The radiation element method by ray emission method, REM2, has been formulated to predict radiative heat transfer in three-dimensional arbitrary participating media with nongray and anisotropically scattering properties surrounded by opaque surfaces. To validate the method, benchmark comparisons were conducted against the existing several radiation methods in a rectangular three-dimensional media composed of a gas mixture of carbon dioxide and nitrogen and suspended carbon particles. Good agreements between the present method and the Monte Carlo method were found with several particle density variations, in which participating media of optical thin, medium, and thick were included. As a numerical example, the present method is applied to predict radiative heat transfer in a boiler model with nonisothermal combustion gas and carbon particles and diffuse surface wall. Elsasser narrow-band model as well as exponential wide-band model is adopted to consider the spectral character of CO2 and H2O gases. The distributions of heat flux and heat flux divergence in the boiler furnace are obtained. The difference of results between narrow-band and wide-band models is discussed. The effects of gas model, particle density, and anisotropic scattering are scrutinized.

Issue Section:
Technical Papers
Keywords:
radiative transfer, 1/f noise, heat treatment, modelling, combustion
Topics:
Anisotropy, Boilers, Electromagnetic scattering, Heat flux, Particulate matter, Radiation (Physics), Radiation scattering, Radiative heat transfer, Scattering (Physics), Carbon, Emissions
1.
Tong, T. W., and Skocypec, R. D., 1992, “Summary on Comparison of Radiative Heat Transfer Solutions for a Specified Problem,” Developments in Radiative Heat Transfer, ASME HTD-Vol. 203, pp. 253–258.
2.
Farmer
,
J. T.
, and
Howell
,
J. R.
,
1994
, “
Monte Carlo Prediction of Radiative Heat Transfer in Inhomogeneous, Anisotropic, Nongray Media
,”
J. Thermophys. Heat Transfer
,
8
, pp.
133
–
139
.
3.
Maruyama
,
S.
,
1993
, “
Radiation Heat Transfer Between Arbitrary Three-Dimensional Bodies with Specular and Diffuse Surfaces
,”
Numer. Heat Transfer, Part A
,
24
, pp.
181
–
196
.
4.
Maruyama
,
S.
, and
Aihara
,
T.
,
1997
, “
Radiation Heat Transfer Between Arbitrary Three-Dimensional Absorbing, Emitting and Scattering Media and Specular and Diffuse Surfaces
,”
ASME J. Heat Transfer
,
119
, pp.
129
–
136
.
5.
Maruyama
,
S.
, and
Higano
,
M.
,
1997
, “
Radiative Heat Transfer of Torus Plasma in Large Helical Device by Generalized Numerical Method REM2,
”
Energy Convers. Manage.
,
38
, pp.
1187
–
1195
.
6.
Guo
,
Z.
,
Maruyama
,
S.
, and
Tsukada
,
T.
,
1997
, “
Radiative Heat Transfer in Curved Specular Surface in Czochralski Crystal Growth Furnace
,”
Numer. Heat Transfer, Part A
,
32
, pp.
595
–
611
.
7.
Fiveland
,
W. A.
, and
Latham
,
C. E.
,
1993
, “
Use of Numerical Modeling in the Design of a Low-NOx Burner for Utility Boilers
,”
Combust. Sci. Technol.
,
93
, pp.
53
–
72
.
8.
Fiveland
,
W. A.
, and
Wessel
,
R. A.
,
1988
, “
Numerical Model for Predicting Performance of Three-Dimensional Pulverized-Fuel Fired Furnaces
,”
ASME J. Eng. Gas Turbines Power
,
110
, pp.
117
–
126
.
9.
Aoki
,
H.
,
Tanno
,
S.
,
Miura
,
T.
, and
Ohnishi
,
S.
,
1992
, “
Three-Dimensional Spray Combustion in a Practical Boiler
,”
JSME Int. J., Ser. II
,
35
, pp.
428
–
434
.
10.
Wiscombe
,
W. J.
,
1977
, “
The Delta-M Method: Rapid Yet Accurate Radiative Flux Calculations for Strongly Asymmetric Phase Functions
,”
J. Atmos. Sci.
,
34
, pp.
1408
–
1442
.
11.
Lee
,
H.
