Research Papers: Radiative Heat Transfer

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.


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

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.

Copyright © 2009 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.



Grahic Jump Location
Figure 1

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

Grahic Jump Location
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.

Grahic Jump Location
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.

Grahic Jump Location
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)

Grahic Jump Location
Figure 5

SEM picture of a single CaCO3 particle

Grahic Jump Location
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)

Grahic Jump Location
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

Grahic Jump Location
Figure 8

Internal absorption and scattering coefficients of CaCO3 particles

Grahic Jump Location
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

Grahic Jump Location
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

Grahic Jump Location
Figure 11

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

Grahic Jump Location
Figure 12

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

Grahic Jump Location
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

Grahic Jump Location
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

Grahic Jump Location
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

Grahic Jump Location
Figure 16

Normalized two-norm of the cumulative distribution functions

Grahic Jump Location
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

Grahic Jump Location
Figure 18

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



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In