Abstract

This work presents an application of a reduced chemical kinetic mechanism using computational singular perturbation (CSP) based on the significant indices of the modes on the evolution of species and the degree of participation of reactions. With this approach, the mechanism of Yang and Pope is reduced to 22 reversible reactions (RR22). In this study, the tabulation of ignition delays is made with Yang and Pope mechanism, GRI 3.0, and the reduced mechanism RR22; the results obtained show a good agreement among the three mechanisms. The “Modèle Intermittent Lagrangien” (MIL) necessary to calculate the chemical source term of the transport equation of the species requires the library of ignition delays determined above and a probability density function (PDF) of the mixture fraction presumed by a beta distribution. The scalar variance, one of the key parameters for the determination of the presumed beta function, is obtained by solving its own transport equation with the unclosed scalar dissipation rate modeled using either an algebraic model or a transport equation. All these models are introduced in the computational fluid dynamics “Code-Saturne” to simulate a turbulent CH4/H2/N2 jet flame (DLR Flame A) performed at the Deutsches Zentrum für Luft-und Raumfahrt (DLR), or German Aerospace Center. A set of comparisons is made and the results of simulations show a good agreement among the three mechanisms as well with the experimental data.

References

1.
Glaude
,
P. A.
,
Warth
,
V.
,
Fournet
,
R.
,
Battin-Leclerc
,
F.
,
Scacchi
,
G.
, and
Côme
,
G. M.
,
1998
, “
Modeling of the Oxidation of N-Octane and N-Decane Using An Automatic Generation of Mechanisms
,”
Int. J. Chem. Kinet.
,
30
(
12
), pp.
949
959
. 10.1002/(SICI)1097-4601(1998)30:12<949::AID-KIN10>3.0.CO;2-G
2.
Smith
,
G. P.
,
Golden
,
D. M.
,
Frenklach
,
M.
,
Moriarty
,
N. W.
,
Eiteneer
,
B.
,
Goldenberg
,
M.
,
Bowmann
,
C. T.
,
Hanson
,
R. K.
,
Song
,
S.
,
Gardinaer
,
W. C.
, and
Lissianski
,
V. V.
,
1998
,
GRI-Mech version 3.0
, http://www.combustion.berkeley.edu/gri-mech/version30/text30.html
3.
Turányi
,
T.
,
1997
, “
Applications of Sensitivity Analysis to Combustion Chemistry
,”
Reliability Eng. Syst. Saf.
,
57
, pp.
41
48
. 10.1016/S0951-8320(97)00016-1
4.
Griffiths
,
J. F.
,
1995
, “
Reduced Kinetic Models and Their Application to Practical Combustion Systems
,”
Prog. Energy Combust. Sci.
,
21
, pp.
25
107
. 10.1016/0360-1285(94)00022-V
5.
Vajda
,
S.
, and
Turányi
,
T.
,
1986
, “
Principal Component Analysis for Reducing the Edelson–Fields-Noyes Model of the Belousov–Zhabotinsky Reaction
,”
J. Phys. Chem.
,
90
, pp.
1664
1670
. 10.1021/j100399a042
6.
Turányi
,
T.
,
1990
, “
Reduction of Large Reaction Mechanisms
,”
New. J. Chem.
,
14
, pp.
795
803
.
7.
Turányi
,
T.
,
1994
, “
Parameterization of Reaction Mechanisms Using Orthonormal Polynomials
,”
Comput. Chem.
,
18
, pp.
45
54
. 10.1016/0097-8485(94)80022-7
8.
Maas
,
U.
, and
Pope
,
S. B.
,
1992
, “
Simplifying Chemical Kinetics: Intrinsic Low-Dimensional Manifolds in Composition Space
,”
Combust. Flame
,
88
, pp.
239
264
. 10.1016/0010-2180(92)90034-M
9.
Maas
,
U.
,
1998
, “
Efficient Calculation of Intrinsic Low-Dimensional Manifolds for the Simplification of Chemical Kinetics
,”
Comput. Visualization Sci.
,
1
(
2
), pp.
69
81
. 10.1007/s007910050007
10.
Max
,
B.
,
1913
, “
Eine Theorie Der Photochemischen Beaktionsgeschwindigkeiten
,”
Z. Phys. Chem.
,
85
, pp.
329
397
.
11.
Chapman
,
D. L.
, and
Underhill
,
L. K.
,
1913
, “
The Interaction of Chlorine and Hydrogen. The Influence of Mass
,”
J. Chem. Soc. Trans.
,
103
, pp.
