In this paper, unsteady impeller-diffuser interaction in a transonic centrifugal compressor stage, which is composed of an impeller with splitter blade and a vaned diffuser, was studied numerically. The unsteady interaction has a significant impact on the time-averaged flow, which are presented by the so-called deterministic correlations in the average-passage equation system (APES) proposed by Adamczyk. Both steady and unsteady simulations were carried out at the design and off-design conditions. Results from the steady and unsteady simulations were compared to highlight the importance of the unsteady interactions and to help assess the shortcomings of simple mixing-plane methods. The comparisons indicate that the unsteady interactions should be considered in the simulations since the differences between the time averaged unsteady results and steady simulation results are significant especially at off-design conditions. Then the interactions between impeller and diffuser were studied in detail to advance the understanding of the flow physics involved. The results show that the impeller/diffuser interaction can affect a range of 30% impeller chord from impeller trailing edge on impeller performance, while whole chord length on diffuser performance. The potential effects of the diffuser cause an unsteady pressure disturbance at the impeller exit, leading to the unsteadiness of impeller load, tip leakage flow and losses. While the unsteadiness of impeller exit flow cause period varieties of inlet flow conditions for the diffuser and have large impacts on diffuser performance. Based on the unsteady results, deterministic correlations in the APES framework were computed and analyzed in order to reveal some shortcomings of present deterministic correlations models and to make some contributions to the modeling development. The distribution characteristics of deterministic correlations were studied. The study indicates that the deterministic correlations in the impeller and diffuser have the similar magnitudes, and that the correlations in the passages have large gradients in circumferential direction and decrease rapidly in flow direction especially in the vaneless space. The deterministic correlations at the impeller/diffuser interface were compared with their spatial correlations using the framework of the deterministic decomposition. The comparisons show that the spatial correlations have some discrepancies with the total deterministic correlations at the impeller/diffuser interface.

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