Growth of Vortices Rolled Up from Deformed Membrane Airfoil with Unsteady Motion

Abstract

Dynamic behavior of vortex ring is the generation of fluid force by the motion and elastic deformation of objects, that why the grasping the behavior of vortex ring is very important. That behavior is measured by the visualization of the flow field around the moving object mainly, and from those results in previous research, it is clarified that the growth of vortex rings is effected by the acceleration and elastic deformation of object. Those results are measured directly, then, there is no established method yet to theoretically grasping the growth of vortex ring using physical property that represent the motion and elastic deformation of object. If it becomes possible to theoretically grasp the growth of vortex ring based on the motion and elastic deformation of objects, it will be possible to indirectly grasp the growth process of a vortex ring from the motion and elastic deformation of object without measuring the flow field of the fluid. In this study, we attempted to theoretically capture the growth of vortex rings generated by downstroke and upstroke of butterfly wing, which occur the different elastic deformation of wing, in terms of the fluid force of added mass flow.