Chemical Kinetics. Xiang Gao1 and Wenting Sun2. School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA 30332. The Global Pathway ...
Using Global Pathway Selection Method to Understand Chemical Kinetics Xiang Gao1 and Wenting Sun2 School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA 30332 The Global Pathway Selection (GPS) algorithm was previously proposed for kinetic mechanism reduction, and in this study it is extended to an analysis approach (GPSA) to understand chemical kinetics. Auto-ignitions associated with the second limit of hydrogen explosion and the negative temperature coefficient (NTC) regime of n-heptane are analyzed as demonstration. GPSA identifies the dominant Global Pathways as a representation of a given complex reacting system. The effects on radical production and consumption and the dominancy of a specific Global Pathway are quantified. Using these quantities, GPSA concludes that the pressure dependent reaction H + O2 +M = HO2 + M is responsible for the second limit of hydrogen explosion, which is consistent with classical theory. For NTC, GPSA suggests that NTC phenomenon is a result of increased dominancy of a radicalconsuming Global Pathway as the initial temperature increases. The two-stage auto-ignition process is analyzed using GPSA as well.
Nomenclature !",$→& '",(,$→& )*+ ,",$ -*+ -$→& .(,$ /( Ω(
= = = = = = = = =
element flux of the eth element from the ith to the jth species. number of the eth atoms transferred from the ith to the jth species in the rth elementary reaction dominancy of a Global Pathway number of the eth atoms in a molecule of the ith species net radical production rate associated with a Global Pathway net radical production rate associated with the conversion from the ith to the jth species the stoichiometric coefficient of the ith species in the rth reaction net reaction rate of the rth reaction net radical production rate of the rth reaction
1. Introduction Numerical simulation plays an increasingly important role in the study of combustion. However, realistic chemical kinetic mechanisms describing the combustion process typically involve hundreds of species and thousands of reactions. Due to their large sizes and complicated coupled relations, it remains a formidable task to extract insights from the reaction system. Systematic and rigorous analytic tools are necessary to obtain useful information from massive simulation datasets. The analysis of chemical kinetics may start from timescale decoupling. One prominent example is Computational Singular Perturbation (CSP) [1], developed in the mid 1980s. CSP decouples fast and slow subspaces (modes) based on Jacobian analysis. The involvement of species and reactions in the fast processes can be identified by the radical pointer and the participation index [2], respectively. The wide applications of CSP include mechanism reduction [3, 4], analysis of flow-chemistry interactions [5], and biochemical systems [6]. Intrinsic low-dimensional manifold (ILDM) [7] is another approach in this category. The identified manifolds represent attractors for the chemical kinetics, thus separating the fast processes, which relax towards the attractors, and the slow ones, which move within the manifolds [8]. This method is then extended to reaction–diffusion manifolds (REDIMs) to tackle the coupling of reaction and diffusion processes [9, 10]. A more recent kinetic analysis method is Chemical 1 2
Graduate Student, 270 Ferst Dr., Atlanta, GA, Student Member. Assistant Professor, 270 Ferst Dr., Atlanta, GA, Member. 1 American Institute of Aeronautics and Astronautics
Explosive Mode Analysis (CEMA) proposed by Lu et al. [11]. It quantifies the timescales related to chemical explosive modes (CEM) based on the eigenvalue analysis of the Jacobian matrix of the chemical source term. Methods to evaluate the contribution of each species or elementary reaction to CEM are provided [11-13]. Such diagnostic techniques provide insights to analyze complex flame dynamics, such turbulent lifted jet flames associated with auto-ignition [13-16]. Besides the methods based on eigenvalue analysis of Jacobian matrix, approaches representing the results with basic physical quantities are available as well. In an investigation of diffusion flame extinction, Won et al. [17] introduced the concept of radical index, which is normalized estimated OH radical formation rate, to quantify the impact of chemical kinetics, and a transport weighted enthalpy, to assess the mass transfer effect. For fuels with distinct chemical properties, a universal correlation between diffusion flame extinction strain rates and the product of radical index and transport-weighted enthalpy has been demonstrated in that work. Sensitivity analysis [18] is another method to analyze the reacting system. However, this method is brute force and very time-consuming, as the number of variables is significant. Furthermore, the coupling relations between variables may not be discovered. Recently, a Global Pathway Selection algorithm (GPS) [19] is proposed to identify important chemical pathways that converting initial reactants to final products, based on atomic flux analysis. Different from the classical Path Flux Analysis algorithm (PFA) [20-23], which considers one or two generations, GPS provides a way to consider the relation between species through all generations (reaction steps). GPS has been used for effective chemical kinetic mechanism reduction [19, 24]. In the present work, GPS method is used as an analytic tool to understand the effect of chemical pathways in ignition process.
