Radiative transfer within non Beerian porous media with semitransparent and opaque phases in non equilibrium: Application to reflooding of a nuclear reactor

Chahlafi, Miloud; Bellet, Fabien; Fichot, F.; Taine, Jean

doi:10.1016/j.ijheatmasstransfer.2012.02.067

Cited by 20 publications

(38 citation statements)

References 26 publications

(58 reference statements)

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“…Most of these studies have concerned semi-transparent media. A generalization of the RTE approach (GRTE) 4 has been derived on opaque/transparent (OT) media [50,51]. Leroy and Taine [52] have also dealt with OT media including conduction and even convection in the fluid, by coupling the GRTE with the Volume Averaging Method; interesting results have been produced on an ideal simple geometry.…”

Section: Introductionmentioning

confidence: 99%

Numerical study of effective heat conductivities of foams by coupled conduction and radiation

Vignoles

Ortona

2016

International Journal of Thermal Sciences

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E↵ective thermal conductivities (ETC) under vacuum were computed numerically on 3D blocks of open-cell foams either obtained by X-ray tomography or generated by Computer-Aided Design (CAD) with ideal geometries.For the first time a Monte-Carlo/Random Walk code accounting for the coupling of conduction in the solid phase and of radiation in the pore space has been used. The whole range of conduction/radiation ratio, parameterized by a Nusselt number, has been scanned; a law relating the ETC to this parameter has been obtained. In all cases the conductive and radiative contributions are additive. The slope of the radiative contribution to the ETC is found to display a distinct behavior, depending on whether radiation or conduction dominates. The low-temperature regime has an emissivity-dependent ETC slope, while the high-temperature regime does not.The critical ratio between both regimes is related to the ratio between cell and strut diameters. In all cases, it is found that the ETC anisotropy decreases with temperature. Closing some windows enhances conduction parallel to the closing walls and reduces radiation perpendicular to them. This e↵ect is shown to influence the ETC eigendirections in actual media.

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Section: Introductionmentioning

confidence: 99%

Numerical study of effective heat conductivities of foams by coupled conduction and radiation

Vignoles

Ortona

2016

International Journal of Thermal Sciences

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“…Statistical techniques of characterisation of the radiative properties of homogenised phases of a porous medium based on extinction cumulative distribution functions G ext ν and scattering cumulative probabilities P sc ν , have been first developed by Tancrez and Taine [1] and used in many recent works, for media with Opaque and Transparent phases [1,2,3,4,5,6] (OT case), with Opaque and Semi Transparent phases [7,8] (OST case), and for media with two Semi Transparent phases or a Semi Transparent phase and a Transparent one [9](ST2 and STT cases). A perfectly homogeneous and isotropic medium, an absorbing gas for instance, follows the extinction Beer's law: Exponential extinction, characterised by an extinction coefficient β ν .…”

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confidence: 99%

“…A perfectly homogeneous and isotropic medium, an absorbing gas for instance, follows the extinction Beer's law: Exponential extinction, characterised by an extinction coefficient β ν . A homogenised phase of porous medium can be: i) Strongly non Beerian [1,4,7,10]; It is the general case; ii) Approximately Beerian, as many 1 foams [2]; iii) Rigorously Beerian, as the space between statistically homogeneous configurations of overlapping or non overlapping spheres [1] or cylinders [9].…”

mentioning

confidence: 99%

Comments over homogenisation scales for interfacial emission and scattering by a divided medium: Beerian and non Beerian behaviours

Dauvois

Zarrouati

Rochais

et al. 2016

International Journal of Heat and Mass Transfer

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International audienceIn statistical methods of characterisation of porous media radiative properties, inter-facial extinction cumulative distribution functions, scattering or absorption cumulative probabilities and general phase functions are generally determined from shots issued from random volume points instead of random interfacial points. Indeed, the first method is numerically much simpler and accurate than the second one. The validity of this approach is discussed and its limitations enhanced for both Beerian and non Beerian homogenised phases, and in the case of a diffuse reflection law or a general one. The explanation of the identity or difference between the results of the two previous types of extinction cumulative distribution functions comes from the comparison between the spatial scale at which these functions are determined and the own scales of the divided medium. The conditions for which a medium follows the Beer's law are then defined in terms of spatial scales. Moreover, the modeling of interfacial emission for a non Beerian homogenised phase is in principle based on the reciprocity theorem and an integral formulation of the Generalised Radiative Transfer Equation. The validity of a simpler approach based on an effective absorption coefficient is also discussed, from the previous analysis. The validity of results of recent works published in IJHMT are finally discussed

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“…The determination of the apparent radiative properties of dispersed media based on media morphology and composition becomes crucial to the accuracy of this approach. This topic has continuously attracted interest from the radiative transfer community due to its large variety of applications such as solar energy conversion [3][4][5] , nuclear technologies [6] , snow physics [7] , and medical applications [8] . The reviews of Viskanta and Mengüç [9] , Baillis and Sacadura [10] , and Bail-lis et al [11] present the theoretical approaches and experimental methodologies for the characterization of spectral, directional apparent radiative properties of particulate and realistic disperse media, such as foams, fibrous materials, various ceramics, polymer coatings containing microspheres, and aerogel super-insulations.…”

Section: Introductionmentioning

confidence: 99%

“…[1,2] ), to multiple intensities approach, previously applied to packed beds (e.g. [6,[34][35][36] ), foams (e.g. [14,18] ) and fibrous media, [33] in order to estimate the applicability of simplifying theoretical approaches for predicting radiative transfer in isotropic fibrous materials consisting of optically large fibers.…”

Section: Introductionmentioning

confidence: 99%

Radiative characterization of random fibrous media with long cylindrical fibers: Comparison of single- and multi-RTE approaches

Randrianalisoa

Haussener

Baillis

et al. 2017

Journal of Quantitative Spectroscopy and Radiative Transfer

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a b s t r a c tRadiative heat transfer is analyzed in participating media consisting of long cylindrical fibers with a diameter in the limit of geometrical optics. The absorption and scattering coefficients and the scattering phase function of the medium are determined based on the discrete-level medium geometry and optical properties of individual fibers. The fibers are assumed to be randomly oriented and positioned inside the medium. Two approaches are employed: a volume-averaged two-intensity approach referred to as multi-RTE approach and a homogenized single-intensity approach referred to as the single-RTE approach . Both approaches require effective properties, determined using direct Monte Carlo ray tracing techniques. The macroscopic radiative transfer equations (for single intensity or two volume-averaged intensities) with the corresponding effective properties are solved using Monte Carlo techniques and allow for the determination of the radiative flux distribution as well as overall transmittance and reflectance of the medium. The results are compared against predictions by the direct Monte Carlo simulation on the exact morphology. The effects of fiber volume fraction and optical properties on the effective radiative properties and the overall slab radiative characteristics are investigated. The single-RTE approach gives accurate predictions for high porosity fibrous media (porosity about 95%). The multi-RTE approach is recommended for isotropic fibrous media with porosity in the range of 79 −95%.

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Radiative transfer within non Beerian porous media with semitransparent and opaque phases in non equilibrium: Application to reflooding of a nuclear reactor

Cited by 20 publications

References 26 publications

Numerical study of effective heat conductivities of foams by coupled conduction and radiation

Numerical study of effective heat conductivities of foams by coupled conduction and radiation

Comments over homogenisation scales for interfacial emission and scattering by a divided medium: Beerian and non Beerian behaviours

Radiative characterization of random fibrous media with long cylindrical fibers: Comparison of single- and multi-RTE approaches

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