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Estimating thrust from shedding vortex surfaces in the wake of a flapping plate

Published online by Cambridge University Press:  04 June 2021

Wenwen Tong ,
Yue Yang Open the ORCID record for Yue Yang [Opens in a new window]  and
Shizhao Wang Open the ORCID record for Shizhao Wang [Opens in a new window]
Wenwen Tong
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing100871, PR China
Yue Yang*
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing100871, PR China CAPT and BIC-ESAT, Peking University, Beijing100871, PR China
Shizhao Wang
Affiliation:
LNM, Institute of Mechanics, Chinese Academy of Sciences, Beijing100190, PR China School of Engineering Sciences, University of Chinese Academy of Sciences, Beijing100049, PR China
*
†Email address for correspondence: [email protected]
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Abstract

We elucidate the vortex dynamics of flows past a flapping plate using the vortex-surface field (VSF) and develop models for estimating thrust from shedding vortex surfaces in wakes. The VSF evolution is calculated from numerical simulation using the immersed boundary method. The VSF visualization reveals that a spoon-like vortex surface dominated by tip vortex lines is formed and periodically shed into the wake owing to the alternating upstroke and downstroke of the flapping plate. We simplify the finite-domain impulse theory based on a particular vortex surface. The simplified theory demonstrates that the force on the plate is only dependent on the vortical impulse and Lamb-vector integral of the vortex surface enclosing the plate. Then, we propose a time-averaged thrust model from near-wake discrete vortex surfaces, where the incorporation of the Lamb-vector integral significantly improves the model estimation from the impulse model. Furthermore, we estimate the mean thrust based on two arbitrary vortex surfaces in the far wake from the linear impulse decay of periodically shedding vortex surfaces, which provides a possible approach to infer the state of the moving body in experimental investigation and practical applications.

JFM classification

Vortex Flows: Vortex dynamics Biological Fluid Dynamics: Propulsion Biological Fluid Dynamics: Swimming/flying
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 920 , 10 August 2021 , A10
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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