2. Methodology 2.1 Global Pathway Selection (GPS) algorithm The detailed methodology of GPS can be found in Ref. [19]. The software of GPS can be downloaded at www.sun.gatech.edu. A brief description, however, is provided as followed. Firstly, the atomic fluxes between each species are calculated from simulation results. Such fluxes form an element flux graph for each considered element (usually carbon, hydrogen, and oxygen for general hydrocarbon system). For these graphs, the nodes are species, and edges are the fluxes between species. The species with significant total atomic flux passing through are identified as hub species. Then, chemical pathways from initial species to final products through these hub species are searched by searching the shortest paths on the element graph. These pathways are referred as Global Pathways. For example, for combustion of H2/air, if HO2 is identified as a hub species, one of its automatically identified global pathways could be: H2àHàHO2àH2O2àOHàH2O
(GP-H2-1)
Each arrow (à) in (GP-H2-1) represents a conversion step between two species. This conversion could involve multiple reactions. For example, the conversion H2àH may involve the reactions H2 + O = H + OH and H2 + OH = H + H2O. For combustion system, multiple global pathways are usually identified, and each global pathway involves several reactions. In previous work [19, 24], the global pathways are used to reduce detailed kinetic mechanisms. The skeletal mechanism can be obtained by removing species and reactions not important to any identified global pathways from the detailed kinetic mechanism. Demonstrations have been given in Ref. [19] and compared with existing mechanism reduction methods to illustrate the accuracy and efficiency of this method. This application shows that GPS is able to pick up important species and reactions from a complex chemical kinetic mechanism. This ability can be further extended as a tool for the analysis of chemical kinetic mechanisms. Global pathway presents the important species and the conversion relationship among them. This method groups the related species together and allows focusing on small number of analysis objects, rather than facing large number of species or reactions in a detailed chemical kinetic mechanism. 2.2 GPS-based analysis (GPSA) framework Based on GPS, a top-down approach to analyze complex reacting system is proposed as illustrated in Figure 1. This approach only focuses on the chemistry aspect. Firstly, for each spatial-temporal point, an element flux graph is 2 American Institute of Aeronautics and Astronautics
built for each considered element from the simulation results. Global Pathways are selected using GPS algorithm from these element flux graphs. These Global Pathways provide a simplified representation of the reacting system, yet reflecting the key chemical information of species conversion. For demonstration purpose, this study only considers auto-ignition process, where radical production is the controlling factor. The selected Global Pathways are then analyzed with respect to their effects on radical production to identify key reaction steps responsible for phenomena of interest. Complex reacting system GPS algorithm Global Pathways as a simplified representation of the complex reacting system
GPSA analysis Key reaction steps controlling phenomena of interest
Figure 1. Framework of GPS-based analysis (GPSA) for complex reacting system The radical analysis is based on the definition of the dominancy of a Global Pathway, )*+ , the net radical production rate associated with a Global Pathway, -*+ , and the net radical production rate associated with a conversion step -$→& . )*+," , is defined as the minimum element flux of the eth element going through a Global Pathway. It represents the rate controlling step of species conversion in a Global Pathway. )*+ = min$,&∈*+ !",$→& where !",$→& is the element flux of the eth element from the ith to the jth species. !",$→& =
(
max 0, '",(,$→& /(
where /( is the instantaneous net reaction rate (mole/s-cm3) of the rth reaction. '",(,$→& is the number of the eth atoms transferred from the ith to the jth species in the rth elementary reaction.
