Chemical Kinetic Model Reduction and Efficient [PDF]

50th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition

Chemical Kinetic Model Reduction and Efficient Implementation Strategies for Hypersonic Propulsion Applications

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50th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition

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n/a Chelliah, Harsha

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Chemical Kinetic Model Reduction and Efficient Implementation Strategies for Hypersonic Propulsion Applications G Esposito ∗ MJ Rahimi † and HK Chelliah

‡

Department of Mechanical and Aerospace Engineering, University of Virginia Charlottesville VA 22904, USA

V Hiremath § and SB Pope

¶

Department of Mechanical and Aerospace Engineering, Cornell University Ithaca NY 14853, USA

D Sheen and W Tsang Chemical and Biochemical Reference Data Division, NIST Gaithersburg, MD 20898, USA

For hypersonic propulsion conditions of interest, several mechanism reduction strategies have been developed by taking advantage of broad range of chemical time scales under high temperature conditions. The reduction methodologies include application of (i) principal component analysis based on sensitivity of ignition, flame propagation, extinction limits and partially-stirred reactor simulations to extract skeletal reaction models, (ii) quasisteady state approximation to obtain reduced reaction models, and (iii) rate-controlled constraint-equilibrium dimension reduction method to represent the chemistry using a reduced set of represented species. In addition, implementation of the in-situ adaptive tabulation approach to partially-stirred reactor simulations has been demonstrated for a set of selected mixing conditions relevant for turbulent reacting flows. In this paper, the above model reduction approaches have been applied to a newly optimized ethylene-air detailed kinetic model.

I.

Introduction

The detailed chemical kinetic models that describe the pyrolytic decomposition of hydrocarbon fuels and subsequent oxidation of H2 /CO/C1 -C4 fuel mixtures typically include over one hundred species in more than one thousand elementary reactions. Under high-temperature conditions, such as those found in combustors of hypersonic vehicles, it is well known that the hydrocarbon pyrolysis reactions are significantly faster than the oxidation of smaller intermediate species, e.g. ethylene.1, 2 Furthermore, if the liquid phase hydrocarbon fuels are to be used for cooling critical components of hypersonic vehicles (e.g. leading edges, combustor walls, etc.), then the endothermic pyrolysis of the fuel molecule will lead to conversion of the fuel molecules to smaller fragments before entering the combustor.3, 4 Considering these operational conditions and knowing that the detailed chemical kinetic models are too large to be implemented in multi-dimensional CFD simulations of reacting flow fields in hypersonic combustors, this paper describes several strategies implemented in improving the accuracy of the relevant fuel pyrolysis chemistry model, optimization of compiled detailed kinetic model, and subsequent reduction of the detailed kinetic model. ∗ Member

AIAA Member AIAA ‡ Professor, Associate Fellow AIAA § Student Member AIAA ¶ Professor, Associate Fellow AIAA † Student

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II.

Detailed Chemical Kinetic Model and Optimization Procedure

The theoretical basis for pyrolytic decomposition of large hydrocarbon fuels to alkyl radicals and subsequent beta-bond scission/isomerization to small unsaturated fragments is fairly well known.5 A key need is the quantitative assignment of actual rate constants at sufficiently high temperatures, with departures from thermal equilibrium requiring consideration of chemical activation. Under an AFOSR and BES/DOE program, we have carried out studies on the pyrolytic decomposition of hydrocarbon radicals up to eight carbon atoms. This represents a combination of single pulse shock tube studies and analysis of the experimental olefinic branching ratios, thus determining high-pressure rate expressions through the solution of the master equation and taking into account energy transfer effects. These results are being extended to derive pressure-dependent rate expressions under many combustion conditions,1, 2 and are directly applicable to the high temperature regime encountered in hypersonic combined-cycle combustors. The detailed chemistry models compiled with updated pyrolytic reaction pathways must simulate the combustion processes of interest in as much detail as possible. The model must include not only the best estimates for the reaction rate parameters, but also their uncertainties and then be subjected to a rigorous, multi-parameter optimization against a set of experimental measurements relevant to the combustion system of interest. The resulting model would therefore reproduce as best as possible the current state of knowledge for that particular combustion system. II.A.

