In this paper, we have used the immersed boundary method to solve the two-dimensional Navier-Stokes equations for two immersed wings performing an idealized 'clap and fling' stroke and a 'fling' half-stroke. We calculated lift coefficients as functions of time per wing for a range of Reynolds numbers (Re) between 8 and 128. We also calculated the instantaneous streamlines around each wing throughout the stroke cycle and related the changes in lift to the relative strength and position of the leading and trailing edge vortices.Our 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 Re=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. In addition, the lift coefficients are not substantially greater in the two-winged case than in the one-winged case. This differs from threedimensional insect flight where the leading edge vortices remain attached to the wing throughout each half-stroke. For Re=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. When averaged over the entire translational part of the stroke, lift coefficients per wing are 35% higher for the twowinged case during a 4.5 chord translation following fling. In addition, lift enhancement increases with decreasing Re. This result suggests that the Weis-Fogh mechanism of lift generation has greater benefit to insects flying at lower Re. Drag coefficients produced during fling are also substantially higher for the two-winged case than the onewinged case, particularly at lower Re.
SUMMARYOf the insects that have been filmed in flight, those that are 1 mm in length or less often clap their wings together at the end of each upstroke and fling them apart at the beginning of each downstroke. This ʻclap and flingʼ motion is thought to augment the lift forces generated during flight. What has not been highlighted in previous work is that very large forces are required to clap the wings together and to fling the wings apart at the low Reynolds numbers relevant to these tiny insects. In this paper, we use the immersed boundary method to simulate clap and fling in rigid and flexible wings. We find that the drag forces generated during fling with rigid wings can be up to 10 times larger than what would be produced without the effects of wing-wing interaction. As the horizontal components of the forces generated during the end of the upstroke and beginning of the downstroke cancel as a result of the motion of the two wings, these forces cannot be used to generate thrust. As a result, clap and fling appears to be rather inefficient for the smallest flying insects. We also add flexibility to the wings and find that the maximum drag force generated during the fling can be reduced by about 50%. In some instances, the net lift forces generated are also improved relative to the rigid wing case. Supplementary material available online at
The smallest flying insects commonly possess wings with long bristles. Little quantitative information is available on the morphology of these bristles, and their functional importance remains a mystery. In this study, we (1) collected morphological data on the bristles of 23 species of Mymaridae by analyzing high-resolution photographs and (2) used the immersed boundary method to determine via numerical simulation whether bristled wings reduced the force required to fling the wings apart while still maintaining lift. The effects of Reynolds number, angle of attack, bristle spacing and wing-wing interactions were investigated. In the morphological study, we found that as the body length of Mymaridae decreases, the diameter and gap between bristles decreases and the percentage of the wing area covered by bristles increases. In the numerical study, we found that a bristled wing experiences less force than a solid wing. The decrease in force with increasing gap to diameter ratio is greater at higher angles of attack than at lower angles of attack, suggesting that bristled wings may act more like solid wings at lower angles of attack than they do at higher angles of attack. In wing-wing interactions, bristled wings significantly decrease the drag required to fling two wings apart compared with solid wings, especially at lower Reynolds numbers. These results support the idea that bristles may offer an aerodynamic benefit during clap and fling in tiny insects.
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