496
508
. 10.1039/CT9130300496
12.
Yu
,
G.
,
Hadi
,
F.
, and
Metghalchi
,
H.
,
2018
, “
Rate-Controlled Constrained-Equilibrium Application in Shock Tube Ignition Delay Time Simulation
,”
ASME J. Energy Resour. Technol.
,
141
(
2
), p.
020801
. 10.1115/1.4041288
13.
Du
,
L.
,
Yu
,
G.
,
Wang
,
Z.
, and
Metghalchi
,
H.
,
2019
, “
The Rate-Controlled Constrained-Equilibrium Combustion Modeling of N -Pentane/Oxygen/Diluent Mixtures
,”
ASME J. Energy Resour. Technol.
,
141
(
8
), p.
082206
. 10.1115/1.4042532
14.
Yu
,
G.
,
Metghalchi
,
H.
,
Askari
,
O.
, and
Wang
,
Z.
,
2018
, “
Combustion Simulation of Propane/Oxygen (With Nitrogen/Argon) Mixtures Using Rate-Controlled Constrained-Equilibrium
,”
ASME J. Energy Resour. Technol.
,
141
(
2
), p.
022204
. 10.1115/1.4041289
15.
Bishnu
,
P.
,
Hamiroune
,
D.
, and
Metghalchi
,
M.
,
2001
, “
Development of Constrained Equilibrium Codes and Their Applications in Nonequilibrium Thermodynamics
,”
ASME J. Energy Resour. Technol.
,
123
(
3
), pp.
214
220
. 10.1115/1.1385517
16.
Hadi
,
F.
, and
Sheikhi
,
M.
,
2016
, “
A Comparison of Constraint and Constraint Potential Forms of the Rate-Controlled Constraint-Equilibrium Method
,”
ASME J. Energy Resour. Technol.
,
138
(
2
), p.
022202
. 10.1115/1.4031614
17.
Nicolas
,
G.
, and
Metghalchi
,
H.
,
2015
, “
Comparison Between RCCE and Shock Tube Ignition Delay Times At Low Temperatures
,”
ASME J. Energy Resour. Technol.
,
137
(
6
), p.
062203
. 10.1115/1.4030493
18.
Nicolas
,
G.
, and
Metghalchi
,
H.
,
2016
, “
Development of the Rate-Controlled Constrained-Equilibrium Method for Modeling of Ethanol Combustion
,”
ASME J. Energy Resour. Technol.
,
138
(
2
), p.
022205
. 10.1115/1.4031511
19.
Janbozorgi
,
M.
,
Gao
,
Y.
,
Metghalchi
,
M.
, and
Keck
,
J. C.
,
2006
, “
Rate-Controlled Constrained-Equilibrium Calculations of Ethanol-Oxygen Mixture
,”
ASME Paper No. IMCEC2006-15667
.
20.
Janbozorgi
,
M.
,
Ugarte
,
S.
,
Metghalchi
,
M.
, and
Keck
,
J. C.
,
2009
, “
Combustion Modeling of Mono-Carbon Fuels Using the Rate-Controlled Constrained-Equilibrium Method
,”
Combust. Flame
,
156
(
10
), pp.
1871
1885
. 10.1016/j.combustflame.2009.05.013
21.
Beretta
,
G.
,
Janbozorgi
,
M.
, and
Metghalchi
,
H.
,
2016
, “
Degree of Disequilibrium Analysis for Automatic Selection of Kinetic Constraints in the Rate-Controlled Constrained-Equilibrium Method
,”
Combust. Flame
,
168
, pp.
342
364
. 10.1016/j.combustflame.2016.02.005
22.
Yu
,
G.
,
Zhang
,
Y.
,
Wang
,
Z.
,
Bai
,
Z.
, and
Metghalchi
,
H.
,
2019
, “
The Rate-Controlled Constrained-Equilibrium Combustion Modeling of N-Butane/ Oxygen/Diluent Mixtures
,”
Fuel
,
239
, pp.
786
793
. 10.1016/j.fuel.2018.11.080
23.
Massias
,
A.
,
Diamantis
,
D.
,
Mastorakos
,
E.
, and
Goussis
,
D. A.
,
1999
, “
An Algorithm for the Construction of Global Reduced Mechanisms with CSP Data
,”
Combust. Flame
,
117
, pp.
