Setup of a numerical methodology for the study of self-pressurization of cryogenic tanks

In this paper, a suitable numerical methodology to predict the thermo-fluid-dynamics within self-pressurized cryogenic tanks is proposed. A comparison towards experimental results of a self-pressurization test case in a ground-based, liquid nitrogen (N₂) tank, subject to an entering heat transfer rate, is carried out in order to select the most promising numerical methodology. The effect of different numerical models and parameters is studied, always adopting the Volume-of-Fluid (VOF) method for tracing the two-phase fluid interface and the Lee model for calculating the phase transition. In particular, the numerical results show that, for the studied test case: (1) the prediction of the pressure rise is not strongly affected by the Lee model parameters, even if they may affect the numerical stability of the computation; (2) the use of a conjugate heat transfer model is necessary in order to represent the liquid temperature stratification close to the free-surface, as the wall heat flux paths play a fundamental role in the heat distribution between the liquid phase and the ullage; (3) a laminar model is more adequate as the turbulent model overestimates convective recirculations in the liquid phase, leading to excessive mixing and resulting in failure to describe temperature stratification close to the free-surface, confirming the results of other papers in the literature; (4) the experimental uncertainty on the entering heat transfer rate may substantially affect the numerical predictions.