In this work, the influence of the radiative properties of coal and ash particles on radiative heat transfer in combustion environments is investigated. Emphasis is placed on the impact on the impact of the complex index of refraction and the particle size on particle absorption and scattering efficiencies. Different data of the complex index of refraction available in the literature are compared, and their influence on predictions of the radiative wall flux and radiative source term in conditions relevant for pulverized coal combustion is investigated. The heat transfer calculations are performed with detailed spectral models. Particle radiative properties are obtained from Mie theory, and a narrow band model is applied for the gas radiation. The results show that, for the calculation of particle efficiencies, particle size is a more important parameter than the complex index of refraction. The influence of reported differences in the complex index of refraction of coal particles on radiative heat transfer is small for particle sizes and conditions of interest for pulverized coal combustion. For ash, the influence of variations in the literature data on the complex index of refraction is larger, here, differences between 10% and 40% are seen in the radiative source term and radiative heat fluxes to the walls. It is also shown that approximating a particle size distribution with a surface area weighted mean diameter, D32, for calculation of the particle efficiencies has a small influence on the radiative heat transfer.

References

References
1.
Goodridge
,
A. M.
, and
Read
,
A. W.
,
1976
, “
Combustion and Heat Transfer in Large Boiler Furnaces
,”
Prog. Energy Combust. Sci.
,
2
(
2
), pp.
83
95
.
2.
Blokh
,
A. G.
,
1988
,
Heat Transfer in Steam Boiler Furnaces
,
Hemisphere Publishing Corporation
,
Washington, DC
.
3.
Denison
,
M. K.
, and
Webb
,
B. W.
,
1993
, “
A Spectral Line-Based Weighted-Sum-of-Gray-Gases Model for Arbitrary RTE Solvers
,”
ASME J. Heat Transfer
,
115
(4), pp.
1005
1012
.
4.
Dombrovsky
,
L. A.
, and
Baillis
,
D.
,
2010
,
Thermal Radiation in Disperse Systems: An Engineering Approach
,
Begell House
,
New York
.
5.
Taine
,
J.
, and
Soufiani
,
A.
,
1999
, “
Gas IR Radiative Properties: From Spectroscopic Data to Approximate Models
,”
Adv. Heat Transfer
,
33
, pp.
295
414
.
6.
Tien
,
C. L.
,
1968
, “
Thermal Radiation Properties of Gases
,”
Adv. Heat Transfer
,
5
, pp.
253
324
.
7.
Tiwari
,
S. N.
,
1978
, “
Models for Infrared Atmospheric Radiation
,”
Adv. Geophys.
,
20
, pp.
1
85
.
8.
Rothman
,
L. S.
,
Gordon
,
I. E.
,
Barber
,
R. J.
,
Dothe
,
H.
,
Gamache
,
R. R.
,
Goldman
,
A.
,
Perevalov
,
V. I.
,
Tashkun
,
S. A.
, and
Tennyson
,
J.
,
2010
, “
HITEMP, the High-Temperature Molecular Spectroscopic Database
,”
J. Quant. Spectrosc. Radiat. Transfer
,
111
(
15
), pp.
2139
2150
.
9.
Coelho
,
P. J.
,
2002
, “
Numerical Simulation of Radiative Heat Transfer From Non-Gray Gases in Three-Dimensional Enclosures
,”
J. Quant. Spectrosc. Radiat. Transfer
,
74
(
3
), pp.
307
328
.
10.
Goutiere
,
V.
,
Liu
,
F.
, and
Charette
,
A.
,
2000
, “
An Assessment of Real-Gas Modelling in 2D Enclosures
,”
J. Quant. Spectrosc. Radiat. Transfer
,
64
(
3
), pp.
299
326
.
11.
Modest
,
M. F.
, and
Zhang
,
H.
,
2002
, “
The Full-Spectrum Correlated-k-Distribution for Thermal Radiation From Molecular Gas-Particulate Mixtures
,”
ASME J. Heat Transfer
,
124
(
1
), pp.
