Numerical simulations of the clap-fling-sweep mechanism of hovering ă insects
Résumé
The Lighthill-Weis-Fogh clap-fling-sweep mechanism is a movement used by ă some insects (Fig. 1) to improve their flight performance. As first ă suggested by Lighthill (1973) [5], this mechanism allows large ă circulations around the wings to be established immediately as they ă start to move. Initially, the wings are clapped. Then they fling open ă like a book, and a non-zero circulation is established around each of ă them. Thus one wing can be considered as the starting vortex for the ă other. Then they sweep apart, carrying these bound vortices and ă generating lift. Since the insect wings have relatively low aspect ratio ă and rotate, 3d effects are important, such as spanwise flow and ă stabilization of the leading edge vortices (Maxworthy, 2007) [6]. To ă explore these effects, we perform direct numerical simulations of ă flapping wings, using a pseudo-spectral method with volume penalization. ă Comparing 2d and 3d simulations for the same setup clarifies the role of ă the three-dimensionality of the wake. Our results show that the 2d ă approximation describes very well the flow during fling, when the wings ă are near, but 3d effects become crucial when the wings move far apart. ă Results of fully three-dimensional numerical simulations of the ă clap-fling-sweep mechanism using a Fourier pseudo-spectral method with ă volume penalization [2] are presented in the following. Figure 2 shows ă the absolute value of the vorticity at three time instants. At t=1.2, ă very strong leading-edge vortices result from the air flow into the ă opening space between the wings. A vortex which reconnects the wing ends ă forms a horseshoe shape at later times. Another interesting point of ă investigation is that not all rotating wings produce stable leading-edge ă vortices.