Computation of the effective thermal conductivity from 3D real morphologies of wood

This work is devoted to the numerical computation of the macroscopic properties of different wood species, namely the porosity and the effective thermal conductivity, following their orthotropic directions. We are interested in typical wood species, such as: spruce, poplar and balsa. First, each sample is scanned at a resolution on the order of the micrometer thanks to a lab X-ray nanotomograph (UltraTom by RX-solutions). Then, a suitable set of 3D image processing operations, coded as a Python script in ImageJ, allows obtaining a digital representation of the 3D morphology. This representation is used as an input mesh for a software developed in house, based on the finite volume method. We derive the macroscopic properties consisting of directional thermal conductivities by achieving the stationary regime. Several numerical experiments are carried out to validate the prediction approach. The focus will be on the effect of the representative elementary volume (REV) on the macroscopic property, which depends on the property itself (porosity, thermal conductivity), the species, and the material direction. An original volume reduction idea is proposed to improve the performance. It consists of amending the form and the size of the REV in the longitudinal direction by assuming that the phases are placed in parallel in this direction. It is numerically shown that this approach has a negligible impact on the property and greatly reduces the computational cost.