The discrete transfer method, often employed to calculate radiative heat transfer in combustion chambers, is not conservative. The reason for this behavior is examined and a conservative formulation is proposed and evaluated. A simple treatment of isotropic scattering media is also presented. The original and the conservative formulation of the method are applied to two-dimensional and three-dimensional enclosures containing a participating medium. It is shown that the accuracy of the original and the conservative formulation is very similar, but the proposed formulation has the advantage of ensuring energy conservation.
1.
Boyd, R. K., and Kent, J. H., 1986, “Three-dimensional Furnace Computer Modelling,” 21st Symposium (Int.) on Combustion, The Combustion Institute, Pittsburgh, PA, pp. 265–274.
2.
Bressloff, N. W., Moss, J. B., and Rubini, P. A., 1995, “Application of a New Weighting Set for the Discrete Transfer Radiation Model,” Proceedings, 3rd European Conference on Industrial Furnaces and Boilers, Lisbon, Portugal.
3.
Carlson, B. G., and Lathrop, K. D., 1968, “Transport Theory—The Method of Discrete Ordinates,” Computing Methods in Reactor Physics, H. Greenspan, C. N. Kelber, and D. Okrent, eds., Gordon & Breach, New York.
4.
Carvalho
M. G.
Coelho
P. J.
1989
, “Heat Transfer in Gas Turbine Combustors
,” Journal of Thermophysics and Heat Transfer
, Vol. 3
, No. 2
, pp. 123
–131
.5.
Carvalho
M. G.
Farias
T.
Fontes
P.
1993
, “Multidimensional Modeling of Radiative Heat Transfer in Scattering Media
,” ASME JOURNAL OF HEAT TRANSFER
, Vol. 115
, pp. 486
–489
.6.
Chai
J. C.
Lee
H. S.
Patankar
S.
1993
, “Ray Effect and False Scattering in the Discrete Ordinates Method
,” Numerical Heat Transfer
, Part B, Vol. 24
, pp. 373
–389
.7.
Chai
J. C.
Lee
H. S.
Patankar
S. V.
1994
, “Finite Volume Method for Radiation Heat Transfer
,” Journal of Thermophysics and Heat Transfer
, Vol. 8
, pp. 419
–425
.8.
Coelho, M. G., Gonc¸alves, J. M., and Carvalho, M. G., 1995, “A Comparative Study of Radiation Models for Coupled Fluid Flow/Heat Transfer Problems,” Proceedings, 9th International Conference for Numerical Methods in Thermal Problems, Vol. IX, Part 1, R. W. Lewis and P. Dubertaki, eds., Pineridge Press, Swansea, pp. 378–389.
9.
Crosbie
A. L.
Schrenker
R. G.
1984
, “Radiative Heat Transfer in a Two-Dimensional Rectangular Medium Exposed to Diffuse Radiation
,” Journal of Quantitative Spectroscopy and Radiative Transfer
, Vol. 31
, No. 4
, pp. 339
–372
.10.
Cumber
P. S.
1995
, “Improvements to the Discrete Transfer Method of Calculating Radiative Heat Transfer
,” International Journal of Heat and Mass Transfer
, Vol. 38
, No. 12
, pp. 2251
–2258
.11.
Fiveland
W. A.
1984
, “Discrete-Ordinates Solutions of the Radiative Transport Equation for Rectangular Enclosures
,” ASME JOURNAL OF HEAT TRANSFER
, Vol. 106
, pp. 699
–706
.12.
Gosman, A. D., Launder, B. E., and Reece, G. J., 1985, Computer-Aided Engineering, Heat Transfer and Fluid Flow, John Wiley & Sons, New York.
13.
Gosman
A. D.
Lockwood
F. C.
Megahed
I. E. A.
Shah
N. G.
1982
, “Prediction of the Flow, Reaction and Heat Transfer in a Glass Furnace
,” Journal of Energy
, Vol. 6
, No. 6
, pp. 353
–360
.14.
Hottel, H. C., and Sarofim, A. F., 1967, Radiative Transfer, McGraw-Hill, New York.
15.
Howell, J. R., 1968, “Application of Monte Carlo to Heat Transfer Problems,” Advances in Heat Transfer, J. P. Hartnett and T. F. Irvine, eds., Vol. 5, Academic Press, New York.
16.
Jamaluddin
A. S.
Smith
P. J.
1988
, “Predicting Radiative Transfer in Rectangular Enclosures Using the Discrete Ordinates Method
,” Combustion Science and Technology
, Vol. 59
, pp. 321
–340
.17.
Lathrop
K. D.
1968
, “Ray Effects in Discrete Ordinates Equations
,” Nuclear Science and Engineering
, Vol. 32
, pp. 357
–369
.18.
Lockwood, F. C., and Shah, N. G., 1981, “A New Radiation Solution Method for Incorporation in General Combustion Prediction Procedures,” 18th Symposium (Int.) on Combustion, The Combustion Institute, Pittsburgh, PA, pp. 1405–1414.
19.
Mengu¨c¸
M. P.
Viskanta
R.
1985
, “Radiative Transfer in Three-Dimen-sional Rectangular Enclosures Containing Inhomogeneous Anisotropically Scattering Media
,” Journal of Quantitative Sprectroscopy and Radiative Transfer
, Vol. 33
, pp. 533
–549
.20.
Modest, M. F., 1993, Radiative Heat Transfer, McGraw-Hill, New York.
21.
Murthy, J. Y., and Choudhury, D., 1992, “Computation of Participating Radiation in Complex Geometries,” HTD-Vol. 203, Developments in Radiative Heat Transfer, ASME, New York, pp. 153–160.
22.
Raithby
G. D.
Chui
E. H.
1990
, “A Finite Volume Method for Predicting Radiant Heat Transfer in Enclosures with Participating Media
,” ASME JOURNAL OF HEAT TRANSFER
, Vol. 112
, pp. 415
–423
.23.
Selc¸uk, N., 1983, “Evaluation of Multi-Dimensional Flux Models for Radiative Transfer in Combustion Chambers: A Review,” AGARD CP-353, Paper No. 28.
24.
Shah, N. G., 1979, “New Method of Computation of Radiation Heat Transfer in Combustion Chambers,” Ph. D. Thesis, Imperial College of Science and Technology, London.
25.
Truelove
J. S.
1988
, “Three-dimensional Radiation in Absorbing-Emitting-Scattering Media using the Discrete-Ordinates Approximation
,” Journal of Quantitative Spectroscopy and Radiative Transfer
, Vol. 39
, No. 1
, pp. 27
–31
.26.
Viskanta
R.
Mengu¨c¸
M. P.
1987
, “Radiation Heat Transfer in Combustion Systems
,” Progress in Energy and Combustion Science
, Vol. 13
, pp. 97
–160
.
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