'",(,$→& =
.(,& ,",&
.(,$ ,",$ 9:;?
.(,9 ,",9
,
.(,& .(,$ < 0
0,
otherwise
where .(,$ is the stoichiometric coefficient of the ith species in the rth reaction (positive for products, negative for reactants) and ,",$ is the number of the eth atoms in a molecule of the ith species. The net radical production rate associated with a Global Pathway, -HI , is defined as the sum of net radical production rate of all reactions involved in this global pathway scaled by its dominancy )*+ -*+ =
)*+ ! 9 ",JKLMNO→9
Ω ( (∈*+
9 !",JKLMNO→9 is the total outgoing element flux of the source of this element graph. The source is the relevant initial reactants. For example, for combustion in air, fuel is the source for carbon graph and oxygen is source for the oxygen graph. Ω ( is the net radical production rate of the rth reaction
Ω ( = /(
Q9 R(,9 9
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Q9 equals 1 if the kth species is a prescribed radical, otherwise it is 0. Though special concern may be necessary to prescribe the radicals, for simplicity, in this work, O, H, and OH are chosen as the prescribed radicals. With -HI , it is clear that which Global Pathways are consuming or producing radicals at a given spatial-temporal point. To get more details, one can investigate each conversion step in a given Global Pathway. Similar to the definition of -HI , the net radical production rate associated with the conversion step from the ith species to the jth species, -$→& , is defined as the sum of net radical production rate of all reactions involved in this conversion step -$→& =
Ω ( (∈ $→&
3. Results and Discussion In the following sections, three combustion system will be investigated using the GPSA analysis methodology. These demonstrations are related to the explosion limit of hydrogen, the negative temperature coefficient (NTC) phenomena of n-heptane. 3.1 The explosion limit of hydrogen The first demonstration is to analyze auto-ignition of stoichiometric H2/air mixture in a constant pressure adiabatic reactor at different reactor pressures using GRI-Mech 3.0 [25]. The initial temperature is 1000K. As shown in Figure 2, the auto-ignition delay of this system is non-monotonically changing with the reactor pressure, consistent with the well-known second explosion limit of H2.
Figure 2. Auto-ignition delays of stoichiometric H2/air at different pressures with initial temperature 1000 K. Different Global Pathways can be identified from simulations at different conditions. This section focuses on the second limit, so the simulation results at 1 atm and 10 atm are further investigated. Considering hydrogen element flux graphs, the most dominant Global Pathway identified at 10 atm is GP-H2-1, and the one at 1 atm is GP-H2-2. The change of dominant Global Pathways is also illustrated by )*+ in Figure 3. H2àHàHO2àH2O2àOHàH2O H2àHàOHàH2O
(GP-H2-1) (GP-H2-2)
-*+ of these Global Pathways are also presented in Figure 3. At 1 atm, as shown in Figure 3(a), at most of the time, both Global Pathways are producing radicals (indicated by positive -*+ ). However, when pressure is increased to 10 atm as shown in Figure 3(b), GP-H2-1 becomes to be the dominant Global Pathway and consumes radicals. The radical destruction processes emerging as pressure increases from 1 atm to 10 atm, is consistent with the increase of ignition delay during the same pressure change as shown in Figure 2.
