The Ignition of C 7 -C 16 Normal and Branched Alkanes at Elevated Pressures

Transcription

1 The Ignition of C 7 -C 16 Normal and Branched Alkanes at Elevated Pressures Matthew A. Oehlschlaeger*, Hsi-Ping S. Shen, Justin Steinberg, and Jeremy Vanderover Department of Mechanical, Aerospace, and Nuclear Engineering Rensselaer Polytechnic Institute Troy, NY Abstract The ignition of several large normal and branched alkanes (C 7 -C 16 ) has been investigated in a heated shock tube at elevated pressures relevant to practical combustion devices. Measurements have been made for n-heptane, n-decane, n- dodecane, n-tetradecane, iso-octane (2,2,4-trimethylpentane), and iso-cetane (2,2,4,4,6,8,8-heptamethylnonane) for Φ = 0.25, 0.5, and 1.0 alkane/air mixtures for pressures from 7 to 60 atm and temperatures from 780 to 1400 K. The measurements are compared to previous data, where available, and to kinetic modeling predictions. The combination of the current data, previous shock tube and rapid compression machine measurements, and kinetic modeling indicate that the differences in reactivity for C 7 and larger normal alkanes is slight, indiscernible within the experimental uncertainties, for mixtures with common carbon content. The data also show that iso-cetane is slightly more reactive than iso-octane under the high- to moderate-temperature conditions ( K) of the measurements made for those compounds. Introduction Commercial liquid transportation fuels (gasoline, jet fuel, and diesel) are comprised of hundreds to thousands of individual hydrocarbon compounds, including high concentrations of larger alkanes. The larger normal alkanes found in transportation fuels are well known to readily ignite at engine conditions, relative to other classes of hydrocarbons (e.g., branched alkanes, cycloalkanes, and aromatics), and thus have low research octane numbers (RONs) and high cetane numbers (CN). On the other hand, larger branched alkanes are more difficult to ignite and have high RONs and low CNs. The reference fuels for RON rating are 2,2,4-trimethylpentane (iso-octane, RON = 100) and n-heptane (RON = 0) and the reference fuels for CN rating are n-hexadecane (ncetane, CN = 100) and 2,2,4,4,6,8,8-heptamethylnonane (iso-cetane, CN = 15); 1-methylnaphthalene (CN = 0) is also a CN reference fuel. N-alkanes are more reactive relative to iso-alkanes at engine conditions primarily due to the more rapid lowtemperature peroxy chemistry that n-alkanes undergo which results in the distinct negative temperature coefficient (NTC) behavior displayed by these fuels [1-2]. Due to the chemical complexity of commercial transportation fuels, efforts have been and are currently being made to develop surrogate mixtures containing a limited number of representative hydrocarbon compounds to mimic the physical and chemical properties of the complete distillate fuels. The common n-alkane representative in gasoline surrogates is n-heptane [3], n- decane and n-dodecane are often chosen as the n-alkane representatives in surrogate jet fuels [4], and candidate n- * Corresponding author: oehlsm@rpi.edu Associated web site: Proceedings of the 6 th U.S. National Combustion Meeting alkane representatives for diesel include n-tetradecane and n-hexadecane (n-cetane) [5]. Iso-octane is an oft-chosen iso-alkane representative in gasoline surrogate [3], while both iso-octane and iso-cetane are candidates for jet fuel surrogates [4], and iso-cetane is appropriate for diesel surrogates [5]. Due to the importance of both branched and normal alkanes, there have been substantial previous efforts aimed at experimental characterization and kinetic modeling of alkane oxidation and ignition kinetics. However, many of the previous efforts have been dedicated to C 10 or smaller compounds and many have been performed at pressures near 1 atm. Previous measurements of ignition delay times for larger alkanes (C 7 and larger) at elevated pressures, characteristic of those found in practical combustion devices (e.g., gas turbine combustors and diesel and spark ignition engines), have been performed in shock tubes [6-25] and rapid compression machines [26-37]. Additionally, there have been many kinetic modeling studies dedicated to alkanes (examples include [20,38-53]); in particular there has been significant kinetic modeling focus on n-heptane and iso-octane, although mechanisms have been developed for alkanes as large as n-hexadecane by several authors [44,47,52-53]. Here recent ignition time measurements for n-heptane, n-decane, n-dodecane, n-tetradecane, iso-octane (2,2,4- trimethylpentane), and iso-cetane (2,2,4,4,6,8,8- heptamethylnonane) are summarized. These experiments expand the database of kinetic targets available for alkane kinetic mechanism development and provide insight into the relative reactivity of alkanes at moderate to high temperatures and elevated pressures important in internal combustion automotive and aero-propulsion engines.

