autoignition of heptanes; experiments and modeling

Autoignition of Heptanes;Experiments and ModelingJOHN M. SMITH, JOHN M. SIMMIE, HENRY J. CURRAN

Chemistry Department, National University of Ireland, Galway, Ireland

Received 19 January 2005; accepted 1 April 2005

DOI 10.1002/kin.20120Published online in Wiley InterScience (www.interscience.wiley.com).

ABSTRACT: There is much interest in determining the influence of molecular structure on therate of combustion of hydrocarbons; the C7H16 isomers of heptane have been selected here asthey exemplify all the different structural elements present in aliphatic, noncyclic hydrocarbons.

With the exception of n-heptane itself, no autoignition studies have been carried outto date on the other isomers of heptane at high temperatures. Therefore, ignition delaytimes were measured for the oxidation of four isomers—n-heptane, 2,2-dimethylpentane, 2,3-dimethylpentane, and 2,2,3-trimethylbutane—under stoichiometric conditions at a reflectedshock pressure of 2 atm, within the temperature range of 1150–1650 K. Measurements underidentical conditions reveal that they all have essentially the same ignition delay time; this con-firms earlier theoretical predictions based purely on detailed chemical kinetic modeling.

The variation of ignition delay times for n-heptane with changing oxygen concentrations andreflected shock pressure was determined and shown to follow expected trends. C© 2005 WileyPeriodicals, Inc. Int J Chem Kinet 37: 728–736, 2005

INTRODUCTION

When a reactive mixture is rapidly heated, it is not un-common to observe no apparent reaction for a time—the ignition delay time—then a rather abrupt increasein the rate of reaction, as indicated by various diagnos-tics such as appearance of products, emission of light,change of pressure, etc. It is quite difficult to deduce areaction mechanism and determine individual rate con-stants from ignition delay times. However, once somekinetic data are available, ignition delay data can bevery useful in modeling, to see if the proposed mech-anism is complete and reasonably correct [1]. In addi-tion, by varying the set of relevant parameters such astemperature and pressure, the ignition time sensitivity

Correspondence to: John M. Simmie; e-mail: [email protected].

Contract grant sponsor: Enterprise Ireland from both BasicResearch and International Collaboration.

Contract grant numbers: SC/1998/409, IC/2001/067.Contract grant sponsor: HEA-PRTLI Cycle-2 (WA-3).

c© 2005 Wiley Periodicals, Inc.

to each parameter may be ascertained, thus enablingthe ignition time of a specific fuel to be determinedover a range of conditions.

The relative simplicity of the experiments coupledwith compounds of huge industrial significance meansthat very many studies on ignition delay times havebeen published even recently [2–27]; Lifshitz summa-rizes many earlier studies [28].

Although much work has been carried out onn-heptane [29–38], a primary reference fuel, there hasnever been a satisfactory study of its isomers whichpossess diverse structural features not present in theparent normal hydrocarbon.

EXPERIMENTAL

The stainless steel shock tube consists of a large, 52 cmdiameter but short, 63 cm driver section coupled via atransition piece to the test section which is 622 cm longand 10.24 cm internal diameter. Pressure transducers(PCB Piezotronics, model 113A21) were set into the

AUTOIGNITION OF HEPTANES; EXPERIMENTS AND MODELING 729

final 50 cm of the test section and were used to timethe incident shock velocity. In order to allow for shockattenuation, the shock velocity at the endwall was cal-culated by extrapolating the incident velocities to theendwall. Reflected shock conditions were calculatedusing the usual one-dimensional shock relations [39]and the application GasEq [40] which requires the ther-modynamics of the input species.

Light emission was measured through a quartz win-dow in the endwall with a fast rise time switchablegain photodetector (Thorlabs, PDA55-EC) and a nar-row bandpass filter centered at 430 ± 10 nm. It is usu-ally assumed that emission from CH∗(A2� ↔ X2�)is responsible [34,41,42]. In addition, some runs wereperformed with a time-resolved intensified charge-coupled device camera (LaVision GmbH, StreakStarS) attached to a grating spectrograph (Acton Research,SpectraPro–300i) to resolve issues such as whetheremission from CH precedes emission from OH [38];we find that these occurred simultaneously.