685
708
. 10.1016/S0010-2180(98)00132-1
24.
Massias
,
A.
,
Diamantis
,
D.
,
Mastorakos
,
E.
, and
Goussis
,
D. A.
,
1999
, “
Global Reduced Mechanisms for Methane and Hydrogen Combustion With Nitric Oxide Formation Constructed With CSP
,”
Combust. Theory Modell.
,
3
, pp.
233
257
. 10.1088/1364-7830/3/2/002
25.
Lam
,
S. H.
,
1993
, “
Using CSP to Understand Complex Chemical Kinetics
,”
Combust. Sci. Tech.
,
89
, pp.
375
404
. 10.1080/00102209308924120
26.
Lam
,
S. H.
, and
Goussis
,
D. A.
,
1994
, “
The CSP Method for Simplifying Kinetics
,”
Int. J. Chem. Kinet.
,
26
, pp.
461
486
. 10.1002/kin.550260408
27.
Awakem
,
D.
,
Obounou
,
M.
, and
Noume
,
H. C.
,
2019
, “
Application of the Computational Singular Perturbation Method to a Turbulent Diffusion CH4/H2/N2 Flame Using OpenFOAM
,”
ASME J. Energy Resour. Technol.
,
141
(
4
), p.
042201
. 10.1115/1.4041841
28.
Yang
,
B.
, and
Pope
,
S. B.
,
1998
, “
An Investigation of the Accuracy of Manifold Methods and Splitting Schemes in the Computational Implementation of Combustion Chemistry
,”
Combust. Flame
,
112
(
1–2
), pp.
16
32
. 10.1016/S0010-2180(97)81754-3
29.
Borghi
,
R.
, and
Gonzalez
,
M.
,
1986
, “
Applications of Lagrangian Models to Turbulent Combustion
,”
Combust. Flame
,
63
, pp.
239
250
. 10.1016/0010-2180(86)90124-0
30.
Borghi
,
R.
,
1988
, “
Turbulent Combustion Modeling
,”
Prog. Energy Combust. Sci.
,
14
, pp.
245
292
. 10.1016/0360-1285(88)90015-9
31.
Obounou
,
M.
,
Gonzalez
,
M.
, and
Borghi
,
R.
,
1994
, “
A Lagrangian Model for Predicting Turbulent Diffusion Flames with Chemical Kinetic Effects
,”
Symposium (International) on Combustion
,
25
(
1
), pp.
1107
1113
.
32.
Fallot
,
L.
,
Gonzalez
,
M.
,
Elamraoui
,
R.
, and
Obounou
,
M.
,
1997
, “
Modelling Finite-Rate Chemistry Effects in Nonpremixed Turbulent Combustion: Test on the Bluff-Body Stabilized Flame
,”
Combust. Flame
,
110
, pp.
298
314
. 10.1016/S0010-2180(97)00077-1
33.
Mouangue
,
R.
,
Obounou
,
M.
,
Gnentedem
,
C.
, and
Njomo
,
D.
,
2010
, “
Numerical Simulation of a Lifted Methane Jet Flame in a Vitiated Coflow: Lagrangian Approach With Detail Chemistry
,”
J. Eng. Appl. Sci.
,
5
(
3
), pp.
211
220
. 10.3923/jeasci.2010.211.220
34.
Gomet
,
L.
,
Robin
,
V.
, and
Mura
,
A.
,
2014
, “
Lagrangian Modelling of Turbulent Spray Combustion Under Liquid Rocket Engine Conditions
,”
Acta Astronautica
,
94
, pp.
184
197
. 10.1016/j.actaastro.2013.08.016
35.
Sanders
,
J. P.
, and
Gökalp
,
I.
,
1998
, “
Scalar Dissipation Rate Modelling in Variable Density Turbulent Axisymmetric Jets and Diffusion Flames
,”
Phys. Fluids
,
10
, pp.
938
948
. 10.1063/1.869616
36.
Mantel
,
T.
, and
Borghi
,
R.
,
1994
, “
A New Model of Premixed Wrinkled Flame Propagation Based on a Scalar Dissipation Equation
,”
Combust. Flame
,
96
, pp.
443
457
. 10.1016/0010-2180(94)90110-4
37.
Jones
,
W. P.
, and
Musonge
,
P.
,
1988
, “
Closure of the Reynolds Stress and Scalar Flux Equations
,”
Phys. Fluids
,
31
, pp.
