Modeling radiative heat transfer in combustion applications involving complex geometries and detailed spectral properties of radiative gaseous species remains a difficult challenge, especially when full coupling with detailed chemistry and fluid dynamics is required. The Monte Carlo method (MCM) usually considered as a reference “exact” method for the computation of radiative transfer is however very demanding in CPU-time. An alternative is the discrete ordinates method (DOM), based on a finite volume approach, that is more suitable for a direct coupling with computational fluid dynamics but may lack accuracy. The aim of the present paper is to propose and demonstrate the efficiency of a methodology for radiative transfer calculation, combining the advantages of both MCM and DOM. In this approach, the fast DOM is used to compute the radiative solution, and its accuracy is controlled by comparison with the exact MCM solution at a selected controlling points. A first application of the proposed methodology to an industrial burner prototype shows its validity and potential for the direct coupling of radiation calculations with unsteady reacting flow computations.

1.
Joseph
,
D.
, 2004, “Modélisation des transferts radiatifs en combustion par méthode aux ordonnées discrètes sur des maillages non structurés tridimensionnels,” Institut National Polytechnique de Toulouse.
2.
Beltrame
,
A.
,
Porshnev
,
P.
,
Merchan-Merchan
,
W.
,
Savelier
,
A.
,
Kennedy
,
L. A.
,
Petrova
,
O.
,
Zhdanok
,
S.
,
Amouri
,
F.
, and
Charon
,
O.
, 2001, “
Soot and NO Formation in Methane-Oxygen Enriched Diffusion Flames
,”
Combust. Flame
0010-2180,
124
, pp.
295
310
.
3.
Hall
,
R. J.
,
Smooke
,
M. D.
, and
Colket
,
M. B.
, 1997, “
Predictions of Soot Dynamics in Opposites Jets Diffusion Flames
,”
Physical and Chemical Aspects of Combustion: A Tribute to Irvin Glassman
,
Academic
,
New York
.
4.
Mbiock
,
M.
, and
Weber
,
R.
, 2000,
Radiation in Enclosures
,
Springer-Verlag
,
Berlin
.
5.
Jensen
,
K. A.
,
Ripoll
,
J. F.
,
Wray
,
A. A.
,
Joseph
,
D.
, and
El Hafi
,
M.
, 2007, “
On Various Modeling Approaches for Radiative Heat Transfer in Pool Fires
,”
Combust. Flame
,
148
(
4
), pp.
263
279
. 0010-2180
6.
de Lataillade
,
A.
,
Dufresne
,
J. L.
,
El Hafi
,
M.
,
Eymet
,
V.
, and
Fournier
,
R.
, 2002, “
A Net Exchange Monte Carlo Approach to Radiation in Optically Thick Systems
,”
J. Quant. Spectrosc. Radiat. Transf.
,
74
(
5
), pp.
563
584
. 0022-4073
7.
Coelho
,
P. J.
,
Perez
,
P.
, and
El Hafi
,
M.
, 2003, “
Benchmark Numerical Solutions for Radiative Heat Transfer in Two-Dimensional Axisymmetric Enclosures With Nongray Sooting Media
,”
Numer. Heat Transfer, Part B
1040-7790,
43
, pp.
425
444
.
8.
Perez
,
P.
,
El Hafi
,
M.
,
Coelho
,
P. J.
, and
Fournier
,
R.
, 2005, “
Accurate Solutions for Radiative Heat Transfer in Two-Dimensional Axisymmetric Enclosures With Gas Radiation and Reflective Surfaces
,”
Numer. Heat Transfer, Part B
,
47
, pp.
39
63
. 1040-7790
9.
Tessé
,
L.
,
Dupoirieux
,
F.
, and
Taine
,
J.
, 2004, “
Monte Carlo Modeling of Radiative Transfer in a Turbulent Sooty Flame
,”
Int. J. Heat Mass Transfer
0017-9310,
47
, pp.
555
572
.
10.
De Lataillade
,
A.
,
Blanco
,
S.
,
Clergent
,
Y.
,
Dufresne
,
J. L.
,
El Hafi
,
M.
, and
Fournier
,
R.
, 2002, “
Monte Carlo Methods and Sensitivity Estimations
,”
J. Quant. Spectrosc. Radiat. Transf.
0022-4073,
75
, pp.