All endwall ignition delay times, τ , for the currentstudy were measured behind the reflected shock, withτ defined as the time interval from shock arrival at theendwall, as indicated by an in situ pressure transducer(Kistler, 601H), to the maximum in the rate of change ofemission with time—a similar definition to the classicwork of Gutman and Matsuda [42] on CO + O →CO2 + h�.

Liquid heptanes, obtained from Sigma-Aldrich in>99% purity, were individually stored in glass bulbsunder vacuum and were subjected to several freeze-pump-thaw degassing cycles prior to use. Due to sat-uration and adsorption effects, the heptane partialpressures were kept significantly below their room tem-perature saturation vapor pressures; fortunately, thesecompounds all have relatively high vapor pressures [43]at room temperature: n-heptane 6.09 kPa (45.7 Torr),2,2-dimethylpentane 14.0 kPa, 2,3-dimethylpentane9.18 kPa, and 2,2,3-trimethylbutane 28.5 kPa all at298 K.

Mixtures of the desired composition were made upin 35 or 50 L tanks with oxygen and argon (both BOC,>99.98%), and sufficient time was allowed to elapse toensure adequate mixing. Prior to each shock, the driverand driven sections of the shock tube were evacuatedindependently to 10−3 and 10−6 Torr, respectively. Thetest section was filled with mixture to initial pressuresof 20–60 Torr—we had previously established that thetube performed satisfactorily in this region by com-paring our measurements with those of Michael andSutherland [44]. Shock waves were generated by fill-ing the driver section with helium gas (BOC CP grade)until a 120 µm polycarbonate diaphragm (ColoprintGmbH, Makrofol DE 7–2) separating the two sections

was burst with the aid of a four-bladed X-shapedcutter.

RESULTS

Comparison with Previous Results

In order to validate our methodology, the recent exper-iments by Horning et al. [36] on n-heptane oxidationwere repeated at an average reflected shock pressureof 1.05 ± 0.1 atm, at equivalence ratios, φ, of 2.0, 1.0,and 0.5—typical mixture composition 0.4% n-heptane,4.4% O2, and the balance argon. The results are in verygood agreement with those of Horning et al., Fig. 1 whoalso used the same definition of the endwall ignitiontime as the one used here. The direct comparison af-forded in this case—the Horning data were obtained ata slightly higher average pressures of 1.25 atm, there-fore his results have been scaled by (1.25/1.05)0.5 toput them on a common footing—means that we canbe confident that our equipment and procedure are per-forming satisfactorily. It is noticeable that the slopesand hence the activation energies recorded by Horningand co-workers [36] are greater than those measuredhere; for example, 45.1 versus 38.0 kcal mol−1 for theφ = 1 points in Fig. 1. This might be taken as an indi-cation that the smaller diameter of our shock tube leadsto a more influential boundary layer [45] which therebyresults in a lower than expected activation energy [27].On the other hand, it can be argued that the Horningdata cover a very narrow range of temperatures andare also faster than ours, that is, are more reactive—suggesting that they are more affected by impurities.Although this latter claim is not supported by the cal-culations of Davidson and Hanson [27] who show thatlow level contamination should not affect results forlarge hydrocarbons like n-heptane.

Horning et al. [36] also reported some experimentsat different reflected shock pressures; these were re-peated here and the results are qualitatively in agree-ment, Fig. 2. In this study, the pressure dependencedetermined is somewhat greater than that found by theStanford group.

The studies of Colket and Spadaccini [8] and thoseof Imbert et al. [38] cannot be compared directly to thisstudy but one can extrapolate their results, see Fig. 3,to these conditions via either Eq. (1):

τ/s = 6.76 × 10−15[C7H16]0.4[O2]−1.2

× exp(+40, 160/RT ) (1)

where the concentrations are in mol cm−3, and thegas constant, R, and hence the activation energy in cal

730 SMITH, SIMMIE, AND CURRAN

Figure 1 Ignition delay times for 0.4% nC7H16, 1.05 ± 0.1 atm in Ar diluent: symbols experiment, — model. φ = 2.0 � thisstudy, � [36]; φ = 1.0 ◦ this study, • [36]; φ = 0.5 � this study, � [36].

mol−1; or Eq. (2):

