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# Tomographic Characterization of a Semitransparent-Particle Packed Bed and Determination of its Thermal Radiative Properties

[+] Author and Article Information
S. Haussener, J. Petrasch

Department of Mechanical and Process Engineering, ETH Zurich, 8092 Zurich, Switzerland

W. Lipiński

Department of Mechanical Engineering, University of Minnesota, Minneapolis, MN 55455

P. Wyss

Department of Electronics/Metrology, EMPA Material Science and Technology, Überlandstrasse 129, 8600 Dübendorf, Switzerland

A. Steinfeld1

Department of Mechanical and Process Engineering, ETH Zurich, 8092 Zurich, Switzerland; Solar Technology Laboratory, Paul Scherrer Institute, 5232 Villigen, Switzerlandaldo.steinfeld@eth.ch

The spectral subscript $λ$ is omitted for brevity.

1

Corresponding author.

J. Heat Transfer 131(7), 072701 (May 04, 2009) (11 pages) doi:10.1115/1.3109261 History: Received May 07, 2008; Revised February 11, 2009; Published May 04, 2009

## Abstract

A two-phase medium consisting of densely packed large nonspherical semitransparent particles in a transparent fluid is considered. Its 3D digital geometry is obtained by computer tomography and employed to numerically calculate its porosity, specific surface, pore and particle size distributions, and the representative elementary volume for continuum domain. The collision-based Monte Carlo method is applied to calculate the probability distribution functions for attenuation path length and direction of incidence at the fluid-solid interface for each phase, which, in turn, are used to derive the extinction and scattering coefficients and the scattering phase functions. The methodology is applied to a packed bed of $CaCO3$ particles, used in industrially relevant high-temperature processes. Spectral and directional dependencies of the radiative properties are analyzed.

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## Figures

Figure 1

Sample of the packed bed of CaCO3 particles: (a) top view photograph, (b) 2D tomographic image, and (c) 3D surface rendering

Figure 2

Normalized histogram of the sample’s absorption values obtained by CT for the void phase (left peak) and for the solid phase (right peak). The bullet indicates the threshold value α/αmax=0.43 used for phase identification.

Figure 4

Opening size distribution functions, f=−dεop(d)/(ε∞dd) of the solid and fluid phases of the CaCO3 packed bed (dh≡dh,pore for fluid and dh≡dh,particle for solid)

Figure 5

SEM picture of a single CaCO3 particle

Figure 7

Spectral directional-hemispherical reflectivities at the specular fluid-solid interface for selected incidence directions, and spectral hemispherical reflectivity of the diffuse fluid-solid interface

Figure 8

Internal absorption and scattering coefficients of CaCO3 particles

Figure 9

Ratio of the scattering efficiency factor obtained for dependent scattering calculated by gas, packed-sphere, liquid, and modified-liquid models to that obtained for independently scattering calculated by the Mie theory

Figure 10

Spectral scattering coefficients of the CaCO3 packed bed for ((a) and (b)) the fluid phase and ((c) and (d)) the solid phase, assuming ((a) and (c)) specularly reflecting particles and ((b) and (d)) diffusely reflecting particles

Figure 12

Probability density functions of the directional cosine of the incident angle at the fluid-solid interface for selected wavelengths

Figure 13

Scattering phase functions of the CaCO3 packed bed versus cosine of the scattering angle for a specularly reflecting solid-fluid interface, at selected wavelengths λ=0.1 μm, 1 μm, 10 μm, and 100 μm

Figure 17

MC (dashed line) and analytically (solid line) calculated phase functions of a particle cloud for fv=1.6×10−3, d=2 μm, n=1.64, and k=2.6×10−5 at λ=1 μm, ρd=0.866, and for specularly and diffusively reflecting particles

Figure 3

(a) Two-point correlation function for the CaCO3 packed bed. The value at r=0 corresponds to the bed porosity. The dashed line indicates the asymptotic value of the function, which corresponds to ε2. (b) Determination of the REV edge length (indicated by the vertical dashed line) by calculating the porosity of ten subvolumes with varying edge lengths l at random locations. The tolerance band for conversion and determination of the REV volume at ε±0.01 is indicated by the two horizontal dashed lines.

Figure 6

Complex refractive index of CaCO3: (solid line) real part obtained experimentally (25), and (dashed line) imaginary part obtained by the Lorentz theory in the spectral range 0.2–6 μm(26) and experimentally in the remaining range (25)

Figure 11

Spectral extinction coefficients of the packed bed: (a) fluid phase and (b) solid phase

Figure 14

Scattering phase functions of the CaCO3 packed bed versus cosine of the scattering angle for a diffusely reflecting solid-fluid interface, at selected wavelengths λ=0.1 μm, 1 μm, 10 μm, and 100 μm

Figure 15

Scattering phase function Φ12 and Φ21 for specular and diffuse fluid-solid interfaces, as a function of the scattering angle cosine, for selected refractive indices n2=1.31, 1.64, and 1.97

Figure 16

Normalized two-norm of the cumulative distribution functions

Figure 18

Normalized mean intensity along three orthogonal directions as a function of sample length

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