Gautam Kalghatgi

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Combustion and Flame 140 (2005) 267–286www.elsevier.com/locate/combustflam

Co-oxidation in the auto-ignition of primary reference fuandn-heptane/toluene blends

Johan Andraea,∗, David Johanssona, Pehr Björnboma, Per Risbergb,Gautam Kalghatgib,c

a Department of Chemical Engineering and Technology, Chemical Reaction Engineering, Royal Institute of Technology,Teknikringen 42, SE-100 44 Stockholm, Sweden

b Department of Machine Design, Internal Combustion Engines, Royal Institute of Technology, SE-100 44 Stockholm, Swedenc Shell Global Solutions, P.O. Box 1, Chester CH1 3SH, UK

Received 30 June 2004; received in revised form 29 October 2004; accepted 24 November 2004

Available online 23 December 2004

Abstract

Auto-ignition of fuel mixtures was investigated both theoretically and experimentally to gain further undering of the fuel chemistry. A homogeneous charge compression ignition (HCCI) engine was run under doperating conditions with fuels of different RON and MON and different chemistries. Fuels consideredprimary reference fuels and toluene/n-heptane blends. The experiments were modeled with a single-zonabatic model together with detailed chemical kinetic models. In the model validation, co-oxidation rebetween the individual fuel components were found to be important in order to predict HCCI experiments,tube ignition delay time data, and ignition delay times in rapid compression machines. The kinetic modeadded co-oxidation reactions further predicted that ann-heptane/toluene fuel with the same RON as theresponding primary reference fuel had higher resistance to auto-ignition in HCCI combustion for lowertemperatures and higher intake pressures. However, for higher intake temperatures and lower intake pren-heptane/toluene fuel and the PRF fuel had similar combustion phasing. 2004 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

Keywords: HCCI; Homogeneous charge compression ignition; Auto-ignition; Fuel chemistry; Primary reference fuels;n-heptane; Toluene; Co-oxidation; CHEMKIN

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1. Introduction

Homogeneous charge compression ignit(HCCI) combustion, first studied over 20 years a[1,2], is a combustion process which utilizes a (moor less) homogeneous fuel/air mixture. Combustioinitiated by auto-ignition of the usually very fuel-lea

* Corresponding author. Fax: +46-8-696-0007.E-mail address: [email protected](J. Andrae).

0010-2180/$ – see front matter 2004 The Combustion Institutdoi:10.1016/j.combustflame.2004.11.009

mixture. It offers a number of benefits over convetional spark-ignition and diesel engines, such as mlower NOx emissions, higher combustion efficienat part load than its SI counterpart, and zero pticulates[3,4]. A disadvantage is the relatively higemissions of unburned hydrocarbons[5], the sourcesbeing quenching wall boundary layers[6] and creviceregions[7,8].

Unlike the diesel and spark-ignition enginewhere the combustion is directly controlled by t

e. Published by Elsevier Inc. All rights reserved.

http://www.elsevier.com/locate/combustflame

mailto:[email protected]

268 J. Andrae et al. / Combustion and Flame 140 (2005) 267–286

CCI

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engine management system, the combustion in Hengines is controlled by its chemical kinetics only[9].Therefore, HCCI engines will have fuel requiremethat differ from diesel and spark-ignition enginand must be properly understood. Clearly the cical problems for HCCI engines are the controlauto-ignition and combustion rate, and increasedderstanding of the chemical kinetic processeslead to auto-ignition is necessary.

Tanaka et al.[10] performed experiments on HCCcombustion in a rapid compression machine (RCwith complex fuels such as cyclic paraffins, olefinand aromatics, which exist in petroleum-based fuThey concluded that for HCCI combustion, the igtion delay and the burn rate could be independecontrolled using various fuel mixtures and additive

However, theoretical studies of auto-ignition wicomplex fuel mixtures and detailed chemistry hanot been investigated much. The main reason foris that the combustion mechanisms have not yet bwell established, especially not for mixtures with amatic and olefins mixed with paraffins. Simmie[11]has given a recent review on the development oftailed chemical models for hydrocarbon fuels.

Internal combustion engines burn blends of lamolecular-weight liquid fuels, a class to which tprimary reference fuels (PRF)n-heptane and isooctane belong. For primary reference fuels both vdetailed[12–17]and reduced or semi-detailed mod[18–21]have been developed.

Klotz et al.[22] developed a mechanism for combustion of toluene-butane blends by merging the nmechanisms for the individual fuel components avalidated the mechanism by carrying out experimein an atmospheric plug-flow reactor at 1170 K. Thdemonstrated that when the chemical interactionstween the fuel components were limited to radipool effects, in order for a merged kinetic mechnism to predict experimental data for fuel blends,blend model should be properly configured to predthe oxidation processes of the neat fuel componeTheir mechanism was not validated against engdata with significantly different pressure and time htories compared to a plug-flow reactor.

Ogink [23] has developed a surrogate kinemechanism for gasoline combustion (iso-octane 5by volume, toluene 35, andn-heptane 10). This reduced mechanism, consisting of around 100 speamong 500 reactions, has mainly been validaagainst shock-tube data and been used in CFDculations to predict gasoline HCCI combustion.

The pioneering work of Leppard[24] consideredauto-ignition during knock and attributed the sentivity of a non-PRF fuel to the differences in the lowtemperature chemistry between such fuels and Pfuels in the negative temperature coefficient, NT

region. Leppard suggested that in the MON test cdition, the NTC region dominates the chemistryPRF fuels and reactions slow down, making PRFels relatively more resistant to knock comparedfuels containing aromatics and olefins. In the ROtest condition the NTC chemistry becomes lessportant so that the PRF fuels lose the advantaghigher resistance to auto-ignition compared to nPRF fuels. Hence a non-PRF fuel has low MON ahigh RON—it is relatively more resistant than a PRfuel to auto-ignition in the RON test than in the MOtest.

In this work we have studied the auto-ignitionfuel blends including mixtures of primary referenfuels andn-heptane/toluene. Emphasis is on detaichemistry modeling and a simpler single-zone phycal model of the engine is used. The chemistry modare validated against shock-tube and rapid compsion machine data and then used to simulate Hexperiments. Our goal is to gain further insight inthe modeling of complex fuel chemistry of fuel blenthat is necessary in order to understand the aignition process. For that purpose we have especinvestigated the role of co-oxidation between the invidual fuel components. An attempt is made to undstand why the same non-PRF fuel behaves like difent PRF fuels under different conditions in termsauto-ignition chemistry.

