ (concave plate) to $150^{\circ }$ (convex plate). Under different bending stiffnesses $K$, three regimes of the propulsive performance in terms of propulsive velocity $U$ and efficiency $\unicode[STIX]{x1D702}$ as a function of $\unicode[STIX]{x1D719}$ are identified. When $K$ is small, moderate and large, the square, convex and concave plate achieves the best performance, respectively. Analyses of vortical structures and velocity fields show that usually the jet behind the plate with the best performance is longest. Besides, the inclination angle of the jet may be small. The different propulsive performances at small and moderate $K$ are mainly attributed to the phase lag of the trailing edge. The force acting on the plate is analysed and it is found that the thrust force is mainly contributed by the normal force. If $U$, $\unicode[STIX]{x1D702}$ and $K$ are rescaled by the normal force and the area moment of the plate, the curves for different $\unicode[STIX]{x1D719}$ almost collapse into a single curve when the bending stiffness coefficient is small or moderate. The scaling confirms that the normal force should be the characteristic fluid force at small or moderate $K$ and the $\unicode[STIX]{x1D719}$ effect is governed by the area moment. The findings may shed some light on the propulsive performance of aquatic animals.

JFM classification

Biological Fluid Dynamics: Propulsion
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 887 , 25 March 2020 , A7
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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