Metamodel-Driven Data Mining Model to Support Three-Dimensional Design of Centrifugal Compressor Stage

The advanced design of a centrifugal compressor with high efficiency and wide operating range is a challenging task due to the complex flow field arising from the three-dimensional geometry, especially for the high-speed, highly loaded centrifugal compressor stage, which typically has a relatively narrow operating range. A great effort has been undertaken recently to solve the time-costly three-dimensional design problem with the assistance of a metamodel. Some effort has been done to gain insight into the design space with the assistance of the data mining method. However, the published works lack any study that systematically performs the data mining between the performance and three-dimensional geometry data due to two unsolved issues, i.e., lack of reliable systematic data mining model and unresolved high-dimensional data problem in the centrifugal compressor community. To tackle these issues, a systematic metamodel-driven data mining (MDDM) model including six general modules (i.e., problem understanding, data understating, metamodeling, data set preparation, knowledge discovery, and deployment) has been proposed and implemented to the knowledge discovery of the well-known Radiver high-speed centrifugal compressor stage. Particular attention has been paid to develop the design principle of operating range extension for the examined high-speed stage. Four specific data mining techniques, i.e., descriptive statistics, self-organization map, k-d tree, and Sobol index, were used for the statistical, correlation, cluster, and sensitivity analysis. The results showed the performance improvement probabilities, the trade-off relationships between efficiency and pressure ratio/operating range, and the characteristic variation of the performance. Specifically, the wide operating range design subspace and the narrow operating range design subspace were split away from the whole design space. In these subspaces, the two most sensitive geometry parameters that controlled the meridional curvature made a large contribution to the stage performance, especially for the meridional curvature at the shroud side near the impeller outlet. The appropriate variation ranges of the two sensitive geometry parameters were recommended, and the flow mechanism behind them was clarified. The statistical results showed that over 90% of the design stages in the recommended variation ranges had a wide operating range. A design case was chosen randomly in the recommended range to verify the performance improvement via computational fluid dynamics (CFD) simulations. The outcomes of this work are particularly relevant for the advanced design of compressors with high efficiency and a wide operating range for flexibility.