2. Experimental procedure

The experiments were conducted in a single cyder engine based on a Scania D12 model, as pathe “Green Car” project involving the Swedish goernment, Volvo, Scania CV, and Shell. The engdetails and fuels studied are given inTables 1 and 2,respectively, and the experimental procedure is smarized below. In a typical experiment the engineand water temperatures are brought up to the oating values, 80◦C for oil and 90◦C for water. The

Table 1Details for the single-cylinder engine based on a Scaniamodel

Compression ratio 16.7Bore 127 mmStroke 154 mmConnecting rod length 255 mmNumber of valves 4Inlet valve opening (IVO) 367 CAD ATCInlet valve closing (IVC) 581 CAD ATCMaximfum inlet valve lit 14.8 mmExhaust valve opening (EVO) 121 CAD ATExhaust valve closing (EVC) 349 CAD ATCMaximum exhaust valve lift 14.8 mm

J. Andrae et al. / Combustion and Flame 140 (2005) 267–286 269

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intake boost pressure and temperature and thegine speed are fixed and the fuel is introduced uauto-ignition takes place as indicated by the presssignal and the increase in power delivered by thegine. The fuel quantity is adjusted until the requirnormalized air fuel ratio,λ, is achieved.λ is the in-verse of the fuel/air equivalence ratio,Φ. Once theengine operating characteristics have stabilized arequired levels a hundred pressure cycles are acquand stored for later analysis. This is repeated forferent fuels under the same operating condition

Table 2Fuels used and their properties

Fuel i-C8H18%vol

n-C7H16%vol

φ-CH3%vol

RON MON

A 94 6 94 94B 84 16 84 84C 25 75 94.2 82.6D 35 65 83.9 73.2

Table 3Operating conditions

Enginespeed, rpm

Intake airtemperature,◦C

Intakepressure,bar (abs)

λ

OP1 900 40 2 4.0OP2 1200 40 2 5.5OP3 900 120 1 3.5OP4 1200 120 1 3.0

engine speed, intake air temperature and pressureexcess air/fuel ratio. Thus different fuels are subjecto the same pressure and temperature history butwill show different auto-ignition behaviors becauthey have different chemistries.

In this paper we consider four operating conditiolisted in Table 3. Two of these conditions, OP1 anOP2, have a high inlet pressure but little heating ofintake air while the other two conditions have a hiintake air temperature with no intake boost. Moreformation of the experiments can be found in[25].

3. Theoretical discussion

3.1. MON, RON, and HCCI-combustion

Fig. 1 shows the bulk gas temperature plottagainst pressure during compression in four differHCCI experiments; also shown are the plots cosponding to the RON and MON tests inferred froinformation in Ref.[24]. These lines are different because of differences in the engine inlet conditionsengine design. In the RON and MON tests thegine is run with a slightly rich mixture, the normalizefuel/air ratio,Φ ∼ 1.1, while the HCCI tests are ruwith a lean mixture(Φ ∼ 0.3). The mixture temperature will follow such a characteristic polytropic line apressure increases but will go above such a line wauto-ignition reactions start. This deviation will ocur at different points depending on the auto-ignit

Fig. 1. Compression temperature versus pressure in different auto-ignition experiments.


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behavior of the fuel/air mixture under the particuoperating condition.

An HCCI engine can be run at a condition suthat fuels of different chemistry will indeed be rankfor auto-ignition phasing according to their RON raing, e.g., condition OP3 (Fig. 6 in Ref.[25]) or theMON rating. However engines can also be run at cditions where fuels of different chemistry cannotranked by either RON or MON alone.

For all practical purposes, for both knock aHCCI, the true auto-ignition quality of a non-PRF fuis given by the octane index

(1)OI = RON− KS,

where sensitivity

(2)S = RON− MON.

S is a measure of the difference in auto-ignition cheistry between PRF and the non-PRF fuel being csidered, on moving from the MON to the RON teconditions; for a PRF fuel,S is zero. For a non-PRFfuel, the OI is the octane number of the PRF fuel wthe equivalent auto-ignition characteristics at the pticular condition.K is a constant depending on thoperating conditions—it is not a property of the fuFrom Fig. 1 it can be seen that for both knock aHCCI, K decreases as we move to a lower polytroi.e., as the temperature for a given pressure decreK is positive or negative depending on whethertemperature for a given pressure is higher or lowthan the condition where the auto-ignition qualitydetermined by RON—inFig. 1, condition OP3 inHCCI tests and the RON line for knock tests. Ttwo lines do not coincide probably because of diffences in mixture strength—K is probably a functionof both the operating polytrope andΦ, for Φ > 0.3.HCCI experiments show thatK depends primarily onthe temperature at a given pressure[26,27] but thereis some evidence thatK also increases asΦ increasesfrom 0.3 to 0.4[26].

HCCI engines can be run at different operatconditions such thatK varies widely. Under conditionOP1, with a high intake pressure, Fuel D, a mixtuof 65% volume toluene and 35% volumen-heptane,with 84 RON and 73 MON was more resistantauto-ignition than iso-octane, PRF100, so thatK was−1.6. However an HCCI engine can be run in sua way thatK > 1 (seeFig. 1), by increasing the intake temperature[26]. In such cases, Fuel D woumatch a PRF fuel of an octane number less thanThus compared to PRF 84, Fuel D becomes morless resistant to auto-ignition depending on whetthe polytrope is below or above the OP3 polytroIn practice, compared to a PRF fuel, a sensitive f(with aromatics, olefins, oxygenates) becomes m

.

resistant to auto-ignition if the pressure is increafor a given temperature, and less resistant to aignition if the temperature is increased for a givpressure.

If the temperature for a given pressure is evlower than in the RON test, the non-PRF fuel wbe even more resistant to auto-ignition compareda PRF fuel of the same RON at this new condition—will match a PRF fuel with an octane number highthan its own RON;K will be negative. Similarly ifthe temperature is increased beyond the MONcondition, the PRF fuels become even more resisto auto-ignition in comparison to sensitive fuels athe sensitive fuel will have an OI less than its MOK will be greater than unity. The effect of pressutemperature, and, to a limited extent, mixture strenon different fuel chemistries must be understoodorder to explain the behavior of non-PRF fuels undifferent conditions.

3.2. Co-oxidation reactions

In a mixture of fuels the obvious chemical copling during the combustion is the radical pool (OH, and H). However, in a mixture consisting of twor more fuel components that is compressed frolow temperature until auto-ignition, there is also tpossibility that chemical interactions are taking plabetween the different fuel components and their racals, Examples of co-oxidation reactions are

(3)RH+ R•1 = R• + R1H

and

(4)R1OO• + RH= R1OOH+ R•,where RH is the fuel, R• is alkyl radical after H ab-straction, and ROO• an alkyl-peroxy radical formedwhen the alkyl radical reacts with molecular oxyge

If co-oxidation reactions are neglected unduestrictions are introduced in the reaction paths fomixture of two fuels compared to the reactionseach of the two fuels alone. This may not be imediately obvious but the following simple exampclearly shows why this is so. Let us assume thatreactants,A andB, both can react to formC:

(5)2A → C; −r1 = k1C2A,

(6)2B → C; −r2 = k2C2B.

If we mix A and B we could assume that onthose reactions occur. This would correspond toincluding co-oxidation reactions. We could alsosume thatA andB can react with each other, corrsponding to including co-oxidation reactions:

(7)A + B → C; −r3 = k3CACB.


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If we consider a mixture ofA andB with total con-centrationCF = CA + CB the reaction rate wouldbecome

−r = −(r1 + r2 + r3) = k1C2A + k2C2

B + k3CACB

(8)= (k1α2 + k2(1− α)2 + k3α(1− α)

)C2

F ,

where

(9)α = CA

CF.

Now let A and B become chemically equal, foexample, assuming that one atom in aB molecule isfrom the same element but another isotope than inA.Then the reaction rate could be written in two way

−r = k1C2F = −(r1 + r2 + r3)

(10)= (k1α2 + k1(1− α)2 + k3α(1− α)

)C2

F .

Hence

(11)k1 = k1

(α2 + 1− 2α + α2 + k3

k1

(α − α2))

,

and

(12)1= (2− n)α2 − (2− n)α + 1,

where

(13)n = k3

k1.

