Development and Validation of a New Method to Model Slip and Work Input for Centrifugal Compressors

Herbert M. Harrison, Purdue University

Abstract

Slip in centrifugal compressors arises from imperfect guidance of the flow by the impeller blades and reduces the work input delivered by the impeller, and slip models are typically used to predict slip in preliminary design. However, slip models are typically calibrated with data that are not representative of modern aerospace compressors (i.e. pumps, turbochargers, or industrial compressors) and do not account for the variation of slip factor with operating condition. A generalized meanline model for centrifugal compressors is developed to interrogate slip in centrifugal compressors from a one-dimensional design perspective. The meanline model is used to investigate the efficacy of slip models for predicting the slip factor and work input of modern, high-speed impellers at design and off-design conditions. Three slip models are used to predict the performance of five impellers, four of which are documented in the open literature. All three slip models generally overpredict the slip factor, and the largest error in the prediction of slip factor typically occurred near design speed. In addition, the analysis shows a close correlation between slip factor and two key design parameters of machine Mach number and loading coefficient over the entire compressor operating range. Finally, error propagation analysis shows that the error in impeller work input is proportional to the error in slip factor scaled by the square of machine Mach number and reveals the inherent challenge of accurate prediction of work input for high-speed machines.Finally, a new method of modeling slip factor and work input for centrifugal compressor impellers is presented. Rather than using geometry to predict the behavior of the flow at the impeller exit, the new method leverages governing relationships to predict the work input delivered by the impeller with dimensionless design parameters. The approach incorporates both impeller geometry and flow conditions and, therefore, is inherently able to predict the slip factor at design and off-design conditions. Five impeller cases are used to demonstrate the efficacy of the method, four of which are well documented in the open literature. Multiple implementations of the model are introduced to enable users to customize the model to specific applications. Significant improvement in the accuracy of the prediction of slip factor and work input is obtained at both design and off-design conditions relative to Wiesner’s slip model. While Wiesner’s model predicts the slip factor of 52% of the data within ±0.05 absolute error, the most accurate implementation of the new model predicts 99% of the data within the same error band. The effects of external losses and flow blockage on the model are considered, and the new model is fairly insensitive to the effects of both phenomena. Finally, detailed procedures to incorporate the new model into a meanline analysis tool are provided in the appendices.

Degree

Ph.D.

Advisors

Srivastava, Purdue University.

Subject Area

Aerospace engineering|Design|Fluid mechanics|Mechanics

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