2 Experimental Ignition times for alkane/air mixtures were measured in the externally heated high-pressure shock tube (constant inner diameter of 5.7 cm, driven section length of 4.11 m, and driver section length of 2.59 m) at Rensselaer Polytechnic Institute that has been previously described [54]. Measurements were made for n-heptane, n-decane, n-dodecane, n-tetradecane, iso-octane (2,2,4- trimethylpentane), and iso-cetane (2,2,4,4,6,8,8- heptamethylnonane) for Φ = 0.25, 0.5, and 1.0 and for pressures from 7 to 60 atm and temperatures from 780 to 1400 K. For a particular set of experiments, the heated shock tube and mixing manifold and vessel temperature was chosen to provide sufficient vapor pressure of the alkane of interest for mixture preparation and to prevent condensation on the shock tube walls. Experiments were performed at a range of shock tube temperatures, from room temperature, for n-heptane and iso-octane, to 160 ºC, for the highest pressure n-tetradecane experiments. The shock tube temperature uniformity was routinely monitored, with non-uniformity within ±2 ºC for all but the highest temperatures. For n-tetradecane experiments performed at a shock tube temperature of 160 ºC the measured temperature non-uniformity was ±4 ºC. The shock tube temperature uniformity was maintained by zone heater/controller system [54]. Fuel/air mixtures were allowed to mix for durations from 15 minutes to 3 hours and at different temperatures to determine if mixing time and heating temperature influenced measured ignition time; no discernable influence was found. Additionally, shock tube experiments were performed for different shock tube temperatures, for like mixtures and reflected shock conditions, with no discernable influence on measured ignition time observed. Ignition times were determined in the reflected shock region using electronically excited OH emission viewed through the shock tube endwall and pressure measurements made using a piezoelectric transducer located in the sidewall at a location 2 cm from the endwall. Example ignition time measurements are shown in Figure 2. Reflected shock conditions were determined using the normal shock relations and measured incident shock velocity. The uncertainty in the reflected shock temperatures and pressure are estimated at 1.5% and 2.0% respectively. Results The ignition time results for Φ = 1.0 are displayed on Arrhenius axes in Figs. 2 and 3 with comparison to previous shock tube and rapid compression machine (RCM) studies performed at elevated pressures, where available, and kinetic modeling predictions from the Lawrence Livermore National Laboratory (LLNL) suite Fig. 1. Example ignition time measurement: Φ = 0.5 isocetane/air. of kinetic mechanisms [41,45,53,55] for both branched (Fig. 2) and normal alkanes (Fig. 3). The estimated uncertainty in the measured ignition times varies from ±15-25%, depending on the fuel, with contributions to uncertainty from: 1) the uncertainty in determination of ignition time based on the ignition time definition and measured pressure and OH emission, 2) uncertainties in the initial reflected shock conditions (mixture composition, temperature, and pressure), and 3) estimated uncertainty due to changes in temperature and pressure due to non-ideal gasdynamic effects. In Figs. 2 and 3 and in subsequent figures ignition times are scaled to the common pressures listed in the figure legends using power-law pressure dependence (τ P n ), determined from regression analysis of experiments performed at a range of pressures (see figure captions for power-law factors), to account for the deviations in reflected shock pressure which result primarily from inconsistent diaphragm rupture that is exacerbated when the shock tube is heated. Literature data was also scaled for variations in experimental pressure using the same powerlaw pressure dependencies. The