Abstract:

The study of flexible flapping wings of natural flyers as well as micro air vehicles remains challenging by the problem's unsteadiness, nonlinearity, moving boundary, and strong fluid-structure interaction. In the talk, I will first introduce a fully-coupled approach to solve flapping-wing aerodynamics. Here, like other immersed-boundary methods, the fluid motion, solid motion, and their interaction are solved together in a single set of equations of motion (i.e. a modified Navier-Stokes equation) on a fixed Eulerian mesh, while the elastic-stress being calculated on a separate Lagrangian mesh and projected back to the Eulerian mesh. Then, I will talk about using an adjoint-based approach for the control and optimization of the shape and moving trajectory of flapping wings. When highly-unsteady flapping wings are considered, the traditional adjoint-based approach used in airfoil design fails even on the definition of sensitivity for the unsteady moving/morphing boundaries. Unsteady mapping function is, in principle, able to handle the moving/morphing boundary but is not feasible by its complexity. Using the idea of non-cylindrical shape (a.k.a tube) analysis, we are able to derive an adjoint-based analysis in a rigorous and simple manner for the optimization of flapping wings. At last, based on the same global definition in numerical simulation, we propose to have a global model reduction by applying POD/Galerkin projection on a uniform Eulerian description of fluid, structure, and the interaction. The simulation method has succeeded in both 2D and 3D flapping wings. There are also preliminary results from the optimization and model reduction approaches.