Continuous-time state-space unsteady aerodynamic modeling based on boundary element method

Abstract

In this paper a continuous-time state-space aerodynamic model is developed based on the boundary element method. Boundary integral equations governing the unsteady potential flow around lifting bodies are presented and modified for thin wing configurations. Next, the BEM discretized problem of unsteady flow around flat wing equivalent to the original geometry is recast into the standard form of a continuous-time state-space model considering some auxiliary assumptions. The system inputs are time derivative of the instantaneous effective angle of attack and thickness/camber correction terms while the outputs are unsteady aerodynamic coefficients. To validate the model, its predictions for aerodynamic coefficients variations due to the various unsteady motions about different wing geometries are compared to the results of the direct BEM computations and verified numerical and theoretical solutions. This comparison indicates a good agreement. Since the resulting aerodynamic model is in the continuous-time domain, it is particularly useful for optimization and nonlinear analysis purposes. Moreover, its state-space representation is the appropriate form for an aerodynamic model in design or control applications.