measured branched alkane ignition times (Fig. 2) show little reduction in overall activation energy (rollover) at the lowest temperatures of the shock tube experiments ( K for these two compounds), indicating that the negative-temperature-coefficient (NTC) behavior is weak at temperatures below 1000 K for these highly branched compounds. The low levels of NTC behavior is also predicted by kinetic modeling performed using the Lawrence Livermore National Laboratory (LLNL) suite of mechanisms [41,45,53,55]. This low level of NTC is due to the slow rate of RO 2 isomerization that occurs in highly branched compounds, due to the lack of secondary and tertiary bonded H atoms available for H-atom transfer in the RO 2 QOOH isomerization. On the other hand, the n-alkane shock tube ignition data exhibits significantly stronger NTC behavior, at the moderate temperatures encountered here and in the lower temperature RCM experiments. 2

3 Fig. 2. Measured iso-octane and iso-cetane/air ignition delay times with comparisons to previous shock tube studies (isooctane) and LLNL kinetic modeling [45,55] (iso-octane and iso-cetane). Iso-octane data scaled to the listed pressures using τ P and iso-cetane data scaled to the listed pressures using τ P to account for deviations in experimental pressure. Fig. 3. Ignition time measurements for Φ = 1.0 n-alkane/air mixtures with comparison to previous shock tube and rapid compression machine studies. All data scaled to the listed pressures using τ P -1 to account for deviations in experimental pressure. The current data for alkane/air mixtures is in good agreement with previous shock tube studies where there is intersection in conditions studied. For iso-octane/air mixtures the data is in good agreement with the previous shock tube studies of Fieweger et al. and Davidson et al., for almost all conditions, indicating that the ignition times for iso-octane/air mixtures at elevated pressures and moderate to high temperatures are well characterized. To our knowledge, the iso-cetane ignition data presented here is the first ignition data for this cetane number reference compound. The comparison of the current n-alkane ignition time measurements with previous shock tube and rapid compression machine (RCM) studies performed at elevated pressures (Fig. 3) shows fairly good agreement in the cases where the measurements are at similar 3

4 pressures. The n-heptane data is in fair agreement with the previous shock tube studies of Ciezki and Adomeit [9] and Gauthier et al. [16] and the RCM data of Silke et al. [34]. The current Φ = 1.0 n-decane data at 40 atm cannot be directly compared to the 50 atm data of Pfahl et al. [10] and the 80 atm data of Zhukov et al. [21] due of the strong dependence of ignition time on pressure in the NTC regime. However, the correlation developed by Olchanski and Burcat [20] to describe their hightemperature n-decane ignition time measurements ( K and 2-10 atm) is in very good agreement with the current data at high-temperature conditions. Finally, there is apparent agreement between the current n-dodecane data with the 20 atm measurements of Vasu et al. [25]. The n-tetradecane measurements are, to our knowledge, the first for any n-alkane larger than C 12. Comparison of alkane reactivity For the purposes of discussing the relative reactivity of the alkane compounds studied, for selected conditions the current ignition time measurements for iso-octane and iso-cetane are compared in Fig. 4, the current ignition time measurements for n-heptane, n-decane, n-dodecane, and n-tetradecane are compared to each other and previous shock tube and RCM studies and kinetic modeling in Fig. 5, and ignition time measurements and modeling for both branched and normal alkanes are compared in Fig. 7. These comparisons allow an assessment of the influence of branching and chain length on reactivity