Generalized radiative transfer equation for porous medium upscaling: Application to the radiative Fourier law

Taine, Jean; Bellet, Fabien; Leroy, Vincent; Iacona, Estelle

doi:10.1016/j.ijheatmasstransfer.2010.05.027

Cited by 40 publications

(62 citation statements)

References 20 publications

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“…However, in the intermediate region there is a discrepancy, that seems to depend on the emissivity. This can be translated by the fact that k + is not a single constant, nor a pure function of the emissivity " as given in classical literature [58], but instead that it is also a function of Nu 0 . Withdrawing the purely conductive contributionk cond and dividing by Nu 0 gives curves like Figure 7, where the obtained k + is plotted against…”

Section: Influence Of Temperature On the Excess Radiative Conductivitymentioning

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: Influence Of Temperature On the Excess Radiative Conductivitymentioning

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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“…Note that the emission term is multiplied by /, to represent the fact that the internal emission in the bulk absorber propagates in the void space only, not in the entire volume (Taine et al, 2010).…”

Section: Two-flux Approximationmentioning

confidence: 99%

The promise and challenge of solar volumetric absorbers

et al. 2014

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“…However, the distribution of scatterers in many media exhibit different forms and degrees of spatial correlation (e.g. clouds [Davis and Marshak 2004;Lovejoy et al 1995], textiles [Coquard and Baillis 2006], porous materials [Bellet et al 2009;Taine et al 2010], or granular aggregates [Meng et al 2015]). This affects light transport, as Figure 4 illustrates; as a consequence, attenuation is no longer exponential, and light extinction becomes non-Poissonian.…”

Section: Effect Of Spatial Correlation On Extinctionmentioning

confidence: 99%

A radiative transfer framework for spatially-correlated materials

2018

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Fig. 1. Spatial correlation in media leads to non-exponential light transport, which significantly affects appearance. The image shows volumetric renderings of translucent dragons made of materials with the same density per unit differential volume µ = 10 (isotropic, albedo Λ = .8), but different correlations. Left: using classic light transport, where material particles are assumed to be uncorrelated. Middle and right: positive and negative correlation, respectively, using our novel framework for spatially-correlated materials. The insets show illustrative views of scatterer correlation for each dragon.We introduce a non-exponential radiative framework that takes into account the local spatial correlation of scattering particles in a medium. Most previous works in graphics have ignored this, assuming uncorrelated media with a uniform, random local distribution of particles. However, positive and negative correlation lead to slower-and faster-than-exponential attenuation respectively, which cannot be predicted by the Beer-Lambert law. As our results show, this has a major effect on extinction, and thus appearance. From recent advances in neutron transport, we first introduce our Extended Generalized Boltzmann Equation, and develop a general framework for light transport in correlated media. We lift the limitations of the original formulation, including an analysis of the boundary conditions, and present a model suitable for computer graphics, based on optical properties of the media and statistical distributions of scatterers. In addition, we present an analytic expression for transmittance in the case of positive correlation, and show how to incorporate it efficiently into a Monte Carlo renderer. We show results with a wide range of both positive and negative correlation, and demonstrate the differences compared to classic light transport.

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Generalized radiative transfer equation for porous medium upscaling: Application to the radiative Fourier law

Cited by 40 publications

References 20 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

The promise and challenge of solar volumetric absorbers

A radiative transfer framework for spatially-correlated materials

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