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Estimating lift from wake velocity data in flapping flight

Published online by Cambridge University Press:  15 April 2019

Shizhao Wang Open the ORCID record for Shizhao Wang [Opens in a new window] ,
Guowei He Open the ORCID record for Guowei He [Opens in a new window]  and
Tianshu Liu Open the ORCID record for Tianshu Liu [Opens in a new window]
Shizhao Wang
Affiliation:
LNM, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China School of Engineering Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
Guowei He
Affiliation:
LNM, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China School of Engineering Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
Tianshu Liu*
Affiliation:
LNM, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China Mechanical and Aerospace Engineering, Western Michigan University, Kalamazoo, MI 49008, USA
*
†Email address for correspondence: tianshu.liu@wmich.edu
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Abstract

The application of the Kutta–Joukowski (KJ) theorem to estimating the lift of a flying animal based on wake velocity fields often leads to significant underprediction of the lift, which is known as the wake momentum paradox. This work attempts to answer the puzzling question on whether the KJ theorem is legitimate in its use for complex viscous unsteady wakes generated by flapping wings. The limitations in applying the KJ theorem to flapping wings are quantitatively examined through numerical simulations of viscous incompressible flows over three flapping wing models. The three flapping wing models studied in this work are a flapping wing with a fixed wingspan, a flapping wing with a dynamically changing wingspan and a dihedral flapping wing. The KJ theorem fails to give a satisfactory prediction of the time-averaged lift unless an effective span length is correctly computed. We propose a wake-sectional Kutta–Joukowski (WS-KJ) model to predict the time-averaged lift, where the effective span length is computed based on the time-averaged distance between the streamwise vorticity centroids in the right and left half sides of the Trefftz plane. The WS-KJ model incorporates the spatial evolutionary effects of the complex vortex structures in the wake and significantly improves the prediction of the time-averaged lift. The physical foundation for such improvement is explored. In addition, the time-dependent amplitude and phase changes of the unsteady lift are discussed as the fluid acceleration effect.

JFM classification

Biological Fluid Dynamics: Swimming/flying

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Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 868 , 10 June 2019 , pp. 501 - 537
Copyright
© 2019 Cambridge University Press 

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