Continuum radiative heat transfer modeling in media consisting of optically distinct components in the limit of geometrical optics

High-resolution X-ray computed tomography is employed to obtain the exact 3D geometrical configuration of porous anisotropic ceria applied in solar-driven thermochemical cycles for splitting H2O and CO2. The tomography data are, in turn, used in direct pore-level numerical simulations for determining the morphological and effective heat/mass transport properties of porous ceria, namely: porosity, specific surface area, pore size distribution, extinction coefficient, thermal conductivity, convective heat transfer coefficient, permeability, Dupuit-Forchheimer coefficient, and tortuosity and residence time distributions. Tailored foam designs for enhanced transport properties are examined by means of adjusting morphologies of artificial ceria samples composed of bimodal distributed overlapping transparent spheres in an opaque medium.

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“…For example, the Planck mean absorption coefficient of CO at 1000 K and 1 atm is 2.1 m

^{- 1}

, calculated based on the HITRAN2004 database [31]. The volume-averaged radiative transfer equation (RTE) is given by [32]. …”

Section: Heat Transfer Characterizationmentioning

confidence: 99%

Effective Heat and Mass Transport Properties of Anisotropic Porous Ceria for Solar Thermochemical Fuel Generation

Haussener

Steinfeld

2012

Materials

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“…RTE has been derived from Maxwell's equations and can, therefore, be assumed to be microphysical in the limit of assumed simplifications [ Mishchenko , 2008; Mishchenko et al , 2011]. Volume averaging of a RTE for each phase (air and ice) in the limit of geometrical optics leads to two coupled volume‐averaged RTEs as described in Lipiński et al [2010a, 2010b] and given by,

\overset{s}{true} \cdot \nabla I_{i}^{} ((), x, \overset{s}{true}) = - β_{i} I_{i}^{} ((), x, \overset{s}{true}) + n_{i}^{2} κ_{i} I_{b, i}^{} ((), x, \overset{s}{true}) + \frac{σ_{s, i i}}{4 π} \int_{4 π} I_{i}^{} ((), x, {\hat{bolds}}_{in}) Φ_{ii} ((), {\hat{bolds}}_{in}, \overset{s}{true}) d Ω_{in} + \frac{σ_{s, j i}}{4 π} \int_{4 π} I_{j}^{} ((), x, {\hat{bolds}}_{in}) Φ_{ji} ((), {\hat{bolds}}_{in}, \overset{s}{true}) d Ω_{in} i, j = 1, 2; i \neq j,

where I i is the volume averaged intensity,

I_{i} = \frac{1}{V} \int_{V} L_{i} d V

, and

σ_{s, i i} = σ_{s,refl, i} + σ_{s, i}, ...

…”

Section: Radiative Transfer Within Snowmentioning

confidence: 99%

“…RTE has been derived from Maxwell's equations and can, therefore, be assumed to be microphysical in the limit of assumed simplifications [Mishchenko, 2008;Mishchenko et al, 2011]. Volume averaging of a RTE for each phase (air and ice) in the limit of geometrical optics leads to two coupled volume-averaged RTEs as described in Lipiński et al [2010aLipiński et al [ , 2010b and given by,…”

Section: Radiative Transfer Within Snowmentioning

confidence: 99%

“…A first approach to account for the complex morphology of snow was introduced in tomography‐based studies [ Kaempfer et al , 2007; Bänniger et al , 2008], where computed tomography (CT) images of the snow microstructure were used as input for the reflectance and transmittance determination by a phenomenological ray‐tracing approach. Recently, a more advanced phenomenological multiphase heat transfer model has been proposed for the radiative characterization of multiphase media in the limit of geometrical optics, assuming independent scattering and neglecting diffraction [ Lipiński et al , 2010a, 2010b]. The model is derived by applying volume‐averaging theory to RTEs valid within each phase and applying the appropriate phase boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Determination of the macroscopic optical properties of snow based on exact morphology and direct pore‐level heat transfer modeling

Haussener¹,

Gergely²,

Schneebeli³

et al. 2012

J. Geophys. Res.

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[1] A multiscale methodology for the determination of the macroscopic optical properties of snow is presented. It consists of solving the coupled volume-averaged radiative transfer equations for two semi-transparent phases -ice and air -by Monte Carlo ray tracing in an infinite slab via direct pore-level simulations on the exact 3D microstructure obtained by computed tomography. The overall reflectance and transmittance are computed for slabs of five characteristic snow types subjected to collimated and diffuse incident radiative flux for wavelengths 0.3-3 mm. The effect of simplifying the snow microstructure and/or the radiative transfer model is elucidated by comparing our results to (i) a homogenized radiation model and considering a particulate medium made of optical equivalent grain size spheres (DISORT), or (ii) a multiphase radiation model considering a packed bed of identical overlapping semi-transparent spheres. The calculations are experimentally validated by transmittance measurements. Significant differences in the macroscopic optical properties are observed when simplifying the snow morphology and the heat transfer model (i.e., homogenized versus multiphase). The proposed approach allows -in addition to determine macroscopic optical properties based on the exact morphology and obtained by advanced heat transfer model -for detailed understanding of radiative heat transfer in snow layers at the pore-scale level.Citation: Haussener, S., M. Gergely, M. Schneebeli, and A. Steinfeld (2012), Determination of the macroscopic optical properties of snow based on exact morphology and direct pore-level heat transfer modeling,

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“…Consalvi et al [3] have first applied to radiative transfer within divided media an approach similar to the volume averaged method of Whitaker and Quintard [4][5][6][7], which is based on the spatial averaging theorem. Other approaches based on this theorem have been developed: i) For statistically isotropic porous media by Lipinski et al [8,9], Randrianalisoa et al [10][11][12], Coquard at al. [13,14], and Gusarov [15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Statistical modelling of radiative transfer within non-Beerian effective phases of macroporous media

Taine

Enguehard

2019

International Journal of Thermal Sciences

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Continuum radiative heat transfer modeling in media consisting of optically distinct components in the limit of geometrical optics

Cited by 41 publications

References 25 publications

Effective Heat and Mass Transport Properties of Anisotropic Porous Ceria for Solar Thermochemical Fuel Generation

Effective Heat and Mass Transport Properties of Anisotropic Porous Ceria for Solar Thermochemical Fuel Generation

Determination of the macroscopic optical properties of snow based on exact morphology and direct pore‐level heat transfer modeling

Statistical modelling of radiative transfer within non-Beerian effective phases of macroporous media

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