POD approach for unsteady aerodynamic model updating

A method for aerodynamic model updating is proposed in this paper. The approach is based upon a correction of the eigenvalues of the reduced order unsteady aerodynamic matrix through an optimization with objective function defined through the difference in the generalized aerodynamic forces or on the aeroelastic poles. The high fidelity model in reduced order form is obtained by the Proper Orthogonal Decomposition (POD) technique applied to the Computational Fluid Dynamics (CFD) Euler-based formulation. Many of the methods that have been developed in the past years for simpler aeroelastic models that use, for example, doublet-lattice method (DLM) aerodynamics, can be adopted for this purpose as well. However, this model is not able to capture shocks and flow separation in transonic flow. The proposed approach performs the updating of the aerodynamic model by imposing the minimization of a global error between target aerodynamic performances, namely, experimental performances, and an aerodynamic model in reduced order form via POD approach. After a general presentation of the application of the POD method to the linearized Euler equations, the optimization strategy is presented. First a simple test on a 2D wing section with theoretical biased data is performed and then the performances of different optimization strategies are tested on a 3D model updated by Wind Tunnel data.