Statistical characterization of near-wall radiative properties of a statistically non-homogeneous and anisotropic porous medium

The radiative properties statistical characterization method of Tancrez and Taine has been extended to statistically anisotropic and non-homogeneous porous media. When a homogenized phase of such a medium does not follow Beer’s law on extinction, extinction and scattering coefficients have no physical meaning: the phase is completely characterised by an extinction cumulative distribution function, a scattering cumulative probability, a general phase function and an effective optical index. A simple expression of the emission source term, in local thermal equilibrium conditions, is given for any non-homogeneous and anisotropic porous medium. The radiative transfer can be modelled by a Generalized Radiative Transfer Equation that is also extended to non-homogeneous porous media. This characterization method has been applied to the radiative properties of a packed bed of opaque and diffuse spherical particles bounded by a wall: the local porosity strongly varies near the wall and the homogenized phase is non Beerian. In the bulk of the medium, Beer’s law becomes valid and extinction, absorption and scattering coefficients have been determined.