Detailed Reaction Model

The detailed reaction model used herein is based on the JetSurF 2.0 high-temperature n-alkane oxidation model.6 In order to reduce the computational complexity of the problem, only the H2 /CO/C1 -C4 submodel is considered here, which consists of 110 species and 784 reactions. This is the same submodel that was used in a recent optimization study,7 with a wide range of validation tests consisting of over 140 sets of global and detailed combustion data.8 The model is untuned except for the H2 /CO chemistry, which was the subject of a comprehensive optimization study conducted previously.9 Furthermore, the H2 /CO chemical rates have been reset to their nominal values.7, 10 Uncertainty factors for the reaction rate parameters range from 1.2 for most of the well-known hydrogen branching reactions to factors of 2 or 4 for some less well-studied reactions.7, 10 II.B.

Optimization Procedure

The optimization of the model was conducted using the Method of Uncertainty Minimization using Polynomial Chaos Expansions (MUM-PCE). This methodology was previously developed in the context of constraining a detailed chemical model by a wide variety of combustion phenomena, including laminar flame speeds and ignition delay7, 10, 11 as well as detailed species measurements in shock tube oxidation.7, 12 As stated above, the chemical model and associated uncertainties must be first compiled. The model can then be thought of as occupying some multi-dimensional space, which includes all possible choices of chemical rate parameters which agree with the model’s uncertainty estimates. The experimental measurements are then simulated in such a way that the variation of the model’s predicted values is known throughout the rate parameter uncertainty space. Some choices of rate parameter values will produce predictions that do not agree with the experimental measurements, and the set of values that remain is called the feasible region.13–15 This feasible region is characterized in MUM-PCE by a multivariate lognormal distribution, which is entirely described by its mean vector and covariance matrix, and are found by means of the rigorous, multi-parameter optimization. The model represented by the mean vector, which is at the center of the feasible region, is the model used here as the detailed or the starting model for reduction.

III.

Skeletal Reaction Models

The newly optimized H2 /CO/C1 -C4 starting chemical kinetic model described above consists of 110 species, including many C5 -C6 species and a related set of C3 -C4 species. Many of these species, e.g. C6 H5 CH2 , lC5 H7 , nC4 H3 , iC4 H5 , pC3 H4 , iC3 H7 , do not play any role in the oxidation of C1 -C4 hydrocarbon molecules of interest in hypersonic propulsion applications, especially under high temperature conditions. In the past, several analytical approaches have been developed to identify such non-contributing species and strip them from the detailed kinetic model. The resulting stripped-down chemical kinetic models are

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commonly identified as skeletal reaction models. The analytical approaches utilized in obtaining skeletal models include heat release flux analysis,16 reaction flux analysis,17 principal component analysis (PCA),18, 19 and directed relation graph (DRG).20 While each approach has its own strengths and weaknesses, in the recent past we have successfully implemented the principal component analysis based on sensitivities (PCAS) of ignition, propagation, and extinction phenomena,19 and this approach is implemented here with extension to partially-stirred reactor simulations. III.A.

Reduction using Principal Component Analysis with Sensitivity (PCAS)

PCAS provides a rigorous approach18 of identifying the dominant reactions and species in a chemical kinetic model under various temporal and spatial conditions as well as distinct combustion phenomena (i.e. ignition, propagation, and extinction) in a combined manner. As shown recently by Esposito and Chelliah,19 the latter is critical for accurate simulation of hypersonic reacting flow regimes sensitive to finite-rate kinetics, such as flame holding and mode transitions. In particular, at critical flame holding conditions, the skeletal model must include the key reactions and species controlling both the ignition and the local extinction phenomena occurring at different spatial regions in the computational domain. In the present implementation of PCA, the response function Q(P) is approximated by18, 19 T