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(a) 1 atm
(b) 10 atm
Figure 3. Hydrogen Global Pathways for ignition at different pressures -$→& for GP-H2-1 and GP-H2-2 during auto-ignition at 10 atm is investigated to extract more details. The slice at temperature rise of 200 K are illustrated in Figure 4. The major reactions contributing to -$→& are listed in in Figure 4 as well. The comparison between -$→& of these two Global Pathways implies that the conversion H à HO2 is related to radical destruction, indicated by the negative -$→& shown in Figure 4(a). This is due to the reaction H+O2+M=HO2+M. This observation agrees with the classical understanding of the second explosion limit [26]. That is, the system changes from explosive to nonexplosive because of the increased radical destruction with the formation of HO2 at elevated pressure conditions. This is through the pressure dependent reaction H+O2+M=HO2+M, which consumes radical H.
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(a) GP-H2-1
(b) GP-H2-2
Figure 4. Conversion steps for different hydrogen Global Pathways The above discussion provides a demonstration of GPSA with a relatively simple reacting system. In next sections, GPSA will be applied on more complex systems. 3.2 The negative temperature coefficient (NTC) regime of n-heptane The NTC regime generally refers to the decrease of reactivity of fuel/air mixture with the increase of temperature within certain temperature range. An example of this phenomenon is the relation between auto-ignition delay and initial temperature, as shown in Figure 5. The simulation is conducted at 1 atm for stoichiometric n-heptane/air mixture using LLNL reduced n-heptane mechanism [27]. As initial temperature increases from 650 to 850K, the ignition delay increases, indicating decreased reactivity of the reactants. Within this NTC regime, two-stage autoignition is observed, as shown by the case of initial temperature 650K and 700K in Figure 6. If the initial temperature is further increased, only one stage ignition is observed, as shown by the case of initial temperature 1000K in Figure 6.
Figure 5. Auto-ignition delays of n-heptane/air at different initial temperature
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Figure 6. Auto-ignition process of n-heptane/air at different initial temperature To analyze NTC with GPSA, the dominant Global Pathways are investigated. Considering carbon element flux graphs, the most dominant one in the first stage ignition is GP-hep-1, and the dominant one at 1000K is GP-hep-2. nC7H16 à C7H15 à C7H15O2 à C7H14OOH à C7H14OOHO2 à nC7ket à CH3COCH2 à CH2CO à HCCO à CO2 nC7H16 à C7H15 à pC4H9 à C2H5 à C2H5O à CH3CHO à CH3CO à CH3 à CH3O à CH2O à HOCH2O à HOCHO à CO2
(GP-hep-1) (GP-hep-2)
The conversion step HCCO à CO2 in GP-hep-1 is via the reaction HCCO + O2 = CO2 + HCO and the conversion step HOCHO à CO2 in GP-hep-2 is via the reaction HOCHO + H = CO2 + H +H2. . These two Global Pathways have different temperature sensitivity. The shared conversion step nC7H16 à C7H15 is via the positively temperature dependent reactions nC7H16 + OH = C7H15 + H2O and nC7H16 + OH = C7H15 + H2O. However, the next conversion step for GP-hep-1, C7H15 à C7H15O2, is via the reaction C7H15 + O2 = C7H15O2, which is assumed to be not sensitive to temperature change by the present kinetic mechanism [27]. Activation energy in Arrhenius expression for this reaction is assumed to be zero. In contrast, the competing reaction C7H15 = pC4H9 + C3H6 is positively dependent on temperature. This implies that GP-hep-1 favors lower temperature to win the competition with GP-hep-2. This argument is consistent with the competition of these two reaction pathways in controlling auto-ignition phenomenon shown in Figure 9. GP-hep-1 is negligible at high initial temperature (e.g. initial temperature 1000K in Figure 9(a)) and only dominates the low temperature region. As temperature increases, GP-hep-2 becomes more dominant. The effects on radical production of these Global Pathways are also different. -$→& and the major reactions contributing to the radical production are illustrated in Figure 7 for a sampling point during the temperature jump of first stage ignition at initial temperature of 650K. The temperature at this moment is 800K. Two Global Pathways share the same major radical-consuming step, which is the H abstraction of fuel, nC7H16 à C7H15. This suggests that the overall reaction rate is controlled by the radical supply to this step. Two Global Pathways differ on the radical production. The reactions producing radicals for GP-hep-1 are associated with large molecules such as the conversion from C7H14OOHO2 to nC7ket and to nC7ket. However, each nC7H16 molecule can only be converted to one molecule of C7H14OOHO2 or nC7ket, which limits the production of radicals. In contrast, most reactions producing radicals for GP-hep-2 are associated with small molecules such as C2H5 and CH3. Every nC7H16 molecule can convert to multiple such smaller molecules. Therefore, GP-hep-2 produces radical more effectively and overall is chain-branching.