The only value that can satisfy Eq.(12) for allvalues ofα is n = 2. The explanation of this mathematical fact that we have to count the third reactwith double reaction rate is that reaction(7) gets re-actants from two different populations of molecuwhile the two first reactions get both reactant mocules from the same population.

A more comprehensive discussion more directo co-oxidation kinetics can be found in[28], whichtreats low-temperature autoxidation of hydrocarband olefins. In that context the importance of coxidation reactions for the chemical kinetics of tautoxidation of mixtures is well established. Morecent work can for example be found in[29–31]whereco-oxidation reactions are used in pseudo-detamechanisms used to describe low-temperature oxtion of hydrocarbons and antioxidants.

4. Modeling procedure

A single-zone modeling approach (no heat trafer, crevices, and charge inhomogeneities) is uThe usefulness of the single-zone assumption iproviding an estimate of ignition delay time as a funtion of thermodynamic conditions in the combustichamber[32].

For problem setup and simulation with detailchemical kinetics we employ the AURORA softwawhich is the perfectly stirred reactor applicationthe CHEMKIN collection[33]. The internal combustion engine model of AURORA is set to solve thequations for a nonisothermal batch reactor (closystem), where the variation of the volume in a cobustion cylinder in an internal combustion engineprovided by the equations in Heywood[34]. Whena mechanism consists ofK species, there is a sof K + 1 nonlinear ordinary differential equationwhich by integration yields the temperature and mfractions. The pressure is calculated with the ideallaw.

As a starting point for detailed chemistry moeling of Fuels A and B (seeTable 2), the latestreaction mechanism from the Lawrence LivermoNational Laboratory (LLNL) combustion chemistgroup [15,16] was used. It consists of 4238 reations among 1034 species, most of them reversiThe chemical interactions betweenn-heptane and isooctane are only through the radical pool in the LLNmechanism.

To model Fuels C and D (seeTable 2) toluenechemistry is needed. As a first step, the detailed meanism from[35] and the detailedn-heptane mechanism version 2 from LLNL[16] were merged. Thetoluene mechanism in[35] has been validated by experiments of toluene oxidation in a an atmosphejet-stirred reactor, by simulating the oxidation of bezene at 0.46 to 10 atm under stirred reactor conditiothe ignition of benzene-oxygen-argon mixtures, athe combustion of benzene in flames. The mermechanism consisted of 619 species among 313actions, most of which were reversible.

All calculations were run on a Dell 650 PrecisioWorkstation at 3.06 GHz with 4 GB of RAM. A typical CPU time was for a run with Fuels A and B arou10 min and for Fuels C and D around 5 min. In the cculations the step size for the ODE solver (DASPin AURORA was 0.1 crank-angle degree, in accdance with the gathered experimental data points.corresponding CPU times for calculations involvisensitivity analysis described below depended oninterval for calculation and size of mechanism, bwere usual within 60 min.

5. Results and discussion

With the assumption that co-oxidation reactioare taking place as described above, these typereactions were added to the initial mechanisms forels A–D. First a validation of the mechanisms (mosthe PRF mechanism as more experimental dataavailable) is performed against shock-tube and racompression machine data. Then the experimen


rimentals in

Fig. 2. Calculated ignition-delay times for primary reference fuel mixtures at constant volume compared with expeshock-tube results from Fieweger et al.[36]. p = 40 bar,λ = 1.0. The LLNL mechanism with added co-oxidations reactionAppendix Aimproves the prediction for PRF80.

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the HCCI-engine are simulated and the impact ofoxidation reactions is discussed.

5.1. Validation of reaction mechanisms

The added co-oxidation reactions for the Pmechanism[15,16] together with their rate constanare listed inAppendix A. Based on[17] and similarreactions found forn-heptane in the LLNL mechanism (e.g., nc7h16+ c7h15-1= c7h15-2+ nc7h16)an activation barrier of 10–14 kcal/mol was takenfor the hydrogen abstraction reactions from isoctane by heptyl radicals (reactions 4239–4254Appendix A). For co-oxidation involving alkylperoxides abstracting hydrogen atoms from iso-octanen-heptane (reactions 4255–4286) a similar activaenergy between 15 and 20 kcal/mol was assumed afor reactions found in the LLNL mechanism forn-heptane and iso-octane (e.g., nc7h16+ c7h15o2-2=c7h15-3+ c7h15o2h-2 and ic8h18+ ac8h17o2=dc8h17+ ac8h17o2h). Also logical activation energies that accounted for the relative strengthprimary, secondary, and tertiary C–H bonds wadopted in the co-oxidation reactions. Consequenas tertiary bonds are weakest, these C–H bobreaking reactions were faster than secondaryprimary ones. Finally co-oxidation reactions involing two other isomers of heptane were assum2,4-dimethylpentane (denoted c7h162-4) and 2

dimethylpentane (denoted neoc7h16) in reacti4287–4370 inAppendix A.

Fig. 2 shows model predictions (constant volumsimulations) of shock-tube data from Fieweger et[36] with and without inclusion of co-oxidation reactions inAppendix A. For PRF0 and PRF100 thmechanism with and without co-oxidation gives bacally the same result as expected. The slight deviafor PRF100 at lower temperatures is due to the formtion of neoc7h16 and c7h162-4 from iso-octanecomposition. However, for the PRF80 mixture theis a significant improvement with co-oxidation reations included and the experimental data can bedicted well. When simulations were conducted wreactions 4287–4370 removed, it could be seenthose reactions were less significant compared toactions 4239–4286 in predicting shock-tube datathe PRF80 mixture.

In Fig. 3 model calculations with the PRF mecanism with and without co-oxidation reactions acompared with ignition delay times measured inrapid compression machine as a function of reseaoctane number[10]. The inclusion of co-oxidation reactions inAppendix A improves the prediction, buthe ignition delay times are still too large comparto the experiments. Tanaka et al.[18] also found bet-ter agreement between model predictions and expmental data by including a coupling reaction betwen-heptane and iso-octane. The shortcoming to pre


machine.
Fig. 3. Predicted ignition-delay times for primary reference fuels as a function of octane number in a rapid compressionp = 1 bar,T = 318 K, λ = 2.5. Filled rings: experimental results from Tanaka et al.[10]. Solid line: LLNL mechanism withadded co-oxidations reactions inAppendix A. Dashed line: LLNL mechanism[16].
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rapid compression machine ignition delay timesleaner mixtures may be due to an-heptane mechanism that is not perfectly tuned under these contions[37].

The same type of co-oxidations was assumedFuels C and D as for the PRF Fuels (seeAppendix B).There are no relevant shock-tube data forn-heptane/toluene blends available in the literature to validthe mechanism in the same way as for PRF fuels.we did perform constant volume calculations for tmerged mechanism with only toluene as reactant,found good agreement with shock-tube experimedata from[38]. When then-heptane/toluene mechnism was constructed the C1–C4 chemistry fromn-heptane was used. The constant volume calculatfor pure toluene were then a check that the ignitdelay times were not affected after this change tooriginal toluene mechanism.

5.2. Comparison between HCCI experiments andcomputed results

All HCCI engine calculations started at 99 cranangle degrees before top dead center. This isthe middle of the compression stroke and beforechemical reaction has had any influence on the hrelease. Also comparison between experimentaland model predictions is more reliable comparedstarting at inlet valve close (IVC) 139 crank-angle dgrees before top dead center (seeTable 1).

