Abstract

A new angular quadrature scheme named Spherical surface Symmetrical equal Dividing (abbreviated to SSDN) is presented. The evaluations of double moments by SSDN and other traditional quadrature sets show that the new SSDN is able to provide good accuracy and compete well with others (as for example the SN and LSN method). Radiative predictions in a black-walled rectangular enclosure containing absorbing-emitting medium indicate that, compared with SN,LSN,TN, and SRAPN, the SSDN can give higher accuracy than SN under some order numbers N. Numerical experiments demonstrate the computational economy of SSDN for some cases.

1.
Carlson, B. G., and Lathrop, K. D., 1968, Computing Methods in Reactor Physics, H. Greenspan, C. N. Kelber, and D. Okrent, eds., Gordon and Breach, New York.
2.
Fiveland
,
W. A.
,
1984
, “
Discrete-Ordinates Solutions of the Radiative Transport Equation for Rectangular Enclosures
,”
ASME J. Heat Transfer
,
106
, pp.
699
706
.
3.
Truelove
,
J. S.
,
1987
, “
Discrete-Ordinates Solutions of the Radiation Transport Equation
,”
ASME J. Heat Transfer
,
109
, pp.
1048
1051
.
4.
Truelove
,
J. S.
,
1988
, “
Three-Dimensional Radiation in Absorbing-Emitting-Scattering Media Using the Discrete-Ordinates Approximation
,”
J. Quant. Spectrosc. Radiat. Transf.
,
39
(
1
), pp.
27
31
.
5.
Vaillon
,
R.
,
Lallemand
,
M.
, and
Lemonnier
,
D.
,
1996
, “
Radiative Heat Transfer in Orthogonal Cuvilinear Coordinates Using the Discrete Ordinates Method
,”
J. Quant. Spectrosc. Radiat. Transf.
,
55
(
1
), pp.
7
17
.
6.
Sakami
,
M.
,
Charette
,
A.
, and
Dez
,
V.
,
1996
, “
Application of the Discrete Ordinates Method to Combined Conductive and Radiative Heat Transfer in a Two-Dimensional Complex Geometry
,”
J. Quant. Spectrosc. Radiat. Transf.
,
56
(
4
), pp.
517
513
.
7.
Koo
,
H.-M.
,
Chiong
,
K.-B.
, and
Song
,
T.-H.
,
1997
, “
Schemes and Application of First and Second-Order Discrete Ordinates Interpolation Methods to Irregular Two-Dimensional Geometries
,”
ASME J. Heat Transfer
,
119
, pp.
730
737
.
8.
Sakami
,
M.
,
Charette
,
A.
, and
Dez
,
V.
,
1998
, “
Radiative Heat Transfer in Three-Dimensional Enclosures of Complex Geometry by Using the Discrete-Ordinates Method
,”
J. Quant. Spectrosc. Radiat. Transf.
,
59
(
1/2
), pp.
117
136
.
9.
Coelho
,
P. J.
,
Goncalves
,
J. M.
, and
Carvalho
,
M. G.
,
1998
, “
Modelling of Radiative Heat Transfer in Enclosures with Obstacles
,”
Int. J. Heat Mass Transf.
,
41
(
1-4
), pp.
745
756
.
10.
Sakami
,
M.
, and
Charette
,
A.
,
1998
, “
A New Differencing Scheme for the Discrete-Ordinates Method in Complex Geometries
,”
Rev. Gen. Therm.
,
37
, pp.
440
449
.
11.
Liu
,
J.
, and
Chen
,
Y. S.
,
1999
, “
Examination of Conventional and Ever-Parity Formulations of Discrete Ordinates Method in A Body-Fitted Coordinates System
,”
J. Quant. Spectrosc. Radiat. Transf.
,
61
(
4
), pp.
417
434
.
12.
Lee
,
C. E.
,
1961
, “
The Discrete SN Approximation to Transport Theory,” LA-2595
, Los Alamos Scientific Laboratory, NM.
13.
