On the relationship between pressure collapse rate and Nusselt number during sloshing in cryogenic liquid hydrogen tanks
Francesco Gambioli, Arnaud G. Malan, Franco Mastroddi
Abstract
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.