(58i) Stability and Bifurcation Analysis of Natural Convection Effects in Liquid Hydrogen Tank Dual Layered Insulations

Liquid hydrogen (LH2) has the highest gravimetric energy density and thus has sparked interest as a mode of transporting hydrogen which is posited to become fuel of the future. One of the challenges in transportation of LH2 is large scale storage because state-of-the-art vacuum technology is not scalable to commercial tank sizes. Non-vacuum technology is needed to design insulation for such cryogenic storage tanks. Insulation can be built in shape of panels or large scale spherical or cylindrical annulus. At large scale (40,000-100,000 m³), the effects of curvature are negligible and thus, study of horizontal insulation panels or layers suffices. These insulation panels are gas saturated porous media. Perlite is an inexpensive porous insulation material that is often utilized in these designs. The choice of the filler gas depends on the cryogenic liquid being insulated. LH2, which is stored at 20K can have insulation layer built from hydrogen or helium filled perlite. While this strategy can be implemented without risking filler gas condensation, it is known that the thermal conductivity of gases is inversely proportional to their molecular weight and boiling point is directly proportional to their molecular weight. Thus, a lighter gas will not condense easily but will have higher conductivity. A dual layer strategy can yield better results for insulation design where, the inner insulation layer that is in contact with the cryogenic liquid can have a lighter gas as a filler gas and the outer layer that is in contact with the ambient environment can have a heavier gas. Hydrogen being the lightest element in the periodic table, has a high thermal conductivity and second lowest liquefaction point. Thus, in the first layer only gaseous hydrogen or helium can be utilized. Dual layer design here enables a thinner and cheaper insulation with inert and inexpensive gas like nitrogen being filled in the second layer. For cryogenic insulation layers, the physical property variation of the filler gas is large. A new approach presented here with a temperature weighted stream-function allows us to investigate the problem neatly without the assumptions of Boussinesq approximation and constant physical properties. We formulate the problem of buoyancy driven natural convection in dual layered insulations with hydrogen and nitrogen as the filler gases. We determine the stability of the conduction state using linear instability theory and the critical Rayleigh number (or permeability) for the onset of convection in the inner or outer layer. Using spectral methods, we show that the bifurcations become sub-critical due to large variations in the physical properties. Thus, the insulation layers must be designed below the limit point of the convective branches. The change of bifurcation from super-critical to sub-critical is important because a design falling in the region where both conductive and convective branches are stable can have problems like migration of cold boundary, leading to ice formation, cryo-pumping and high boil-off.