The rate-controlled constrained-equilibrium (RCCE) model reduction scheme for chemical kinetics provides acceptable accuracies in predicting hydrocarbon ignition delays by solving a smaller number of differential equations than the number of species in the underlying detailed kinetic model (DKM). To yield good approximations, the method requires accurate identification of the rate controlling constraints. Until recently, a drawback of the RCCE scheme has been the absence of a systematic procedure capable of identifying optimal constraints for a given range of thermodynamic conditions and a required level of approximation. A recent methodology has proposed for such identification an algorithm based on a simple algebraic analysis of the results of a preliminary simulation of the underlying DKM, focused on the degrees of disequilibrium (DoD) of the individual chemical reactions. It is based on computing an approximate singular value decomposition of the actual degrees of disequilibrium (ASVDADD) obtained from the DKM simulation. The effectiveness and robustness of the method have been demonstrated for methane/oxygen ignition by considering a C1/H/O (29 species/133 reactions) submechanism of the GRI-Mech 3.0 scheme and comparing the results of a DKM simulation with those of RCCE simulations based on increasing numbers of ASVDADD constraints. Here, we demonstrate the new method for shock-tube ignition of a natural gas/air mixture, with higher hydrocarbons approximately represented by propane according to the full (53 species/325 reactions) GRI-Mech 3.0 scheme including NOx formation.

References

References
1.
Beretta
,
G. P.
,
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
.
2.
Keck
,
J. C.
, and
Gillespie
,
D.
,
1971
, “
Rate-Controlled Partial-Equilibrium Method for Treating Reacting Gas Mixtures
,”
Combust. Flame
,
17
(2), pp.
237
241
.
3.
Keck
,
J. C.
,
1979
, “
Rate-Controlled Constrained Equilibrium Method for Treating Reactions in Complex Systems
,”
The Maximum Entropy Formalism
,
R. D.
Levine
and
M.
Tribus
, eds.,
MIT Press
,
Cambridge, MA
, pp.
219
245
.
4.
Beretta
,
G. P.
, and
Keck
,
J. C.
,
1986
, “
The Constrained-Equilibrium Approach to Nonequilibrium Dynamics
,”
Second Law Analysis and Modeling
, Vol.
3
,
R. A.
Gaggioli
, ed.,
ASME
,
New York
, pp.
135
139
.
5.
Law
,
R.
,
Metghalchi
,
M.
, and
Keck
,
J. C.
,
1989
, “
Rate-Controlled Constrained Equilibrium Calculations of Ignition Delay Times in Hydrogen-Oxygen Mixtures
,”
Symp. (Int.) Combust.
,
22
(1), pp.
1705
1713
.
6.
Keck
,
J. C.
,
1990
, “
Rate-Controlled Constrained-Equilibrium Theory of Chemical Reactions in Complex Systems
,”
Prog. Energy Combust. Sci.
,
16
(2), pp.
125
154
.
7.
Bishnu
,
P.
,
Hamiroune
,
D.
,
Metghalchi
,
H.
, and
Keck
,
J. C.
,
1997
, “
Constrained-Equilibrium Calculations for Chemical Systems Subject to Generalized Linear Constraints Using the NASA and STANJAN Equilibrium Programs
,”
Combust. Theory Modell.
,
1
(3), pp.
295
312
.
8.
Hamiroune
,
D.
,
Bishnu
,
P.
,
Metghalchi
,
H.
, and
Keck
,
J. C.
,
1998
, “
Rate-Controlled Constrained-Equilibrium Method Using Constraint Potentials
,”
Combust. Theory Modell.
,
2
(1), pp.
81
94
.
9.
Yousefian
,
V.
,
1998
, “
A Rate-Controlled Constrained-Equilibrium Thermochemistry Algorithm for Complex Reacting Systems
,”
Combust. Flame
,
115
(1–2), pp.
66
80
.
10.
Janbozorgi
,
M.
,
Ugarte
,
S.
,
Metghalchi
,
H.
, and
Keck
,
J. C.
,
2009
, “
Combustion Modelling of Mono-Carbon Fuels Using the Rate-Controlled Constrained-Equilibrium Method
,”
Combust. Flame
,
156
(10), pp.
1871
1885
.
11.
Beretta
,
G. P.
,
Keck
,
J. C.
,
Janbozorgi
,
M.
, and
Metghalchi
,
H.