at the elevated pressure conditions studied. It should be pointed out that the mixtures studied all have approximately common carbon content regardless of the size of the alkane. For example, a Φ =1.0 n-heptane/air mixture contains 1.874% molar n-heptane (nc 7 H 16 ) while a Φ = 1.0 iso-cetane/air mixture contains % molar iso-cetane (ic 16 H 34 ). While the n-heptane mixture contains more than twice the fuel molecules contained in the iso-cetane mixture, the two mixtures differ in carbon atom content by only 3.6%. Thus, differences in reactivity are related primarily to differences in oxidation chemistry and not mixture exothermicity. As illustrated in Fig. 4, the experiments and kinetic modeling results from the LLNL mechanisms [45,55] show that the ignition delay times for iso-octane are % longer than those for iso-cetane in the temperature range of the measurements ( K for conditions displayed). At lower temperatures in the NTC regime the LLNL predicted difference is larger, with iso-octane ignition times up to a factor of three longer than those for iso-cetane. At the moderate temperatures for which experimental data were obtained, the difference in reactivity between iso-cetane and iso-octane can be attributed the smaller fraction of primary H atoms contained in iso-cetane (27 of 34 primary H atoms) relative to iso-octane (15 of 18 primary H atoms), which allows faster H-atom abstraction. Additionally, the alkyl Fig. 4. Comparison of Φ = 1.0 iso-octane/air and isocetane/air ignition times: experiments (scaled to 40 atm to account for deviations in pressure) and kinetic modeling based on LLNL mechanisms [45,55]. radicals formed by H-atom abstraction from iso-cetane (C 16 H 33 ) form a larger fraction of H atoms during their fragmentation relative to those alkyl radicals formed by H-atom abstraction from iso-octane (C 8 H 17 ). The H atoms formed in this fragmentation process provide chain branching through H + O 2 OH + O increasing the population of the reactive radical pool. It should be noted that the difference in iso-octane and iso-cetane reactivity is relatively small at the high to moderate temperatures studied here. The deviation in the simulated ignition times for isooctane and iso-cetane at temperatures below that studied here, exhibited in Fig. 4, is due to the faster rate of alkylperoxy isomerization (RO 2 QOOH), which controls radical production in the low-temperature oxidation sequence (R + O 2 RO 2 QOOH (+O 2 ) OOQOOH 2OH + products); see Fig. 6 for schematic of these reaction paths consistent with that presented by several kinetic modeling groups [47,52-53]. Alkylperoxy isomerization is faster in the iso-cetane peroxy reaction sequence than that for iso-octane due to the three CH 2 groups appropriately spaced in iso-cetane for sixmembered transition states for RO 2 isomerization between CH 2 groups [41]. The comparisons made for n-alkanes (Fig. 5) show that nearly all of the ignition time measurements made at Φ = 1.0 and near 12 atm fall within bands representing ±40% in measured ignition time. The lone set of data that falls outside of this band is the n-heptane data of Ciezki and Adomeit [9]. There is, perhaps, a slight decrease in reactivity with increasing chain length in Figure 6. However, the decrease is very slight and this observation is influenced by the ignition time data for n-heptane reported by Ciezki and Adomeit [9], which is longer than both the current and Gauthier et al. [16] n-heptane data when scaled using τ P -1. The coupled uncertainty resulting from the comparison of ignition time measurements made in different facilities using different 4

