A radiative conductivity model is developed for porous media with a solid opaque phase and a transparent fluid phase. In a first step, an effective semi transparent medium occupying the volume of the real fluid phase is characterized, assuming the validity of the Beer's laws. For example, rod bundles in squared or triangular configurations can be directly characterized by effective strongly anisotropic extinction, absorption and scattering coefficients, optical index and phase function, which depends on both the incident and scattering unit vectors, by generalizing the Radiative Distribution Function Identification method of Tancrez and Taine (2004). The validity and accuracy of the associated Beer's laws are discussed in this case. In a second step, at the limit of an optically thick porous medium, an original model based on a perturbation method of the Radiative Transfer Equation directly leads to the determination, under an accurate validity criterion, of a radiative conductivity tensor for the fluid phase. Examples of results are given in the case of rod bundles versus porosity, specific area and local wall absorptivity.
Radiative transfer within non Beerian porous media with semitransparent and opaque phases in non equilibrium: Application to reflooding of a nuclear reactor.
AbstractA local radiative transfer model is developed for strongly anisotropic porous media with an opaque phase and a mixture of two semitransparent phases. At the optically thick limit, the homogenized phase associated with the opaque interfaces is characterized by generalized extinction and scattering coefficients at equilibrium, a phase function and an effective refraction index, by following the model of Taine et al. [1] for non Beerian media. The radiative transfer model is based on a Radiative Transfer Equation (RTE) with three source terms, which are associated with the temperature fields of the opaque interfaces and the two semitransparent phases. This RTE has been solved by a perturbation technique, which allows radiative interfacial fluxes and radiative powers per unit volume, that are exchanged between phases, to be computed at local scale. The main contributions are obtained at zeroth order perturbation. Corrective contributions at first order perturbation are also determined: Radiative fluxes and powers are then expressed from coupled Fourier's laws, which are characterized by radiative conductivity tensors associated with each phase.Illustrative results are given for the radiative modeling of reflooding of a damaged * Corresponding author
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