A DEM/FFT approach to simulate the effective thermal conductivity of granular media

A numerical method to compute the Effective Thermal Conductivity (ETC) of granular media surrounded by a stagnant fluid is presented. Based on the geometry and size of grains, a Representative Volume Elements (RVE) of the granular media is created using the Discrete Element Method (DEM) while the ETC of this RVE is estimated with Fast Fourier Transform (FFT) computations. To bridge the gap between the DEM and the FFT, a discretization algorithm (voxelization of convex polyhedra) was developed. Since their physical properties are poorly defined, "fuzzy" voxels associated with solid-gas interfaces or solid-solid contacts, domains inherent in a granular medium, are clearly identified during this step. The assignment of extreme properties to these voxels, assuming negligible radiation, allows to establish lower and upper ETC bounds. This methodology is applied to granular media of Uranium dioxide particles immersed in stagnant Helium; packed beds for which experimental data are available in the literature. First, the effect of RVE and discretization sizes on the simulated ETC are investigated and optimal values of RVE size and discretization ratio are defined. Next, the significant deviation of simulated DEM-FFT ETC bounds, observed at high solid to gas conductivity contrasts, exhibits the key role of interfaces on the computed ETCs. An improved modelling of solid-gas interfaces based on the Knudsen effect and a modelling correction for solid-solid interfaces is therefore proposed. The new modelling is shown to adequately bound and estimate the ETC of considered granular media at high (similar to 100) solid to gas thermal conductivity contrasts.