τ/µs = 1.206 × 10−5[nC7H16]0.92[O2]−1.41[Ar]0.09

× exp(+26, 922/T ) (2)

where the concentrations are in mol m−3.For φ = 2, these results are in good agreement with

those of Colket and Spadaccini but are significantlyfaster at other stoichiometries. In the other case there

Figure 2 Ignition delay times at 0.4% nC7H16, φ = 1.0, in Ar diluent: symbols experiment, — model. 1 atm � this study, �[36]; 2 atm ◦ this study, • [36].

is substantially good agreement at φ ≤ 1 but quite se-vere disagreement at φ = 2. Similar conclusions canbe reached if comparison is made to much earlier workof Burcat et al. [46].

One can also use the Horning et al. [36] correlation,Eq. (3):

τ/s = 4.54 × 10−14[nC7H16]0.95[O2]−1.58

× exp(+45, 000/RT ) (3)


Figure 3 Autoignition of n-heptane: — [16], – – – [38], · · · [8].

where the concentrations are in mol cm−3, and, thegas constant and activation energy are in cal mol−1, tomatch against these results, see the solid lines in Fig. 3.As is evident the agreement is quite good.

Influence of Oxygen Concentration

The initial oxygen concentration normally has amarked effect upon the magnitude of the ignition de-lay. So, a series of experiments were devised to testthe dependence on oxygen concentration by keepingthe concentration of n-heptane constant at 0.4% andincreasing oxygen from 2.2%, φ = 2.0, through 4.4%,φ = 1.0, to 8.8%, φ = 0.5, Fig. 1.

The results show that the ignition delay time de-creases with increasing oxygen concentration or de-creasing equivalence ratio, therefore showing a nega-tive oxygen concentration dependence. This is quitetypical behavior for hydrocarbon oxidation at hightemperatures.

Influence of Final Pressure

The effect of pressure on the ignition delay time forstoichiometric n-heptane, 0.4% fuel and 4.4% O2, wastested by varying the final reflected shock pressure from1 to 2 atm, Fig. 2. An increase in the pressure results ina decrease in the measured ignition delay time, there-fore we expect a negative pressure dependency on themeasured ignition delay. Hence the rate of oxidationincreases with increasing pressure.

In order to express the ignition time as a functionof pressure, a multiple regression analysis was carriedout on stoichiometric n-heptane data at 1 and 2 atm.The following correlation formula (r2 = 0.978) wasobtained:

τ/µs = 10(−3.30 ± 0.04) p(−0.468 ± 0.043)

× exp[(+20, 650 ± 139)/T ] (4)

where p is in atmospheres.If a similar treatment is applied to the data of

Horning et al. [36], then the following equation is ar-rived at

τ/µs = 10(−4.79 ± 0.15) p(−0.531 ± 0.03)

× exp[(+24, 060 ± 215)/T ] (5)

Hence, the values obtained are quite similar to theones from this study; although one would have pre-dicted by inspection of Fig. 2 that the Horning datawould have a smaller pressure dependence. Clearlythere is a compensation effect between the variablesof pressure and temperature which blur the multipleregression analysis.

Global Correlation

A simple approach to interpreting ignition delay datahas been to derive algebraic correlation formulas whichexpress the ignition time as a function of key param-eters. An advantage of establishing such correlations


is that the sensitivity of the ignition time to a givenparameter, for example reactant concentrations ortemperature is revealed. The experimental ignition de-lay dependence on the temperature and the concentra-tions of compound, oxygen, and diluent is normallyrepresented according to a variant of the Arrheniusexpression:

τ = A[X ]α[O2]β[Ar]γ exp(+E/RT ) (6)

where τ is the ignition delay, A is an empirically deter-mined constant, T is the temperature of the gas behindthe reflected shock wave in kelvin, R is the universalgas constant, E is the activation energy in the sameunits. α, β, and γ are the power dependencies of theignition delays on the compound, oxygen, and argonconcentrations respectively. The concentrations whichappear in the above equation are those of the initialcomponents behind the reflected shock front and arecomputed on the basis of frozen chemistry.