Q(P) ≈ (∆P) ST S (∆P) = q(P),

(1)

where P is the normalized kinetic parameter vector (k = 1, ..., r) and S is a matrix made of a collection of sensitivity coefficient matrices sj stacked in a column, whose elements are defined as, sjik =

∂ ln fi (xj ) . ∂ ln Pk

(2)

Here fi is any appropriate target function evaluated at a specific spatial or temporal location xj . By performing a spectral analysis of ST S it is possible to decompose q(P) as, q(P) =

r ∑

2

λk (∆Ψk ) ,

(3)

k=1

where λk is the set of real eigenvalues sorted according to descending order, starting with the largest eigenvalue. The vector components Ψ = UT P are the original parameter vector transformed through normalized eigenvector matrix U and are called principal components. Since the eigenvectors are normalized, the values of λk control the magnitude of q(P) and the eigenvectors define which parameters P are grouped together. ¯ on the eigenvalues defines which parameter groups related to all λk > λ ¯ play the Setting a threshold λ most important role in the response function. Moreover, another threshold (¯ u) on the values of eigenvector components uk corresponding to the λk , discriminates influential reactions within every contributing mode. III.A.1.

Combined skeletal model based on ignition, propagation, and extinction

In applying PCAS, Eq. (1) can be derived based on a single phenomenon, i.e. ignition or extinction, or combination of several phenomena. This can be easily accomplished because of the generality of the definition of Q in Eq. (1). For example, a combined response function QC (P) can be constructed as QC (P) ≈ [(∆P)T ST S(∆P)]phen

1

+ [(∆P)T ST S(∆P)]phen

2

+ ...,

(4)

where S can be related to sensitivity of any response function of any phenomena i. In the following sections, the errors associated with model reduction via PCAS based on the analysis of single phenomenon or combined phenomena are presented. III.B. III.B.1.

Application of PCAS Premixed Ignition and Flame Propagation Analysis

In high-speed reacting flows with relatively long mixing time scales compared to the advection time scales, homogeneous ignition chemistry can describe the induction length or the location where intense reaction

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occur. For this reason, accurate prediction of homogeneous ignition phenomenon under various initial conditions (i.e. temperature, pressure, and equivalence ratios) and fuel-air mixtures have received considerable attention. In particular, considerable effort has been devoted to measurement of ignition delay times in shock tubes as well as temporal evolution of temperature and species, providing a valuable database for chemical kinetic model optimization. For example, Hong et al.21 have proposed a new hydrogen kinetic model based on the ignition delay and speciation information. Burke et al.22 have also used the same ignition database together with their high-pressure flow reactor database to develop a slightly modified hydrogen kinetic model. Finally, the MUM-PCE optimization approach described above has been used to optimize a H2 /CO/C1 -C4 kinetic model that included the new experimental data by Hong et al.,21 and this new H2 /CO/C1 -C4 kinetic model is used here to extract skeletal reaction models using the PCAS methodology. For atmospheric pressure mixtures of ethylene and air with ϕ=0.5 to 1.5 and initial temperatures between 900 to 2000 K, Fig. 1 shows the L2-norm error in predicting ignition delay, defined by19 [∫ ||ϵign ||L2 =

ϕb

ϕa

∫

Tb Ta

(

τign,skel − τign,det τign,det

]1/2

)2 dT dϕ

,

(5)

as the number of species of the kinetic model is reduced from 110 species to 30 species. These results are consistent with the L2-norm errors reported in a recent paper by Esposito and Chelliah19 that employed a previously optimized C1 -C4 model.11 If PCAS reduction is performed based on sensitivities of ignition analysis only, then for species greater than 33 yields errors less than 1%. The traditional semi-log plot of ignition delay vs. inverse temperature show that predictions using such skeletal models are indistinguishable from the detailed model (not shown here for brevity). For a 30 species skeletal model, the error is estimated to be about 6%. More importantly, the errors associated with such skeletal models are generally well within the experimental uncertainties.21 8 Ignition Combined

7 6

4

||ε

ign

||

L2

5

3 2 1 0 30

35

40

45

# species

Figure 1. For a stoichiometric ethylene-air mixture at p =1 atm, the reduction error for ignition vs. the number of species in the skeletal model based ignition sensitivity analysis. Combined skeletal models are based on sensitivities of ignition, propagation, and extinction.

