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Reduced High-Temperature Combustion Chemistry
Models of Jet Fuels
Yang Gao1, Rui Xu2, Hai Wang2, Tianfeng Lu1*
1 Department of Mechanical Engineering, University of Connecticut
191 Auditorium Road Unit 3139, Storrs, CT 06269-3139
2 Department of Mechanical Engineering, Stanford University
452 Escondido Mall, Stanford CA 94305-3032
Abstract—In the present study, reduced kinetic models,
including fuel-specific reduced models and a universal reduced
foundational fuel chemistry model for jet fuel combustion, are
developed based on the recently developed HyChem models.
The HyChem approach takes advantage of the de-coupling
between fuel pyrolysis and oxidation of the pyrolysis products
that underlies the basic physics of real, liquid fuel combustion
processes and the diagnostic capabilities currently available.
The resulting HyChem model of real jet fuels is comprised of a
“1-species” lumped model of a jet fuel and a detailed
foundational reaction model for the pyrolysis and oxidation
H2/CO/C1-4/one-ring aromatics, and is thus already
substantially reduced in size. The foundational fuel chemistry
model may be further reduced through skeletal reduction using
directed relation graph (DRG) and sensitivity analysis, and
timescale reduction using the linearized quasi-steady state
approximations (LQSSA). This two-stage reduction approach
is applied on one conventional and two alternative jet fuels,
resulting in fuel-specific reduced models with 31, 26, and 31
species, respectively. A universal reduced model with 35 species
is further proposed for the three fuels, which features
programmable fuel thermodynamic and transport properties
and fuel cracking reaction parameters, as well as a shared
reduced oxidation core for the fuel cracking products. The fuel-
specific and universal reduced models are validated against the
detailed HyChem models for auto-ignition, perfectly stirred
reactors (PSR), 1-D laminar premixed flame speed, and
extinction of premixed and non-premixed counterflow flames.
I. INTRODUCTION
Jet fuels are comprised of a large number of components
with different chemical and physical properties. In addition,
combustion of jet fuels results in myriad intermediate species
during the pyrolysis and oxidation processes. As such it is
highly challenging to model the chemical kinetic behaviors of
real jet fuels. Recently, a hybrid approach, “HyChem,” was
proposed to model high-temperature combustion of practical
jet fuels [1, 2], and HyChem models have been developed for
multiple real jet fuels. The HyChem approach takes
advantage of the de-coupling between fuel pyrolysis and
oxidation of the pyrolysis products that underlies the basic
physics of real, liquid fuel combustion processes and the
diagnostic capabilities currently available. The resulting
HyChem model of real jet fuels is comprised of a lumped
model of fuel pyrolysis and a detailed foundational reaction
model for the pyrolysis and oxidation of the primary
intermediates of jet fuel pyrolysis and oxidative pyrolysis.
Key species include hydrogen, methane, ethylene, propene,
iso-butene, 1-butene, benzene and toluene. Because the
lumped model is essentially a 1-species model, the HyChem
models are already extremely compact. In essence, the
approach uses the physical phenomenon to derive the lower-
dimension model, rather than starting at a higher complexity
(e.g., using the surrogate and detailed reaction mechanism
approach).
The HyChem model for each fuel consists of 119 species
and 843 reactions, in which seven lumped reaction steps are
used to describe the fuel pyrolysis, and the oxidation kinetics
of the fuel pyrolysis products is described by USC Mech II
[3]. The kinetic parameters of the HyChem model were
determined though time-history data of shock-tube and flow-
reactor experiments. The HyChem models have been
validated against a variety of experiments, including ignition
delay, laminar flame speed, and counterflow extinction [1, 2].
The emphasis of the current work is the reduction of the
foundational fuel chemistry model. In particular, compact
reduced models are developed based on the HyChem models
for three target fuels to obtain CFD-amenable models for
more efficient simulations. The three target fuels include a
conventional petroleum-derived Jet-A fuel (POSF10325, Cat
A2), and two alternative jet fuels: one (POSF11498, Cat C1)
features a low derived cetane number (DCN) and is composed
of highly branched iso-alkanes, and the other (POSF12345,
Cat C5) features similar chemical properties but vastly
different physical properties (flat boiling curve) with Cat A2.
More details of the fuels can be found in Refs. [4, 5].
II. METHODOLOGIES AND RESULTS
A. Fuel-specific reduced HyChem models
The reduction is based on reaction states sampled from
auto-ignition and perfectly stirred reactors (PSR). The
reduction parameter range covers pressure of 0.5-30 atm,
equivalence ratio of 0.5-1.5, initial temperature of 1000-1600
K for auto-ignition, and inlet temperature of 300 K for PSR.