Attempting to correlate our dataset with Eq. (6) isnot useful since essentially only the oxygen concentra-tion and the temperature are changing across the set.Analysis of a more limited version of the correlationformula

τ = 10B[O2]α exp(+E/RT )

now does give a good correlation, r2 = 0.947:

τ = 10−4.29 ± .139[O2]−1.50 ± .034

× exp[(+20, 643 ± 189)/T ] (7)

Figure 4 n-Heptane correlation: � φ = 2.0, ◦ φ = 1.0, � φ = 0.5.

where τ is measured in microseconds, concentration inmol m−3, and temperature in kelvin. If one defines aconcentration-corrected ignition delay time as

β = τ

[X]α[O2]b[Ar]c= A exp

(E

RT

)(8)

then all the experimental data can be expressed in asingle correlating expression:

lnβ = ln A +(

E

R

)(1

T

)(9)

All 140 runs were plotted according to Eq. (9); it canbe seen that the plot is quite linear, r2 value of 0.975,with a slope which equates to an activation energy of41.0 ± 0.01 kcal mol−1, Fig. 4.

Results for Heptane Isomers

The ignition delay times for very nearly stoichiometricmixtures of four heptane isomers were determined atreflected shock pressures of 2.0 ± 0.2 atm, Fig. 5. Ineach case the mixture composition was 1.49% hep-tane, 16.0% O2, and the balance of 82.5% Ar; thiswas chosen to mirror the values used by Westbrooket al. [47]. In retrospect, this mixture composition wasnot a good choice since departure from ideal one-dimensional shock wave theory increases as the per-centage of monoatomic gas decreases.

Linear regression analysis of each dataset gives(with correlation coefficients of 0.993, 0.975, 0.990,


Figure 5 Heptane experimental (points) and model-predicted (lines) ignition delay times at 1.89% fuel, P5 = 2.0 ± 0.2 atm,and φ = 1.0 in Ar: — � n-heptane, · · · � 2,3-dimethylpentane, — • 2,2-dimethylpentane, – – – ∇ 2,2,3-trimethylbutane.

and 0.982 respectively):

n-Heptane log(τ/µs)

= (7325 ± 103)/T − (3.15 ± 0.08)

2,2-Dimethylpentane log(τ/µs)

= (7253 ± 198)/T − (2.91 ± 0.14)

2,3-Dimethylpentane log(τ/µs)

= (6208 ± 110)/T − (2.20 ± 0.08)

2,2,3-Trimethylbutane log(τ/µs)

= (5881 ± 169)/T − (1.98 ± 0.12)

Hence the activation energies range from 26.9 kcalmol−1 for 223TMB to 33.5 kcal mol−1 for n-heptane.

DISCUSSION

Kinetic Modeling

Detailed chemical kinetic modeling was performed us-ing the HCT modeling code [48]. The detailed chem-istry is based on the hierarchical nature of hydro-carbon combustion systems with a detailed hydro-gen/oxygen submechanism [49] together with detailedchemistry to describe C1–C7 hydrocarbon fuels [50–54]. A fuller description of the mechanism develop-ment and methodology used is given in the paper byWestbrook et al. [47]. The mechanisms developed for

each heptane isomer included only high temperaturechemistry, i.e. the addition of C7 alkyl radicals tomolecular oxygen and subsequent alkylperoxyl radi-cal chemistry was not included. The rate constant ex-pressions used for unimolecular fuel decomposition,hydrogen atom abstraction reactions etc. are consis-tent with those described in a recent study of iso-octane oxidation [54]. Thermochemistry for the speciesis based on the group additivity methods of Benson[55] using the THERM package of Ritter and Bozzelli[56,57].

Model predictions for the normal heptane isomerare in excellent agreement for the leanest mixture withφ = 0.5 but less so for the stoichiometric and richmixtures, Fig. 1, although the general trend is verywell reproduced. The trend with reflected shock pres-sure is also in quite good agreement with our data(Fig. 2).

A comparison of model-predicted ignition delaytimes with the experimental results is given in Fig. 5.With the possible exception of n-heptane which has theshortest ignition delay times, the three other isomershave very similar values. Overall, there is good agree-ment between the model predictions and the experi-mental results. At low temperatures (1150–1250 K),the model predictions are consistently slower thanthose observed experimentally for all fuels. At tem-peratures above 1250 K, the model captures the rela-tive reactivity of the fuels very well in that at 1400 Kfor example, n-heptane is fastest to ignite, then 2,3-dimethylpentane, followed by 2,2-dimethylpentane,


with 2,2,3-trimethylbutane slowest to ignite. Interest-ingly Westbrook et al. [47] in a detailed chemical ki-netic modeling study had predicted that

it is very difficult to distinguish between the different iso-mers . . . indicating that all of the isomers ignite at nearly thesame rate.

