This paper reports on analyses and optimization studies of problems associated with liquid hydrogen thermal stratification and self-pressurization in cryogenic vessels. Three different pressure rise models were employed to calculate the self-pressurization and boil-off rates. These are a homogeneous model, a surface-evaporation model, and a thermal stratification model. The first two models are based on the assumption that no temperature gradients exist in the tank, while the thermal stratification model takes the temperature distribution into account. Employing the thermal stratification model, temperature gradients and their effect on the pressure rise rates in liquid hydrogen tanks are analyzed.

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