Also shown in Fig. 1 are the errors associated with PCAS based skeletal models with combined sensitivities of ignition, propagation, and extinction. These results indicate that even smaller errors are possible for skeletal models with species over 37, but a sudden increase in the error to about 6% is observed as the number of species is reduced to below 37. Figure 2a shows a similar plot for L2 norm-error on flame propagation velocity, defined as19 ||ϵprop ||L2

 ∫ =

ϕb ϕa

(

0 0 − SL,det SL,skel 0 SL,det

)2

1/2 dϕ

,

(6)

for ethylene-air mixtures of ϕ=0.5 to 1.5 with p=1 atm and T0 =300 K, as the number of species is reduced using the PCAS approach. For propagation, the results show that the departure from the detailed model is less than 4% for a 36 species skeletal model, which is less than the experimental uncertainty. The skeletal model based on the combined sensitivity analysis show a similar trend as the reduction solely based on

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propagation analysis. A comparison of the predicted burning velocity of ethylene-air mixtures obtained using the detailed model and a 37 species combined skeletal model is shown on Fig. 2a indicating excellent agreement over a wide range of equivalence ratios. 70

0.08 Propagation Combined

0.07

60

0.06

50 SL [cm/s]

0.04

40

0

||εprop||L2

0.05

0.03

30

0.02

20 0.01 0 30

Detailed Combined 35

40

45

10 0.5

1 φ

# species

(a)

1.5

(b)

Figure 2. For an ethylene-air mixture at p =1 atm and T0 = 300K, (a) the reduction error for propagation vs. the number of species in the skeletal model based on sensitivity of propagation and (b) a comparison of the predicted burning velocity as a function of equivalence ratio (ϕ) using the detailed model and a combined skeletal model having 37 species. Combined skeletal models are based on sensitivities of ignition, propagation, and extinction.

III.B.2.

Non-premixed Extinction Analysis

Previous studies on supersonic non-premixed reacting shear layers have shown that apart from the induction phenomenon, local extinction plays a critical role in the overall reaction progress and thus the combustion efficiency.23 Furthermore, reduced kinetic models derived solely from ignition or flame propagation fail to accurately predict the extinction limits, mainly because the premixed ignition and flame propagation data do not show any sensitivity to some of the fuel rich chemistry.19 For example, a recent global sensitivity study on non-premixed ethylene-air extinction limits have shown that the reaction C2 H3 +H=H2 CC+H2 is sensitive for extinction but has a very low sensitivity ranking in either ignition or flame propagation.24 Two key factors have contributed to excluding extinction from kinetic model optimizations, namely computational cost and lack of experimental data with well-defined uncertainties. We have addressed some of these shortcomings25 and have applied the PCAS methodology based on sensitivity of extinction strain rate to extract skeletal reaction models using the updated H2 /CO/C1 -C4 kinetic model. Figure 3a shows the corresponding error in predicting extinction limit, defined as19 ϵext =

aext,skel − aign,det , aext,det

(7)

as the number of species in the skeletal model is reduced to 30. As shown before,19 it is evident from Fig. 3a that the extinction limit is the most restrictive in terms of determining the size of the skeletal reaction model. A comparison of the peak flame temperature vs. local flow strain rate about the extinction point is shown in Fig. 3b indicates that the 37 species combined model departs from the detailed model by about 3%, again well within the uncertainty of recent experiments.25 III.B.3.