Skeletal reduction with directed relation graph (DRG) [6] and
sensitivity analysis [7] is first applied to eliminate
unimportant species and reactions from the detailed HyChem
models. In DRG, H radical is selected as the starting species
and an error threshold of 0.3 is specified for all the three target
fuels. After the skeletal reduction with DRG, the resulting
skeletal models are further reduced with sensitivity analysis
with ignition delay and extinction residence time of PSR as
target parameters. Fig. 1 shows the accumulative worst-case
relative error in the target parameters as function of the
number of retained species in sensitivity analysis for Cat A2,
with the vertical dashed line indicating the error threshold.
The error threshold for each fuel in sensitivity analysis is
chosen where the rapid increase in worst-case error of target
parameters starts to occur, that is 20% for A2 and C5, and
35% for C1, respectively. The final skeletal models consist of
41, 34, and 41 species for Cat A2, C1, and C5, respectively.
As the last step in the skeletal reduction, reactions
unimportant for all the remained species are eliminated by
comparing the contribution of each reaction to each remained
species using an error threshold of 20% [8]. In the second-
stage of the reduction, linearized quasi-steady-state
approximations (LQSSA) [9] are further applied on 10, 8, and
10 global QSS species for Cat A2, C1, and C5, respectively.
The QSS species are removed from the transport equations
and are analytically solved using internal algebraic equations
with a graph-based method [9]. Table I provides the summary
of the detailed, skeletal and reduced models for the three
target fuels.
Fig. 2 shows selected validations of the reduced and
skeletal models against the detailed HyChem models for Cat
A2, C1, and C5 for ignition delay and laminar flame speed.
The reduced and skeletal models agree well with the detailed
models over a wide range of conditions. Fig. 3 compares the
maximum temperature of the flame as function of the
reciprocal strain rate for non-premixed and premixed flames.
The reduced models agree tightly with the detailed models
along the entire curves including the turning points, which are
the nominal extinction states of the flames, with the worst-
case relative error being approximately 15%.
B. A universal reduced HyChem model
Because the oxidation cores for the three target fuels are
largely identical, a universal skeletal model is developed by
combining the oxidation cores of three target fuels and using
programmable fuel properties and fuel cracking reactions.
Procedurally, the three skeletal models are first merged to
obtain a universal skeletal oxidation core with 47 species and
263 reactions after removing 37 reactions that are
unimportant for all the three fuels. The three target fuels and
their fuel-specific cracking reactions are replaced with 1
nominal fuel species and 7 nominal fuel cracking reactions,
of which the rates and stoichiometric coefficients are
evaluated using a special subroutine. Among the 48 species
(including the nominal fuel) in the universal skeletal model,
13 species are identified to be global QSS species, and a 35-
species universal reduced model is finally obtained.
Fig. 4 shows selected validations of the 35-species
universal reduced model with Cat A2, C1, and C5 as the fuel
respectively against the detailed models for ignition delay and
laminar flame speed. It is seen that the universal reduced
models agree slightly better with the detailed models than the
fuel-specific reduced models.
Fig.1 Accumulative worst-case error in the target parameters in sensitivity
analysis as function of the number of retained species in the skeletal model
for Cat A2.
TABLE I. Sizes of the detailed, skeletal and reduced HyChem models
Cat A2
Cat C1
Cat C5
Species &
Reactions
Species &
Reactions
Species &
Reactions
Detailed
119
843
119
843
119
843
Skeletal
41
202
34
182
41
200
Reduced
31
26
31
Fig. 2 Ignition delay (left) and laminar flame speed (right) at pressure of
0.5, 1, 5, and 30 atm for Cat A2, C1, and C5, calculated with the detailed
(solid lines), skeletal (dashed lines) and reduced (symbols) models,
respectively.
A2
Error tolerance 20%
Last removed 19%
Next test 33%
A2/air
= 1
C1/air
= 1
C5/air
= 1
Auto-ignition
Ignition delay (s)
Ignition delay (s)
Ignition delay (s)
1000/T (K-1)
1000/T (K-1)
1000/T (K-1)
A2/air
T0= 300 K
C1/air
T0= 300 K
C5/air
T0= 300 K
Laminar flame speed
Equivalence ratio
Equivalence ratio
Equivalence ratio
Laminar flame speed (cm)
Laminar flame speed (cm)
Laminar flame speed (cm)
Fig. 3 Comparison of the maximum temperature, Tmax, in counterflow non-
premixed (left) and premixed (right) flames as function of the reciprocal
strain rate for Cat A2, C1, and C5, calculated with the detailed (solid lines)
and reduced (symbols) models, respectively.