, and
Buckius
,
R. O.
,
1982
, “
Scaling Anisotropic Scattering in Radiation Heat Transfer for a Planar Medium
,”
ASME J. Heat Transfer
,
104
, pp.
68
–
75
.
12.
Kim
,
T.-K.
, and
Lee
,
H. S.
,
1990
, “
Scaled Isotropic Results for Two-Dimensional Anisotropic Scattering Media
,”
ASME J. Heat Transfer
,
112
, pp.
721
–
727
.
13.
Maruyama, S., 1997, “Radiative Heat Transfer in a Layer of Anisotropic Scattering Fog Subjected to Collimated Irradiation,” Proc., 2nd Int. Symposium on Radiation transfer, Aug., Kasadasi, Turkey.
14.
Maruyama
,
S.
,
1998
, “
Radiation Heat Transfer in Anisotropic Scattering Media With Specular Boundary Subjected to Collimated Irradiation
,”
Int. J. Heat Mass Transfer
,
41
, pp.
2847
–
2856
.
15.
Edwards
,
D. K.
, and
Balakrishnan
,
A.
,
1973
, “
Thermal Radiation by Combustion Gases
,”
Int. J. Heat Mass Transf.
,
12
, pp.
25
–
40
.
16.
Hsu, P.-F., Tan, Z., and Howell, J. R., 1992, “Application of the YIX Method to Radiative Heat Transfer Within a Mixture of Highly Anisotropic Scattering Particles and Non-Gray Gas,” Developments in Radiative Heat Transfer, ASME HTD-Vol. 203, pp. 285–300.
17.
Yuen, W. W., Ma, A. K., and Takara, E. E., 1992, “Evaluation of Radiative Heat Transfer Using the Generalized Zonal Method and the Absorption Mean Beam Length Concept,” Developments in Radiative Heat Transfer, ASME HTD-Vol. 203, pp. 265–273.
18.
Maruyama, S., Ukaku, M. and Aihara, T., 1995, “Radiative Heat Transfer of Non-Uniform, Non-Gray, Absorbing, Emitting and Scattering Media Using Band Models,” Proc., 32nd National Heat Transfer Symposium of Japan, Yamaguchi, pp. 591–592.
19.
Siegel, R., and Howell, J. R., 1992, Thermal Radiation Heat Transfer, 3rd Edition, Chap. 13, Hemisphere, Washington, DC.
20.
Foster
,
P. J.
, and
Howarth
,
C. R.
,
1968
, “
Optical Constants of Carbons and Coals in the Infrared
,”
Carbon
,
6
, pp.
719
–
729
.
21.
Menguc
,
M. P.
, and
Viskanta
,
R.
,
1985
, “
Radiative Transfer in Three-Dimensional Rectangular Enclosures Containing Inhomogeneous, Anisotropically Scattering Media
,”
J. Quant. Spectrosc. Radiat. Transf.
,
33
, pp.
533
–
549
.
22.
Chai
,
J. C.
,
Lee
,
H. S.
, and
Patankar
,
S. V.
,
1993
, “
Ray Effect and False Scattering in the Discrete Ordinates Method
,”
Numer. Heat Transfer, Part B
,
24
, pp.
373
–
3899
.
23.
Omori, T., Murakami, S., Katoh, S., Choi, C. K., and Kobayashi, H., 1992, “Coupled Simulation of Convective and Radiative Heat Transfer in Enclosed Space: Accuracy of Shape Factors Obtained by Monte Carlo Method,” Proc., Air-Con. Sanit. Eng. Japan, pp. 653–656.
24.
Smyth
,
K. C.
,
Miller
,
J. H.
,
Dorfman
,
R. C.
,
Mallard
,
W. G.
, and
Santoro
,
A. R.
,
1985
, “
Soot Inception in a Methane/Air Diffusion Flame as Characterized by Detailed Species Profiles
,”
Combust. Flame
,
62
, pp.
157
–
181
.
25.
Maruyama, S., and Wu, H., 2000, “Comparison of The Absorption Coefficient, Spectral and Total Emissivities of Participating Gases at High Temperature by LBL Analysis and Gas Models,” Proc. 4th JSME-KSME Thermal Engineering Conference, Vol. 1, pp. 223–228.
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