Rotordynamic Stability Predictions for Centrifugal Compressors Using a Bulk-Flow Model to Predict Impeller Shroud Force and Moment Coefficients

An analysis is developed for a compressible bulk-flow model of the leakage path between a centrifugal-compressor impeller’s shroud and its housing along the impeller’s front and back sides. This development is an extension of analyses performed first by Childs (1989, ASME J. Vib. Acoust., Stress, Reliab. Des., 111, pp. 216–225) for pump impellers. The bulk-flow model is used to predict reaction force and moment coefficients for the impeller shroud. A labyrinth seal code developed by Childs and Scharrer ( 1986, ASME Trans. J. Eng. Gas Turbines Power, 108, pp. 325–331) is used to calculate the rotordynamic coefficients developed by the labyrinth seals in the compressor stage and also provides a boundary condition for the shroud calculations. Comparisons between the measured shroud moment coefficients by Yoshida et al. (1996, Proceedings of the 6th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery, 2, pp. 151–160) and model predictions show reasonable agreements for the clearance flow and reaction moments. For the conditions considered, low Mach number flow existed in the shroud clearance areas and compressible-flow and incompressible-flow models produced similar predictions. Childs’ model predictions for the direct damping and cross-coupled stiffness coefficients of a pump impeller produced reasonable agreement; hence the present model was validated to the extent possible. A rotor model consisting of an overhung impeller stage supported by a nominally cantilevered rotor was analyzed for stability using the present bulk-flow model and an API standard Wachel–von Nimitz formula model (1981, J. Petrol. Technol., pp. 2252–2260). The bulk-flow model predicted significantly higher onset speeds of instability. Given that some compressors have been predicted to be comfortably stable using API standard Wachel–von Nimitz formula but have been unstable on the test stand, these results suggest that unidentified destabilizing forces and or moments are present in compressors. Seal rub conditions that arise from surge events and increase the seal clearances are simulated, showing that enlarged clearances increase the preswirl at the seals, thus increasing these seal’s destabilizing forces and reducing stability margins. These results are consistent with field experience. Predictions concerning the back shroud indicate that shunt-hole injection mainly acts to enhance stability by changing the flow field of the division wall or balance piston seals, not by influencing the back-shroud’s forces or moments. Effective swirl brakes at these seals also serve this purpose.