The pressure and the average cylinder tempture have been measured in HCCI experimentsdifferent fuels of different chemistries[25]. Howeverin engines, the charge is not truly homogeneous[39]primarily because the fresh charge mixes withresidual gases from the previous cycle. Hence aignition should start at these hot spots[40] whosetemperature would be higher than the average, btemperature. The difference,�T , between the temperature of the hot spot and the bulk temperatshould be larger, the cooler the intake charge. Hewe assume that�T at 99◦ before top dead centeour initial point in the calculation is∼45 K for OP1and∼25 K for OP3. These chosen values for�T arearbitrary but without such an increment on the msured temperature, especially Fuel A (PRF 94)Fuel D could not be made to ignite at OP1 and Oeven when they actually did ignite in experiments.

In Figs. 4 and 5predicted and experimental presures are plotted against crank angle for Fuels Aand C, D, respectively, for operating condition O(high intake temperature/low intake ressure). The cresponding curves for Fuels B and D at operating cdition OP1 (low inlet temperature/high inlet pressuare shown inFig. 6. Both simulations with and without added co-oxidation reactions inAppendices Aand B are shown. Obviously the single-zone mooverpredicts the pressure rise during auto-ignitionthis is of minor importance in this work where thtime of auto-ignition is more relevant.


P3 (lowr)

P3 (lowis

Fig. 4. Experimental and calculated pressures for Fuels A and B as a function of crank angle for operating condition Ointake pressure/high intake temperature). Initial temperature and pressure at the start of calculations (99◦ before top dead centeis 472 K, 1.74 bar for Fuel B and 455 K, 1.37 bar for Fuel A, respectively. ATDC, after top dead center.

Fig. 5. Experimental and calculated pressures for Fuels C and D as a function of crank angle for operating condition Ointake pressure/high intake temperature). Temperature and pressure at the start of calculations (99◦ before top dead center)472 K and 1.74 bar, respectively.

onssesn

Comparing Fuel B inFig. 4 (OP3) andFig. 6(OP1) shows that adding the co-oxidation reacti

does not change ignition delay at OP3 but decreaignition delay at OP1. After addition of co-oxidatio


P1 (highis

Fig. 6. Experimental and calculated pressures for Fuels B and D as a function of crank angle for operating condition Ointake pressure/low intake temperature). Temperature and pressure at the start of calculations (99◦ before top dead center)415 K and 3.34 bar, respectively.

P1ore.e-on

innd

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sednlyex-for

theasew-omesx-rlierfseee insult

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reactions the change of reactivity of Fuel B from Oto OP3 agrees better with experiments than befFor Fuels C and D the inclusion of co-oxidation ractions significantly improves the model predictifor OP3 (seeFig. 5). In fact, Fuel C did not evenignite without adding the co-oxidation reactionsAppendix B. The kinetic models with co-oxidatioreaction give similar ignition delay for Fuel B anFuel D at OP3.

Fig. 6shows that adding co-oxidation reactionsFuel D decreases the ignition delay at OP1. Both wand without co-oxidation reaction we get that Fuehas about 5 CAD less ignition delay than Fuel DOP1 (seeFig. 6).

Figs. 7 and 8show the heat-release rates (J/deg)for Fuels B and D for conditions OP3 and OP1,spectively. The modeled heat-release rates havemultiplied by 0.1 and 0.2 for OP3 and OP1, resptively, a consequence of using a single-zone mothat overpredicts the heat release rate. The simuland experimental ignition delays are close to eother at OP3 and that in both experiments and simtions Fuel B ignites more than 5 CAD before Fuel DOP1. However, the simulated ignition delay increabetween OP3 and OP1 for Fuel D while it was maiunchanged for Fuel B. On the other hand, theperimental ignition delay was mainly unchangedFuel D while it decreased for Fuel B.

Moreover, the mechanisms cannot predicttrends in comparing the low-temperature heat relefor the fuels at OP1. The model predicts that lotemperature heat release starts earlier and bechigher for Fuel D compared to Fuel B, while the eperiments predict that the heat release starts eafor Fuel B than for Fuel D with similar amounts oenergy released by low-temperature chemistry (Fig. 8). The double peaks for the main heat releasFig. 8are predicted by the model and are not a reof bad resolution.

Thus, by adding co-oxidation reactions to thenetic models, we could predict that the differenceignition delay between Fuel B and D, evident at codition OP1, disappears for condition OP3. This wnot possible without co-oxidation reactions. Howevthe changes of ignition delays for each fuel did nagree well with experimental data. This may havedo with the difficulty in determining the most apprpriate starting temperatures for the simulationsto inhomogeneities of the charges, including hot-sformation, in the HCCI experiments.

The results for OP2 and OP4 not shown in figuwere in accordance with the results discussed abfor OP1 and OP3. In addition to trends regardcombustion phasing with and without co-oxidatireactions, the model could in line with experimepredict that Fuel C did not ignite for OP1 and O(high intake pressure/low intake temperature).


ting9

Fig. 7. Experimental and calculated heat release rate (J/deg) for Fuels B and D as a function of crank angle for operacondition OP3 (low intake pressure/high intake temperature). Temperature and pressure at the start of calculations (9◦ beforetop dead center) is 472 K and 1.74 bar, respectively.

elP1and

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iner,co-

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ayser-

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el Bthe

co-

-orion

ith

-oupen--

en-

ro-pidereh a

5.3. Conversion of individual fuel components

Fig. 9 shows the conversion of the individual fucomponents for Fuel B calculated for conditions Oand OP3. Different trends can be seen for OP1OP3. As could be expected fromFig. 4 showing thepressure, for OP3 there is no difference in the reswith or without co-oxidation reactions. One likeexplanation is that OP3 is in the negative tempeture coefficient (NTC) region[24,41] for this typeof fuel and that the effect of new reaction pathscompensated by the effect of those parts in the meanism that gives NTC behavior. For OP1 on the othand, the difference is evident. Fuel B experiencool flame behavior and around 40% ofn-heptane(nc7h16) is consumed. On turning off the reactionsAppendix Athe cool flame response is much weakalthough present. This indicates the importance ofoxidation between iso-octane (ic8h18) andn-heptane(nc7h16) for OP1.

As already noted in the theoretical discussabove, the increased conversion of both fuel comnents is simply the effect of new reaction paths beadded for both components. Obviously this geneeffect is important since it decreases ignition delsignificantly resulting in better agreement with expiments.

Fig. 10shows a bar plot of the fractional contribtion of the production of c7h15-2 radicals from 99

20 crank-angle degrees before top dead center, Fuand OP1. The bars are calculated by normalizingintegral of rate of production (mol/(cm3 s)) for themost important reactions. As would be expected,oxidation reactions with iso-octane andn-heptane areimportant prior to auto-ignition.

