A novel method, the Double Rays Method (DRM), is proposed to capture the discontinuous nature of the radiation intensity, in order to reduce false scattering of the discrete ordinates method (DOM). Numerical tests demonstrate that the DRM successfully removes false scattering in all the two-dimensional test problems discussed in this paper. The effect of false scattering on the computational results in two-dimensional situations is investigated with the DRM. False scattering plays a double role: when the boundary emits radiation in a limited number of directions, or when the irradiation comes from a limited number of directions, it produces a smeared intensity field and radiative heat flux distribution, and thus must be removed. In the case of diffuse boundary, however, false scattering plays a useful role and thus should be retained.
Issue Section:
Radiative Heat Transfer
Keywords:
Heat Transfer,
Modeling,
Numerical Methods,
Radiation,
Scattering,
scattering,
interpolation,
heat radiation
1.
Fiveland
, W. A.
, 1987
, “Discrete Ordinate Methods for Radiative Heat Transfer in Isotropically and Anisotropically Scattering Media
,” ASME J. Heat Transfer
, 109
, pp. 809
–812
.2.
Truelove
, J. S.
, 1987
, “Discrete-Ordinates Solutions of the Radiative Transport Equation
,” ASME J. Heat Transfer
, 109
(4
), pp. 1048
–1051
.3.
Fiveland, W. A., 1991, “The Selection of Discrete Ordinate Quadrature Sets for Anisotropic Scattering,” in Fundamental of Radiation Heat Transfer, ASME HTD-Vol. 160, ASME, New York, pp. 89–96.
4.
El Wakil, N., and Sacadura, J. F., 1992, “Some Improvements of the Discrete Ordinates Method for the Solution of the Radiative Transport Equation in Multidimensional Anisotropically Scattering Media,” in Developments of Radiative Heat Transfer, ASME HTD-Vol. 203, ASME, New York, pp. 119–127.
5.
Thurgood
, C. P.
, Pollard
, A.
, and Becker
, H. A.
, 1995
, “The TN Quadrature Set for the Discrete Ordinate Method
,” ASME J. Heat Transfer
, 117
(4
), pp. 1068
–1070
.6.
Koch
, R.
, Krebs
, W.
, Wittig
, S.
, and Viskanta
, R.
, 1995
, “Discrete Ordinates Quadrature Scheme for Multidimensional Radiative Transfer
,” J. Quant. Spectrosc. Radiat. Transf.
, 53
(4
), pp. 353
–372
.7.
Li
, B.-W.
, Yao
, Q.
, Cao
, X.-Y.
, and Cen
, K.-F.
, 1998
, “A New Discrete Ordinate Quadrature Scheme for Three-Dimensional Radiative Heat Transfer
,” ASME J. Heat Transfer
, 120
(2
), pp. 514
–518
.8.
Liu
, F.
, Becker
, H. A.
, and Polland
, A.
, 1996
, “Spatial Differencing Schemes of the Discrete Ordinates Method
,” Numer. Heat Transfer, Part B
, 30
(1
), pp. 23
–43
.9.
Cheong
, K.-B.
, and Song
, T.-H.
, 1997
, “An Alternative Discrete Ordinates Method With Interpolation and Source Differencing for Two-Dimensional Radiative Transfer Problem
,” Numer. Heat Transfer, Part B
, 32
(1
), pp. 107
–125
.10.
Pessoa-Filho
, J. B.
, and Thynell
, S. T.
, 1997
, “An Approximate Solution to Radiative Transfer in Two-Dimensional Rectangular Enclosures
,” ASME J. Heat Transfer
, 119
(4
), pp. 738
–745
.11.
Sakami
, M.
, and Charrette
, A.
, 1998
, “A New Differencing Scheme for the Discrete Ordinates in Complex Geometry
,” Rev. Gen. Therm.
, 37
(3
), pp. 440
–449
.12.
Mohamad
, A. A.
, 1998
, “Local Analytical Discrete Ordinate Method for the Solution of the Radiative Transfer Equation
,” Int. J. Heat Mass Transf.
, 39
(9
), pp. 1859
–1864
.13.
Fiterman
, A.
, and Ben-Zvi
, R.
, 1999
, “Dots: Pseudo-Time-Stepping Solution of the Discrete Equations
,” Numer. Heat Transfer, Part B
, 35
(1
), pp. 163
–183
.14.
Selcuk
, N.
, and Kirbas
, G.
, 2000
, “The Method of Lines Solution of the Discrete Ordinates Method for Radiative Heat Transfer in Enclosures
,” Numer. Heat Transfer, Part B
, 37
(1
), pp. 107
–125
.15.
Kim
, Il-K.
, and Kim
, W.-D.
, 2001
, “A Hybrid Spatial Differencing Schemes for Discrete Ordinates Method in 2D Rectangular Enclosures
,” Int. J. Heat Mass Transf.
, 4
(4
), pp. 575
–586
.16.
Raithby
, G. D.
, and Chui
, E. H.
, 1990
, “A Finite-Volume Method for Predicting a Radiative Heat Transfer in Enclosures with Participating Media
,” ASME J. Heat Transfer
, 112
(2
), pp. 415
–423
.17.
Chai
, J. C.
, Lee
, H. S.
, and Patankar
, S. V.
, 1994
, “Finite-Volume Method for Radiation Heat Transfer
,” J. Thermophys. Heat Transfer
, 8
(3
), pp. 419
–425
.18.
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
(2
), pp. 373
–389
.19.
Ramankutty
, M. A.
, and Crosbie
, A. L.
, 1997
, “Modified Discrete Ordinates Solution of Radiative Transfer in Two-Dimensional Rectangular Enclosures
,” J. Quant. Spectrosc. Radiat. Transf.
, 57
, pp. 107
–140
.20.
Baek
, S. W.
, Byun
, D. Y.
, and Kang
, S. J.
, 2000
, “The Combined Monte-Carlo and Finite-Volume Method for Radiation in a Two-Dimensional Irregular Geometry
,” Int. J. Heat Mass Transf.
, 43
(13
), pp. 2337
–2344
.21.
Thynell
, S. T.
, 1998
, “Discrete-Ordinates Method in Radiative Heat Transfer
,” Int. J. Eng. Sci.
, 35
(12–14
), pp. 1651
–1675
.22.
Crosbie
, A. L.
, and Schrenker
, R. G.
, 1984
, “Radiative Transfer in a Two-Dimensional Rectangular Medium Exposed to Diffuse Radiation
,” J. Quant. Spectrosc. Radiat. Transf.
, 31
(4
), pp. 339
–372
.23.
Thynell
, S. T.
, and O¨zisik
, N. N.
, 1987
, “Radiation Transfer in Isotropically Scattering, Rectangular Enclosures
,” J. Thermophys. Heat Transfer
, 1
(1
), pp. 69
–76
.24.
Chai
, J. C.
, Patankar
, S. V.
, and Lee
, H. S.
, 1994
, “Evaluation of Spatial Differencing Practices for the Discrete Ordinates Method
,” J. Thermophys. Heat Transfer
, 8
(1
), pp. 140
–144
.Copyright © 2002
by ASME
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