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The Two Element in Series (TEIS) and Two Zone models stand out as powerful tools that enable deeper understanding of compressor stage designs after they have been tested. The insights gained from these investigations have aided in improving new stage designs. Up to now, it has only been possible to use the TEIS and Two Zone models for analysis of test data due to the inability to predict the four required input parameters for untested machines. Empirical models for the TEIS and Two Zone model input parameters, ETAa5, ETAb5, Chi5, and DELTA5p, for two different types of vaned diffusers, channel and cascade, are proposed. These models were developed with frozen impeller modeling. This is the first time that modeling the TEIS and Two Zone input parameters has been attempted for vaned diffusers and impeller-diffuser coupling was not considered in this initial investigation. The centrifugal compressor experimental data used in the model building was obtained from Concepts NREC, an industry sponsor. Each dataset provided was evaluated for quality and reliability and only the data deemed reliable were used in the model building databases. The empirical models presented are built solely on this higher quality data. Seven models are proposed for use in predicting the TEIS and Two Zone model input parameters ETAa5, ETAb5, Chi5, and DELTA5p. Models for ETAa5, ETAb5, and DELTA5p are specific to the type of vane present in the diffuser, while the model for Chi5 is common to both diffuser types. These are the first models ever built for the TEIS and Two Zone model inputs applied to channel and cascade diffusers and become a benchmark for future studies. The work with these models is not complete, however. The databases are not of a size that data could be withheld from empirical model building for the express purpose of validation. Instead the model performance is evaluated by applying all of the models, simultaneously, to the database from which they were built. The determination of the effectiveness of the combined modeling is based on the average error across the entire speedline. The models proved to be effective and a contributing step to employing such models for use in future compressor design.

The Two-Element In Series (TEIS) and Two-Zone models have been used successfully for over twenty years to model test data for radial flow compressors and pumps. The models can also be used to predict the performance of new machines provided that the model inputs can be accurately specified. Unfortunately, use of the TEIS and Two-Zone models as a predictive tool has been limited because an accurate and broadly applicable method of predicting the modeling parameters, etaA, etaB, chi and d2p does not exist. Empirical models have been developed to predict the TEIS and Two-Zone modeling parameters based on a large database of centrifugal pump and compressor test results. These test data were provided by ConceptsNREC and have been collected over the past 40 years. The database consists of a wide range of machines including some that were designed and tested by ConceptsNREC and others from the open literature. Only cases with a vaneless diffuser or volute have been included in the analysis to avoid any possible impeller-diffuser interactions. From the database, models for all of the TEIS and Two-Zone parameters have been derived using basic regression techniques. Three different models are proposed for each of the two TEIS modeling parameters, etaA and etaB. One model for pumps, another for compressors, and a combined model applicable for all machines is given. For the Two-zone parameters, chi and d2p, a single set of models was developed to represent the design point performance and another showing how chi and d2p vary off-design. The combined models for etaA and EtaB are 30% and 70% more accurate than the current state-of-the-art models, respectively. The new models account for the variance in chi and d2p at off-design flow conditions and further refine the accuracy of the overall prediction by correctly modeling the loss mechanisms in the impeller passage. Validation work has shown that the set of models that predict etaA, etaB, chi and d2p can be solved to consistently produce sensible results and yield a reasonable "blind" prediction of the performance of a wide range of radial compressors and pumps. These models constitute the first broadly applicable method for predicting the required TEIS and Two-Zone variables and are sufficiently accurate to provide initial performance estimates of new impeller designs