Generalized Equation for Thermal Conductivity of MLI at Temperatures From 20K to 300K

Multilayer insulation (MLI) has the lowest thermal conductivity of any currently used insulation in high vacuum environments and is used in cryogenic insulation system to minimize heat leaks in liquid hydrogen storage tanks. MLI consists of highly reflective radiation shields separated by spacers or insulation. The thermal conductivity of MLI varies with both temperature and vacuum level. Most published apparent thermal conductivities were measured for temperatures between 80K and 300K; some of the published data were for temperatures between 20K and 80K. Since the temperature of liquid hydrogen is 20K and the storage tanks are exposed to ambient air, it is essential to know the thermal performance of MLI for the temperature range of 20K to 300K. In addition, in order to provide a detailed temperature distribution and to optimize insulation systems with respect to the number of layers of MLI, layer density, insulation weight, and separator configuration, the layer-by-layer thermal performance of MLI has to be established for efficient storage tank design. A general equation for thermal conductivity was developed based on heat transfer principles for a wide range of temperature differences and vacuum levels. The equation consists of four heat transfer modes: 1) thermal radiation between two adjacent reflectors, 2) thermal radiation absorbed by spacers 3) gas conduction, and 4) solid spacer conduction. The equation can be applied for the temperature ranges of liquid hydrogen up to ambient, and for pressure ranges between 1.33 mPa to 1.33 kPa (0.01 millitorr and 10 torr). The predicted layer-by-layer temperatures, heat fluxes and apparent thermal conductivities using the developed thermal conductivity equation show very good agreement with measured data between the temperatures of 80K and 300K at the various pressure levels. When the equation was applied for a temperature of 20K, heat fluxes increased due to the larger temperature difference, while apparent thermal conductivities decreased due to the lower cold side temperature.