Partially-Stirred Reactor Analysis

The above flame propagation and extinction predictions were based on laminar flows controlled by molecular mixing. However, real supersonic combustors are known to operate under intense turbulent mixing conditions.23 For such reacting turbulent flows, the partially-stirred reactor (PaSR) configuration has been used in the past to better understand the coupling between chemical reactions and the mixing of species in a computationally efficient manner.26, 27 Here, we have considered such a case and applied the PCAS approach to extract skeletal reaction models based on PaSR simulations with assumed mixing time scales. The specific conditions considered in the present PaSR simulations consist of mixing an incoming stream of fresh stoichiometric mixture of ethylene-air at T0 =1200 K and p=1 atm with a pilot stream at equilibrium 5 of 9

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12

2050

Extinction Combined

Detailed Combined

10

2000

1950

max T [K]

|εext|

8

6

1900

4

1850

2

1800

0 30

35

40

45

1750 500

# species

(a)

1000 a [1/s]

1500

(b)

Figure 3. For an ethylene-air non-premixed flame at p =1 atm and T0 300K, (a) the percentage reduction error for extinction vs. the number of species in the skeletal model based on sensitivities of extinction and (b) a comparison of the predicted maximum flame temperature vs. flow strain rate using the detailed model and a combined skeletal model having 37 species. Combined skeletal models are based on sensitivities of ignition, propagation, and extinction.

state (i.e. equilibrium temperature of 2724 K). The ratio of the mass flow rates of the two streams is specified to be 90% to 10%. At t=0, the reactor is specified to be composed of the unreacted stoichiometric mixture of ethylene and air at 1200 K and 1 atm. The residence time is specified to be 100 µsec, with mixing time of 10 µsec and pairing time of 10 µsec with 100 simulated particles, similar to those assumed by Hiremath et al.28 The error estimate between the detailed model and the skeletal or reduced model, is defined as28 ϵP aSR =

r r [zdetailed (∆t) − zreduced (∆t)]rms , r r [zdetailed (∆t) − zdetailed (0)]rms

(8)

√ ∑N where z r is the specific moles of represented (or transported) species. Here, []rms is defined as ( N1 n=1 ||z (n) (t)||2 ). Figure 4a indicates that a skeletal model with about 22 species can predict the induction process of a PaSR reactor with less than 5% departure from the detailed model. Unfortunately, no experiments exist for this hypothetical flow configuration to specify a cap on the error limit. Figure 4a also shows that the 37 species combined skeletal model (based on sensitivities of ignition, propagation, and extinction, but excluding PaSR sensitivities) derived using the PCAS approach is capable of predicting the PaSR evolution with an error of about 1%. Skeletal models with less than 22 species show a dramatic increase in predicted error of PaSR simulations indicating the removal critical species from the mechanism. Alternatively, evaluating the concentration of species about this threshold via QSSA or RCCE provides a mechanism to maintain a low PaSR error as discussed in next section.

IV.

Reduced Reaction Models

In the above skeletal model reduction, the species not contributing to the overall reaction pathways were completely removed from the kinetic model. These reactions can be considered as either having negligible flux or being too slow (i.e. frozen) under all spatial and temporal conditions of interest. On the other hand, there are other reactions or group of reactions that are much faster than the physical or fluid dynamical time scales of the combustor which can be considered to be in partial equilibrium, but cannot be eliminated from the model. Such fast reactions are the source of stiffness in solving reacting flows. Methods of decoupling such fast reactions from fluid dynamical processes have been investigated over many decades, leading to further reduction of the size of the kinetic model as well as the stiffness. Such models are commonly identified as reduced reaction models. Here, we have considered two approaches of obtaining such reduced reaction models, namely (i) quasi steady-state approximation (QSSA) and (ii) rate-controlled constraint-equilibrium approximation (RCCE).

