Modelling thermal conductivity of porous core systems for vacuum insulation panels

Abstract

Vacuum insulation panels (VIPs) are one of the most advanced and expensive insulation technologies, which achieve exceptionally low thermal conductivities of up to 0.004 W/(m·K) within a compact space. Modelling the thermal conductivity of core materials is essential for understanding their internal heat transfer mechanisms, enabling the development and optimisation of low-cost, sustainable, and durable cores of VIPs. The core material of VIPs is typically made of porous media since the voids within the porous structure not only reduce the density but also restrict both gaseous and solid heat transfer within the core. Existing models often fall short in efficiently capturing the complex interplay of heat transfer mechanisms within diverse porous structures, particularly across a wide range of pressure and for non-ideal porous structures. The particles forming the core are generally spherical or flaky in shape. Therefore, this study designs a two-dimensional Voronoi structure and a set of three-dimensional granular structures to construct physical models for analysing heat transfer. The proposed structures can be customised to reflect the morphological characteristics. The modelling work includes three components: conduction, convection, and radiation. For solid thermal conduction, this study employs either the Lattice Boltzmann method (LBM) or the finite element method (FEM), depending on the characteristic length of the solid skeleton. Then, a multiscale analytical model and numerical models are developed for calculating gas conduction and convection. Finally, the Rosseland approximation is applied to materials when FTIR data is available; If not, an improved radiation model combining the Watson model and physical structures is developed in this study to predict the radiative thermal conductivity of porous media. This study first examines the thermal conductivity variations of multiscale porous media, using fumed silica as a case study, with gas pressure as the primary variable. The model effectively captures the morphological characteristics of the material and has been validated across a full range of pressure conditions. Compared to existing studies on fumed silica, the proposed model achieves more accurate and reasonable predictions. In the pressure range from 0.01 to 0.8 atm, where thermal conductivity changes sharply, the model maximum error does not exceed 3%. This study further investigates the heat transfer behaviour of flaky porous media, exemplified by expanded perlite powder, by developing an innovative hybrid model to achieve a balance between predictive accuracy and computational complexity from vacuum to atmospheric pressure. At higher pressures (0.0001 to 0.05 atm, where Knudsen number < 0.1), all experimental results fall within the prediction range of the numerical model, while at lower pressures (> 0.05 atm, where Knudsen number > 0.1), the analytical model demonstrates deviations from the experimental values ranging between 5% and 17%. Subsequently, the model is applied to investigate the effects of morphological parameters on the effective thermal conductivity and offers practical advice into optimising the thermal performance of flaky porous media. Finally, this study develops a thermal conductivity model for granular porous media, using glass beads as an example, under vacuum conditions to investigate the influence of morphological characteristics on effective thermal conductivity and identify the most suitable three-dimensional geometric structure to represent their solid skeleton. A scaling model is first introduced by analysing the nonlinear relationship between contact thermal conduction and contact radius, significantly reducing the computational complexity with a maximum error of 1%. Five geometric structures are then employed to predict the conductive and radiative thermal conductivity with varying porosities. The results show that the aggregation structure provides the most accurate predictions for high-porosity (> 47.6%, porosity of simple cubic packing) structures with an average error of 12.7%; the dumping structure is optimal for packed beds (≈ 40%) with an average error of 9.2%, particularly for radiative thermal conductivity, In conclusion, this thesis presents a comprehensive modelling framework that addresses critical gaps in the thermal conductivity modelling of porous VIP core materials. By integrating analytical and numerical methods with advanced material characterisation and physical representation techniques, this study provides practical approaches for calculating the thermal conductivity of porous media cores. The developed modelling framework offers a powerful tool for the rational design and optimisation of VIP core materials with tailored thermal performance, which can contribute to the development of more energy-efficient and cost-effective insulation solutions for the industries.