5 techniques and the uncertainties resulting from applying τ P -1 scaling at all temperatures, which is a gross simplification for the large temperature range represented in Fig. 5, certainly is near or greater than ±40% in ignition time. Additionally, the kinetic modeling predictions for n- heptane and n-tetradecane of Curran et al. [41] and Westbrook et al. [53] (LLNL), are in fairly good accord with the measured ignition times and show negligible difference in reactivity at both high and low temperatures with increasing chain length. The maximum predicted difference in ignition time between n-heptane and n- tetradecane by the LLNL mechanisms is 30% in the NTC region. Hence, both experiment and kinetic modeling indicate that the differences in reactivity for these larger n-alkanes are very slight for mixtures of common carbon content. The similarity in reactivity for these compounds for a broad range of temperatures can be understood through the schematic of the major alkane reaction paths displayed in Fig. 6. At temperatures below 1400 K the n-alkanes are primarily consumed via H-atom abstraction by small radicals (O, H, OH, HO 2, CH 3, and others) to produce alkyl radicals; at T > 1400 K n-alkane thermal decomposition competes. At higher temperatures (T > K) these alkyl radicals primarily decompose, which can be proceeded by isomerization (H-atom transfer), to produce olefins, most of which are ethylene and propene [56-57] for all n-alkanes regardless of chain length. Therefore, at higher temperatures the intermediate olefin pool for all n-alkanes is similar, provided that the mixtures are of common carbon content, and therefore the measured and modeled ignition times are very similar. At lower temperatures (T < K) the alkyl radicals add directly to O 2 to form alkylperoxy radicals Fig. 5. Comparison of n-alkane/air ignition measurements and kinetic modeling near 12 atm. The solid lines represent a ±40% band in ignition time, which most of the data falls within. O 2 RH R RO 2 QOOH O 2 OOQOOH olefin + R olefin + HO 2 ketohydroperoxide + OH OH + radical cyclic ether + OH β-scission products + R Fig. 6. The primary reaction pathways for alkane oxidation. (RO 2 ) which can dissociate back to alkyl and O 2 or isomerize to form hydroperoxy alkyl radicals (QOOH), which is rapid for n-alkanes relative to iso-alkanes. The QOOH can add an additional O 2 to form hydroperoxy peroxy (OOQOOH) which can quickly isomerize to a ketohydroperoxide and an OH radical. The ketohydroperoxide can decompose to form a second OH radical and another radical. In total, this reaction sequence produces three radicals from the original alkyl radical and thus chain low-temperature radical branching. This reaction sequence occurs at temperatures lower than 800 K. At moderate temperatures ( K) the lowtemperature branching reaction pathway competes with the dissociation of QOOH to form different products: olefins and HO 2, cyclic ethers and OH, and β-scission products and alkyl radicals. This moderate temperature pathway results in no radical branching and thus lower reactivity is observed at moderate temperatures, in the negative temperature coefficient (NTC) regime, than at lower temperatures where QOOH + O 2 is faster than QOOH decomposition. At the transition from the NTC regime to the high-temperature regime decomposition of hydrogen peroxide, H 2 O 2 + M 2OH + M, begins to become fast enough to enhance the radical pool and results end of the NTC regime (~ K) and a return to the traditional increase in reactivity with increasing temperature observed in the high-temperature regime (T > 1000 K). Hydrogen peroxide is formed via the sequence QOOH olefin + HO 2 followed by n- alkane + HO 2 alkyl + H 2 O 2. The similarity of the measured ignition times in all the experimental studies shown in Fig. 5 for temperatures less than 1000 K implies that the moderate- and lowtemperature reaction pathways and rates are not strongly influenced by n-alkane chain length for C 7 and larger n- alkanes. In particular, reactions involving internal isomerization (RO 2 QOOH and OOQOOH OH + 5