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(a) GP-hep-1
(b) GP-hep-2
Figure 7. Conversion steps for different n-heptane Global Pathways With the above knowledge about the temperature sensitivity and radical production of these Global Pathways, NTC can be better analyzed using GPSA. -*+ for both Global Pathways during the first stage ignition is illustrated in Figure 8 for initial temperature 650K. More complete auto-ignition process is shown in Figure 9 for initial temperature 650, 750, and 1000K. Figure 8 indicates that GP-hep-1 is the dominant Global Pathway during the first stage ignition. GP-hep-2 is negligible. As GP-hep-1 is not chain-branching as discussed above, this Global Pathway is consuming radicals, indicated by the negative -*+ shown in Figure 8. This implies that, the radical consumption due to GP-hep-1 is the reason of the termination of the first stage ignition. This termination effect favors higher initial temperature as the major radical consumption step, nC7H16 à C7H15, is positively temperature dependent as noted above. In contrast, the radical production steps of GP-hep-1 are less sensitive to temperature. This is because they are limited by the conversion step C7H15 à C7H15O2, which is not sensitive to temperature as noted above. Therefore, as initial temperature increases, the consumption of radical is promoted and the first stage ignition become less self-sustained so it is terminated earlier. This explains the observation in Figure 6 that, as initial temperature increases from 650 to 750K, less fuel is consumed during the first stage ignition, and lower temperature is reached. To sum up, GP-hep-1 consumes radical and controls the termination of the first stage ignition. This termination effect is promoted by higher initial temperature within the NTC regime.
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Figure 8. n-heptane Global Pathways for the first stage ignition at 650K
(a) 650 K
(a) 750 K
(b) 1000 K
Figure 9. n-heptane Global Pathways for ignition at different initial temperatures The second stage ignition involves the competition between GP-hep-1 and GP-hep-2. As shown in Figure 9, GPhep-1 is dominant at the beginning but GP-hep-2 starts to dominate as temperature increases. This is expected as GP-hep-1 favors low temperature in the competition with GP-hep-2 as noted above. As initial temperature increases from 650 to 750K, both the final temperature and temperature rise at the end of first stage ignition decreased. As a result of this lower temperature during the induction period of the second stage ignition, GP-hep-1 become more dominant during this period comparing to the case at 650K. As GP-hep-1 is consuming radicals, while GP-hep-2 is producing radicals, this increased dominancy of GP-hep-1 reduces the reactivity of mixture, indicated by the 9 American Institute of Aeronautics and Astronautics
increased ignition delay from 0.12s to 0.22s as temperature increases from 650K to 750K. To sum up, the second stage is controlled by the competition between GP-hep-1 and GP-hep-2. Higher initial temperature terminates the first stage ignition earlier as noted above, resulting lower temperature for the second stage ignition. This helps GPhep-1 to be more dominate and reduces the reactivity of the reactants. This reduced reactivity due to higher initial temperature is the NTC phenomena. As initial temperature further increases, GP-hep-2 becomes more dominant even at the early period. When GPhep-1 becomes negligible comparing to GP-hep-2, the auto-ignition process is not terminated by GP-hep-1, and therefore there is no two-stage auto-ignition. One example is the case of initial temperature 1000K shown in Figure 9. The auto-ignition is one-stage and GP-hep-2 is negligible.
