San Andres employed the NBS software package MIPROPS to account for density's dependence on pressure in the simulation of liquid annular seals. His example on a LH2 seal showed a significant change in the mass coefficient compared to a constant density model. San Andres, Yang, and Childs extended this analysis by including the pressure and temperature dependence of density, specific heat, viscosity, volumetric expansion, and thermal conductivity in a coupled solution of the energy, momentum, and continuity equations. Their example showed very significant changes in stiffness and inertia for a high speed (38,000 rpm), large L/D ratio (0.5) LOX seal, as compared to their constant temperature results. The current research rederived the San Andres-Yang-Childs (SYC) analysis and extended it to include not only the Moody friction model of SYC but also the Hir's friction model. The derivation begins with obtaining the local differential equations of continuity, momentum, and energy conservation in the seal. These equations are averaged across the film thickness to obtain the resulting 'bulk flow' differential equations. Shear stress and convective heat loss through the stator (seal) and rotor are related to the Moody and Hir's friction factor model. The Holman analogy is employed to relate heat conduction in or out of the fluid film's boundary layer to the friction induced shear stress.
