Centrifugal impellers are inevitably subjected to manufacturing uncertainties during the machining process due to many factors. Such manufacturing uncertainties resulting in geometrical variations lead to impeller performance degradation. For a transonic impeller, the complexity of the flow field may amplify this deterioration. In view of this, it is important to have a clear understanding of the effect caused by manufacturing uncertainties. However, relevant studies are rare and lack consideration of realistic manufacturing uncertainties. Furthermore, the high dimensionality caused by high-fidelity uncertainty model makes the computational fluid dynamics (CFD) unaffordable, making the development of high-efficiency and high-fidelity method for high-dimensionality uncertainty quantification (UQ) problems become urgent.

To tackle these limitations, a group of 92 machined centrifugal impellers were scanned, and a statistical model of realistic manufacturing uncertainties was built. With the combination of the CFD simulations and Non–Intrusive Polynomial Chaos (NIPC) methods, the influence of manufacturing uncertainties on the polytropic efficiency and flow field of a transonic centrifugal impeller was quantified. To achieve a good trade-off between the computational efficiency and accuracy for the UQ, a Dual Dimensionality Reduction (DDR) method was proposed, by which the dimensionality of the spatially varying input, i.e., the manufacturing error field, was reduced to 3. The results showed that the manufacturing errors of machined impellers follow Gaussian distributions with a mean error of zero and a shape increased standard deviation near the blade leading edge. The polytropic efficiency of the examined impeller exhibited a negatively skewed distribution and the mean efficiency was reduced by 0.34%. The flow mechanisms behind the performance degradations mainly lay in the increased shock losses near the blade tip and separation losses near the hub. The present study provides a fundamental contribution to the uncertainty quantification of turbomachinery and establishes a theoretical foundation for the development of robust centrifugal impellers.

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