On the complex interplay of temperature, phase change and natural convection in self-pressurization-an investigation using segregated modeling
Accurate prediction of self-pressurization in cryogenic tanks requires resolving the coupled effects of heat ingress, natural convection, and phase change. This work introduces a segregated numerical framework in which the liquid and vapor phases are treated with incompressible and compressible solvers, respectively, and the liquid-vapor interface is modeled as a sharp boundary subject to energy-jump conditions derived from first principles, without accommodation or tuning coefficients. Conjugate heat transfer through the tank walls is accounted for by solving the heat-conduction equation in the solid domain rather than prescribing external heat-flux conditions. The framework is validated against laboratory-scale LN2 and large-scale LH2 experiments, reproducing the spatio-temporal evolution of pressure and temperature without adjustable parameters. In both settings, the simulations identify two distinct regimes in self-pressurization: an initial heating-driven phase that establishes a self-similar temperature profile in the vapor, followed by an evaporation-driven phase in which the pressure rise is governed by the saturation relation. The comparison between these largely different scales motivated a revised scaling for self-pressurization, based on ullage thermodynamics. Finally, the influence of buoyancy was examined by reducing the strength of the gravitational body force, which revealed that natural convection modifies the duration of the transient heating phase but has a limited impact on the long-term pressurization rate. This analysis also clarifies the mechanism controlling the development of thermal stratification in the liquid. Overall, the segregated approach provides a predictive, parameter-free tool for analyzing cryogenic storage and offers a physically grounded basis for scaling self-pressurization across fluids, geometries, and heat-flux conditions.