Influence of boundary conditions on computation of the effective thermal conductivity of foams

Abstract

Accurate numerical simulation of the effective thermal conductivity (ETC) of 3D pore-scale foam models requires a judicious choice of boundary conditions, as the computational domains are often smaller than the representative volume element, giving rise to considerable edge effects. Within the finite element homogenization framework, a set of mixed boundary conditions are considered alongside the usual uniform and periodic boundary conditions. Validity criteria and order relations, demonstrated from entropy-based principles, are numerically verified on unit cell-based geometries, random virtual periodic foams, and non-periodic tomography-reconstructed foams of equivalent microstructure. A statistical treatment based on the integral range provides confidence intervals for the estimated ETC. For foam samples with random homogeneous porosity, the mixed boundary conditions are shown to fulfill the macrohomogeneity condition and thus provide thermodynamically valid ETC estimates. For periodic foams with irregular microstructure, the ETC is very slightly underestimated under the mixed boundary conditions. For non-periodic geometries, it is shown that periodic boundary conditions-commonly viewed as the reference-underestimate the ETC due to boundary geometry mismatch, while the mixed boundary conditions give a more accurate and precise estimate.

Computational Model of Effective Thermal Conductivity of Green Insulating Fibrous Media

“…Li et al [ 20 ] determined both the in- and out-of-plane thermal conductivities of composites using the representative volume element (REV) technique with two-unit cells created at varied scales and periodic boundary conditions. However, as heterogeneous media can have prohibitively large representative elementary volume (REV) sizes due to the randomness of the microstructure (non periodic), it is often necessary to estimate the true effective thermal conductivity (ETC) based on the apparent thermal conductivity (ATC) of computational domains (elementary volume) smaller than RVE, for which different boundary conditions may provide different results [ 21 ]. Thus, in this current paper, particular attention is placed on the precision of the numerical results and the influence of the choice and size of the computational representative elementary volume (REV).…”

“…We propose considering two types of elementary volume: usual cubic or slice. Until now, elementary cubic volumes [ 21 ] have generally been considered, and there has been virtually no previous work on the influence of REV volume shape. This is an innovative aspect of this article, which aims to show the influence and importance of the choice of volume shape.…”

Effect of the shape and the distribution of cells on the effective thermal conductivity of polyurethane foam

“…20,21 The generation of the REVs is based on a pavement of unit cells: Kelvin cell, 7,22 Gibson and Ashby cell, 10 and the spherical cell. 6,23 Spherical constructions are used to model polymeric foam without considering the struts' shape and dimensions. 24 Then, heuristic constructions such as Kelvin structure 7,22,25 are widely used and can give a good approximation to realistic microstructure, but it is still limited to closed or open cell foam.…”

“…Several studies use numerical periodic homogenization to compute the effective thermal conductivity either for composite materials 19 or for foams 20,21 . The generation of the REVs is based on a pavement of unit cells: Kelvin cell, 7,22 Gibson and Ashby cell, 10 and the spherical cell 6,23 . Spherical constructions are used to model polymeric foam without considering the struts' shape and dimensions 24 .…”

Modelling of thermal conductivity and nonlinear mechanical behavior of straw insulation composite by a numerical homogenization approach

“…This special class of porous materials with cellular microstructure have been extensively studied by using periodic homogenization method. Low et al 2020 [33] studied the influence of boundary conditions on the computation of the effective thermal conductivity of foams with a high porosity of 74%. Three types of foam geometries were used, namely, unit cell-based structures, digitally generated periodic foams, and tomography-reconstructed real foams.…”