Analyzing Mistuning of Bladed Disks by Symmetry and Reduced-Order Areodynamic Modeling

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Shapiro, B. and K. Willcox. Analyzing Mistuning of Bladed Disks by Symmetry and Reduced-Order Areodynamic Modeling. Journal of Propulsion and Power, vol19, no2, pg307-311, March-April 2003.



The mistuned behavior of bladed disks is analyzed and optimized using an unsteady, transonic, computational fluid dynamic model (CFD). This result is enabled by the integration of two frameworks: the first is based on symmetry arguments and an eigenvalue/vector perturbation scheme, while the second is a reduction technique based on the proper orthogonal decomposition (POD). The first framework reduces the complexity of the problem, reveals engineering trade offs and suggests the existence of an intentional robust mistuning which improves both stability and forced response with respect to random variations in blade parameters. The second framework permits the reduction of state-of-the-art computational fluid dynamic codes to reduced-order models, which capture the accuracy of the original simulation but fit within the mistuning analysis framework. Together, these methodologies allow the analysis of a transonic, bladed disk with stiffness mistuning (see Fig. 1).Moreover, because of the low order of the aeroelasticmodel, a robust control¹ uncertainty analysis can be used to prove that the intentional mistuning suggested by the symmetry analysis framework is indeed robust. Hence this paper contains the first rigorous demonstration that intentional mistuning can robustly improve both the stability and forced response for a model that includes sophisticated aerodynamic effects.