Figs. 11 and 12show the conversion of the individual fuel components for Fuel D calculated fconditions OP3 and OP1, respectively. The initiatof toluene is the formation of benzyl (PHCH2) andhydroperoxy radicals by the reaction of toluene woxygen:

TOLUEN + O2 = PHCH2 + HO2. (14)

Reaction(14) can begin at relatively low temperatures since the C–H bonds of the methyl grin toluene have unusually low bond dissociationergy [41]. As the radical pool builds by the lowtemperature oxidation ofn-heptane, the reaction

TOLUEN + OH = PHCH2 + H2O (15)

starts to dominate the toluene consumption and bzyl production. This in turn will inhibitn-heptane ox-idation as toluene competes withn-heptane for OHradicals. Benzyl radicals, the product in reaction(15),are less reactive compared to heptyl radicals pduced byn-heptane and OH. Note that there is a rapartial conversion at an early CAD, and then this a plateau in toluene conversion combined wit


ting9

ngle for

Fig. 8. Experimental and calculated heat release rate (J/deg) for Fuels B and D as a function of crank angle for operacondition OP1 (high intake pressure/low intake temperature). Temperature and pressure at the start of calculations (9◦ beforetop dead center) is 415 K and 3.34 bar, respectively.

Fig. 9. Calculated conversion for individual fuel components of Fuel B (ic8h18 and nc7h16) as a function of crank aOP3 and OP1.

onhethe

on-

slow n-heptane conversion until the final conversiof toluene is taking place at a much later CAD. Tplateau in toluene conversion may be an effect of

thermal stability of the benzyl radicals due to electrdelocalization[41] resulting in an equilibrium condition.


99–20

ngle for

Fig. 10. Contribution of different reactions to overall rate of production for the c7h15-2 radical: Fuel B, OP1, Intervalcrank angles before top dead center.

Fig. 11. Calculated conversion for individual fuel components of Fuel D (nc7h16 and c6h5ch3) as a function of crank a
OP3.
to

ncerad-

-ind--

With co-oxidation reactions it is, accordingthe model, possible for benzyl radicals to attackn-heptane resulting in higher net fuel conversion sithese reactions consume a relative stable benzyl

ical while producing a reactive heptyl. The following reactions of heptyl will then produce OH thatturn will convert more toluene into benzyl, accoring to reaction(15), leading to the higher initial con


ngle for
Fig. 12. Calculated conversion for individual fuel components of Fuel D (nc7h16 and c6h5ch3) as a function of crank aOP1.
rebe

ex-arts

i-

nter,liz-

tn-ile-

-ity

atrm

re

first-s

i-

-

ul-lu-

ds-alityor-ke

blesare

version of both fuels that can be seen inFigs. 11and 12.

Note that the partialn-heptane conversion is mopronounced at OP1 than at OP3. Again this maydue to compensation of some of that effect bypected NTC behavior at OP3 conditions by some pof then-heptane oxidation mechanism[24,41].

Fig. 13 shows a bar plot of the fractional contrbution of the production of benzyl (PHCH2) from99 to 28 crank-angle degrees before top dead ceFuel D and OP1. The bars are calculated by normaing the integral of rate of production (mol/cm3 s) forthe most important reactions.Fig. 13supports the facthat reaction(15) above is the dominant path for bezyl production when the radical pool builds up, whreactions 1–4 inAppendix Bdominates the consumption of benzyl.

5.4. Sensitivity analysis

To further examine the fuel chemistry in the lowtemperature region prior to auto-ignition, a sensitivanalysis was carried out.

The system of ordinary differential equations thdescribe the physical problem are of the general fo

(16)dϕ

dt= F(ϕ, t, a),

where ϕ, in this case, is the vector of temperatuand mass fractions. The parametera represents the

rate expressions for the gas-phase reactions. Theorder sensitivity coefficient matrix is then defined a

(17)wj,i = ∂ϕ

∂αi,

where the indicesj andi refer to the dependent varables and reactions, respectively.

Differentiating Eq.(17) with respect to the preexponentialsAi yields

(18)dwj

dt= ∂F

∂ϕ· wj,i + ∂F j

∂αi.

In DASPK, the sensitivity equations are solved simtaneously with the dependent variables of the sotion itself. The Jacobian matrix∂F/∂ϕ in Eq. (18)is exactly the one that is required by the backwardifferentiation formula method in solving the originmodel problem, so it is readily available for sensitivcomputation. The raw sensitivity coefficients are nmalized in the form of logarithmic derivates to mathem more useful, e.g., for species mass fractions

(19)∂ lnYk

∂ lnαi

∣∣∣∣F

= αi

Yk

∂Yk

∂αi

∣∣∣∣F

.

Although the gas-phase species solution variaare mass fractions, the sensitivity coefficientscomputed in terms of mole fractions as follows,

αi

Xk

∂Xk

∂αi

∣∣∣∣F

= αi

Yk

∂Yk

∂αi

∣∣∣∣F

− αiW̄

Kg∑j=1

1

Wj

∂Yk

∂αi

∣∣∣∣F

,

(20)


l

1.

Fig. 13. Contribution of different reactions to overall rate of production for the benzyl (PHCH2) radical: Fuel D, OP1, interva99–28 crank angles before top dead center.

Fig. 14. Normalized first-order sensitivity coefficients of the OH radical with respect to preexponentials for Fuel B at OP−20CA ATDC, T = 826 K,p = 46.5 bar.

sr

erct

tiv-

whereXk are the mole fractions,Wj are the speciemolecular weights, andW̄ is the mean moleculaweight of the mixture.

Fig. 14shows a bar plot of normalized first-ordsensitivity coefficients of the OH– radical with respeto preexponentials for Fuel B at OP1. The sensi


1.
Fig. 15. Normalized first-order sensitivity coefficients of the OH radical with respect to preexponentials for Fuel D at OP−28CA ATDC, T = 751 K,p = 31.3 bar.
nk-owntednsi-

t-then-nk

owne

di-oreis-an

ion.

Di-ure,chlownothent

a-

genter-

on–gengenaro-oci-

ostessrom

use-reeas-rgyefin.ento

enlly

al--vee ofss

ity calculation was done between 22 and 20 craangles before top dead center and the position shin Fig. 14is 20◦ before top dead center. It can be nothat co-oxidation reactions are among the most setive for building up the radical pool.

In Fig. 15 shows a bar plot of normalized firsorder sensitivity coefficients of the OH radical wirespect to preexponentials for Fuel D at OP1. The ssitivity calculation was done between 30 and 28 craangles before top dead center and the position shin Fig. 15 is 28◦ before top dead center. It can bnoted that co-oxidation reactions 1–4 inAppendix Bare among the most sensitive for building up the racal pool as they transform benzyl radicals to the mreactive heptyl radicals. This also supports the dcussion above that co-oxidation reactions lead toincreased OH production and a faster fuel convers

5.5. An attempt at chemical explanation of theco-oxidation effects

The ignition delays of Fuels B (PRF84) and(toluene/n-heptane, RON84) in the HCCI experments are almost equal at OP3 (low intake presshigh intake temperature) while Fuel B ignites muearlier than Fuel D at OP1 (high intake pressure,intake temperature). Thus their ignition delays docorrespond to their RON or MON. This raises tquestion if co-oxidation reactions could be importa

for this behavior. The following discussion summrizes our attempt to answer this question.

