Mathematical Modelling of Thermal Stratification in a Cryogenic Propellant Tank

Cryogenic tanks used for space applications are filled with sub-cooled cryogenic propellants, whose liquid-vapor interface remains undisturbed for long periods of time prior to launch. During this period, substantial amount of heat leaks into the tank from external sources such as solar and ambient convective fluxes, even though the tank is well insulated. This results in thermal stratification near the liquid vapour interface. A transient, two-phase, thermodynamic model of stratification in a cryogenic tank is developed, considering propellant boundary layer flow due to natural convection close to tank wall. Continuity, momentum, energy and mass transfer equations are solved using finite difference-based formulations of SINDA/FLUINT simulator. The analytical model is validated with test results reported in literature. Subsequently, studies are carried out to investigate the effect of liquid sub-cooling in propellant tank on stratified mass and liquid temperature profile. The study shows that sub-cooling of cryogenic tank leads to significant increase in stratified mass.