On the Relationship Between Pressure Collapse Rate and Nusselt Number During Sloshing in Cryogenic Liquid Hydrogen Tanks

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 (). A method for estimating 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 × 105 down to 7.58 × 103—reflecting the transient nature of the phenomenon.