n-heptane has 10 secondary carbon–hydrobonds and 6 primary ones. Iso-octane has onetiary carbon–hydrogen bond, two secondary carbhydrogen bonds, and 15 primary carbon–hydrobonds. Toluene has three primary carbon–hydrobonds and five carbon–hydrogen bonds on thematic nucleus. Due to the increasing bond dissation energies free radicals abstract hydrogen measily from the tertiary carbon–hydrogen bonds, leasily from the secondary bonds, and least easily fthe primary bonds in iso-octane andn-heptane. Theabstraction of hydrogen from the aromatic nuclein toluene is very difficult and may almost be nglected while abstraction of hydrogen from the thprimary carbon–hydrogen bonds would be the eiest case according to the bond dissociation enethat is 5 kcal/mol less for a primary bond in toluenthan for a tertiary carbon–hydrogen bond in a parafHowever, the benzyl radicals formed after hydrogabstraction from toluene are thermally stable dueelectron delocalization and their reaction with oxygat auto-ignition temperatures is thermodynamicaless favored. They will preferably take part in radicradical reactions[41]. The radicals formed from isooctane andn-heptane, on the other hand, will hanumerous reaction paths available. However, somthe reaction paths inn-heptane oxidation and to a le


ionlled

-an

fromoxy

inase.om

edso-

oreiona-usns

so-se

.ureble1,

ingighthe

flu-uld

CIhisla-rgeheereilel Dbe

etic

enithom-ant

i-bem-r.to

ro-ionCI

ri-/that

iorturenin-the

rchishthee

up-orIm-nsw-ed

extent in iso-octane oxidation result in a moderator decrease of the oxidation rate, within the so-caNTC temperature region[41].

If we compare an iso-octane/n-heptane mixturewith a toluene/n-heptane mixture the addition of cooxidation reactions to the kinetic models would methat we add steps where free radicals generatedn-heptane, such as heptyl, hydroperoxy, and alkradicals, may abstract hydrogen from iso-octanethe first case and from toluene in the second cAlso radicals generated from iso-octane and frtoluene may abstract hydrogen fromn-heptane. How-ever, the number of reaction paths for radicals formby hydrogen abstraction is much higher in the ioctane case than in the toluene case. Furthermthe benzyl radicals formed by hydrogen abstractfrom toluene have a limited power to initiate oxidtion chain reactions due their thermal stability. Thwe would expect that if we add co-oxidation reactioto the kinetic models outside the NTC region the ioctane/n-heptane mixture would appear to increamore in reactivity than the toluene/n-heptane mixtureSuch an effect would occur at high intake pressand low intake temperature (OP1) due to favoraconditions for low-temperature chemistry since OPunlike OP3, is outside the NTC region. When addco-oxidation reactions at low intake pressure and hintake temperature (OP3), the conditions are inNTC region and the iso-octane/n-heptane mixturewould not increase in reactivity while then-heptane/toluene would do so to some extent due to less inence of the NTC effects. Such an explanation woagree well with Leppard’s work[24] as discussed inthe introduction.

Obviously the experimental results in the HCtests concerning Fuels B and D are in line with targument if some of the deviations between simutions and experiments could be explained by chainhomogeneity and the formation of hot spots. Texperimental results show that the two fuels wmore equal in terms of ignitions delays at OP3 whFuel B had much shorter ignition delays than Fueat OP1. In the simulations this behavior could only

seen if co-oxidation reactions were used in the kinmodels.

6. Conclusions

Auto-ignition of fuel mixtures including primaryreference fuels andn-heptane/toluene blends has bemodeled with detailed chemical kinetics together wa single-zone adiabatic model, and the results cpared with experimental data. The most importfindings are summarized below.

• The addition of co-oxidation reactions to the knetic model improved the prediction of shock-tudata for PRF80 and ignition delay times in rapid copression machines as a function of octane numbe

• By adding co-oxidation reactions, analogousthe corresponding reactions in autoxidation of hydcarbons, a significant improvement of the predictof the general trend of auto-ignition phasing in HCcombustion of fuel mixtures was found.

• The model could, in agreement with the expements, predict that iso-octane/n-heptane and toluenen-heptane with research octane number 84 (notethe motor octane number for such a toluene/n-heptanemixture is 73) have a similar auto-ignition behavat low intake pressure and high intake temperawhile iso-octane/n-heptane auto-ignites earlier thatoluene/n-heptane at high intake pressure and lowtake temperature. This could only be predicted byuse of co-oxidation reactions.

Acknowledgments

Financial support from the Swedish ReseaCouncil under Contract No. 2002-5807, the Swedgovernment, Volvo, Scania CV, and Shell under“Green Car” project is gratefully acknowledged. Walso thank Professor Hans-Erik Ångström for his sport, Eric Lycke in the engine laboratory at KTH fhis help, and guest researcher Matthew Bardsley,perial College, for his help in conducting calculatiowithin a summer project. Finally we thank the revieers for valuable comments that significantly improvthe quality of our paper.

ism
Appendix ARate constants for added co-oxidation reactions betweenn-heptane (nc7h16) and iso-octane (ic8h18) to the LLNL mechan[15,16]
4239. ic8h18+ c7h15-1= nc7h16+ ac8h17 9.00E+11 0.0 13500.04240. ic8h18+ c7h15-1= nc7h16+ bc8h17 2.00E+11 0.0 11200.04241. ic8h18+ c7h15-1= nc7h16+ cc8h17 1.00E+11 0.0 9000.04242. ic8h18+ c7h15-1= nc7h16+ dc8h17 6.00E+11 0.0 13500.04243. ic8h18+ c7h15-2= nc7h16+ ac8h17 9.00E+11 0.0 14500.04244. ic8h18+ c7h15-2= nc7h16+ bc8h17 2.00E+11 0.0 11200.04245. ic8h18+ c7h15-2= nc7h16+ cc8h17 1.00E+11 0.0 10000.0

(continued on next page)


Appendix A (continued)

