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The Lighthill–Weis-Fogh clap–fling–sweep mechanism revisited

Published online by Cambridge University Press:  26 April 2011

D. KOLOMENSKIY ,
H. K. MOFFATT ,
M. FARGE  and
K. SCHNEIDER
D. KOLOMENSKIY*
Affiliation:
M2P2–CNRS, Universités d'Aix-Marseille, 38 rue Joliot-Curie, 13451 Marseille CEDEX 20, France
H. K. MOFFATT
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
M. FARGE
Affiliation:
LMD–IPSL–CNRS, Ecole Normale Supérieure, 24 rue Lhomond, 75231 Paris CEDEX 5, France
K. SCHNEIDER
Affiliation:
M2P2–CNRS, Universités d'Aix-Marseille, 38 rue Joliot-Curie, 13451 Marseille CEDEX 20, France CMI, Université de Provence, 39 rue Joliot-Curie, 13453 Marseille CEDEX 13, France
*
†Email address for correspondence: [email protected]
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Abstract

The Lighthill–Weis-Fogh ‘clap–fling–sweep’ mechanism for lift generation in insect flight is re-examined. The novelty of this mechanism lies in the change of topology (the ‘break’) that occurs at a critical instant tc when two wings separate at their ‘hinge’ point as ‘fling’ gives way to ‘sweep’, and the appearance of equal and opposite circulations around the wings at this critical instant. Our primary aim is to elucidate the behaviour near the hinge point as time t passes through tc. First, Lighthill's inviscid potential flow theory is reconsidered. It is argued that provided the linear and angular accelerations of the wings are continuous, the velocity field varies continuously through the break, although the pressure field jumps instantaneously at t = tc. Then, effects of viscosity are considered. Near the hinge, the local Reynolds number is very small and local similarity solutions imply a logarithmic (integrable) singularity of the pressure jump across the hinge just before separation, in contrast to the ‘negligible pressure jump’ of inviscid theory invoked by Lighthill. We also present numerical simulations of the flow using a volume penalization technique to represent the motion of the wings. For Reynolds number equal to unity (based on wing chord), the results are in good agreement with the analytical solution. At a realistic Reynolds number of about 20, the flow near the hinge is influenced by leading-edge vortices, but local effects still persist. The lift coefficient is found to be much greater than that in the corresponding inviscid flow.

JFM classification

Aerodynamics: Aerodynamics Low-Reynolds-number flows: Low-Reynolds-number flows Biological Fluid Dynamics: Swimming/flying
Type
Papers
Information
Journal of Fluid Mechanics , Volume 676 , 10 June 2011 , pp. 572 - 606
Copyright
Copyright © Cambridge University Press 2011

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References

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Kolomenskiy et al, supplementary material

Numerical simulation of the flow during fling and during sweep at Reynolds number Re=1. The wings break apart at time t=1.0805. Vorticity, stream function and pressure fields are shown in sequence. Above the hinge, the flow during the whole process is as expected from the local analysis. At t=0.82, when the angle of incidence equals 45°, the vorticity and the pressure just above the hinge point change sign, hence the pressure becomes positive. Below the hinge, the local solution is only valid at t>0.92, when the angle of incidence is larger than 51.3°. However, the pressure below the hinge point changes sign from positive to negative already at t=0.3. When the wings sweep apart at t>1.0805, the dominant contribution to the flow near the trailing edges is due to the outward translation velocity of the wings. The streamlines form closed loops below the trailing edges, but these are not detached eddies, because the vorticity still reaches its extreme values on the wing surfaces. The pressure becomes negative above as well as below the trailing edges.

Download Kolomenskiy et al, supplementary material(Video)
Video 6.6 MB

Kolomenskiy et al, supplementary material

Numerical simulation of the flow during fling and during sweep at Reynolds number Re=1. The wings break apart at time t=1.0805. Vorticity, stream function and pressure fields are shown in sequence. Above the hinge, the flow during the whole process is as expected from the local analysis. At t=0.82, when the angle of incidence equals 45°, the vorticity and the pressure just above the hinge point change sign, hence the pressure becomes positive. Below the hinge, the local solution is only valid at t>0.92, when the angle of incidence is larger than 51.3°. However, the pressure below the hinge point changes sign from positive to negative already at t=0.3. When the wings sweep apart at t>1.0805, the dominant contribution to the flow near the trailing edges is due to the outward translation velocity of the wings. The streamlines form closed loops below the trailing edges, but these are not detached eddies, because the vorticity still reaches its extreme values on the wing surfaces. The pressure becomes negative above as well as below the trailing edges.

Download Kolomenskiy et al, supplementary material(Video)
Video 3.8 MB

Kolomenskiy et al. supplementary material

Flow field during fling and during sweep at Reynolds number Re=20. Vortices are swept from the leading edges, and they influence the flow above the hinge point. However, local effects dominate in a small neighbourhood of the trailing edges

Download Kolomenskiy et al. supplementary material(Video)
Video 6.5 MB

Kolomenskiy et al. supplementary material

Flow field during fling and during sweep at Reynolds number Re=20. Vortices are swept from the leading edges, and they influence the flow above the hinge point. However, local effects dominate in a small neighbourhood of the trailing edges

Download Kolomenskiy et al. supplementary material(Video)
Video 3.7 MB