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RESEARCH PAPERS: Solution Methods

Radiative Transfer in Dispersed Media: Comparison Between Homogeneous Phase and Multiphase Approaches

[+] Author and Article Information
Jaona Randrianalisoa

CETHIL UMR5008, CNRS, INSA-Lyon, Université Lyon 1, F-69621 Villeurbanne, Francejaona.randrianalisoa@insa-lyon.fr

Dominique Baillis

CETHIL UMR5008, CNRS, INSA-Lyon, Université Lyon 1, F-69621 Villeurbanne, France

J. Heat Transfer 132(2), 023405 (Dec 09, 2009) (11 pages) doi:10.1115/1.4000237 History: Received December 03, 2008; Revised June 15, 2009; Published December 09, 2009; Online December 09, 2009

The radiative transfer in dispersed media in the geometric optic regime is investigated through two continuum-based approaches. The first one is the traditional treatment of dispersed media as continuous and homogeneous systems, referred here as the homogeneous phase approach (HPA). The second approach is based on a separate treatment of the radiative transfer in the continuous and dispersed phases, referred here as the multiphase approach (MPA). The effective radiative properties involved in the framework of the HPA are determined using the recent ray-tracing (RT) method, enabled to overcome the modeling difficulties such as the dependent scattering effects and the misunderstanding of the effective absorption coefficient. The two modeling approaches are compared with the direct Monte Carlo simulation. It is shown that (i) the HPA combined with effective radiative properties, such as those from the RT method, is satisfactory in analyzing the radiative transfer in dispersed media constituting of transparent, semitransparent, or opaque particles. Therefore, the use of more complex continuum models such as the dependence included discrete ordinate method (Singh, B. P., and Kaviany, M., 1992, “Modelling Radiative Heat Transfer in Packed Beds  ,” Int. J. Heat Mass Transfer, 35, pp. 1397–1405) is not imperative anymore. (ii) The MPA, though a possible candidate to handle nonequilibrium problems, is suitable if the particle (geometric) backscattering is weak or absent. It is the case, for example, for dispersed media constituted of opaque particles or air bubbles. However, caution should be taken with the MPA when dealing with the radiative transfer in dispersed media constituted of nonopaque particles having refractive indexes greater than that of the continuous host medium.

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Figures

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Figure 1

Illustration of the ray-tracing algorithm on a 2D dispersed medium

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Figure 2

(a) Effective absorption coefficients of dispersed media of large spheres with relative refractive index n1/n0=1.5 at the wavelength λ=πμm. Circle symbols with dash lines: the ray-tracing prediction and star symbols with dot lines: the independent scattering model. (b) Effective scattering coefficients of dispersed media of large spheres with relative refractive index n1/n0=1.5 at the wavelength λ=πμm. Circle symbols with dash lines: the ray-tracing prediction, star symbols with dot lines: the independent scattering model, and solid line: theoretical solution from Eq. 10.

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Figure 3

(a) Effective phase function of dispersed media of transparent particles with relative refractive index n1/n0=1.5. (b) Effective phase function of dispersed media of transparent particles with relative refractive index n1/n0=2/3.

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Figure 4

(a) Schematization of a thin slab of a heterogeneous medium and (b) modeling of a thin slab of heterogeneous according to the MPA

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Figure 5

(a) Radiation extinction in the matrix substance at the abscise z. Absorption (left); scattering by reflection (center); and scattering by transmission (right). (b) Radiation extinction in the particle substance at the abscise z. Absorption (left); scattering by reflection (center); and scattering by transmission (right).

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Figure 6

MPA effective phase functions of dispersed media of transparent particles with relative refractive index n1/n0=1.5

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Figure 7

(a) Directional transmittances and reflectances through slabs of suspension of nonabsorbing particles with n1=1.5 in a semitransparent host medium with n0=1. (b) Directional transmittances and reflectances through slabs of totally reflecting particles in a semitransparent host medium with n0=1. (c) Directional transmittances and reflectances through slabs of semitransparent matrixes with n0=1.5 embedding nonabsorbing air bubbles with n1=1.

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Figure 8

(a) Hemispherical transmittances through samples of opaque particles of uniform reflectivities ρ0=0.9 in a host medium with n0=1.0. (b) Hemispherical reflectances through samples of opaque particles of uniform reflectivities ρ0=0.9 in a host medium with n0=1.0.

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Figure 9

(a) Hemispherical transmittances through samples of semitransparent matrix with n0=1.5 embedding air bubbles with n1=1.0. (b) Hemispherical reflectances through samples of semitransparent matrix with n0=1.5 embedding air bubbles with n1=1.0.

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Figure 10

(a) Hemispherical transmittances through samples of semitransparent particles with n1=1.5 in suspension in a host medium with n0=1.0. (b) Hemispherical reflectances through samples of semitransparent particles with n1=1.5 in suspension in a host medium with n0=1.0.

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