Analysis of natural convection effects in non-vacuum-based insulation layers of large-scale liquid hydrogen tanks

This work examines natural convection effects in the non-vacuum-based dual insulation layers of liquid hydrogen storage tanks. Specifically, we consider a dual-layer insulation system in which the inner layer (near the cold boundary) is a hydrogen-filled porous material, while the outer layer (near the warm boundary) is a nitrogen-filled porous medium. We use linear instability theory to determine the critical Rayleigh number for the onset of convective motions, accounting for full physical property variation. We show that the highly unstable density stratification can lead to sub-critical bifurcations and the co-existence of conduction and convective states. We present computed bifurcation diagrams, along with flow patterns and temperature profiles of the emerging convective states. Due to sub-critical bifurcations, in order to avoid convective motions and minimize the boil-off rate, the insulation needs to be designed such that the Rayleigh number is below the limit point of the convective branch.