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.

1.
Schunk
,
L.
,
Haeberling
,
P.
,
Wepf
,
S.
,
Wuillemin
,
D.
,
Meier
,
A.
, and
Steinfeld
,
A.
, 2008, “
A Receiver-Reactor for the Solar Thermal Dissociation of Zinc Oxide
,”
ASME J. Sol. Energy Eng.
0199-6231,
130
, p.
021009
.
2.
Wieckert
,
C.
,
Frommherz
,
U.
,
Kräupl
,
S.
,
Guillot
,
E.
,
Olalde
,
G.
,
Epstein
,
M.
,
Santen
,
S.
,
Osinga
,
T.
, and
Steinfeld
,
A.
, 2007, “
A 300 kW Solar Chemical Pilot Plant for the Carbothermic Production of Zinc
,”
ASME J. Sol. Energy Eng.
0199-6231,
129
, pp.
190
196
.
3.
von Zedtwitz
,
P.
, and
Steinfeld
,
A.
, 2005, “
Steam-Gasification of Coal in a Fluidized-Bed/Packed-Bed Reactor Exposed to Concentrated Thermal Radiation-Modeling and Experimental Validation
,”
Ind. Eng. Chem. Res.
,
44
, pp.
3852
3861
. 0888-5885
4.
Piatkowski
,
N.
, and
Steinfeld
,
A.
, 2008, “
Solar-Driven Coal Gasification in a Thermally Irradiated Packed-Bed Reactor
,”
Energy Fuels
0887-0624,
22
, pp.
2043
2052
.
5.
Osinga
,
T.
,
Lipiński
,
W.
,
Guillot
,
E.
,
Olalde
,
G.
, and
Steinfeld
,
A.
, 2006, “
Experimental Determination of the Extinction Coefficient for a Packed-Bed Particulate Medium
,”
Exp. Heat Transfer
0891-6152,
19
, pp.
69
79
.
6.
Zhao
,
C. Y.
,
Lu
,
T. J.
, and
Hodson
,
H. P.
, 2004, “
Thermal Radiation in Ultralight Metal Foams With Open Cells
,”
Int. J. Heat Mass Transfer
0017-9310,
47
, pp.
2927
2939
.
7.
Kamiuto
,
K.
,
Iwamoto
,
M.
,
Nishimura
,
T.
, and
Sato
,
M.
, 1991, “
Radiation-Extinction Coefficients of Packed-Sphere Systems
,”
J. Quant. Spectrosc. Radiat. Transf.
0022-4073,
45
, pp.
93
96
.
8.
Chen
,
J.
, and
Churchill
,
S.
, 1963, “
Radiant Heat Transfer in Packed Beds
,”
AIChE J.
0001-1541,
9
, pp.
35
41
.
9.
Tancrez
,
M.
, and
Taine
,
J.
, 2004, “
Direct Identification of Absorption and Scattering Coefficients and Phase Function of a Porous Medium by a Monte Carlo Technique
,”
Int. J. Heat Mass Transfer
0017-9310,
47
, pp.
373
383
.
10.
Yang
,
Y.
,
Howell
,
J.
, and
Klein
,
D.
, 1983, “
Radiative Heat Transfer Through a Randomly Packed Bed of Spheres by the Monte Carlo Method
,”
ASME J. Heat Transfer
,
105
, pp.
325
332
. 0022-1481
11.
Argento
,
C.
, and
Bouvard
,
D.
, 1996, “
A Ray Tracing Method for Evaluating the Radiative Heat Transfer in Porous Media
,”
Int. J. Heat Mass Transfer
0017-9310,
39
, pp.
3175
3180
.
12.
Chan
,
C.
, and
Tien
,
C.
, 1974, “
Radiative Transfer in Packed Spheres
,”
ASME J. Heat Transfer
,
96
, pp.
52
58
. 0022-1481
13.
Brewster
,
M.
, and
Tien
,
C.
, 1982, “
Radiative Transfer in Packed Fluidized Beds—Dependent Versus Independent Scattering
,”
ASME J. Heat Transfer
,
104
, pp.
573
579
. 0022-1481
14.
Tien
,
C.