6 ketohydroperoxide), the rates of which are dependent on the length of R for smaller molecules, must not be strongly dependent on length, for C 7 and larger alkyls. This conclusion is consistent with the premise that reactions proceeding through cyclic transition states typically proceed through 5-8 member rings and in the case of larger alkanes the addition of chain length does not add probable isomerization pathways. Finally, the comparison of normal and branched alkane measurements and kinetic modeling (Fig. 7) illustrate slight reactivity differences for temperatures less than 1000 K with divergence at lower temperatures due to the influence of low-temperature peroxy chemistry as previously discussed. At moderate temperatures ( K) the measurements indicate that the ignition times for n-alkanes are slightly longer than those for iso-cetane and slightly shorter than those for iso-octane. These differences are small, within the uncertainty bounds at some temperatures. However, the slight reactivity difference between iso-cetane and n-alkanes (n-decane in Fig. 7) in this temperature range is also predicted by the LLNL mechanisms and can be attributed to differences in the rates of thermal decomposition for these two compounds which plays a secondary role to H-atom abstraction in fuel consumption for temperatures from K where the differences are observed. Fig. 7. Comparison of Φ = 1.0 iso-octane/air, isocetane/air, n-decane, and n-dodecane ignition times: experiments and kinetic modeling based on LLNL mechanisms [45,53,55]. Summary New ignition time measurements for iso-octane, isocetane, n-heptane, n-decane, n-dodecane, and n- tetradecane have been performed at conditions of relevance to practical combustion devices. Measurements were made for Φ = 0.25, 0.5, and 1.0 n-alkane/air mixtures at pressures from 7 to 60 atm and temperatures from 780 to 1400 K. The experiments for iso-cetane and n-tetradecane are, to our knowledge, the first ignition time measurements for these compounds. These experiments greatly extend the database of kinetic targets available for transportation fuel relevant alkanes and provide insight into the relative reactivity of alkanes. The results presented here are part of an ongoing effort to characterize the ignition of larger hydrocarbons found in and representative of those found in liquid transportation fuels. Other studies include measurements for cyclo-alkanes and aromatics. We are presently working towards extending these measurements to larger compounds (n-hexadecane, 1-methylnaphthalene) and mixtures. Acknowledgement This work was supported by the U.S. Air Force Office of Scientific Research (Grant No. FA ) with Dr. Julian Tishkoff as technical monitor. References [1] C.K. Westbrook, Proc. Combust. Inst. 28 (2000) [2] J.A. Miller, M.J. Pilling, J. Troe, Proc. Combust. Inst. 30 (2005) [3] W.J. Pitz, N.P. Cernansky, F.L. Dryer, F.N. Egolfopoulos, J.T. Farrell, D.G. Friend, H. Pitsch, SAE Paper , [4] M. Colket, J.T. Edwards, S. Williams, N.P. Cernansky, D.L. Miller, F.N. Egolfopoulos, P. Lindstedt, K. Seshadri, F.L. Dryer, C.K. Law, D.G. Friend, D.B. Lenhert, H. Pitsch, A. Sarofim, M. Smooke, W. Tsang, AIAA Paper AIAA , [5] J.T. Farrell, N.P. Cernansky, F.L. Dryer, D.G. Friend, C.A. Hergart, C.K. Law, R. McDavid, C.J. Mueller, H. Pitsch, SAE Paper , [6] A.C. Nixon, G.H. Ackerman, L.E. Faith, R.D. Hawthorn, H.T. Henderson, A.W. Ritchie, L.B. Ryland, U.S. Air Force Technical Report AFAPL- RF , [7] D.J. Vermeer, J.W. Meyer, A.K. Oppenheim, Combust. Flame 18 (1972) [8] A. Burcat, R.F. Farmer, R.A. Matula, Int. Sym. Shock Tubes and Waves 13 (1982) [9] H.K. Ciezki, G. Adomeit, Combust. Flame 93 (1993) [10] U. Pfahl, K. Fieweger, G. Adomeit, Proc. Combust. Inst. 26 (1996) [11] K. Fieweger, R. Blumenthal, G. Adomeit, Combust. Flame 109 (1997) [12] M.B. Colket, L.J. Spadaccini, J. Prop. Power 17 (2001) [13] C.K. Westbrook, W.J. Pitz, H.J. Curran, J. Boercker, W. Kunrath, Int. J. Chem. Kinet. 33 (2001) [14] D.C. Horning, D.F. Davidson, R.K. Hanson, J. Prop. Power 18 (2002) [15] B. Imbert, L. Catoire, N. Chaumeix, C. Paillard, J. Prop. Power 20 (2004)

