Numerical Study of Flexible Flapping Wing Propulsion

Abstract

In this study, a strong-coupling approach is applied to simulate highly flexible flapping wings interacting with fluid flows. Here, the fluid motion, solid motion, and their interaction are solved together by a single set of equations of motion on a fixed Eulerian mesh, with the elastic stress being solved on a Lagrangian mesh and projected back to the Eulerian mesh. To provide necessary flapping mechanism, control cells are implemented in solid area (i.e., the wing) as skeleton. The moving trajectory of the skeleton is therefore prescribed by a conventional direct-forcing type of immersed boundary method, while the rest of the wing moves passively through elasticity and fluid-structure interaction. This combined algorithm is then used to study the propulsion characteristics of flexible flapping wings with different elastic moduli and at different flapping frequencies and amplitudes. A two-dimensional NACA0012 airfoil is chosen as a model wing, and it is under active plunging defined by control cells and corresponding passive pitching motion. With different input parameters, very different wake structures can be observed. As a result, the coupled plunging-pitching motion can be either drag-producing or thrust-producing. Finally, passive pitching angle θ and nominal angle of attack α for flexible wings are defined to characterize the flapping motion. It is found that θ needs to be greater than 0.26 and α needs to be greater than 0.3 to generate thrust instead of drag for the flapping motion within the current parametric matrix.