The blade geometric variations are usually ignored in the prediction of bladed disk aerodynamic damping values. This situation is the result of the high computational cost associated with the full-annulus unsteady flow CFD models required to account for these blade geometric differences. This paper presents an approach that can account for these geometric differences with high fidelity and at a reasonable one-time cost. The approach is based on the use of the influence-coefficient (IC) method together with a set of sensitivity coefficients defined for the blade geometry changing effects. The sensitivity coefficients make use of a set of principal component analysis (PCA) modes that describe the measured blade geometry variation. Once the sensitivity coefficients are determined, they are used to construct the IC matrices and to predict the aerodynamic damping values associated with the geometrically mistuned disk. The currently proposed method is unique in two aspects. The first is to follow the observed physics while making assumptions in the linearization process to reduce the number of required sensitivity coefficients. The second is to construct the multiblade CFD model, with blades of different geometries, in a unique way to reduce the data generation costs. Two IC approximation formulas were developed. If NP denotes the number of PCA modes used to describe the blade geometric variation, one formula reduces the number of required multiblade unsteady CFD models from (NP +1)  to (NP +1) , the other reduces the number of CFD models from (NP +1)  to NP +1. Results obtained from these two formulas are compared and validated.
A Fast Influence Coefficient Method for Aerodynamically Mistuned Disks Aeroelasticity Analysis
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Hsu, K., and Hoyniak, D. (August 26, 2011). "A Fast Influence Coefficient Method for Aerodynamically Mistuned Disks Aeroelasticity Analysis." ASME. J. Eng. Gas Turbines Power. December 2011; 133(12): 122502. https://doi.org/10.1115/1.4004110
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