4246. ic8h18+ c7h15-2= nc7h16+ dc8h17 6.00E+11 0.0 14500.04247. ic8h18+ c7h15-3= nc7h16+ ac8h17 9.00E+11 0.0 14500.04248. ic8h18+ c7h15-3= nc7h16+ bc8h17 2.00E+11 0.0 11200.04249. ic8h18+ c7h15-3= nc7h16+ cc8h17 1.00E+11 0.0 10000.04250. ic8h18+ c7h15-3= nc7h16+ dc8h17 6.00E+11 0.0 14500.04251. ic8h18+ c7h15-4= nc7h16+ ac8h17 9.00E+11 0.0 14500.04252. ic8h18+ c7h15-4= nc7h16+ bc8h17 2.00E+11 0.0 11200.04253. ic8h18+ c7h15-4= nc7h16+ cc8h17 1.00E+11 0.0 10000.04254. ic8h18+ c7h15-4= nc7h16+ dc8h17 6.00E+11 0.0 14500.04255. ac8h17o2+ nc7h16= ac8h17o2h+ c7h15-1 3.15E+13 0.0 17500.04256. ac8h17o2+ nc7h16= ac8h17o2h+ c7h15-2 2.10E+13 0.0 15500.04257. ac8h17o2+ nc7h16= ac8h17o2h+ c7h15-3 2.10E+13 0.0 15500.04258. ac8h17o2+ nc7h16= ac8h17o2h+ c7h15-4 1.05E+13 0.0 15500.04259. bc8h17o2+ nc7h16= bc8h17o2h+ c7h15-1 3.15E+13 0.0 17500.04260. bc8h17o2+ nc7h16= bc8h17o2h+ c7h15-2 2.10E+13 0.0 15500.04261. bc8h17o2+ nc7h16= bc8h17o2h+ c7h15-3 2.10E+13 0.0 15500.04262. bc8h17o2+ nc7h16= bc8h17o2h+ c7h15-4 1.05E+13 0.0 15500.04263. cc8h17o2+ nc7h16= cc8h17o2h+ c7h15-1 3.15E+13 0.0 17500.04264. cc8h17o2+ nc7h16= cc8h17o2h+ c7h15-2 2.10E+13 0.0 15500.04265. cc8h17o2+ nc7h16= cc8h17o2h+ c7h15-3 2.10E+13 0.0 15500.04266. cc8h17o2+ nc7h16= cc8h17o2h+ c7h15-4 1.05E+13 0.0 15500.04267. dc8h17o2+ nc7h16= dc8h17o2h+ c7h15-1 3.15E+13 0.0 17500.04268. dc8h17o2+ nc7h16= dc8h17o2h+ c7h15-2 2.10E+13 0.0 15500.04269. dc8h17o2+ nc7h16= dc8h17o2h+ c7h15-3 2.10E+13 0.0 15500.04270. dc8h17o2+ nc7h16= dc8h17o2h+ c7h15-4 1.05E+13 0.0 15500.04271. c7h15o2-1+ ic8h18= ac8h17+ c7h15o2h-1 1.21E+14 0.0 18500.04272. c7h15o2-2+ ic8h18= ac8h17+ c7h15o2h-2 1.21E+14 0.0 18500.04273. c7h15o2-3+ ic8h18= ac8h17+ c7h15o2h-3 1.21E+14 0.0 18500.04274. c7h15o2-4+ ic8h18= ac8h17+ c7h15o2h-4 1.21E+14 0.0 18500.04275. c7h15o2-1+ ic8h18= bc8h17+ c7h15o2h-1 3.06E+13 0.0 15500.04276. c7h15o2-2+ ic8h18= bc8h17+ c7h15o2h-2 3.06E+13 0.0 15500.04277. c7h15o2-3+ ic8h18= bc8h17+ c7h15o2h-3 3.06E+13 0.0 15500.04278. c7h15o2-4+ ic8h18= bc8h17+ c7h15o2h-4 3.06E+13 0.0 15500.04279. c7h15o2-1+ ic8h18= cc8h17+ c7h15o2h-1 1.53E+13 0.0 14500.04280. c7h15o2-2+ ic8h18= cc8h17+ c7h15o2h-2 1.53E+13 0.0 14500.04281. c7h15o2-3+ ic8h18= cc8h17+ c7h15o2h-3 1.53E+13 0.0 14500.04282. c7h15o2-4+ ic8h18= cc8h17+ c7h15o2h-4 1.53E+13 0.0 14500.04283. c7h15o2-1+ ic8h18= dc8h17+ c7h15o2h-1 8.07E+13 0.0 18500.04284. c7h15o2-2+ ic8h18= dc8h17+ c7h15o2h-2 8.07E+13 0.0 18500.04285. c7h15o2-3+ ic8h18= dc8h17+ c7h15o2h-3 8.07E+13 0.0 18500.04286. c7h15o2-4+ ic8h18= dc8h17+ c7h15o2h-4 8.07E+13 0.0 18500.04287. ic8h18+ xc7h15= c7h162-4+ ac8h17 9.00E+11 0.0 13500.04288. ic8h18+ xc7h15= c7h162-4+ bc8h17 2.00E+11 0.0 11200.04289. ic8h18+ xc7h15= c7h162-4+ cc8h17 1.00E+11 0.0 9000.04290. ic8h18+ xc7h15= c7h162-4+ dc8h17 6.00E+11 0.0 13500.04291. ic8h18+ yc7h15= c7h162-4+ ac8h17 9.00E+11 0.0 14500.04292. ic8h18+ yc7h15= c7h162-4+ bc8h17 2.00E+11 0.0 11200.04293. ic8h18+ yc7h15= c7h162-4+ cc8h17 1.00E+11 0.0 10000.04294. ic8h18+ yc7h15= c7h162-4+ dc8h17 6.00E+11 0.0 14500.04295. ic8h18+ zc7h15= c7h162-4+ ac8h17 9.00E+11 0.0 14500.04296. ic8h18+ zc7h15= c7h162-4+ bc8h17 2.00E+11 0.0 11200.04297. ic8h18+ zc7h15= c7h162-4+ cc8h17 1.00E+11 0.0 10000.04298. ic8h18+ zc7h15= c7h162-4+ dc8h17 6.00E+11 0.0 14500.04299. ic8h18+ xc7h15o2= ac8h17+ xc7h15o2h 1.21E+14 0.0 18500.04300. ic8h18+ yc7h15o2= ac8h17+ yc7h15o2h 1.21E+14 0.0 18500.04301. ic8h18+ zc7h15o2= ac8h17+ zc7h15o2h 1.21E+14 0.0 18500.04302. ic8h18+ xc7h15o2= bc8h17+ xc7h15o2h 5.60E+13 0.0 15500.04303. ic8h18+ yc7h15o2= bc8h17+ yc7h15o2h 5.60E+13 0.0 15500.0




