Computational Model of Porous Media Using True 3-D Images

Abstract

Thermally conductive foams are being developed for many engineering applications; and there is a need to develop analytical models to predict the thermal properties of such porous media. Most of the current models are based on volume averaging techniques, and often assume simple, ideal shapes for the pore geometry. The method described in this chapter focuses on modeling the thermal and flow properties of foams on the basis of its true microstructure. The approach is to take a three dimensional solid model of a real foam, obtained by imaging techniques, and use it as the basis for the numerical solution of the transport phenomena. This is a micro-model, in which the thermal phenomena are modeled at the pore level of the foam. The model is computationally intensive, as can be expected; but it does not require semi-empirical or experimentally derived constants such as permeability to derive a solution. By incorporating the effect of the true pore geometry on the thermal transport and fluid flow in the foam, this model is able to determine the thermal conductivity, permeability, friction factor and heat transfer coefficients. Graphitic carbon and silicon carbide foams are used in this study, but the approach that is described is quite general and can be applied to other porous media; it may also be applied to composites that contain phases with distinct boundaries at the micro-level.

Nanocarbons for the Development of Advanced Catalysts

“…In these cases, it is necessary to investigate the thermal profile in CNT/SiC foams or monoliths and to optimize the preparation in relation to this aspect, but this is an area scarcely investigated. Current advances in CFD (computational fluid dynamics) of porous media 184 should be integrated into design of CNT/SiC foams or monoliths to optimize the performances.…”

On the Influence of Boundary Conditions when Determining Transport Coefficients from Finite Samples of Porous Media: Assessment for Tomographic Images of Real Materials

“…The correlation function is isotropic and exponentially dacaying, with a decay length l c = 4p x . Thus, the sample size can be expressed as [128l c ] 3 . The second one is a Bentheim sandstone (BS), with porosity 0.232, studied in [32].…”

“…Examples of applications can be found in [4,10,11,18,30] for [P/P], in [3,7,32] for [D/P] and in [6,11,14,21,26] for [D/D]. Although the idea of a self-consistent scheme is very common in theoretical models for the conductivity of composites such as those of Bruggeman [8] or Landauer [19], it seems that its numerical counterpart [E+P] has not been implemented in earlier works for the upscaling of conduction properties (but it is in [14] for the upscaling of the Stokes flow equations).…”

“…Again, this introduces directional constraints and the eigen-directions of Λ Λ Λ or K can only be found aligned with the artificial planes of symmetry. Various ad-hoc methods can be found where [P/P] is applied to Ω supplemented with upstream and/or downstream layers of a homogeneous material, in order ensure the connection of the conductive paths on the inlet and outlet sides of Ω [3,30]. Finally, a counterpart of [D/D] was considered in [26] where the normal flux instead of the temperature is prescribed on the boundaries,…”