On the complex interplay of temperature, phase change and natural convection in self-pressurization-an investigation using segregated modeling

TL;DR

The paper develops a parameter-free, segregated CFD framework that couples an incompressible liquid solver with a compressible vapor solver, enforcing phase change via energy-jump conditions at a sharp liquid–vapor interface and resolving conjugate heat transfer through tank walls. Validation against lab-scale LN$_2$ and large-scale LH$_2$ experiments shows accurate prediction of pressure and temperature evolution without tuning, revealing two self-pressurization regimes: an initial heating-dominated transient followed by an evaporation-dominated quasi-steady state. A novel ullage-based scaling is proposed, collapsing regime transitions across fluids and geometries with a transition at $\hat{t}_* \approx 0.2$, and a simple relation enabling evaporation-rate estimation from measured $\frac{dp}{dt}$ in the evaporation-dominated regime. The study also finds that natural convection primarily alters the transient duration but barely affects long-term pressurization, and clarifies the thermodynamic origin of liquid stratification, offering a physically grounded basis for scaling and design of cryogenic storage under non-venting conditions.

Abstract

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.

Figures (14)

• Figure 1: Schematic of the difference between the traditional Volume of Fluid (VOF) approach, on the left and the segregated solver, on the right. The red solid line at the interface in the segregated solver highlights the discrete boundary surface at the liquid–vapor interface where mass and energy exchange due to evaporation and/or condensation is enforced (see Section \ref{['sec:CFD_coupling']}).
• Figure 2: Pressurization curve $p(t)$ from large-scale experiments contrasted with numerical simulations using the VOF approach and Lee phase-change model (Equation \ref{['eq:lee_model']}) for various accommodation coefficients $C$. The markers are shown only for plotting purposes.
• Figure 3: Comparison of computational cost of simulating the large-scale test using the segregated solver and VOF+KTG techniques across four mesh resolutions. Mesh sizes: $M_0 = 7.5\, k$, $M_1 = 16.7\, k$, $M_2 = 29.9\, k$, $M_3 = 66.7\, k$ cells.
• Figure 4: Mesh sensitivity analysis for the segregated solver in the large-scale test in terms of pressure (a) and temperature evolution (b) in the vapor phase for various mesh resolutions: $M0 \, (\Delta x = 10\, \mathrm{mm})$ with $7.4$k cells, $M1\, (5\, \mathrm{mm})$ with $17.2$k cells, $M2\, (2\, \mathrm{mm})$ with $39.6$k cells, $M3\, (1\, \mathrm{mm})$ with $61.4$k cells, $M4\, (0.5\, \mathrm{mm})$ with $84.62$k cells, and $M5\, (0.25\, \mathrm{mm})$ with $107.6$k cells. The markers are shown only for plotting purposes.
• Figure 5: Detailed visualization of the mesh in the thermal boundary layer in the large-scale test case.