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PaSR skeletal combined

20

2400 2200 temperature (K)

reduction error (%)

25

15 10 5 0 20

2000 1800

detailed combined PaSR skeletal 35 species PaSR skeletal 24 species PaSR skeletal 20 species

1600 1400

25

30 35 # species

1200 0

40

1

2

3

time (s)

(a)

4 −4 x 10

(b)

Figure 4. For a PaSR simulation with two streams consisting of stoichiometric mixture of ethylene-air at T0 =1200K and a pilot stream at equilibrium conditions (a) the reduction error vs. the number of species based on sensitivities of PaSR and (b) a comparison of the predicted temperature of the PaSR as a function of time using the detailed model, several skeletal models, and combined skeletal model having 37 species. Combined skeletal model is based on sensitivities of ignition, propagation, and extinction.

IV.A.

Quasi Steady State Approximation

The concept of deriving simplified chemical kinetic models based on the quasi-steady-state approximation (QSSA) for selected intermediate chemical species dates back to the early 1900’s. While early investigations were motivated by the lack of chemical kinetic data, the recent efforts on mechanism reduction29, 30 were driven by the computational difficulty associated with the implementation of rather large detailed chemical kinetic models in CFD simulations. Systematic development of reduced reaction models require identification of species in steady state under a broad range of conditions and expression of the fastest reaction rate in each steady state relationship in terms of the slower reactions. The latter step leads to a reduction of the stiffness of the kinetic model. An automated method of analyzing ignition, flame propagation, and flame extinction results and the development of reduced reaction by applying QSSA concepts were recently demonstrated by Zambon and Chelliah.31 This approach was first applied to a detailed ethylene-air model proposed by Wang et al.8 generating a series of reduced reaction models ranging from 15 to 18 species (plus 4 if chemical element conservations were not imposed in the computations) with both explicit or implicit solutions of algebraic relationships. This approach was later extended to a recently optimized ethylene model11 yielding a 20 (plus 4) species reduced reaction model. Both sets of reduced models have successfully predicted the ignition, propagation, and extinction phenomena in good agreement with the base detailed model. However, as discussed in section II, the detailed models continue to evolve with availability of well defined experimental data. Furthermore, in the previous QSSA work,31 PaSR results were not included in the analysis. Thus, QSSA based reduced reaction models have performed somewhat poorly, yielding about 7% reduction-tabulation error in PaSR simulations,28 but computationally yielded much better performance in retrieving chemical source terms. Our near term objective is to apply the QSSA methodology to the newly optimized H2 /CO/C1 -C4 detailed kinetic model used here and include PaSR analysis in addition to the standard ignition, propagation, and extinction analysis. IV.B.

Rate-Controlled Constraint-Equilibrium with ISAT

The RCCE concept is somewhat similar to the QSSA except that the, instead of assuming the nontransported to be steady-state, they assumed to be in a constraint chemical equilibrium state, which is determined by using the potential element method. Although the approach was first proposed by Keck and Gillepsie in 1971,32 the lack of an efficient method of identifying the constraint relationships hindered the application of this methodology. However, recently a new efficient algorithm was developed using RCCE for minimization of the error of PaSR simulations as the number of represented species were reduced from the detailed model.33 This algorithm was further improved recently by Hiremath et al.28 who introduced a computationally efficient greedy algorithm with local improvement (GALI) that is used here. A comparison 7 of 9

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reduction-tabulation error (percentage)

of the error of PaSR simulations with the computationally efficient insitu adaptive tabulation (ISAT) as a function of the number of represented (or transported) species in the RCCE simulations is shown in Fig. 5. Note that in Fig. 5, zreduced in Eq. (8) is replaced with zreduced−tabulation . The results clearly show that by retaining the information of species associated with fast reactions via RCCE minimizes the reductiontabulation error to about 5% with 20 represented species in the model. More importantly, the tabulation error is shown to be less than 1% with a drastic reduction in computational cost.28 5.0 ISAT ISAT+SKELETAL ISAT+RCCE

4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5

18

20

22

24

26

28

30

32

34

# represented species

Figure 5. Reduction-tabulation error vs. the number of species using RCCE-GALI-ISAT algorithms, for a PaSR simulation with two streams consisting of stoichiometric mixture of ethylene-air at T0 =1200K and a pilot stream at equilibrium conditions. Also shown is the error of using 37 species skeletal model derived from PCAS approach and errors associated with ISAT implementations.

