Geometric Control Theoretic Formulation Applied to the Analysis of Pitching and Plunging Airfoils

The unsteady aerodynamics of a two-dimensional pitching-plunging airfoil are modeled using a state space system. This computationally inexpensive model, simpler than the current classical theories of unsteady aerodynamics, is an output-based model, providing only the dynamics of certain output variables, without reconstructing the entire flow field.Due to the simplicity of the system, it allows for the analytical study of the behavior of four outputs: lift, drag, circulation and point of separation. In order to capture the nonlinearities of the complex unsteady flow, the four outputs are analyzed using some of the tools provided by the geometric control theory. The results are then studied in a fluid dynamics framework to determine if the unsteady motion of the airfoil can provide an enhancement of the mentioned parameters