, 1988, “
Thermal Radiation in Packed and Fluidized Beds
,”
ASME J. Heat Transfer
,
110
, pp.
1230
1242
. 0022-1481
15.
Coquard
,
R.
, and
Baillis
,
D.
, 2004, “
Radiative Characteristics of Opaque Spherical Particles Beds: A New Method of Prediction
,”
J. Thermophys. Heat Transfer
0887-8722,
18
, pp.
178
186
.
16.
Coquard
,
R.
, and
Baillis
,
D.
, 2005, “
Radiative Characteristics of Beds of Spheres Containing an Absorbing and Scattering Medium
,”
J. Thermophys. Heat Transfer
0887-8722,
19
, pp.
226
234
.
17.
Petrasch
,
J.
,
Wyss
,
P.
, and
Steinfeld
,
A.
, 2007, “
Tomography-Based Monte Carlo Determination of Radiative Properties of Reticulate Porous Ceramics
,”
J. Quant. Spectrosc. Radiat. Transf.
0022-4073,
105
, pp.
180
197
.
18.
Zeghondy
,
B.
,
Iacona
,
E.
, and
Taine
,
J.
, 2006, “
Determination of the Anisotropic Radiative Properties of a Porous Material by Radiative Distribution Function Identification (RDFI)
,”
Int. J. Heat Mass Transfer
0017-9310,
49
, pp.
2810
2819
.
19.
Stanmore
,
B.
, 2005, “
Review—Calcination and Carbonation of Limestone During Thermal Cycling for CO2 Sequestration
,”
Fuel Process. Technol.
,
86
, pp.
1707
1743
. 0378-3820
20.
Farmer
,
J. T.
, and
Howell
,
J. R.
, 1998, “
Comparison of Monte Carlo Strategies for Radiative Transfer in Participating Media
,”
Adv. Heat Transfer
0065-2717,
31
, pp.
333
429
.
21.
Modest
,
M.
, 2003,
Radiative Heat Transfer
, 2nd ed.,
Academic
,
San Diego
.
22.
Berryman
,
J.
, and
Blair
,
S.
, 1986, “
Use of Digital Image Analysis to Estimate Fluid Permeability of Porous Material: Application of Two-Point Correlation Functions
,”
J. Appl. Phys.
0021-8979,
60
, pp.
1930
1938
.
23.
Petrasch
,
J.
,
Wyss
,
P.
,
Stämpfli
,
R.
, and
Steinfeld
,
A.
, 2008, “
Tomography-Based Multiscale Analyses of the 3D Geometrical Morphology of Reticulated Porous Ceramics
,”
J. Am. Ceram. Soc.
,
91
, pp.
2659
2665
. 0002-7820
24.
2003,
Handbook of Fluidization and Fluid-Particle Systems
,
W. C.
Yang
, ed.,
Marcel Dekker
,
New York
.
25.
Palik
,
E.
, 2003,
Handbook of Optical Constants of Solids
,
Academic
,
San Diego
.
26.
Querry
,
M.
,
Osborne
,
G.
,
Lies
,
K.
,
Jordon
,
R.
, and
Coveney
,
R.
, 1978, “
Complex Refractive Index of Limestone in the Visible and Infrared
,”
Appl. Opt.
,
17
, pp.
353
356
. 0003-6935
27.
Rodriguez-Navarro
,
C.
,
Rodriguez-Navarro
,
A.
,
Elert
,
K.
, and
Sebastian
,
E.
, 2004, “
Role of Marble Microstructure in Near-Infrared Laser-Induced Damage During Laser Cleaning
,”
J. Appl. Phys.
0021-8979,
95
(
7
), pp.
3350
3357
.
28.
Bohren
,
C.
, and
Huffman
,
D.
, 2004,
Absorption and Scattering of Light by Small Particles
, 3rd ed.,
Wiley
,
New York
.
29.
Tien
,
C. L.
, and
Drolen
,
B. L.
, 1987, “
Thermal Radiation in Particulate Media With Dependent and Independent Scattering
,”
Annu. Rev. Numer. Fluid Mech. Heat Transfer
0892-6883,
1
, pp.
1
32
.
You do not currently have access to this content.