V.

Conclusions

A newly optimized H2 /CO/C1 -C4 detailed chemical kinetic model involving 110 species in 784 reactions was employed to derive skeletal and reduced reaction models for the accurate simulation of ethylene and other smaller fuel molecule oxidation relevant for hypersonic propulsion applications. The model reductions were accomplished by applying PCAS, QSSA, and RCCE methodologies. Without applying QSSA or RCCE methodologies, model reductions via PCAS show that to achieve an error less than 5%, the skeletal model requires retaining 37 species for extinction, 35 species for propagation, 33 species for ignition, and 23 species for the PaSR case considered. It was also shown that with the application of QSSA or RCCE, errors less than 5% can be achieved with models consisting of about 20 species. Such models, coupled with efficient ISAT algorithms can drastically reduce the computational cost associated with evaluation of chemical source terms in high-speed turbulent reacting flow simulations.

Acknowledgements This research was sponsored by the National Center for Hypersonic Combined Cycle Propulsion grant FA 9550-09-1-0611. The technical monitors on the grant are Chiping Li (AFOSR) and Aaron Auslender and Rick Gaffney (NASA). SPB has financial interest in Ithaca Combustion Enterprise, LLC, which has licensed the software ISAT-CK and CEQ used in this work.

References 1 W Tsang, JA Walker, and JA Manion. The decomposition of normal hexyl radicals. Proceedings of the Combustion Institute, 31(1):141 – 148, 2007. 2 W Tsang, WS McGivern, and JA Manion. Multichannel decomposition and isomerization of octyl radicals. Proceedings of the Combustion Institute, 32(1):131 – 138, 2009. 3 H Lander and AC Nixon. Endothermic fuels for hypersonic vehicles. J. of Aircraft, 8(4):200–207, 1971. 4 DR Sobel and LJ Spadaccini. Hydrocarbon fuel cooling technologies for advanced propulsion. ASME-95-GT-226, 1995. 5 I Glassman and R Yetter. Combustion, 4th Ed. Academic Press, 2008. 6 H Wang, E Dames, B Sirjean, DA Sheen, R Tangko, A Violi, JYW Lai, FN Egolfopoulos, DF Davidson, RK Hanson, CT Bowman, CK Law, W Tsang, NP Cernansky, DL Miller, and RP Lindstedt. A high-temperature chemical kinetic model ofnalkane (up ton-dodecane), cyclohexane, and methyl-, ethyl-,n-propyl andn-butyl-cyclohexane oxidation at high temperatures, jetsurf version 2.0, 2010. 7 DA Sheen and H Wang. Combustion kinetic modeling using multispecies time histories in shock-tube oxidation of heptane. Combustion and Flame, 158(4):645–656, 2011.

