The goal of the present study is to quantify the uncertainty in the aerodynamic performance of a centrifugal compressor stage with curvilinear impeller blades, due to impeller manufacturing variability. Impellers with curvilinear element blades allow a greater control of secondary flows with respect to impellers having ruled blades. High flow coefficient impellers for centrifugal compressors exhibit larger secondary flow than medium or low flow coefficient impellers, due to the stronger curvature of the flow path and the larger blade height for the same external diameter. Thus curvilinear blade impellers allow to improve the efficiency and range of high flow coefficient centrifugal compressor stages. As the design of these impellers is more complex than the design of ruled blade impellers, it is important to estimate the impact of the impeller manufacturing variability on the performance of the full stage. Sampling methods are often used in uncertainty propagation studies. However, sampling based approaches require a very large number of samples to have an accurate estimate of the performance uncertainty. 3D steady RANS computations are necessary to capture the impact of the geometric variability of the curvilinear blade impeller, on the stage performance. Thus, sampling methods would require an excessive computational time. In this work, the Polynomial Chaos Expansion (PCE) method with arbitrary probability distributions, implemented in DAKOTA, is used to reduce the number of runs required for the uncertainty quantification study. Manufacturing measurement data are been used to derive the histograms of the main impeller design parameters. From these histograms, numerically-generated orthogonal polynomials are computed for each parameter using a discretized Stieltjes procedure. Stochastic expansion methods such as PCE suffer from the curse of dimensionality, i.e., an exponential increase in the number of runs as the number of uncertain parameters increases. To mitigate the curse of dimensionality, sparse grids are used, which allow a drastic reduction of the number of runs. The results of the study show that the performance variability is small, thus our design with curvilinear element blades is robust with respect to impeller manufacturing variability. Using Sobol indices, we also rank the design parameters according to their impact on the performance variability.
