A novel approach to thermal insulation modelling in soft and medium vacuum insulation systems

The accuracy of vacuum-dependent models for predicting thermal performance of Multi-Layer Insulation (MLI) and other layered insulation systems is critical for the development of novel solutions in the aerospace and energy sectors, particularly long distance superconductors and cryogenic transfer lines. This paper presents a review of the current state of the art in cryogenic vacuum insulation systems and their associated modelling techniques and test methods. Current modelling techniques, namely the Lockheed and McIntosh MLI models, are compared to cryogenic, boil-off calorimeter test data for 3 types of MLI from the current literature. Both current models provide acceptable accuracy at high vacuum pressures but deviate from the test data when gas conduction becomes the dominant heat transfer mechanism ($Kn\le 1$). Neither of the current models follow the characteristic S-curve observed by researchers during insulation tests. This paper presents the introduction of a novel modelling approach for layered insulation systems though changes to the current state of the art, specifically at soft ($p_{vac}\le 7.5\times {10}^5\text{ mTorr}$) and medium vacuum ($p_{vac}\le 7.5\times {10}^2\text{ mTorr}$) pressures, by substituting the gas conduction term in both equations with alternative terms based on the system Knudsen number (Kn) and molecule mean free path (l). This results in a stronger pressure dependence across the vacuum regime. Both modified models exhibited the characteristic S-curve with significantly reduced errors over the entire range.