Theoretical investigation on heat leakage distribution between vapor and liquid in liquid hydrogen tanks

As a key factor affecting thermal behaviors of liquid hydrogen (LH₂) tanks, heat leakage plays an important role in accurate prediction of pressure build-up for safe storage and transportation of LH₂. Uniform heat flux between vapor and liquid in LH₂ tanks is widely adopted as thermal boundary condition in predicting pressure build-up process. However, a distribution of heat flux between vapor and liquid was observed during the self-pressurization process in the experimental test. In light of this, an analytically theoretical model of revealing the energy exchange process among the vapor, liquid and inner wall is proposed to investigate the heat leakage distribution ratio (HDR) between vapor and liquid in LH₂ tanks. The feasibility of the model is validated by the experimental results from NASA. In the whole self-pressurization process of 25,000 s, HDR reduces from 0.803 to 0.235 under a liquid fill ratio of 90% and a total heat leakage of 71.3 W. The results show that the existence of inner wall and different thermal properties between the vapor and liquid make the heat leakage flux non-uniformly distributed into the vapor and liquid. And the geometric structure of tank, thermal properties and initial states of the vapor and liquid have a significant effect on HDR. When coupling the model with thermal multi-zone model, the relative error in pressure prediction is reduced by 61.8% against experimental results. Benefiting from the coupled model, the relative error in pressure prediction caused by the uniform heat flux boundary condition reduces from 90.16% to 8.15%. The present work establishes theoretical foundation on analyzing heat leakage distribution between the vapor and liquid for LH₂ tanks, and provides useful guidance on modifying boundary conditions in accurately predicting thermal behaviors of LH₂ tanks.