Bulk-Flow analysis for force and moment coefficients of a shrouded centrifugal compressor impeller
Gupta, Manoj Kumar
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An analysis is developed for a compressible bulk-flow model of the leakage path between a centrifugal compressor's impeller shroud and housing along the front and back side of the impeller. This is an extension of analysis performed first by Childs (1989) for a shrouded pump impeller and its housing considering an incompressible fluid, and then later by Cao (1993) using a compressible bulk flow model for the shroud of a cryogenic fluid pump. The bulk-flow model is used to develop a reaction force and moment model for the shroud of a centrifugal compressor by solving the derived governing equations and integrating the pressure and shear stress distribution. Validation is done by comparing the results to published measured moment coefficients by Yoshida et al. (1996). The comparison shows that the shroud casing clearance flow and the fluid force moment can be simulated by the bulk flow model fairly well. An Iwatsubo-based labyrinth seal code developed by Childs and Scharrer (1986) is used to calculate the rotordynamic coefficients developed by the labyrinth seals in the compressor. Tangential force and transverse moment components acting on the rotor are found to have a destabilizing influence on the rotor for a range of precession frequencies. Rotordynamic coefficients are derived for a single stage of a multistage centrifugal compressor, and a comparison is made to stability predictions using Wachel's coefficient using the XLTRC (rotordynamic FEA code). For the model employed, Wachel's model predicts a slightly lower onset speed of instability. The results also show that leakage that flows radially inwards on the back shroud has a greater destabilizing influence than leakage flow that is radially outwards. Seal rub conditions are simulated by increasing the clearance and simultaneously decreasing the tooth height, which increased the leakage and the swirl tothe eye seal inlet; and therefore reduced stability. Calculated results are provided for different seal clearances and tooth height, for seal and shroud forces and moments.