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8 H Wang, X You, AV Joshi, SG Davis, A Laskin, FN Egolfopoulos, and CK Law. Usc mech version ii. high-temperature combustion reaction model of h2/co/c1-c4 compounds., 2007. 9 SG Davis, AV Joshi, H Wang, and FN Egolfopoulos. An optimized kinetic model of h2/co combustion. Proceedings of the Combustion Institute, 30:1283–1292, 2005. 10 DA Sheen and H Wang. The method of uncertainty quantification and minimization using polynomial chaos expansions. Combustion and Flame, 158(12):2358–2374, 2011. 11 DA Sheen, X You, H Wang, and T Løv˚ as. Spectral uncertainty quantification, propagation and optimization of a detailed kinetic model for ethylene combustion. Proceedings of the Combustion Institute, 32(1):535–542, 2009. 12 R Tangko, DA Sheen, and H Wang. Combustion kinetic modeling using multispecies time-histories in shock-tube oxidation of n-dodecane, 2011. 13 M Frenklach, A Packard, P Seiler, and R Feeley. Collaborative data processing in developing predictive models of complex reaction systems. International Journal of Chemical Kinetics, 36(1):57–66, Jan 2004. 14 T Russi, A Packard, R Feeley, and M Frenklach. Sensitivity analysis of uncertainty in model prediction. Journal of Physical Chemistry A, 2008. 15 P Seiler, M Frenklach, A Packard, and R Feeley. Numerical approaches for collaborative data processing. Optimization and Engineering, 7(4):459–478, Dec 2006. 16 H Wang and M Frenklach. Detailed reduction of reaction mechanisms for flame modeling. Combustion and Flame, 1991. 17 W Sun, Z Chen, X Gou, and Y Ju. A path flux analysis method for the reduction of detailed chemical kinetic mechanisms. Combustion and Flame, 157(7):1298 – 1307, 2010. 18 S Vajda, P Valko, and T Turanyi. Principal component analysis of kinetic models. International Journal of Chemical Kinetics, 17(1):55–81, 1985. 19 G Esposito and HK Chelliah. Skeletal reaction models based on principal component analysis: Application to ethyleneair ignition, propagation, and extinction phenomena. Combustion and Flame, 158(3):477 – 489, 2011. 20 T Lu and CK Law. A directed relation graph method for mechanism reduction. Proceedings of the Combustion Institute, 30(1):1333–1341, 2005. 21 Z Hong, DF Davidson, and RK Hanson. An improved H2/O2 mechanism based on recent shock tube/laser absorption measurements. Combustion and Flame, 158(4):633–644, April 2011. 22 M Burke, M Chaos, Y Ju, FL Dryer, and S Klippenstein. Comprehensive H2/O2 Kinetic Model for High-Pressure Combustion. to appear in Combustion and Flame, June 2011. 23 JP Drummond and MH Carpenter. Mixing and mixing ehhancement in supersonic reacting flowfields. Progress in Astronautics and Aeronuatics - High-speed flight propulsion systems (SN Murthy and ET Curran, eds., 137:383–455, 1991. 24 G Esposito and HK Chelliah. A global sensitivity study of extinction limits of non-premixed ethylene/air flames. In preparation, 2011. 25 BG Sarnacki, G Esposito, R Krauss, and HK Chelliah. Extinction Limits and Associated Uncertainties of Non-Premixed Counterflow Flames of Methane, Ethylene, Propylene and n-Butane in Air. to appear in Combustion and Flame, 2011. 26 SM Correa. Turbulence-chemistry interactions in the intermediate regime of premixed combustion. Combustion and Flame, 93:41–60, 1993. 27 SB Pope. Computationally efficient implementation of combustion chemistry using in situ adaptive tabulation. Combustion Theory and Modelling, 1:41–63, 1997. 28 V Hiremath, Z Ren, and SB Pope. Combined dimension reduction and tabulation strategy using isat-rcce-gali for the efficient implementation of combustion chemistry. Combustion and Flame, 158(11):2113 – 2127, 2011. 29 M Smooke. Reduced kinetic mechanisms and asymptotic approximations for methane-air flames: a topical volume. Reduced Kinetic Mechanisms and Asymptotic Approximations for Methane-Air Flames, 1991. 30 N Peters and B Rogg. Reduced kinetic mechanisms for applications in combustion systems. Lecture Notes in Physics, 1993. 31 AC Zambon and HK Chelliah. Explicit reduced reaction models for ignition, flame propagation, and extinction of c2h4/ch4/h2 and air systems. Combustion and Flame, 150(1-2):71–91, 2007. 32 JC Keck and D Gillespie. Rate-controlled partial-equilibrium method for treating reacting gas mixtures. Combust. Flame, 17:237–241, 1971. 33 V Hiremath, Z Ren, and SB Pope. Combustion Theory and Modelling, 14(5):619–652, 2010.

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