Time-domain analysis of the load distribution in wings using the lifting-line theory and the Wagner's Function

Abstract

The combination of high aspect ratio wings with advanced materials presented on modern aircraft leads to structural systems susceptible to large displacements when loaded, which must be considered on the aircraft performance evaluation and its dynamic response. The analysis of this complex system requires the coupling of aerodynamic and structural models into an aeroelastic model. In particular, the time-domain analysis of the wing aeroelastic response requires an unsteady aerodynamic model to predict the spanwise wing loading history. Combining a lifting-line model with a two-dimensional transient lift coefficient is effective in describing the wing unsteady behavior. In this context, the present project aims to develop an aerodynamic model for the non-stationary analysis of wings combining the Prandtl's lifting-line theory with the Wagner's function. Wagner's function allows describing an airfoil's non-stationary behavior and can be combined with the lifting-line model. The development of the unsteady lifting prediction model results in a Volterra-Fredholm integro-differential equation. Galerkin method with linear shape functions enables to obtain the spanwise circulation distribution. Runge-Kutta schema will be adopted for time-domain integration. An existing Python code to predict the steady response of finite wings using the Galerkin method will be modified to include the transient effects. Finally, the developed computational model will be applied to and compared with some cases of oscillating wings reported in the literature.