Stratified Two-Phase Flow in Annular Seals

A new mathematical theory for the analysis of leakage rate behavior of annular shaft seals operating in the two-phase regime is presented which is based on the stratified flow of the boiling liquid and vapor phases. The flow is presumed to be axisymmetric, steady, and so rapid as to be turbulent. A set of governing equations for film-averaged liquid and vapor properties is developed. The streams are assumed to be adiabatic and moving at different average velocities. Effects of heat generation due to viscous dissipation and of interfacial mass transfer are accounted for fully. The methods of calculation for leakage under choked and unchoked conditions are explained. Many numerical results of leakage rate calculations for cryogenic oxygen are presented and are compared to corresponding results from a homogeneous-equilibrium flow model. Parametric studies show that leakage is fairly insensitive to the arrangement of the liquid and vapor phases within the seal.