Nonlinear aeroelastic modelling and analysis of a geometrically nonlinear wing with combined unsteady sectional and lifting line aerodynamics

This research develops a novel geometrically nonlinear aeroelastic model of a cantilevered flexible wing capable of capturing unsteady aerodynamics with finite span effects. The structural model is developed using a Chebyshev-Ritz approach with the ONERA unsteady aerodynamic formulation coupled to a three-dimensional wing analysis based on the lifting line approach. The resulting system describing the evolution of the generalised structural coordinates and the aerodynamic states is formulated as a continuous state space model. The model is validated against experimental results from the wind tunnel testing of a highly flexible wing demonstrator at the University of Bristol. The numerical results are computed by applying a numerical continuation procedure, exercising the benefits of the state space formulation. The extensive numerical-experimental comparative analysis includes the bifurcation characteristics of the system and the behaviour of the aeroelastic modes. The developed model reflected the experimentally identified bifurcation behaviour. The predicted variations of the flutter onset speed with the wing root pitch angles were found to be within 5% of the experimental values. The model also correctly captured the post-flutter Limit Cycle Oscillation (LCO). This work further showed that the predicted flutter speeds are sensitive to the semi-empirical coefficients present in the ONERA unsteady aerodynamics formulation. Consequently, further calibration of the model was based on the analysis of the experimental flutter speeds and airspeed-driven eigenvalue variations. This approach was necessitated by the influence of application-specific conditions (e.g., the Reynolds number) on the unsteady aerodynamic characteristics. Despite this limitation, the tuned model agreed with the experimental observations across a wide range of test conditions. The approaches presented in this work can benefit multiple applications during research on geometrically nonlinear wings, such as the analysis of root causes influencing critical aeroelastic phenomena or design of aeroelastic control laws.