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Surrogate Modeling of Manufacturing Variation Effects on Unsteady Interactions in a Transonic Turbine

This effort develops a surrogate modeling approach for predicting the effects of manufacturing variations on performance and unsteady loading of a transonic turbine. Computational fluid dynamics (CFD) results from a set of 105 as-manufactured turbine blade geometries are used to train and validate the surrogate models. Blade geometry variation is characterized with point clouds gathered from a structured light, optical measurement system and as-measured CFD grids are generated through mesh morphing of the nominal design grid data. Principal component analysis (PCA) of the measured airfoil geometry variations is used to create a reduced basis of independent surrogate model parameters. It is shown that the surrogate model typically captures between 60% and 80% of the CFD predicted variance. Three new approaches are introduced to improve surrogate effectiveness. First, a zonal PCA approach is defined which investigates surrogate accuracy when limiting analysis to key regions of the airfoil. Second, a training point reduction strategy is proposed that is based on the k–d tree nearest neighbor search algorithm and reduces the required training points up to 38% while only having a small impact on accuracy. Finally, an alternate reduction approach uses k-means clustering to effectively select training points and reduces the required training points up to 66% with a small impact on accuracy.