PREDICTED ROTORDYNAMIC BEHAVIOR OF A LABYRINTH SEAL AS ROTOR SURFACE SPEED APPROACHES MACH 1
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Prior one-control-volume (1CV) models for rotor-fluid interaction in labyrinth seals produce synchronously-reduced (at running-speed), frequency-independent stiffness and damping coefficients. The 1CV model, consisting of a leakage equation, a continuity equation, and a circumferential-momentum 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 1CV fluid-mechanic model continues to be valid, the calculated rotordynamic coefficients become strongly frequency dependent. A solution is developed for the reaction-force components for a range of precession frequencies, producing frequency-dependent stiffness and damping coefficients. They can be used to define a Laplace-domain transfer-function model for the reaction-force/rotor-motion components. Calculated rotordynamic results are presented for a simple Jeffcott rotor acted on by a labyrinth seal. The seal radius Rs and running speed cause the rotor surface velocity Rs to equal the speed of sound c0 at = 58 krpm. Calculated synchronous-response results due to imbalance coincide for the synchronously-reduced and the frequency-dependent models. For an inlet preswirl ratio of 0.5, both models predict the same log decs out to 14.5 krpm. The synchronously-reduced 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 frequency-dependent model predicts an OSI of 65 krpm. The frequency-dependent models predict small changes in the rotors damped natural frequencies. The synchronously-reduced model predicts large changes. The stability-analysis results show that a frequency-dependent 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 Rs = 0.26 c0.