In this remarkable paper, which does not containany experiments against which their conclusions canbe tested, they also predict activation energies of ap-proximately 40 kcal mol−1 for each compound.

Westbrook et al. [47] point out that the chain-branching reaction

H + O21→ O + OH

and the termination step

CH3 + CH32→ C2H6

are the key to understanding this high-temperaturechemistry. They argue that the formation of a numberof alkyl radicals from the parent compound will leadto the formation of H-atoms from some of the alkylradicals—and hence assist ignition via reaction (1)—but other radicals will lead to methyl radicals whichdelay ignition via reaction (2). The proportions of eachformed for this set of isomers are essentially the sameand hence the ignition times will also be the same.They illustrate this argument by considering just twoof the radicals that can be formed by H-atom abstractionfrom 2-methylhexane; 2-methylhept-1-yl (top), and2-methylhept-5-yl (bottom) in Fig. 6.

The 2-methylhept-1-yl radical can decompose toproduce propene, two molecules of ethylene, and ahydrogen atom. However, the 2-methylhept-5-yl rad-ical leads to the formation of two propene moleculesand a methyl radical. Hence, formation of the 2-methyl-hept-1-yl radical accelerates ignition while formationof a 2-methylhept-5-yl radical inhibits the overall re-activity of the system.

It is remarkable too that the Westbrook study pre-dicts 2,2-dimethylpentane and 2,4-dimethylpentane to

Figure 6 Radical decomposition routes.

be the two slowest isomers to ignite. Modeling stud-ies show that fuel consumption is achieved by H-atomabstraction by hydrogen atoms and to a lesser extentby hydroxyl radicals. In addition, unimolecular fueldecomposition contributes about 15–20% dependingon the temperature. Of the four isomers studied here,2,2-dimethylpentane is consistently slower over the en-tire temperature range, with only 2,2,3-trimethylbutaneslightly slower than 2,2-dimethylpentane. Westbrooket al. argued that of the 16 available H-atoms for ab-straction, 14 lead to the formation of methyl radicalsvia β-scission and chain termination, while the otherisomers have, at most, 10 H atoms leading to chaintermination.

Westbrook et al. also explain the relative unre-activity of 2,2,3-trimethylbutane. Initial examinationwould suggest that, based on above arguments, 2,2,3-trimethylbutane should be more reactive than the otherisomers as 15 of its 16 available H atoms lead to alkylradicals which, following β-scission, produce H atomswhich should lead to chain branching. However, alkylradical β-scission in this case also leads to high con-centrations of isobutene which is resistant to oxidation[58].

Although the detailed mechanisms reproduce theexperimental data reasonably accurately, some im-provement in predicted delay times is possible. For ex-ample, the mechanism predicts shorter ignition times(faster reaction) for rich n-heptane mixtures than thosemeasured (Fig. 1). Improvement may be achieved byslight variations in the rate constants used for abstrac-tion of a hydrogen atom from the parent alkane by O andH atoms and/or hydroxyl, hydroperoxyl, and methylradicals, as all of these are not accurately known. Inaddition, pressure-dependent rate constants, includingfalloff, might lead to better agreement between modeland experiment for the branched heptane isomers.

CONCLUSION

A new shock tube has been commissioned and usedto measure ignition delay times under reflected shockconditions. Experimental data taken by Horning et al.[16] for n-heptane have been reproduced in order tovalidate the experimental technique. Mixtures of 0.4%n-heptane in argon diluent were studied at a reflectedshock pressure of 1.0 atm at equivalence ratios of 0.5,1.0, and 2.0, Fig. 1. In addition, experiments wereperformed under stoichiometric conditions at reflectedshock pressures of 1.0, 2.0, and 4.0 atm, Fig. 2. It wasfound that under all conditions, very good agreementwas found between the current data and that recordedby Horning et al. [16], although ignition delay times


in this study are consistently slightly longer than thosemeasured by Horning et al.