Fig. 4 Ignition delay (left) and laminar flame speed (right) at pressure of
0.5, 1, 5, and 30 atm for Cat A2, C1, and C5, calculated with the detailed
(solid lines) and universal reduced (symbols) models, respectively.
III. CONCLUSIONS
The detailed HyChem models for real jet fuels, including
Cat A2, C1, and C5, are systematically reduced for high-
temperature applications using DRG, sensitivity analysis and
LQSSA. Fuel-specific reduced models with 31, 26, and 31
species are obtained for Cat A2, C1, and C5, respectively. In
addition, a 35-species universal reduced model is obtained
using programmable fuel properties and fuel cracking
reactions. The reduced models are validated against the
detailed HyChem models for 0-D homogenous reactors,
including auto-ignition and PSR, and 1-D diffusive systems,
including laminar flame speed and extinction of premixed
and non-premixed counterflow flames. The validation results
show good agreements between the detailed and reduced
models over a wide range of parameters. The compact
reduced models are amenable for efficient CFD simulations
with real fuel chemistry.
ACKNOWLEDGMENT
This work was supported by NASA NRA NNX15AU96A
and NNX15AV05A under the technical monitoring of Dr.
Jeff Moder, and by the US AFOSR under grant numbers
FA9550-14-1-0235 and FA9550-16-1-0195 under technical
monitoring of Dr. Chiping Li.
REFERENCES
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Egolfopoulos, Evidence supporting a simplified approach to modeling high-
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Meeting, Maryland, April 23-26, 2017.
[2] R. Xu, D. Chen, K. Wang, Y. Tao, J. K. Shao, T. Parise, Y. Zhu, S.
Wang, R. Zhao, D. J. Lee, F. N. Egolfopoulos, D. F. Davidson, R. K.
Hanson, C. T. Bowman, H. Wang, HyChem model: application to
petroleum-derived jet fuels, in: 10th U.S. National Combustion Meeting,
Maryland, April 23-26, 2017.
[3] H. Wang, X. You, A. Joshi, S. Davis, A. Laskin, F. Egolfopoulos, C.
Law USC Mech Version II. High-Temperature Combustion Reaction Model
of H2/CO/C1-C4 Compounds. http://ignis.usc.edu/USC_Mech_II.htm
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0 1 2 3 4 5 6 7 8 9 10
1500
1600
1700
1800
1900
2000
2100
2200
10 atm
Tmax (K)
Reciprocal strain rate (ms)
1 atm
0 1 2 3 4 5 6 7 8 9 10
1500
1600
1700
1800
1900
2000
2100
2200
10 atm
Tmax (K)
Reciprocal strain rate (ms)
1 atm
Twin jets: A2/air
Tin = 300 K, = 0.7
50% A2 +N2vs. Air
Tin = 300 K
0 1 2 3 4 5 6 7 8 9 10
1500
1600
1700
1800
1900
2000
2100
2200
10 atm
Tmax (K)
Reciprocal strain rate (ms)
1 atm
50% C1 +N2vs. Air
Tin = 300 K
0 1 2 3 4 5 6 7 8 9 10
1500
1600
1700
1800
1900
2000
2100
2200
10 atm
Tmax (K)
Reciprocal strain rate (ms)
1 atm
Twin jets: C1/air
Tin = 300 K, = 0.7
0 1 2 3 4 5 6 7 8 9 10
1500
1600
1700
1800
1900
2000
2100
2200
10 atm
Tmax (K)
Reciprocal strain rate (ms)
1 atm
50% C5 +N2vs. Air
Tin = 300 K
0 1 2 3 4 5 6 7 8 9 10
1500
1600
1700
1800
1900
2000
2100
2200
10 atm
Tmax (K)
Reciprocal strain rate (ms)
1 atm
Twin jets: C5/air
Tin = 300 K, = 0.7
A2/air
T0= 300 K
Equivalence ratio
Laminar flame speed (cm)
C1/air
T0= 300 K
Equivalence ratio
Laminar flame speed (cm)
C5/air
T0= 300 K
Equivalence ratio
Laminar flame speed (cm)
Laminar flame speed
Ignition delay (s)
A2/air
= 1
1000/T (K-1)
Ignition delay (s)
C1/air
= 1
1000/T (K-1)
Ignition delay (s)
C5/air
= 1
1000/T (K-1)
Auto-ignition