THERMAL EFFECTS IN CRYOGENIC LIQUID ANNULAR SEALS .1. THEORY AND APPROXIMATE SOLUTION

A thermohydrodynamic (THD) analysis is introduced for calculation of t he performance characteristics of cryogenic liquid annular seals in th e turbulent flow regime. A full-inertial bulk-flow model is advanced f or momentum conservation and energy transport. The liquid material pro perties depend on the local absolute pressure and temperature. Heat fl ow to the rotor and stator is modeled by bulk-flow heat transfer coeff icients. An approximate analytical solution is obtained to the governi ng equations when the seal operates at a steady-state and concentric c ondition. The temperature-rise in the fluid film of a cryogenic liquid seal is found to be composed of four sources due to viscous dissipati on, pressure extrusion work, surface heat transfer and kinetic energy variation. For incompressible adiabatic flows, the fluid temperature r ises linearly along the axial direction. The approximate analytical so lution provides a useful tool for preliminary design and a better unde rstanding of seal performance. Full numerical predictions of load, lea kage, temperature, and rotordynamic coefficients for a high speed liqu id oxygen seal are given in Part II to show the importance of thermal effects on seal performance. The accuracy of the approximate concentri c seal analysis is then demonstrated by comparison to the results from the full numerical solution.