529
538
.
11.
Roger
,
M.
,
Blanco
,
S.
,
El Hafi
,
M.
, and
Fournier
,
R.
, 2005, “
Monte Carlo Estimates of Domain Deformation Sensitivities
,”
Phys. Rev. Lett.
0031-9007,
95
, p.
180601
.
12.
Modest
,
M. F.
, 2003,
Radiative Heat Transfer
,
3rd ed.
,
McGraw-Hill
,
New York
.
13.
Liu
,
J.
,
Shang
,
H. M.
,
Chen
,
Y. S.
, and
Wang
,
T. S.
, 2000, “
Development of an Unstructured Radiation Model Applicable for Two Dimensional Planar, Axisymmetric and 3-Dimensional Geometries
,”
J. Quant. Spectrosc. Radiat. Transf.
,
66
, pp.
17
33
. 0022-4073
14.
Joseph
,
D.
,
El Hafi
,
M.
,
Fournier
,
R.
, and
Cuenot
,
B.
, 2005, “
Comparison of Three Spatial Differencing Schemes in Discrete Ordinates Method Using Three-Dimensional Unstructured Meshes
,”
Int. J. Therm. Sci.
,
44
(
9
), pp.
851
864
. 1290-0729
15.
Lockwood
,
F. C.
, and
Shah
,
N. G.
, 1981, “
A New Radiation Solution Method for Incorporation in General Combustion Prediction Procedures
,” 18th Symposium (International) on Combustion, The Combustion Institute, pp.
1405
1409
.
16.
Perez
,
P.
, 2003, “
Algorithmes de synthèse d’images et propriétés spectrales des gaz de combustion: méthode de Monte Carlo pour la simulation des transferts radiatifs dans les procédés à haute température
,” Institut National Polytechnique de Toulouse.
17.
Liu
F.
, 1999, “
Numerical Solutions of Three-Dimensional Non-Grey Gas Radiative Transfer Using the Statistical Narrow-Band Model
,”
ASME J. Heat Transfer
0022-1481,
121
, pp.
200
203
.
18.
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
0017-9310,
40
(
4
), pp.
987
991
.
19.
Chandrashekhar
,
S.
, 1950,
Radiative Transfer
,
Clarendon
,
Oxford
.
20.
Koch
,
R.
, and
Becker
,
R.
, 2003, “
Evaluation of the Quadrature Schemes for the Discrete Ordinates Method
,”
Proceedings of Eurotherm73 on Computational Thermal Radiation in Participating Media
, Eurotherm Series No. 11,
P.
Lybaert
,
V.
Feldheim
,
D.
Lemonnier
, and
N.
Selçuk
, eds.,
Elsevier
,
Paris
, pp.
59
74
.
21.
Ströhle
,
J.
,
Schnell
,
U.
, and
Hein
,
K. R. G.
, 2001, “
A Mean Flux Discrete Ordinates Interpolation Scheme for General Coordinates
,” Third International Conference on Heat Transfer, Antalya.
22.
Liu
,
F.
,
Smallwood
,
G. J.
, and
Gülder
,
Ö. L.
, 2000, “
Application of the Statistical Narrow-Band Correlated-k Method to Low-Resolution Spectral Intensity and Radiative Heat Transfer Calculations—Effects of the Quadrature Scheme
,”
Int. J. Heat Mass Transfer
,
43
, pp.
3119
3135
. 0017-9310
23.
Liu
,
F.
,
Smallwood
,
G. J.
, and
Gülder
,
Ö. L.
, 2001, “
Application of the Statistical Narrow-Band Correlated-k Method to Non-Grey Gas Radiation in CO2–H2O Mixtures: Approximate Treatments of Overlapping Bands
,”
J. Quant. Spectrosc. Radiat. Transf.
,
68
, pp.
401
417
. 0022-4073
24.
Hottel
,
H. C.
, and
Sarofim
,
A. F.
, 1967,
Radiative Transfer
,
McGraw-Hill
,
New York
.
25.
Green
,
J. S. A.
, 1967, “
Division of Radiative Streams Into Internal Transfer and Cooling to Space
,”
Q. J. R. Meteorol. Soc.
0035-9009,
93
, pp.
