Predicted Rotordynamic Behavior of a Labyrinth Seal as Rotor Surface Speed Approaches Mach 1
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Prior onecontrolvolume (ICV) models for rotorfluid interaction in labyrinth seals produce synchronouslyreduced (at runningspeed), frequencyindependent stiffness and damping coefficients. The ICV model, consisting of a leakage equation, a continuity equation, and a circumferentialmomentum equation (for each cavity) was stated to be invalid for rotor surface speeds approaching the speed of sound. However, the present results show that, while the ICV fluidmechanic model continues to be valid, the calculated rotordynamic coefficients become strongly frequency dependent. A solution is developed for the reactionforce components for a range of precession frequencies, producing frequencydependent stiffness and damping coefficients. They can be used to define a Laplacedomain transferfunction model for the reactionforce/rotormotion components. Calculated rotordynamic results are presented for a simple Jeffcott rotor acted on by a labyrinth seal. The seal radius Rs and running speed ω cause the rotor surface velocity Rsω to equal the speed of sound c0, at ω=58 krpm. Calculated synchronousresponse results due to imbalance coincide for the synchronouslyreduced and the frequencydependent models. For an inlet preswirl ratio of 0.5, both models predict the same log decs out to ω≈14.5 krpm. The synchronouslyreduced model predicts an onset speed of instability (OSI) at 15 krpm, but a return to stability at 45 krpm, with subsequent increases in log dec out to 65 krpm. The frequencydependent model predicts an OSI of 65 krpm. The frequencydependent models predict small changes in the rotor's damped natural frequencies. The synchronouslyreduced model predicts large changes. The stabilityanalysis results show that a frequencydependent labyrinth seal model should be used if the rotor surface speed approaches a significant fraction of the speed of sound. For the present example, observable discrepancies arose when Rsω = 0.26 c 0. Copyright © 2009 by ASME.
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Thorat, M. R., & Childs, D. W.
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International Standard Book Number (ISBN) 13
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