MICROSCALE DIRECT CALCULATION OF SOLID PHASE CONDUCTIVITY OF VORONOI'S FOAMS

The effects of cell randomness and sample size on thermal conductivity of cellular foams were investigated through the finite-element method (FEM) applied to numerical samples generated by the perturbed Voronoi tessellation method. The three-dimensional aspect of cellular materials, the nature of cells (opened or closed), the distribution of cell volume, and the randomness of the cell shape and location were taken into account. For the model validation, a comparative study with experimental and existing numerical results of open-cell (metallic and ceramic) foams and closed-cell (polymer) foams was carried out. The smallness of the sample size leads to an under- or overprediction, depending on the cell nature, of their thermal conductivities. This size effect comes mainly from the dependence of the sample porosity on its size for a fixed cell wall thickness or strut cross-section area. The size effect becomes negligible when samples, the representative elementary volume (REV), contain tens of cells along each volume side. The cell randomness (in terms of shape and location), captured here through the cell size standard deviation of the Gaussian-normal distribution, leads to a cell volume dispersion, and more particularly, the apparition of small cell volume. These last are characterized by small cell faces and short face edges, which provoke a decrease of the foam thermal conductivities. The cell randomness effects are more important for open-cell structures than for closed-cell structures. The proposed approach predicts perfectly the numerical results of the volume-finite method applied to numerical foams generated from the X-ray computed tomography technique. The suitability of the current approach for predicting thermal conductivity of both open- and closed-cell foams is confirmed by the satisfactory agreement between calculations and measurements in wide temperature and porosity ranges.