371
372
.
26.
Cherkaoui
,
M.
,
Dufresne
,
J. L.
,
Fournier
,
R.
,
Grandpeix
,
J. Y.
, and
Lahellec
,
A.
, 1996, “
Monte Carlo Simulation of Radiation in Gases With a Narrow-Band Model and a Net-Exchange Formulation
,”
ASME J. Heat Transfer
0022-1481,
118
, pp.
401
407
.
27.
Dufresne
,
J. -L.
,
Fournier
,
R.
, and
Grandpeix
,
J. -Y.
, 1999, “
Inverse Gaussian K-Distributions
,”
J. Quant. Spectrosc. Radiat. Transf.
,
61
, pp.
433
441
. 0022-4073
28.
Schönfeld
,
T.
, and
Rudgyard
,
M.
, 1999, “
Steady and Unsteady Flows Simulations Using the Hybrid Flow Solver AVBP
,”
AIAA J.
,
37
(
11
), pp.
1378
1385
. 0001-1452
29.
Roux
,
S.
,
Lartigue
,
G.
,
Poinsot
,
T.
,
Meier
,
U.
, and
Bérat
,
C.
, 2005,
“Studies of Mean and Unsteady Flow in a Swirled Combustor Using Experiments, Acoustic Analysis and Large Eddy Simulations
,”
Combust. Flame
0010-2180,
141
, pp.
40
54
.
30.
Angelberger
,
C.
,
Egolfopoulos
,
F.
, and
Veynante
,
D.
, 2000, “
Large Eddy Simulations of Chemical and Acoustic Forcing of a Premixed Dump Combustor
,”
Flow, Turbul. Combust.
,
65
(
2
), pp.
205
222
. 1386-6184
31.
Colin
,
O.
,
Ducros
,
F.
,
Veynante
,
D.
, and
Poinsot
,
T.
, 2000, “
A Thickened Flame Model for Large Eddy Simulations of Turbulent Premixed Combustion
,”
Phys. Fluids
1070-6631,
12
(
7
), pp.
1843
1863
.
32.
Selle
,
L.
,
Lartigue
,
G.
,
Poinsot
,
T.
,
Koch
,
R.
,
Schildmacher
,
K. U.
,
Krebs
,
W.
,
Prade
,
B.
,
Kaufmann
,
P.
, and
Veynante
,
D.
, 2004, “
Compressible Large Eddy Simulations of Turbulent Combustion on Complex Geometries on Unstructured Meshes
,”
Combust. Flame
0010-2180,
137
, pp.
489
505
.
33.
Goncalves dos Santos
,
R.
,
Lecanu
,
M.
,
Ducruix
,
S.
,
Gicquel
,
O.
, and
Veynante
,
D.
, 2005, “
Large Eddy Simulations of Combustion/Radiative Heat Transfers Coupling Using the Specialized Communication Language CORBA
,” The Cyprus International Symposium on Complex Effects in Large Eddy Simulations, Limassol, Cyprus, Sept. 20–25.
34.
Gonçalves dos Santos
,
R.
,
Ducruix
,
S.
,
Gicquel
,
O.
, and
Veynante
,
D.
, 2006, “
Large Eddy Simulations of Turbulent Combustion Including Radiative Heat Transfers Using Specialised Communication Languages
,” 11th International Conference on Numerical Combustion, Granada, Spain.
35.
Gonçalves dos Santos
,
R.
,
Ducruix
,
S.
,
Gicquel
,
O.
,
Joseph
,
D.
,
El Hafi
,
M.
, and
Veynante
,
D.
, 2007, “
Large-Eddy Simulations Including Radiative Heat Transfer
,” Third European Combustion Meeting, Chania, Crete, Apr. 11–13, Paper No. 23–3.
36.
Goncalves dos Santos
,
R.
,
Lecanu
,
M.
,
Ducruix
,
S.
,
Gicquel
,
O.
,
Iacona
,
E.
, and
Veynante
,
D.
, 2008, “
Coupled Large Eddy Simulations of Turbulent Combustion and Radiative Heat Transfer
,”
Combust. Flame
,
152
(
3
), pp.
387
400
. 0010-2180
You do not currently have access to this content.