Lathrop
,
K. D.
, and
Carlson
,
B. G.
,
1965
, “
Discrete Ordinates Angular Quadrature of the Neutron Transport Equation,” LA-3168
, Los Alamos Scientific Laboratory, NM.
14.
Fiveland
,
W. A.
,
1987
, “
Discrete-Ordinates Methods for Radiative Heat Transfer in Isotropically Scattering Media
,”
ASME J. Heat Transfer
,
109
, pp.
809
812
.
15.
Jamaluddin
,
A. S.
, and
Smith
,
P. J.
,
1988
, “
Predicting Radiative Transfer in Rectangular Enclosures Using the Discrete Ordinate Method
,”
Combust. Sci. Technol.
,
59
, pp.
321
340
.
16.
Jamaluddin
,
A. S.
, and
Smith
,
P. J.
,
1988
, “
Predicting Radiative Transfer in Axisymmetric Cylindrical Enclosures Using the Discrete Ordinate Method
,”
Combust. Sci. Technol.
,
62
, pp.
173
181
.
17.
Tan
,
Z.
, and
Howell
,
J. R.
,
1990
, “
New Numerical Method for Radiation Heat Transfer in Nonhomogeneous Participating Media
,”
J. Thermophys. Heat Transfer
,
4
(
4
), pp.
419
424
.
18.
Hsu
,
P.-F.
,
Tan
,
Z.
, and
Howell
,
J. R.
,
1993
, “
Radiative Transfer by the YIX Method in Nonhomogeneous, Scattering, and Nongray Media
,”
J. Thermophys. Heat Transfer
,
7
(
3
), pp.
487
495
.
19.
Fiveland, W. A., 1991, “The Selection of Discrete Ordinate Quadrature Sets for Anisotropic Scattering,” Fundamentals of Radiation Heat Transfer, ASME-HTD-160.
20.
Wakil, N. El., 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,” Developments in Radiative Heat Transfer, ASME HTD-203, pp. 119–127.
21.
Koch
,
R.
,
Krebs
,
W.
,
Wittig
,
S.
, and
Viskanta
,
R.
,
1995
, “
Discrete Ordinates Quadrature Schemes for Multidimensional Radiative Transfer
,”
J. Quant. Spectrosc. Radiat. Transf.
,
53
(
4
), pp.
353
372
.
22.
Thurgood
,
C. P.
,
Pollard
,
A.
, and
Becker
,
H. A.
,
1995
, “
The TN Quadrature Set for the Discrete Ordinate Ordinates Method
,”
ASME J. Heat Transfer
,
117
, pp.
1068
1070
.
23.
Li
,
Ben-Wen
,
Yao
,
Qiang
,
Cao
,
Xin-Yu
, and
Cen
,
Ke-Fa
,
1998
, “
A New Discrete Ordinates Quadrature Scheme for Three-Dimensional Radiative Heat Transfer
,”
ASME J. Heat Transfer
,
120
, pp.
514
518
.
24.
Li
,
Ben-Wen
,
Zhou
,
Jun-Hu
,
Cao
,
Xin-Yu
, and
Cen
,
Ke-Fa
,
2000
, “
Successive Spherical Rings Arithmetic Progression Dividing Discrete Ordinates Method and Its Comparison with TN Set
,”
Int. J. Transport Phenomena
,
2
, pp.
231
239
.
25.
Chai
,
J. C.
,
Lee
,
H. S.
, and
Patankar
,
S. V.
,
1994
, “
Improved Treatment of Scattering Using the Discrete Ordinates Method
,”
ASME J. Heat Transfer
,
116
, pp.
260
263
.
26.
Selcuk
,
N.
,
1985
, “
Exact Solution for Radiative Heat Transfer in Box-Shaped Furnaces
,”
ASME J. Heat Transfer
,
107
, pp.
648
655
.
27.
Selcuk
,
N.
, and
Kayakol
,
N.
,
1997
, “
Evaluation of Discrete Ordinates Method for Radiative Transfer in Rectangular Furnaces
,”
Int. J. Heat Mass Transf.
,
40
(
2
), pp.
213
222
.
You do not currently have access to this content.