30
38
.
12.
Johansson
,
R.
,
Leckner
,
B.
,
Andersson
,
K.
, and
Johnsson
,
F.
,
2011
, “
Account for Variations in the H2O to CO2 Molar Ratio When Modelling Gaseous Radiative Heat Transfer With the Weighted-Sum-of-Grey-Gases Model
,”
Combust. Flame
,
158
(
5
), pp.
893
901
.
13.
Solovjov
,
V. P.
,
Andre
,
F.
,
Lemonnier
,
D.
, and
Webb
,
B.
,
2016
, “
The Generalized SLW Model
,”
J. Phys.: Conf. Ser.
,
676
(
1
), p.
012022
.
14.
Gronarz
,
T.
,
Habermehl
,
M.
, and
Kneer
,
R.
,
2016
, “
Modeling of Particle Radiative Properties in Coal Combustion Depending on Burnout
,”
Heat Mass Transfer
(preprint).
15.
Brewster
,
M. Q.
, and
Kunitomo
,
T.
,
1984
, “
The Optical Constants of Coal, Char and Limestone
,”
ASME J. Heat Transfer
,
106
(
4
), pp.
678
683
.
16.
Manickavasagam
,
S.
, and
Mengüç
,
M. P.
,
1993
, “
Effective Optical Properties of Pulverized Coal Particles Determined From FT-IR Spectrometer Experiments
,”
Energy Fuels
,
7
(
6
), pp.
860
869
.
17.
Kim
,
C.
, and
Lior
,
N.
,
1995
, “
Easily Computable Good Approximations for Spectral Radiative Properties of Particle-Gas Components and Mixture in Pulverized Coal Combustors
,”
Fuel
,
66
(
12
), pp.
277
280
.
18.
Bäckström
,
D.
,
Gall
,
D.
,
Pushp
,
M.
,
Johansson
,
R.
,
Andersson
,
K.
, and
Pettersson
,
J. B. C.
,
2015
, “
Particle Composition and Size Distribution in Coal Flames—The Influence on Radiative Heat Transfer
,”
Exp. Therm. Fluid Sci.
,
64
, pp.
70
80
.
19.
Foster
,
P. J.
, and
Howarth
,
C. R.
,
1968
, “
Optical Constants of Carbons and Coals in the Infrared
,”
Carbon
,
6
(
5
), pp.
719
729
.
20.
Im
,
K. H.
, and
Ahluwalia
,
R. K.
,
1993
, “
Radiation Properties of Coal Combustion Products
,”
Int. J. Heat Mass Transfer
,
36
(
2
), pp.
293
302
.
21.
Liu
,
F.
, and
Swithenbank
,
J.
,
1993
, “
The Effects of Particle Size Distribution and Refractive Index on Fly-Ash Radiative Properties Using a Simplified Approach
,”
Int. J. Heat Mass Transfer
,
36
(
7
), pp.
1905
1912
.
22.
Goodwin
,
D. G.
, and
Mitchner
,
M.
,
1989
, “
Flyash Radiative Properties and Effects on Radiative Heat Transfer in Coal-Fired Systems
,”
Int. J. Heat Mass Transfer
,
32
(
4
), pp.
627
638
.
23.
Wall
,
T. F.
,
Lowe
,
A.
,
Wibberley
,
L. J.
,
Mai-Viet
,
T.
, and
Gupta
,
R. P.
,
1981
, “
Fly Ash Characteristics and Radiative Heat Transfer in Pulverized-Coal-Fired Furnaces
,”
Combust. Sci. Technol.
,
26
(
3–4
), pp.
107
121
.
24.
Lohi
,
A.
,
Wynnyckyj
,
J. R.
, and
Rhodes
,
E.
,
1992
, “
Spectral Measurement of the Complex Refractive Index of Fly Ashes of Canadian Lignite and Sub-Bituminous Coals
,”
Can. J. Chem. Eng.
,
70
(
4
), pp.
751
758
.
25.
