Phase Change and Choked Flow Effects on Rotordynamic Coefficients of Cryogenic Annular Seals

The present work deals with the numerical analysis of phase change effects and choked flow on the rotordynamic coefficients of cryogenic annular seals. The analysis is based on the “bulk flow” equations, with the energy equation written for the total enthalpy, and uses an estimation of the speed of sound that is valid for single- or two-phase flow as well. The numerical treatment of choked flow conditions is validated by comparisons with the experimental data of Hendricks (1987, “Straight Cylindrical Seal for High-Performance Turbomachines,” NASA Technical Paper No. 1850) obtained for gaseous nitrogen. The static characteristics and the dynamic coefficients of an annular seal working with liquid or gaseous oxygen are then investigated numerically. The same seal was used in previous analyses performed by Hughes et al. (1978, “Phase Change in Liquid Face Seals,” ASME J. Lubr. Technol., 100, pp. 74–80), Beatty and Hughes (1987, “Turbulent Two-Phase Flow in Annular Seals,” ASLE Trans., 30(1), pp. 11–18), and Arauz and San Andrés (1998, “Analysis of Two Phase Flow in Cryogenic Damper Seals. Part I: Theoretical Model,” ASME J. Tribol., 120, pp. 221–227 and 1998, “Analysis of Two Phase Flow in Cryogenic Damper Seals. Part 2: Model Validation and Predictions,” ASME J. Tribol., 120, pp. 228–233). The flow in the seal is unchoked, and rotordynamic coefficients show variations, with the excitation frequency depending if the flow is all liquid, all gas, or a liquid-gas mixture. Finally, the pressure ratio and length of the previous seal are changed in order to promote flow choking in the exit section. The rotordynamic coefficients calculated in this case show a dependence on the excitation frequency that differ from the unchoked seal.