Microstructure effects on thermal conductivity of open-cell foams generated from the Laguerre–Voronoï tessellation method

• Realistic virtual open-cell foams are generated using Laguerre–Voronoï tessellation method.
• D numerical model based on volume averaging and finite element methods is proposed to predict effective thermal conductivity.
• Predicted thermal conductivities match well experimental data of aluminum and ceramic foams at 300 K and over the porosity range 75–96%.
• Representative element volume based on thermal conductivity analysis should contain about nine cells along each volume side.
• The non-uniformity of axial cross-sectional area of struts reduces drastically the effective thermal conductivity.

The effects of microstructure on the thermal conductivity of open-cell structures are investigated using a numerical approach. They include sample size, cell arrangement, and non-uniformity of strut cross-sectional area. The approach combines the Laguerre–Voronoï tessellation method for generating volumetric digitalized foam samples and the finite-element method for solving the heat transfer problem and thus for computing thermal properties. It is shown that (i) the apparent thermal conductivity is size dependent for small sample volumes. The size effect becomes negligible when the volume element representing the sample contains more than nine cells along the edge side and we can refer to effective thermal conductivity. (ii) The non-uniformity of axial strut cross-sectional area causes a strong thermal resistance along the strut axis and consequently, a decrease of the effective thermal conductivity. And (iii) From comparison between regular Kelvin's cells and random monomodal cell structures, the arrangement of cells has little influence on the effective thermal conductivity of open-cell foams. This is explained by the similarity of their tortuosity values (skeleton tortuosity about 1.4). The suitability of the current approach for predicting effective thermal conductivity of open-cell foams is confirmed by the satisfactory agreement between numerical calculations and measurements over the porosity range 75–96%.