4304. ic8h18+ zc7h15o2= bc8h17+ zc7h15o2h 5.60E+13 0.0 15500.04305. ic8h18+ xc7h15o2= cc8h17+ xc7h15o2h 2.80E+13 0.0 14500.04306. ic8h18+ yc7h15o2= cc8h17+ yc7h15o2h 2.80E+13 0.0 14500.04307. ic8h18+ zc7h15o2= cc8h17+ zc7h15o2h 2.80E+13 0.0 14500.04308. ic8h18+ xc7h15o2= dc8h17+ xc7h15o2h 8.07E+13 0.0 18500.04309. ic8h18+ yc7h15o2= dc8h17+ yc7h15o2h 8.07E+13 0.0 18500.04310. ic8h18+ zc7h15o2= dc8h17+ zc7h15o2h 8.07E+13 0.0 18500.04311. ac8h17o2+ c7h162-4= ac8h17o2h+ xc7h15 6.30E+13 0.0 17500.04312. ac8h17o2+ c7h162-4= ac8h17o2h+ yc7h15 6.30E+13 0.0 15500.04313. ac8h17o2+ c7h162-4= ac8h17o2h+ zc7h15 6.30E+13 0.0 16500.04314. bc8h17o2+ c7h162-4= bc8h17o2h+ xc7h15 6.30E+13 0.0 17500.04315. bc8h17o2+ c7h162-4= bc8h17o2h+ yc7h15 6.30E+13 0.0 15500.04316. bc8h17o2+ c7h162-4= bc8h17o2h+ zc7h15 6.30E+13 0.0 16500.04317. cc8h17o2+ c7h162-4= cc8h17o2h+ xc7h15 6.30E+13 0.0 17500.04318. cc8h17o2+ c7h162-4= cc8h17o2h+ yc7h15 6.30E+13 0.0 15500.04319. cc8h17o2+ c7h162-4= cc8h17o2h+ zc7h15 6.30E+13 0.0 16500.04320. dc8h17o2+ c7h162-4= dc8h17o2h+ xc7h15 6.30E+13 0.0 17500.04321. dc8h17o2+ c7h162-4= dc8h17o2h+ yc7h15 6.30E+13 0.0 15500.04322. dc8h17o2+ c7h162-4= dc8h17o2h+ zc7h15 6.30E+13 0.0 16500.04323. ic8h18+ nc7h15= neoc7h16+ ac8h17 9.00E+11 0.0 13500.04324. ic8h18+ nc7h15= neoc7h16+ bc8h17 2.00E+11 0.0 11200.04325. ic8h18+ nc7h15= neoc7h16+ cc8h17 1.00E+11 0.0 9000.04326. ic8h18+ nc7h15= neoc7h16+ dc8h17 6.00E+11 0.0 13500.04327. ic8h18+ oc7h15= neoc7h16+ ac8h17 9.00E+11 0.0 14500.04328. ic8h18+ oc7h15= neoc7h16+ bc8h17 2.00E+11 0.0 11200.04329. ic8h18+ oc7h15= neoc7h16+ cc8h17 1.00E+11 0.0 10000.04330. ic8h18+ oc7h15= neoc7h16+ dc8h17 6.00E+11 0.0 14500.04331. ic8h18+ pc7h15= neoc7h16+ ac8h17 9.00E+11 0.0 14500.04332. ic8h18+ pc7h15= neoc7h16+ bc8h17 2.00E+11 0.0 11200.04333. ic8h18+ pc7h15= neoc7h16+ cc8h17 1.00E+11 0.0 10000.04334. ic8h18+ pc7h15= neoc7h16+ dc8h17 6.00E+11 0.0 14500.04335. ic8h18+ qc7h15= neoc7h16+ ac8h17 9.00E+11 0.0 14500.04336. ic8h18+ qc7h15= neoc7h16+ bc8h17 2.00E+11 0.0 11200.04337. ic8h18+ qc7h15= neoc7h16+ cc8h17 1.00E+11 0.0 10000.04338. ic8h18+ qc7h15= neoc7h16+ dc8h17 6.00E+11 0.0 14500.04339. neoc7h16+ ac8h17o2= nc7h15+ ac8h17o2h 1.17E+14 0.0 17500.04340. neoc7h16+ bc8h17o2= nc7h15+ bc8h17o2h 1.17E+14 0.0 17500.04341. neoc7h16+ cc8h17o2= nc7h15+ cc8h17o2h 1.17E+14 0.0 17500.04342. neoc7h16+ dc8h17o2= nc7h15+ dc8h17o2h 1.17E+14 0.0 17500.04343. neoc7h16+ ac8h17o2= oc7h15+ ac8h17o2h 2.60E+13 0.0 15500.04344. neoc7h16+ bc8h17o2= oc7h15+ bc8h17o2h 2.60E+13 0.0 15500.04345. neoc7h16+ cc8h17o2= oc7h15+ cc8h17o2h 2.60E+13 0.0 15500.04346. neoc7h16+ dc8h17o2= oc7h15+ dc8h17o2h 2.60E+13 0.0 15500.04347. neoc7h16+ ac8h17o2= pc7h15+ ac8h17o2h 2.60E+13 0.0 15500.04348. neoc7h16+ bc8h17o2= pc7h15+ bc8h17o2h 2.60E+13 0.0 15500.04349. neoc7h16+ cc8h17o2= pc7h15+ cc8h17o2h 2.60E+13 0.0 15500.04350. neoc7h16+ dc8h17o2= pc7h15+ dc8h17o2h 2.60E+13 0.0 15500.04351. neoc7h16+ ac8h17o2= qc7h15+ ac8h17o2h 3.90E+13 0.0 17500.04352. neoc7h16+ bc8h17o2= qc7h15+ bc8h17o2h 3.90E+13 0.0 17500.04353. neoc7h16+ cc8h17o2= qc7h15+ cc8h17o2h 3.90E+13 0.0 17500.04354. neoc7h16+ dc8h17o2= qc7h15+ dc8h17o2h 3.90E+13 0.0 17500.04355. ic8h18+ nc7h15o2= nc7h15o2h+ ac8h17 2.52E+14 0.0 18500.04356. ic8h18+ oc7h15o2= oc7h15o2h+ ac8h17 2.52E+14 0.0 18500.04357. ic8h18+ pc7h15o2= pc7h15o2h+ ac8h17 2.52E+14 0.0 18500.04358. ic8h18+ qc7h15o2= qc7h15o2h+ ac8h17 2.52E+14 0.0 18500.04359. ic8h18+ nc7h15o2= nc7h15o2h+ bc8h17 2.60E+13 0.0 15500.04360. ic8h18+ oc7h15o2= oc7h15o2h+ bc8h17 2.60E+13 0.0 15500.04361. ic8h18+ pc7h15o2= pc7h15o2h+ bc8h17 2.60E+13 0.0 15500.0



s


4362. ic8h18+ qc7h15o2= qc7h15o2h+ bc8h17 2.60E+13 0.0 15500.04363. ic8h18+ nc7h15o2= nc7h15o2h+ cc8h17 1.30E+13 0.0 14500.04364. ic8h18+ oc7h15o2= oc7h15o2h+ cc8h17 1.30E+13 0.0 14500.04365. ic8h18+ pc7h15o2= pc7h15o2h+ cc8h17 1.30E+13 0.0 14500.04366. ic8h18+ qc7h15o2= qc7h15o2h+ cc8h17 1.30E+13 0.0 14500.04367. ic8h18+ nc7h15o2= nc7h15o2h+ dc8h17 1.68E+14 0.0 18500.04368. ic8h18+ oc7h15o2= oc7h15o2h+ dc8h17 1.68E+14 0.0 18500.04369. ic8h18+ pc7h15o2= pc7h15o2h+ dc8h17 1.68E+14 0.0 18500.04370. ic8h18+ qc7h15o2= qc7h15o2h+ dc8h17 1.68E+14 0.0 18500.0

kf = AT n exp(−E/RT ).A units mol cm s K;E units cal/mol.

Appendix BRate constants for added co-oxidation reactions betweenn-heptane (n-C7H16) and toluene (φ-CH3) to merged neat mechanismfor individual fuels[16,35]

A n E

1. φ-CH2 + nc7h16= φ-CH3 + c7h15-1 7.50E+11 0.0 80002. φ-CH2 + nc7h16= φ-CH3 + c7h15-2 5.00E+11 0.0 70003. φ-CH2 + nc7h16= φ-CH3 + c7h15-3 5.00E+11 0.0 70004. φ-CH2 + nc7h16= φ-CH3 + c7h15-4 2.50E+11 0.0 70005. c7h15o2-1+ φ-CH3 = φ-CH2 + c7h15o2h-1 3.00E+12 0.0 120006. c7h15o2-2+ φ-CH3 = φ-CH2 + c7h15o2h-2 3.00E+12 0.0 120007. c7h15o2-3+ φ-CH3 = φ-CH2 + c7h15o2h-3 3.00E+12 0.0 120008. c7h15o2-4+ φ-CH3 = φ-CH2+ c7h15o2h-4 3.00E+12 0.0 120009. φ-CH2 + c7h15o2-1= c7h15o-1+ φ-CH2O 3.00E+12 0.0 12000

10. φ-CH2 + c7h15o2-2= c7h15o-2+ φ-CH2O 3.00E+12 0.0 1200011. φ-CH2 + c7h15o2-3= c7h15o-3+ φ-CH2O 3.00E+12 0.0 1200012. φ-CH2 + c7h15o2-4= c7h15o-4+ φ-CH2O 3.00E+12 0.0 12000

kf = AT n exp(−E/RT ).A units mol cm s K;E units cal/mol.

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