4. Conclusion The GPS-based analysis (GPSA) approach provides a systematical tool to analyze complex reacting system. The system is simplified as a limited number of Global Pathways. The analysis is conducted by investigating the effects on radical production and consumptions, and the dominancy of these Global Pathways. The number of variables to be investigated is significantly reduced. This feature becomes advantageous when reacting system involve mechanisms of large size of complex chemistry kinetics. For the second hydrogen explosion limit, GPSA concludes that this is caused by a radical-consuming Global Pathway (GP-H2-1) which becomes dominant as pressure increases, due to the pressure dependent reaction H+O2+M=HO2+M. This is consistent with the classical explanation. For the negative temperature coefficient (NTC) phenomena, GPSA suggests that this is caused by the increased dominancy of a radical-consuming Global Pathway (GP-hep-1). It terminates the first stage ignition and forms two-stage ignition process. This termination effect is decreased as initial temperature increases, which results in an increased dominancy of this Global Pathway during the second stage ignition. This reduces the reactivity of the reactants and the increased auto-ignition delay as a result of increased initial temperature is the NTC phenomena.
Reference: [1] Lam, S., and Goussis, D., "Understanding complex chemical kinetics with computational singular perturbation," Symposium (International) on Combustion. Vol. 22, Elsevier, 1989, pp. 931-941. [2] Lam, S., and Goussis, D., "The CSP method for simplifying kinetics," International Journal of Chemical Kinetics Vol. 26, No. 4, 1994, pp. 461-486. [3] Lu, T., Ju, Y., and Law, C. K., "Complex CSP for chemistry reduction and analysis," Combustion and Flame Vol. 126, No. 1, 2001, pp. 1445-1455. [4] Valorani, M., Creta, F., Goussis, D. A., Lee, J. C., and Najm, H. N., "An automatic procedure for the simplification of chemical kinetic mechanisms based on CSP," Combustion and Flame Vol. 146, No. 1, 2006, pp. 29-51. [5] Valorani, M., Najm, H. N., and Goussis, D. A., "CSP analysis of a transient flame-vortex interaction: time scales and manifolds," Combustion and Flame Vol. 134, No. 1, 2003, pp. 35-53. [6] Goussis, D. A., and Najm, H. N., "Model reduction and physical understanding of slowly oscillating processes: the circadian cycle," Multiscale Modeling & Simulation Vol. 5, No. 4, 2006, pp. 1297-1332. [7] Maas, U., and Pope, S. B., "Simplifying chemical kinetics: intrinsic low-dimensional manifolds in composition space," Combustion and flame Vol. 88, No. 3, 1992, pp. 239-264. [8] Maas, U., "Efficient calculation of intrinsic low-dimensional manifolds for the simplification of chemical kinetics," Computing and Visualization in Science Vol. 1, No. 2, 1998, pp. 69-81. [9] Bykov, V., and Maas, U., "The extension of the ILDM concept to reaction–diffusion manifolds," Combustion Theory and Modelling Vol. 11, No. 6, 2007, pp. 839-862. [10] Bykov, V., and Maas, U., "Problem adapted reduced models based on Reaction–Diffusion Manifolds (REDIMs)," Proceedings of the Combustion Institute Vol. 32, No. 1, 2009, pp. 561-568.
