Aerodynamic forces on a flat plate undergoing asynchronous sinusoidal heaving and pitching motion

Unsteady aerodynamic has drawn a lot of attentions in recent years given its implication in biological fluid dynamics, such as the flight of insects and birds. Its fundamental physic is a dynamical system that the flow dynamic and the unsteady motion of solid objects are coupled. We numerically investigated a flat plate immersed in a steady freestream undergoing flapping motions. Computational fluid dynamics (CFD) with finite volume method is implemented to solve two-dimensional Navier–Stokes equations for Reynolds number 600~900. Both cross-stream translation and pitching motions are set to be sinusoidal and a phase difference is introduced. We explored a range of motion frequency and phase angle; and the transition for drag becoming thrust is identified. Additionally, we modeled the same problem using a discrete vortex method. Conventional CFD using a Eulerian mesh for these unsteady problems are generally expansive and time-consuming. Discrete vortex method serves as a reduced-order model in Lagrangian sense, and is right for vortex-dominated flows such as massive separation flows or vortex shedding. Despite the inviscid nature, vortex methods capture the essential interplay between vortices shed from both the leading and trailing edges. The forces computed using vortex method are compared and validated with the CFD result.