Unsteady aerodynamic models for agile flight at low reynolds numbers

The goal of this work is to develop low-order models for the unsteady aerodynamic forces on a small wing in response to agile maneuvers and gusts. In a previous study, it was shown that Theodorsen's and Wagner's unsteady aerodynamic models agree with force data from DNS for pitching and plunging maneuvers of a 2D flat plate at Reynolds numbers between 100 and 300 as long as the reduced frequency k is not too large, k < 2, and the effective angle-of-attack is below the critical angle. In this study reduced order models are obtained using an improved method, the eigensystem realization algorithm (ERA), which is more efficient to compute and fits within a standard control design framework. For test cases involving pitching and plunging motions, it is shown that Wagner's indicial response is closely approximated by ERA models of orders 4 and 6, respectively. All models are tested in a framework that decouples the longitudinal flight dynamic and aerodynamic models, so that the aerodynamics are viewed as an input-output system between wing kinematics and the forces generated. Lagrangian coherent structures are used to visualize the unsteady separated flow.