3589
3604
. 10.1063/1.866876
38.
Meier
,
W.
,
Barlow
,
R. S.
,
Chen
,
Y.-L.
, and
Chen
,
J.-Y.
,
2000
, “
Raman/Rayleigh/LIF Measurements in a Turbulent CH4/H2/N2 Jet Diffusion Flame: Experimental Techniques and Turbulence–Chemistry Interaction
,”
Combust. Flame
,
123
(
3
), pp.
326
343
. 10.1016/S0010-2180(00)00171-1
39.
Schneider
,
Ch.
,
Dreizler
,
A.
, and
Janicka
,
J.
,
2003
, “
Flow Field Measurements of Stable and Locally Extinguishing Hydrocarbon-Fuelled Jet Flames
,”
Combust. Flame
,
135
(
1–2
), pp.
185
190
. 10.1016/S0010-2180(03)00150-0
40.
Noume
,
H.
,
Bomba
,
V.
, and
Obounou
,
M.
,
2020
, “
Numerical Investigation of a Turbulent Jet Flame with a Compact Skeletal Mechanisms
,”
ASME J. Energy Resour. Technol.
,
142
(
3
), p.
032206
. 10.1115/1.4044556
41.
Pitsch
,
Heinz
,
2000
, “
Unsteady Flamelet Modeling of Differential Diffusion in Turbulent Jet Diffusion Flames
,”
Combust. Flame
,
123
, pp.
358
374
. 10.1016/S0010-2180(00)00135-8
42.
Pitsch
,
H.
, and
Peters
,
N.
,
1998
, “
A Consistent Flamelet Formulation for Non-Premixed Combustion Considering Differential Diffusion Effects
,”
Combust. Flame
,
114
, pp.
26
40
. 10.1016/S0010-2180(97)00278-2
43.
Lindstedt
,
R. P.
, and
Ozarovsky
,
H. C.
,
2005
, “
Joint Scalar Transported PDF Modeling of Non Piloted Turbulent Diffusion Flames
,”
Combust. Flame
,
143
, pp.
471
490
. 10.1016/j.combustflame.2005.08.030
44.
Ihme
,
M.
,
Pitsch
,
H.
, and
Bodony
,
D.
,
2009
, “
Radiation of Noise in Turbulent Non-Premixed Flames
,”
Proc. Combust. Inst.
,
32
(
1
), pp.
1545
1553
. 10.1016/j.proci.2008.06.137
45.
Emami
,
M. D.
, and
Eshghinejad Fard
,
A.
,
2012
, “
Laminar Flamelet Modeling of a Turbulent CH4/H2/N2 Jet Diffusion Flame Using Artificial Neural Networks
,”
Appl. Math. Modell.
,
36
(
5
), pp.
2082
2093
. 10.1016/j.apm.2011.08.012
46.
Fairweather
,
M.
, and
Woolley
,
R. M.
,
2004
, “
First-order Conditional Moment Closure Modeling of Turbulent, Nonpremixed Methane Flames
,”
Combust. Flame
,
138
, pp.
3
19
. 10.1016/j.combustflame.2004.03.001
47.
Wang
,
H.
, and
Pope
,
S. B.
,
2011
, “
Large Eddy Simulation/Probability Density Function Modeling of a Turbulent CH4/H2/N2 Jet Flame
,”
Proc. Combus. Inst.
,
33
(
1
), pp.
1319
1330
.
48.
EDF R and D
, “
Code Saturne 3.0 Theory and Programmer’s Guide
,”
Technical Report
. http:www.code-saturne.org
49.
Alim
,
M. A.
, and
Malalasekera
,
W.
,
2005
, “
Transport and Chemical Kinetics of H2/N2 Jet Flame: A Flamelet Modelling Approach With Nox Prediction
,”
J. Naval Architecture Mar. Eng.
,
2
(
1
), pp.
33
40
.
50.
McGuirk
,
J. J.
, and
Rodi
,
W.
,
1979
, “The Calculation of Three Dimensional Turbulent Free Jets,”
F.
Durst
,
B. E.
Launder
,
F. W.
Schmidt
, and
J. H.
Whitelaw
, eds,
Turbulent Shear Flows I
,
Springer
,
Berlin, Heidelberg
, pp.
71
83
.
51.
Villermaux
,
J.
,
1986
,
Encyclopedia of Fluid Mechanics
,
Gulf Publishing Co.
,
West Orange, NJ
, p.
707
.
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