On the validity of purely thermodynamic descriptions of two-phase cryogenic fluid storage

This paper presents a comprehensive analysis of the transport processes that control the self-pressurization of a cryogenic storage tank in normal gravity. A lumped thermodynamic model of the vapour region is coupled with the Navier-Stokes and energy equations governing heat, mass and momentum transport in the liquid. These equations are discretized using a Galerkin finite-element method with implicit time integration. Three case studies are considered based on three different heating configurations imposed on the tank wall: liquid heating, vapour heating and uniform heating. For each case, the pressure and temperature rise in the vapour and the flow and temperature distributions in the liquid are determined. Results are compared to a lumped thermodynamic model of the entire tank. It is shown that the final rate of pressure rise is about the same in each case and close to that predicted by thermodynamics even though the actual pressures are different because of varying degrees of thermal stratification. Finally, a subcooled liquid jet is used to mix the liquid and limit the pressure rise. Even so, there is still some thermal stratification in the liquid, and as a result the final vapour pressure depends on the particular heat distribution.