Vortex Ring Formed by a Butterfly Wing and Dynamic Forces

Abstract

Butterfly generates unsteady dynamic fluid force with a pair of vortex rings. In order to elucidate the flight mechanism of butterflies, it is necessary not only to clarify the vortex rings formed around the wings but also elucidate the characteristics of the unsteady fluid force generated by the flapping motion. By applying the momentum theory to the vortex rings formed during flapping motion, it is possible to estimate the force generated by flapping motion. In this study, we reconstruct a pair of vortex rings formed by flapping motion based on a small number of visualization results and elucidate dynamic fluid force characteristics. A part of estimation result of Lift estimated by the rough shape vortex rings generated by downstroke and upstroke do not match with the direct measurement result. But not only the peak value of estimation result of Lift is near with the direct measurement result quantitatively but also the value of estimation result between upstroke is a small negative as well as the direct measurement result. Although there is a phase difference between the estimation result and direct measurement result, there is a qualitative and quantitative agreement between estimation results and direct measurement result. From those results, butterfly generate the unsteady dynamic Lift between downstroke, especially at butterfly spread wing maximum (t/T = 0.40). After that, the unsteady dynamic Lift decrease and become 0 at upstroke.