Efficient Aircraft Flutter Analysis using Model Order Reduction with Error Estimation

Fast and accurate aircraft flutter analysis in the transonic regime remains an open problem due to the high computational cost of accurately modelling transient aerodynamic forces. In this thesis, a methodology for flutter prediction with the application of model order reduction with error estimation is presented to reduce computational cost while achieving user desired accuracy. The methodology is shown to be computationally efficient, minimize the requirement for user knowledge, and provide user-prescribed accuracy for flutter prediction relative to the high-dimensional aeroelastic model. The Euler equations are used to model the aerodynamics, which are linearized about a nonlinear steady-state solution and reduced using a projection-based model order reduction approach. The resulting aerodynamic ROM is coupled to a structural model to form the primal aeroelastic ROM. The aeroelastic ROM is of low order, allowing for a computationally efficient parameter sweep of the aeroelastic eigenproblem to determine the flutter point. A dual-weighted residual-based error estimator is presented which approximates the error in the eigenvalues obtained from the primal aeroelastic ROM relative to the true eigenvalues from the high-dimensional aeroelastic model. This error estimator makes use of a dual aeroelastic ROM to approximate the dual solution. A second error estimator is presented which approximates the error in the predicted flutter point relative to the true flutter point from the high-dimensional model. By combining the aforementioned algorithmic elements, a ROM-based flutter methodology with error estimation is developed. The proposed method provides the user with approximate aeroelastic eigenvalues, an approximate flutter point, and an estimate of the error in both these quantities. Flutter analyses are presented for several test cases. Both the eigenvalue and flutter point error estimators are shown to have good agreement with the true error. For the test cases presented, the cost of computing the flutter point at a given Mach number is equivalent to the cost of approximately 4 to 15 steady nonlinear flow evaluations of the high-dimensional Euler equations. When compared to a POD-based ROM approach, the proposed method achieves comparable or faster computational times for similar levels of error while additionally providing error estimates for flutter analysis.

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