Thermal Effects in Cryogenic Liquid Annular Seals—Part II: Numerical Solution and Results

A numerical thermohydrodynamic model for solution of the nonlinear differential equations describing the turbulent flow of a single-phase, cryogenic liquid annular seal is presented. A perturbation method is used for calculation of the zeroth and first-order flow solutions to determine the seal steady-state response and dynamic force coefficients. Numerical predictions for a high speed liquid oxygen seal with a roughened stator surface show that, relative to an isothermal-barotropic fluidmodel, the adiabatic THD solution presents a significant temperature-rise with a profound effect on the liquid material properties and seal performance characteristics. The calculations show the onset of two-phase flow conditions at moderate eccentricities despite the large pressure differential across the seal. Comparisons of the static performance characteristics for the reference seal show excellent agreement between the approximate analytical solution developed in Part I and the full numerical results.