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Pressure collapse in sloshing cryogenic liquid hydrogen tanks is a challenge for existing models, which often diverge from experimental data. This paper presents a novel lumped-parameter model that overcomes these limitations. Based on a control volume analysis, our approach simplifies the complex, non-equilibrium physics into a single dimensionless ordinary differential equation governing the liquid’s temperature. We demonstrate this evolution is controlled by one key parameter: the interfacial Nusselt number ( N u ). A method for estimating N u directly from pressure data is also provided. Validated against literature data, the model predicts final tank temperatures with deviation of 0.88K ( < 5% relative error) from measurements, thereby explaining the associated pressure collapse. Furthermore, our analysis reveals that the Nusselt number varies significantly during a single sloshing event—with calculated values ranging from a peak of 5.81 × 10 5 down to 7.58 × 10 3 —reflecting the transient nature of the phenomenon.
Gambioli et al. (Wed,) studied this question.