,
2012
, “
The Rate-Controlled Constrained-Equilibrium Approach to Far-From-Local-Equilibrium Thermodynamics
,”
Entropy
,
14
(2), pp.
92
130
.
12.
Janbozorgi
,
M.
, and
Metghalchi
,
H.
,
2012
, “
Rate-Controlled Constrained-Equilibrium Modeling of H-O Reacting Nozzle Flow
,”
J. Propul. Power
,
28
(4), pp.
677
684
.
13.
Nicolas
,
G.
,
Janbozorgi
,
M.
, and
Metghalchi
,
H.
,
2014
, “
Constrained-Equilibrium Modeling of Methane Oxidation in Air
,”
ASME J. Energy Resour. Technol.
,
136
(3), p.
032205
.
14.
Nicolas
,
G.
, and
Metghalchi
,
H.
,
2015
, “
Comparison Between RCCE and Shock Tube Ignition Delay Time at Low Temperatures
,”
ASME J. Energy Resour. Technol.
,
137
(6), p.
062203
.
15.
Gyftopoulos
,
E. P.
, and
Beretta
,
G. P.
,
2005
,
Thermodynamics: Foundations and Applications
,
Dover Publications
,
Mineola, NY
.
16.
Beretta
,
G. P.
, and
Gyftopoulos
,
E. P.
,
2015
, “
What Is a Chemical Equilibrium State?
,”
ASME J. Energy Resour. Technol.
,
137
(2), p.
021008
.
17.
Beretta
,
G. P.
, and
Gyftopoulos
,
E. P.
,
2004
, “
Thermodynamic Derivations of Conditions for Chemical Equilibrium and of Onsager Reciprocal Relations for Chemical Reactors
,”
J. Chem. Phys.
,
121
(6), pp.
2718
2728
.
18.
Beretta
,
G. P.
,
2009
, “
Nonlinear Quantum Evolution Equations to Model Irreversible Adiabatic Relaxation With Maximal Entropy Production and Other Nonunitary Processes
,”
Rep. Math. Phys.
,
64
(1–2), pp.
139
168
.
19.
Hiremath
,
V.
,
Ren
,
Z.
, and
Pope
,
S. B.
,
2011
, “
Combined Dimension Reduction and Tabulation Strategy Using ISAT-RCCE-GALI for the Efficient Implementation of Combustion Chemistry
,”
Combust. Flame
,
158
(1), pp.
2113
2127
.
20.
Martin
,
C. D.
, and
Porter
,
M. A.
,
2012
, “
The Extraordinary SVD
,”
Am. Math. Mon.
,
119
(10), pp.
838
851
.
21.
Wold
,
S.
,
Esbensen
,
K.
, and
Geladi
,
P.
,
1987
, “
Principal Component Analysis
,”
Chemom. Intell. Lab. Syst.
,
2
(1–3), pp.
37
52
.
22.
Smith
,
G. P.
,
Golden
,
D. M.
,
Frenklach
,
M.
,
Moriarty
,
N. W.
,
Eiteneer
,
B.
,
Goldenberg
,
M.
,
Bowman
,
C. T.
,
Hanson
,
R. K.
,
Song
,
S.
,
Gardiner
,
W. C.
, Jr
.,
Lissianski
,
V. V.
, and
Qin
,
Z.
, 2017, “GRI-Mech 3.0,” accessed Nov. 17, 2017, http://combustion.berkeley.edu/gri-mech/version30/text30.html
23.
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
.
24.
Hadi
,
F.
,
Janbozorgi
,
M.
,
Sheikhi
,
R.
, and
Metghalchi
,
H.
,
2016
, “
A Study of Interactions Between Mixing and Chemical Reaction Using the Rate-Controlled Constrained-Equilibrium Method
,”
J. Non-Equilib. Thermodyn.
,
41
(4), pp.
257
278
.
25.
Beretta
,
G. P.
,
2014
, “
Steepest Entropy Ascent Model for Far-Nonequilibrium Thermodynamics: Unified Implementation of the Maximum Entropy Production Principle
,”
Phys. Rev. E
,
90
, p.
042113
.
26.
Montefusco
,
A.
,
Consonni
,
F.
, and
Beretta
,
G. P.
,
2015
, “
Essential Equivalence of the General Equation for the Nonequilibrium Reversible-Irreversible Coupling (GENERIC) and Steepest-Entropy-Ascent Models of Dissipation for Nonequilibrium Thermodynamics
,”
Phys. Rev. E
,
91
(4), p.
042138
.
You do not currently have access to this content.