Numerical Simulation of Sloshing-Induced and Static Thermodynamic Responses in a Liquid Helium Storage Tank

Liquid helium storage tanks undergo coupled heat ingress, thermal stratification, self-pressurization, and sloshing, but the empirical phase-change frequency used in conventional Lee models limits their reproducibility. This study couples the volume-of-fluid method, a layer-by-layer multilayer insulation/liquid nitrogen shield heat leak model, and a calibrated temperature-dependent Lee closure. The complete correlation, coefficients, evaporation adjustment factor (χ = 0.1), phase change sources, saturation relation, and latent heat source are reported. The full field after 3 h of static heat ingress is mapped into a 30 s sinusoidal sloshing calculation at 0.6 Hz and 0.3 g. In the liquid helium self-pressurization benchmark, the relative deviation of the average pressurization rate decreases from 39.64% for the best tested fixed-frequency Lee case (1.0 × 10−4 s−1) to 14.32% for the calibrated closure. After 3 h, the vapor pressure reaches 81,332.53 Pa and the average liquid centerline temperature gradient reaches 18.00 × 10−4 K/m. Sloshing produces an interfacial mixing layer approximately 0.43 m thick. The simulated pressure signals exhibit only a small downward drift; because time step sensitivity and global mass/energy balance data are unavailable, no numerically resolved pressure drop magnitude is claimed. The reported sloshing results are limited to the two-dimensional transverse plane model.