In addition, a comparative study of four heptane iso-mers, n-heptane, 2,2-dimethyl pentane, 2,3-dimethylpentane, and 2,2,3-trimethyl butane was performed at1.49% fuel, unit stoichiometry, and at an average re-flected shock pressure of 1.0 atm, Fig. 5. It was foundthat at low temperatures (1150–1300 K), all isomershad almost identical ignition delay times. At tempera-tures above 1300 K, n-heptane is fastest to ignite with2,2- and 2,3-dimethylpentane slightly slower and 2,2,3-trimethylbutane slightly slower still. These data weresimulated using a mechanism published by Westbrooket al. [47] with good agreement observed between ex-periment and model (Fig. 5).

BIBLIOGRAPHY

1. Simmie, J. M. Prog Energy Combust Sci 2003, 29, 599–634.

2. Borisov, A. A.; Skachkov, G. I.; Troshin, K. Y. ChemPhys Rep 2000, 18 1665–1682.

3. Cadman, P.; Thomas, G. O.; Butler, P. Phys Chem ChemPhys 2000, 2, 5411–5419.

4. Jee, S. B.; Kim, K.; Shin, K. S. Bull Korean Chem Soc2000, 21, 1015–1019.

5. Won, S. J.; Ryu, J. C.; Bae, J. H.; Kim, Y. D.; Kang,J. G. Bull Korean Chem Soc 2000, 21, 487–492.

6. Burcat, A.; Dvinyaninov, M.; Olchanski, E. Int J ChemKinet 2001, 33, 491–508.

7. Cadman, P. Phys Chem Chem Phys 2001, 3, 4301–4309.8. Colket, M. B.; Spadaccini, L. J. J Propulsion Power 2001,

17, 315–323.9. Ikeda, E.; Mackie, J. C. Z Phys Chem 2001, 215, 997–

1009.10. Kim, K.; Shin, K. S. Bull Korean Chem Soc 2001, 22,

303–307.11. Qin, Z. W.; Yang, H. X.; Gardiner, W. C. Combust Flame

2001, 124, 246–254.12. Servaites, J.; Krier, H.; Melcher, J. C.; Burton, R. L.

Combust Flame 2001, 125, 1040–1054.13. Zhang, F.; Akbar, R.; Thibault, P. A.; Murray, S. B. Shock

Waves 2001, 10, 457–466.14. Benkiewicz, K.; Hayashi, A. K. Fluid Dynamics Res

2002, 30, 269–292.15. Cadman, P.; Bambrey, R. J.; Box, S. K.; Thomas, G. O.

Combust Sci Technol 2002, 174, 111–127.16. Horning, D. C.; Davidson, D. F.; Hanson, R. K. J Propul-

sion Power 2002, 18, 363–371.17. Kim, H.; Pae, S.; Min, K. Combust Sci Technol 2002,

174, 221–238.18. Lamoureux, N.; Paillard, C. E.; Vaslier, V. Shock Waves

2002, 11, 309–322.19. Lamoureux, N.; Paillard, C. E. Shock Waves 2003, 13,

57–68.

20. MacNamara, J. P.; Simmie, J. M. Combust Flame 2003,133, 231–239.

21. Mikolaitis, D. W.; Segal, C.; Chandy, A. J PropulsionPower 2003, 19, 601–606.

22. Toland, A.; Simmie, J. M. Combust Flame 2003, 132,556–564.

23. Wang, B. L.; Olivier, H.; Gronig, H. Combust Flame2003, 133, 93–106.

24. Zhukov, V. P.; Sechenov, V. A.; Starikovskii, A. Y.Combustion Explosion Shock Waves, 2003, 39, 487–495.

25. Huang, J.; Hill, P. G.; Bushe, W. K.; Munshi, S. R. Com-bust Flame 2004, 136, 25–42.

26. Zhukov, V. P.; Sechenov, V. A.; Starikovskii, A. Y. Com-bust Flame 2004, 136, 257–259.

27. Davidson, D. F.; Hanson, R. K. Int J Chem Kinet 2004,36, 510–523.

28. Lifshitz, A. In Handbook Shock Waves. Ben-Dor, G.;Igra, O.; Elperin, T. (Eds.) Academic Press: New York,2001; Vol. 3, Ch. 165.

