Natural convection effects in insulation layers of spherical cryogenic storage tanks

Natural convection effects in the insulation layers of spherical storage tanks are studied for different cryogenic fluids and tank sizes or curvatures. The non-vacuum-based insulation layers of these tanks are made of gas-filled porous materials such as perlite or glass bubbles. The large temperature difference that can exist between the inner cold wall and outer hot wall may create convective patterns with a multi-cellular flow within the insulation-filled annulus and lead to a higher boil-off rate and cryo-pumping effects. A main objective in the design of these systems is the elimination of the convective patterns by a proper choice of insulation properties. This work examines the impact of the insulation permeability or the Rayleigh number (Ra) on the type of convective flows for liquified natural gas (LNG) and liquid hydrogen (LH2) spherical storage tanks. Bifurcation diagrams of possible solutions are generated by numerical solutions of the governing equations at different Ra numbers. It is found that as Ra increases, new convective cells emerge near the south pole of the insulation layer due to unstable density stratification and lead to the distortion of isotherms, bringing the cold boundary towards the external hot boundary. When the temperature difference is large as in the case of LNG and LH2 tanks, there exist regions of multiple solutions in which multi-cell convective solutions may co-exist with a crescent-shaped weakly convective solution. In order to eliminate the possibility of multi-cell convection, inversion of the cold boundary, and reduce the boil-off rate, the Ra value of the insulation system should be below the limit point of the convective branch.