Analysis of slip factors in CFD calculations – Assessment of literature models

Slip modelling enhances the accuracy of pressure rise and power predictions in the preliminary design of compressor stages. In the literature, several models like the Stodola, Pfleiderer, Wiesner-Busemann and Qiu model are published. All of them are semi-empirical models considering the flow phenomena, which lead to outlet flow deviation. Nevertheless, the data and DOE are fixed to the compressor test data in the literature. In this paper, a CFD-based DOE with a thousand centrifugal compressor impellers and a large variation in compressor design parameters is calculated. This data forms the basis for an assessment of the literature models as well as the introduction of an own CFD-based slip model. In a first step, an automated simulation workflow for centrifugal compressor impellers is described in detail. Overall, seven geometrical parameters as well as the flow coefficient are analyzed. The geometrical parameters are the blade number, outlet blade angle, outlet blade curvature, rake angle, tip clearance, blade thickness as well as mean diameter ratio. The CFD setup is validated with focus on the slip factor based on the data of the Eckardt impellers. A design of experiments (DOE) with Latin Hypercube Sampling and 1000 sample points is calculated. For the assessment of the literature models, the root mean square error (RMSE) and maximum error quantify the slip model performance statistically. A ranking of the four models is conducted and high inaccuracies in specific parameter ranges are detected and explained. Based on this assessment and the flow phenomena in centrifugal compressor impellers, an own CFD-based slip model is developed. The applicability is high due to the similarities to the Wiesner-Busemann and Qiu model.