Unsteady Lifting-Line Theory for Camber Morphing Wings State-Space Aeroelastic Modeling

Abstract

A novel frequency-domain analytical-numerical model for the aerodynamic solution of camber morphing wings is developed. The model combines an unsteady lifting-line formulation with Küssner–Schwarz aerodynamic theory to provide the pressure distribution and thus the transcendental aerodynamic matrix that relates the generalized aerodynamic forces to the Lagrangian coordinates of a given wing structural dynamics model. The state-space form of the aerodynamic loads is obtained from the rational matrix approximation of the aerodynamic matrix. This, combined with the wing structural dynamics operator, can readily provide the state-space form of the aeroelastic problem. To assess the accuracy of the proposed aerodynamic solution method, numerical investigations are performed. These consist of its application to several conventional wing configurations and wings with camber morphing, followed by the comparisons of the corresponding solutions with the predictions given by a well-validated panel-method solver for potential flows. These results are shown to be in very good agreement, thus demonstrating that the proposed approach can capture the effects due to wing tapering, sweep angle, and camber morphing, while requiring a remarkably lower computational effort. The excellent accuracy of a few-pole finite-state approximation of the aerodynamic matrix is finally proven for a swept wing with camber morphing.