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[11] Lu, T., Yoo, C. S., Chen, J., and Law, C. K., "Three-dimensional direct numerical simulation of a turbulent lifted hydrogen jet flame in heated coflow: a chemical explosive mode analysis," Journal of Fluid Mechanics Vol. 652, 2010, pp. 45-64. [12] Luo, Z., Yoo, C. S., Richardson, E. S., Chen, J. H., Law, C. K., and Lu, T., "Chemical explosive mode analysis for a turbulent lifted ethylene jet flame in highly-heated coflow," Combustion and Flame Vol. 159, No. 1, 2012, pp. 265-274. [13] Shan, R., Yoo, C. S., Chen, J. H., and Lu, T., "Computational diagnostics for n-heptane flames with chemical explosive mode analysis," Combustion and Flame Vol. 159, No. 10, 2012, pp. 3119-3127. [14] Yang, S., Wang, X., Yang, V., Sun, W., and Huo, H., "Comparison of Flamelet/Progress-Variable and Finite-Rate Chemistry LES Models in a Preconditioning Scheme," 55th AIAA Aerospace Sciences Meeting, Gaylord Texan, Grapevine, Texas, 2017. [15] Gao, X., Zhai, J., Sun, W., Ombrello, T., and Carter, C., "The Effect of Ozone Addition on Autoignition and Flame Stabilization," 54th AIAA Aerospace Sciences Meeting. 2016, p. 0960. [16] Gao, X., Sun, W., Ombrello, T., and Carter, C., "The Effect of Ozonolysis Activated Autoignition on Jet Flame Dynamics," 55th AIAA Aerospace Sciences Meeting. Gaylord Texan, Grapevine, Texas, 2017, p. 0960. [17] Won, S. H., Dooley, S., Dryer, F. L., and Ju, Y., "A radical index for the determination of the chemical kinetic contribution to diffusion flame extinction of large hydrocarbon fuels," Combustion and Flame Vol. 159, No. 2, 2012, pp. 541-551. [18] Turányi, T., "Sensitivity analysis of complex kinetic systems. Tools and applications," Journal of Mathematical Chemistry Vol. 5, No. 3, 1990, pp. 203-248. [19] Gao, X., Yang, S., and Sun, W., "A global pathway selection algorithm for the reduction of detailed chemical kinetic mechanisms," Combustion and Flame Vol. 167, 2016, pp. 238-247. [20] Sun, W., Chen, Z., Gou, X., and Ju, Y., "A path flux analysis method for the reduction of detailed chemical kinetic mechanisms," Combustion and Flame Vol. 157, No. 7, 2010, pp. 1298-1307. [21] Yang, S., Yang, V., Sun, W., Nagaraja, S., Sun, W., Ju, Y., and Gou, X., "Parallel On-the-fly Adaptive Kinetics for Nonequilibrium Plasma Discharges of C2H4/O2/Ar Mixture," 54th AIAA Aerospace Sciences Meeting, San Diego, California, 2016, AIAA 2016-0195. [22] Yang, S., Ranjan, R., Yang, V., Menon, S., and Sun, W., "Parallel On-the-fly Adaptive Kinetics in Direct Numerical Simulation of Turbulent Premixed Flame," Proceedings of the Combustion Institute, 2016. doi:10.1016/j.proci.2016.07.021 [23] Yang, S., Ranjan, R., Yang, V., Sun, W., and Menon, S., "Extinction and re-ignition predictions of a time-evolving turbulent non-premixed flame: sensitivity to chemical kinetics models," Combustion and Flame (submitted), 2016. [24] Coogan, S., Gao, X., McClung, A., and Sun, W., "Evaluation of Kinetic Mechanisms for Direct Fired Supercritical OxyCombustion of Natural Gas," ASME Turbo Expo 2016: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2016, pp. V04AT04A037-V04AT04A037. [25] Smith, G. P., Golden, D. M., Frenklach, M., Moriarty, N. W., Eiteneer, B., Goldenberg, M., Bowman, C. T., Hanson, R. K., Song, S., and Gardiner Jr, W. C., "GRI-Mech 3.0," URL: http://www/. me. berkeley. edu/gri_mech Vol. 51, 1999, p. 55. [26] Law, C. K. Combustion physics: Cambridge university press, 2010. [27] Seiser, R., Pitsch, H., Seshadri, K., Pitz, W., and Gurran, H., "Extinction and autoignition of n-heptane in counterflow configuration," Proceedings of the Combustion Institute Vol. 28, No. 2, 2000, pp. 2029-2037.
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