Gupta
,
R. P.
, and
Wall
,
T. F.
,
1985
, “
The Optical Properties of Fly Ash in Coal Fired Furnaces
,”
Combust. Flame
,
61
(
2
), pp.
145
151
.
26.
Boothroyd
,
S. A.
, and
Jones
,
A. R.
,
1986
, “
A Comparison of Radiative Characteristics for Fly Ash and Coal
,”
Int. J. Heat Mass Transfer
,
29
(
11
), pp.
1694
1654
.
27.
Buckius
,
R. O.
, and
Hwang
,
D. C.
,
1980
, “
Radiation Properties for Polydispersions: Application to Coal
,”
ASME J. Heat Transfer
,
102
(
1
), pp.
99
103
.
28.
Johansson
,
R.
,
Andersson
,
K.
, and
Johnsson
,
F.
,
2012
, “
Influence of Ash Particles on Radiative Heat Transfer Under Air- and Oxy-Fired Conditions
,”
37th Clearwater Clean Coal Conference
, Clearwater, FL.http://publications.lib.chalmers.se/publication/171387-influence-of-ash-particles-on-radiative-heat-transfer-in-air-and-oxy-fired-conditions
29.
Mie
,
G.
,
1908
, “
Beiträge zur Optik Trüber Medien, Speziell Kolloidaler Metallösungen
,”
Ann. Phys.
,
330
(
3
), pp.
377
445
.
30.
Gronarz
,
T.
,
Schnell
,
M.
,
Siewert
,
C.
,
Schneiders
,
L.
,
Schröder
,
W.
, and
Kneer
,
R.
,
2017
, “
Comparison of Scattering Behaviour for Spherical and Non-Spherical Particles in Pulverized Coal Combustion
,”
Int. J. Therm. Sci.
,
111
, pp.
116
128
.
31.
Bohren
,
C. F.
, and
Huffman
,
D. R.
,
1983
,
Absorption and Scattering of Light by Small Particles
(Wiley Science Paperback Series),
Wiley
,
New York
.
32.
Modest
,
M.
,
2013
,
Radiative Heat Transfer
,
3rd
ed.,
Elsevier, Amsterdam
,
The Netherlands
.
33.
Mätzler
,
C.
,
2002
, “
MATLAB Functions for Mie Scattering and Absorption
,” Institute of Applied Physics, University of Bern, Bern, Switzerland.
34.
Chang
,
H.
, and
Charalampopoulos
,
T. T.
,
1990
, “
Determination of the Wavelength Dependence of Refractive Indices of Flame Soot
,”
Proc. R. Soc. London A
,
430
(
1880
), pp.
577
591
.
35.
Maron
,
N.
,
1990
, “
Optical Properties of Fine Amorphous Carbon Grains in the Infrared Region
,”
Astrophys. Space Sci.
,
172
(
1
), pp.
21
28
.
36.
Dombrovsky
,
L. A.
,
2012
, “
The Use of Transport Approximation and Diffusion-Based Models in Radiative Transfer Calculations
,”
Comput. Therm. Sci.
,
4
(
4
), pp.
297
315
.
37.
Malkmus
,
W.
,
1967
, “
Random Lorentz Band Model With Exponential-Tailed S−1 Line-Intensity Distribution Function
,”
J. Opt. Soc. Am.
,
57
(
3
), pp.
323
329
.
38.
Soufiani
,
A.
, and
Taine
,
J.
,
1997
, “
High Temperature Gas Radiative Property Parameters of Statistical Narrow-Band Model for H2O, CO2 and CO, and Correlated-K Model for H2O and CO2
,”
Int. J. Heat Mass Transfer
,
40
(
4
), pp.
987
991
.
39.
Johansson
,
R.
,
Leckner
,
B.
,
Andersson
,
K.
, and
Johnsson
,
F.
,
2013
, “
Influence of Particle and Gas Radiation in Oxy-Fuel Combustion
,”
Int. J. Heat Mass Transfer
,
65
, pp.
143
152
.
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