Non-Oberbeck-Boussinesq effects and sub-critical primary bifurcations in porous media convection

Abstract

Large temperature variations and highly unstable density stratification may exist between the cold and hot boundaries of the porous non-vacuum gas filled insulation layers of cryogenic storage tanks. For example, the density can vary by about a factor 3 in N2 filled liquefied natural gas (LNG) tank insulation layers and factor 15 in H2 filled liquid hydrogen (LH2) tank insulation layers. In such cases, the bifurcation of the convective states from the conduction state could be sub-critical leading to sudden jumps and hysteresis effects in heat transfer and boil-off rates. This work examines the impact of large physical property variation and non-Oberbeck-Boussinesq (non-OB) effects on the nature of bifurcation of convective states in gas filled porous insulation layers. Specifically, we show that the well-known super-critical (pitchfork) bifurcation of convective states that appear under the OB approximation changes to sub-critical bifurcation when the temperature difference exceeds a critical value. Further, under such large temperature variations, the emerging convective solutions could be highly asymmetric with center of circulation much closer to the cold boundary. We present linear stability results, local bifurcation analysis as well as numerical simulations of the full model equations for the two selected LNG and LH2 cases.