An Analysis of a Symmetric Flapping Model: A Symmetry-Breaking Mechanism and Its Universality

抄録

We analyse a simple two-dimensional flapping model, two swinging rigid plates joined together on a hinge, to understand dynamical interaction between separation vortices and flapping wings. To make the problem clear, we assume a symmetric situation in which the flapping motion is completely symmetric with respect to up and down directions. By simulating this model using a discrete vortex method, we found a new type of symmetry-breaking mechanism that allows to achieve a mean speed in one direction. The most important factor in determining the behavior of the model is the nature of the flow following the second downstroke, in which the wing produces significant lift through its interaction with the separation vortices. The condition for the symmetry-breaking is also examined. At least two coherent vortices must coexist in fluid, and the intertial mass in a nondimensional form must be larger than a critical value. Two nondimensional parameters are introduced to describe the detail.