Unsteady Lifting Line Theory Using the Wagner Function for the Aerodynamic and Aeroelastic Modeling of 3D Wings

A method is presented to model the incompressible, attached, unsteady lift and pitching moment acting on a thin three-dimensional wing in the time domain. The model is based on the combination of Wagner theory and lifting line theory through the unsteady Kutta-Joukowski theorem. The results are a set of closed-form linear ordinary differential equations that can be solved analytically or using a Runge-Kutta-Fehlberg algorithm. The method is validated against numerical predictions from an unsteady vortex lattice method for rectangular and tapered wings undergoing step or oscillatory changes in plunge or pitch. Further validation is demonstrated on an aeroelastic test case of a rigid rectangular finite wing with pitch and plunge degrees of freedom.