Conference PaperPDF Available

Reduced High-Temperature Combustion Chemistry Models of Jet Fuels

Authors:
  • Convergent Science Inc

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.
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
AbstractIn 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.
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Tmax (K)
Reciprocal strain rate (ms)
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Twin jets: A2/air
Tin = 300 K, = 0.7
50% A2 +N2vs. Air
Tin = 300 K
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Tmax (K)
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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
... To facilitate the DNS study of fuel cracking behaviors, a 25-species reduced model for n-butane/air combustion is further developed. The fast fuel cracking assumption under high-T conditions are validated in 0-D, 1-D, and a 2-D DNS.In Chapter 3, highly compact reduced models with approximately 30 species are developed for high-T combustion of several representative real jet fuels based on the HyChem models[77,78] which consist of lumped fuel cracking steps and a detailed oxidation core for small molecules.In Chapter 4, an 86-species reduced model and a 99-species skeletal model for ethylene/air combustion with polycyclic aromatic hydrocarbons (PAHs) are developed for efficient CFD simulations of sooting flames. In Chapter 5, the previous developed species bundling approach is extended, and three new approaches are proposed to further reduce the computational cost of the MAD model. ...
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In this work we introduce an unconventional approach to modeling the high-temperature combustion chemistry of multicomponent real fuels. The hybrid chemistry (HyChem) approach decouples fuel pyrolysis from the oxidation of fuel decomposition intermediates. The thermal decomposition and oxidative thermal decomposition processes are modeled by seven lumped reaction steps in which the stoichiometric and reaction rate coefficients may be derived from experiments. The oxidation process is described by detailed chemistry of foundational hydrocarbon fuels. We present results obtained for three petroleum-derived fuels: JP-8, Jet A and JP-5 as examples. The experimental observations show only a small number of intermediates are formed during thermal decomposition under pyrolysis and oxidative conditions, and support the hypothesis that the stoichiometric coefficients in the lumped reaction steps are not a strong function of temperature, pressure, or fuel-oxidizer composition, as we discussed in a companion paper. Modeling results demonstrate that HyChem models are capable of predicting a wide range of combustion properties, including ignition delay times, laminar flame speeds, and non-premixed flame extinction strain rates of all three fuels.
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The ignition temperatures of nitrogen-diluted 1,3-butadiene by heated air in counterflow were experimentally determined for pressures up to 5 atmospheres and pressure-weighted strain rates from 100 to 250s−1. The experimental data were compared with computational results using the mechanism of Laskin et al. [A. Laskin, H. Wang and C.K. Law, Int. J. Chem. Kinet. 32 (10) (2000) 589–614], showing that while the overall prediction is approximately within the experimental uncertainty, the mechanism over-predicts ignition temperature by about 25–40K, with the differences becoming larger at high pressure/low temperature region. Sensitivity analyses for the near-ignition states were performed for both reactions and diffusion, which identified the importance of H2/CO chain reactions, three 1,3-butadiene reaction pathways, and the binary diffusion between 1,3-butadiene and N2 on ignition. The detailed mechanism, consisting of 94 species and 614 reactions, was then simplified to a skeletal mechanism consisting of 46 species and 297 reactions by using a new reduction algorithm combining directed relation graph and sensitivity analysis. The skeletal mechanism was further simplified to a 30-step reduced mechanism by using computational singular perturbation and quasi-steady-state assumptions. Both the skeletal and reduced mechanisms mimic the performance of the detailed mechanism with good accuracy in both homogeneous and heterogeneous systems.
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A 55-species reduced mechanism for n-heptane oxidation was derived from a 188-species skeletal mechanism, which was previously obtained from a detailed mechanism consisting of 561 species using a directed relation graph (DRG). This reduced mechanism was derived by first obtaining a skeletal mechanism with 78 species using DRG-aided sensitivity analysis. The unimportant reactions were eliminated by using the importance index defined in computational singular perturbation (CSP), with a newly posited restriction to treat each reversible reaction as a single reaction. An isomer lumping approach, also developed in the present study, then groups the isomers with similar thermal and diffusion properties so that the number of species transport equations is reduced. It was found that the intragroup mass fractions of the isomers can be approximated as constants in the present reduced mechanism, leading to a 68-species mechanism with 283 elementary reactions. Finally, 13 global quasi-steady-state species were identified using a CSP-based time-scale analysis, resulting in the 55-species reduced mechanism, with 283 elementary reactions lumped into 51 semiglobal steps. Validation of the reduced mechanism shows good agreement with the detailed mechanism for both ignition and extinction phenomena. The inadequacy of the detailed mechanism in predicting the experimental laminar flame speed is also demonstrated.
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A systematic approach was developed to obtain analytic solutions for the concentrations of the quasi steady state (QSS) species in reduced mechanisms. The nonlinear algebraic equations for the QSS species concentrations were first approximated by a set of linear equations, and the linearized quasi steady state approximations (LQSSA) were then analytically solved with a directed graph, namely a QSSG, which was abstracted from the inter-dependence of QSS species. To obtain analytic solutions of high computational efficiency, the groups of strongly connected QSS species were first identified in the QSSG. The inter group couplings were then resolved by a topological sort, and the inner group couplings were solved with variable elimination by substitution. An efficient algorithm was developed to identify a near-optimal sequence for the variable elimination process. The proposed LQSSA-QSSG method was applied to generate a 16-step reduced mechanism for ethylene/air, and good accuracy and high efficiency were observed in simulations of auto-ignition and perfectly stirred reactors with the reduced mechanism.
Law USC Mech Version II. High-Temperature Combustion Reaction Model of H2/CO/C1-C4 Compounds
  • H Wang
  • X You
  • A Joshi
  • S Davis
  • A Laskin
  • F Egolfopoulos
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
Reciprocal strain rate (ms) 1
  • T Max
10 atm T max (K) Reciprocal strain rate (ms) 1 atm 0 1 2 3 4 5 6 7 8 9 10