Impact of Realistic Manufacturing Uncertainties on the Aerodynamic Performance of a Transonic Centrifugal Impeller

The centrifugal compressor is a core component in turbochargers, shaft aeroengines, industrial gas compressors, aircraft cabin cooling units, microturbines and industrial refrigeration plants. During the machining process of centrifugal compressors, deviations from the nominal design geometry are commonly incurred due to the presence of manufacturing variabilities. Such manufacturing variabilities are randomly distributed over the blade surface, which can result in compressor performance degradations and pose a significant threat to the high efficiency, stability, and reliable operation of compressors. Therefore, it is important to consider the effect of manufacturing variabilities as early as possible in the compressor design process. However, most of the relevant studies have been conducted based on simplified uncertainty models of the manufacturing variabilities. Few efforts have been devoted to the analysis or design of centrifugal compressors considering the realistic stochastic nature of manufacturing variabilities. The purpose of this paper is twofold; the first goal is to investigate the effect of realistic manufacturing variabilities on the aerodynamic performance and flow field of a transonic compressor impeller, while the second goal is focused on a robust design optimization of the impeller in order to enhance its performance robustness in the presence of manufacturing variabilities.

In order to provide a realistic basis for the uncertainty modeling of the manufacturing variabilities, blades from a set of 92 centrifugal impellers of the same nominal geometry were first scanned using a Coordinate Measuring Machine (CMM) to obtain the actual blade geometries and measured data for the manufacturing variabilities. Statistical analysis of the results for the group of impellers showed that the geometry variation at individual points on the blade surface followed a normal distribution with zero mean. Based on the measurement data, a non-stationary Gaussian random process with Karhunen-Loeve (K-L) expansion was used to build an error field to construct virtual blade profiles with manufacturing variabilities, which effectively reduced the dimensionality required to describe the whole blade surface.

To further reduce the dimensionality for uncertainty quantification (UQ), a sensitivity analysis was undertaken in a feature space to determine which mode of the error field had most influence on the aerodynamic performance. Then, a non-intrusive polynomial chaos (NIPC) method was employed to statistically evaluate the aerodynamic performance and flow field of the compressor impeller. The results showed that the averaged impeller polytropic efficiency was decreased by 0.34% due to manufacturing variabilities, while the average value of total pressure ratio for the set of impellers deviated only slightly from the nominal.

The UQ method was combined with a metamodel-based design optimization system to produce an optimized impeller geometry that gave robust performance in spite of geometric variations due to manufacturing. The support vector regression (SVR) model was built to link the geometric design variables to the coefficients of the polynomial chaos expansion of the statistical response. The results showed that the optimized blade had enhanced efficiency when averaged over the range of manufacturing variabilities as well as less sensitivity to variabilities.

The present study has made a fundamental contribution to the uncertainty quantification and design optimization of turbomachinery and laid a theoretical foundation for the development of advanced centrifugal impellers that give robust performance in the presence of stochastic manufacturing variabilities.