Vortex dynamics and dynamic fluid forces by a flapping butterfly wing

An elastic moving airfoil is superior to a rigid moving airfoil because the deformation of its shape enables it to generate a larger fluid force. Membrane airfoils, such as butterfly wings, perform well even in low Reynolds number flows and have thus attracted attention. Previous studies have shown that the flapping motion of a butterfly generates a pair of vortex rings. However, it is difficult to determine the entire vortex ring structure and estimate the dynamic fluid force. In this study, we clarify the dynamic behavior of vortex rings generated by the flapping motion of a butterfly and the associated dynamic lift. Two-dimensional particle image velocimetry is used to visualize the flow field around a butterfly wing in two cross sections. The dynamic lift is estimated from the parameters of a pair of vortex rings measured from two directions. The estimation results indicate that the amplitude of dynamic lift is the largest before the butterfly wing reaches the horizontal position in each stroke. In addition, the degree of development of the vortex ring circulation and the projected area on the horizontal plane are the largest before the butterfly reaches the horizontal position, except for the projected area of the vortex ring during the upstroke. Both the dynamic lift and the parameters for the vortex rings are different between the downstroke and the upstroke. It is believed that these differences are mainly caused by the different degrees of elastic deformation of the butterfly wing on the downstroke and the upstroke.