29. Orr, C. R. Proc Combust Inst 1963, 9, 1034–1045.30. Levinson, G. S. Combust Flame 1964, 9, 63–72.31. Vermeer, D. J.; Meyer, J. W.; Oppenheim, A. K. Combust

Flame 1972, 18, 327–336.32. Coats, C. M.; Williams, A. Proc Combust Inst 1978, 17,

611–621.33. Ciezki, H.; Adomeit, G. In 16th International Sympo-

sium on Shock Tubes Waves, 1987; pp. 481–486.34. Ciezki, H.; Adomeit, G. Combust Flame 1993, 93, 421–

433.35. Davidson, D. F.; Horning, D. C.; Hanson, R. K.; Hitch,

B. In 22nd International Symposium on Shock Waves,1999; paper 360.

36. Horning, D. C.; Davidson, D. F.; Hanson, R. K. In 23rdInternational Symposium on Shock Waves, 2001; paper5732.

37. Herzler, J.; Jerig, L.; Roth P. (in review).38. Imbert, B.; Catoire, L.; Chaumeix, N.; Paillard, C. J Prop

Power 2004, 20, 415–426.39. Ben-Dor, G.; Igra, O.; Elperin T. (Eds.). Handbook of

Shock Waves, Vol. 1: Theoretical, Experimental and Nu-merical Techniques, Academic Press: New York, 2001;Emanuel G., Ch. 3.1, pp. 185–262.

40. Morley, C. http://www.c.morley.ukgateway.net/gseqrite.html.

41. Bowman, C. T.; Seery, D. J. Combust Flame 1968, 12,611–614.

42. Gutman, D.; Matsuda, S. J Chem Phys 1970, 52, 4122–4132.

43. Lide, D. R. (Ed.). Handbook of Chemistry and Physics,77th ed.; 1997.

44. Michael, J. V.; Sutherland, J. W. Int J Chem Kinetics1986, 18, 409–436.

45. Petersen, E. L.; Hanson, R. K. Shock Waves 2001, 10,405–420.

46. Burcat, A.; Farmer, R. C.; Matula, R. A. In Proceedingsof the 13th International Symposium on Shock Tubesand Shock Waves, 1981; pp. 826–833.


47. Westbrook, C. K.; Pitz, W. J.; Curran, H. J.; Boercker,J.; Kunrath, E. Int J Chem Kinet 2001, 33, 868–877.

48. Lund, C. M.; Chase, L. Lawrence Livermore NationalLaboratory Report; UCRL-52504, revised 1995.

49. O Conaire, M.; Curran, H. J.; Simmie, J. M.; Pitz, W. J.;Westbrook, C. K. Int J Chem Kinet 2004, 36, 603–622.

50. Curran, H. J.; Gaffuri, P.; Pitz, W. J.; Westbrook, C. K.Combust Flame 1998, 114, 149–177.

51. Wang, S.; Miller, D. L.; Cernansky, N. P.; Curran, H. J.;Pitz, W. J.; Westbrook, C. K. Combust Flame 1999, 118,415–430.

52. Ribaucour, M.; Minetti, R.; Sochet, L. R.; Curran, H. J.;Pitz, W. J.; Westbrook, C. K. Proc Combust Inst 2001,28, 1671–1678.

53. Curran, H. J.; Gaffuri, P.; Pitz, W. J.; Westbrook, C.K.; Leppard, W. R. Proc Combust Inst 1996, 26, 2669–2677.

54. Curran, H. J.; Gaffuri, P.; Pitz, W. J.; Westbrook, C. K.Combust Flame 2002, 129, 253–280.

55. Benson, S. W. Thermochemical Kinetics; Wiley:New York, 1976.

56. Ritter, E. R.; Bozzelli, J. W. Int J Chem Kinet 1991, 23,767–778.

57. Lay, T.; Bozzelli, J. W.; Dean, A. M.; Ritter, E. R. J PhysChem 1995, 99, 14514–14527.

58. Curran, H. J.; Dunphy, M. P.; Simmie, J. M.; Westbrook,C. K.; Pitz, W. J. Proc Combust Inst 1992, 24, 769–776.

autoignition of heptanes; experiments and modeling

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