Analysis and Validation of a Unified Slip Factor Model for Impellers at Design and Off-Design Conditions

This paper presents a unified slip model for axial, radial, and mixed-flow impellers. The core assumption of the model is that the flow deviation or slip velocity at impeller exit is mainly originated from the blade loading near the discharge of an impeller and its subsequent relative eddy in the impeller passage. The blade loading is estimated and then used to derive the slip velocity using Stodola’s assumption. The final form of the slip factor model can be successfully related to Carter’s rule [1] for axial impellers and Stodola’s [2] slip model for radial impellers, making the case for this model to be applicable to axial, radial, and mixed-flow impellers. Unlike conventional slip factor models for radial impellers, the new slip model suggests that the flow coefficient at the impeller exit is an important variable for the slip factor when there is significant blade turning at the impeller discharge. This explains the interesting off-design trends for slip factor observed from experiments, such as the rise of the slip factor with flow coefficient in the Eckardt A impeller [3]. Extensive validation results for this new model are presented in this paper. Several cases are studied in detail to demonstrate how this new model can capture the slip factor variation at the off-design conditions. Furthermore, a large number of test data from more than 90 different compressors, pumps, and blowers were collected. Most cases are radial impellers, but a few axial impellers are also included. The test data and model predictions of the slip factor are compared at both design and off-design flow conditions. In total, over 1,650 different flow conditions are evaluated. The unified model shows a clear advantage over the traditional slip factor correlations, such as the Busemann-Wiesner model [4], when off-design conditions are considered.