7 [16] B.M. Gauthier, D.F. Davidson, R.K. Hanson, Combust. Flame 139 (2004) [17] D.F. Davidson, B.M. Gauthier, R.K. Hanson, Proc. Combust. Inst. 30 (2005) [18] J. Herzler, L. Jerig, P. Roth, Proc. Combust. Inst. 30 (2005) [19] J.M. Smith, J.M. Simmie, H.J. Curran, Int. J. Chem. Kinet. 37 (2005) [20] E. Olchanski, A. Burcat, Int. J. Chem. Kinet. 38 (2006) [21] V.P. Zukhov, V.A. Sechenov, A.Yu. Starikovski, Combust. Flame 153 (2008) [22] D.F. Davidson, D.R. Haylett, R.K. Hanson, Combust. Flame 155 (2008) [23] V.P. Zukhov, V.A. Sechenov, A. Yu. Starikovski, Combust. Flame 153 (2008) [24] D.F. Davidson, D.R. Haylett, R.K. Hanson, Combust. Flame 155 (2008) [25] S.S. Vasu, D.F. Davidson, Z. Hong, V. Vasudevan, R.K. Hanson, Proc. Combust. Inst. 32 (2009), [26] M.P. Halstead, L.J. Kirsch, C.P. Quinn, Combust. Flame 30 (1977) [27] J.F. Griffiths, P.A. Halford-Maw, D.J. Rose, Combust. Flame 95 (1993) [28] R. Minetti, M. Carlier, M. Ribaucour, E. Therssen, L.R. Sochet, Combust. Flame 102 (1995) [29] Minetti, R.; Ribaucour, M.; Carlier, M.; Sochet, L.R. Combust. Sci. Technol. 1996, 113, [30] R. Minetti, M. Carlier, M. Ribaucour, E. Therssen, L.R. Sochet, Proc. Combust. Inst. 26 (1996) [31] J.F. Griffiths, P. Halford-Maw, C. Mohamed, Combust. Flame 111 (1997) [32] C.K. Westbrook, W.J. Pitz, J.E. Boercker, H.J. Curran, J.F. Griffiths, C. Mohamed, M. Ribaucour, Proc. Combust. Inst. 29 (2002) [33] S. Tanaka, F. Ayala, J.C. Keck, J.B. Heywood, Combust. Flame 132 (2003) [34] E.J. Silke, H.J. Curran, J.M. Simmie, Proc. Combust. Inst. 30 (2005) [35] X. He, M.T. Donovan, B.T. Zigler, T.R. Palmer, S.M. Walton, M.S. Wooldridge, A. Atreya, Combust. Flame 142 (2005) [36] S.M. Walton, X. He, B.T. Zigler, M.S. Wooldridge, A. Atreya, Combust. Flame 150 (2007) [37] K. Kumar, Ph.D. Thesis, Case Western Reserve University, [38] C.V. Callahan, T.J. Held, F.L. Dryer, R. Minetti, M. Ribaucour, L.R. Sochet, T. Faravelli, P. Gaffuri, E. Ranzi, Proc. Combust. Inst. 26 (1996) [39] G.M. Côme, V. Warth, P.A. Glaude, R. Fournet, F. Battin-LeClerc, G. Scacchi, Proc. Combust. Inst. 26 (1996) [40] E. Ranzi, T. Faravelli, P. Gaffuri, A. Sogaro, A. D Anna, Combust. Flame 108 (1997) [41] H.J. Curran, P. Gaffuri, W.J. Pitz, C.K. Westbrook, Combust. Flame 114 (1998) [42] S.G. Davis, C.K. Law, Proc. Combust. Inst. 27 (1998) [43] R.P. Lindstedt, L.Q. Maurice, J. Prop. Power 16 (2000) [44] R. Fournet, F. Battin-Leclerc, P.A. Glaude, B. Judenherc, V. Warth, G.M. Côme, G. Scacchi, A. Ristori, G. Pengloan, P. Dagaut, M. Cathonnet Int. J. Chem. Kinet. 33 (2001) [45] H.J. Curran, P. Gaffuri, W.J. Pitz, C.K. Westbrook, Combust. Flame 129 (2002) [46] F. Buda, R. Bounaceur, V. Warth, P.A. Glaude, R. Fournet, F. Battin-Leclerc, Combust. Flame 142 (2005) [47] E. Ranzi, A. Frassoldati, S. Granata, T. Faravelli, Ind. Eng. Chem. Res. 44 (2005) [48] S. Touchard, R. Fournet, P.A. Glaude, V. Warth, F. Battin-Leclerc, G. Vanhove, M. Ribaucour, R. Minetti, Proc. Combust. Inst. 30 (2005) [49] P. Dagaut, M. Cathonnet, Prog. Energy Combust. Sci. 36 (2006) [50] Y. Muharam, J. Warnatz, J. Phys. Chem. Chem. Phys. 9 (2007) [51] F. Battin-Leclerc, Prog. Energy Combust. Sci. 34 (2008) [52] J. Biet, M.H. Hakka, V. Warth, P.-A. Glaude, F. Battin-Leclerc, Energy Fuels 22 (2008) [53] C.K. Westbrook, W.J. Pitz, O. Herbinet, H.J. Curran, E.J. Silke, Combust. Flame 156 (2009) [54] H.-P.S. Shen, M.A. Oehlschlaeger, Combust. Flame, doi: /j.combustflame , to appear. [55] C.K. Westbrook, W.J. Pitz, iso-cetane mechanism, personal communication. [56] W. Tsang, J.A. Walker, J.A.Manion, Proc. Combust. Inst. 31 (2007) [57] D.C. Horning, Ph.D. Thesis, Stanford University, Stanford, CA,