Title: A computational fluid dynamics study of 'clap and fling' in the
smallest flying insects.

Abstract:

Tiny flying insects augment the lift forces generated during flapping
flight by clapping their wings together at the beginning of each
downstroke. This behavior has been termed 'clap and fling' or 'clap and
peel.' The fluid dynamic process through which additional lift is
generated has been termed the Weis-Fogh mechanism. At the beginning of the
downstroke, the wings initially fling apart by rotating about the common
trailing edge. During this rotation, large attached leading edge vortices
form on each wing, and the leading edge vortex of one wing acts as the
starting vortex of the other wing. Since these vortices are mirror images
of each other, the circulation about the pair of wings remains zero. As a
result, trailing edge vortices are not needed to conserve circulation, and
indeed they are not initially formed. This is significant because both
leading and trailing edge vortices are formed by a single wing in pure
translation, resulting in smaller lift forces.

In this study, the immersed boundary method was used to solve the
two-dimensional Navier-Stokes equations with two immersed wings performing
an idealized clap and fling stroke. Lift coefficients were calculated as
functions of time per wing for a range of Reynolds numbers (8 - 128).
These results show that lift generation per wing during the clap and
fling of two wings when compared to the average lift produced by one wing
with the same motion falls into two distinct patterns. For Reynolds
numbers of 64 and higher, lift is initially enhanced during the rotation
of two wings when lift coefficients are compared to the case of one wing.
Lift coefficients after fling and during the translational part of the
stroke oscillate as the leading and trailing edge vortices are alternately
shed, and are not substantially greater than the one-winged case. For
Reynolds numbers of 32 and lower, lift coefficients per wing are also
enhanced during wing rotation when compared to the case of one wing
rotating with the same motion. Remarkably, lift coefficients following
two-winged fling during the translational phase are also enhanced when
compared to the one-winged case. Indeed, they begin about 70% higher than
the one-winged case during pure translation. Lift enhancement also
increases with decreasing Reynolds number, suggesting that the Weis-Fogh
mechanism of lift generation has greater benefit to insects flying at
lower Reynolds numbers. Indeed, it appears that all insects that fly at
very low Reynolds numbers use clap and fling, while the majority of flying
insects do not.