Computational Modeling of Thermal Phenomena in Nanomaterials for Building Applications

Comparative study of a cubic, Kelvin and Weaire-Phelan unit cell for the prediction of the thermal conductivity of low density silica aerogels

“…Next to this, due to the pore size distribution effect, the values for D are larger at lower densities for real aerogels which is, to our knowledge, for the first demonstrated for foam-like structures. Also, in a previous study [19], at densities below 90 kg.m -3 , it was challenging to create structures because of geometrical constraints in the corners of the cubic unit cell. As the actual pores are more likely to correspond to a spherical instead of a cubical shape, the Kelvin cell is introduced which is more or less a draped shape of a sphere while a cubic unit cell has a more deviant bounding box shape.…”

“…Each term in this formula can be calculated individually and depends on the assumed bead diameter dp and pitch between the beads. We refer to [15] and [19] for more detailed calculations dependent on the overlap a/dp, Fig. Consequently, the overlap becomes more important for larger bead diameters.…”

“…This can be explained by the change of the interatomic spacing which becomes larger if the bead diameter is larger. Then, while the volumetric resistance is taken as constant [19], the interatomic spacing due to space and transmission resistances are higher too, which lead to a higher inter-atomic spacing in general. From Eq.…”

“…As the actual pores are more likely to correspond to a spherical instead of a cubical shape, the Kelvin cell is introduced which is more or less a draped shape of a sphere while a cubic unit cell has a more deviant bounding box shape. Modelling a sphere like void inside a cubic unit cell led to air filling inner corners [19] and consequently an underestimation of the amount of solid in the unit cell which lowers the density significantly for the same D. In other words, for an identical density, the D value of a Kelvin cell is larger with respect to the cubic unit cell. For this reason, the Kelvin cell is a more representative model than a cubic unit cell and hence gains lower deviations from the state-of-the-art relation.…”

“…Finite volume simulations were carried out to calculate the thermal flow as in [19]. The working principle is as follows.…”