ABSTRACTAn ignition delay correlation was developed for a toluenereference fuel (TRF) blend that is representative ofautomotive gasoline fuels exhibiting two-stage ignition.Ignition delay times for the autoignition of a TRF 91 blendwith an antiknock index of 91 were predicted throughextensive chemical kinetic modeling in CHEMKIN for aconstant volume reactor. The development of the correlationinvolved determining nonlinear least squares curve fits forthese ignition delay predictions corresponding to differentinlet pressures and temperatures, a number of fuel-airequivalence ratios, and a range of exhaust gas recirculation(EGR) rates. In addition to NO X control, EGR isincreasingly being utilized for managing combustion phasingin spark ignition (SI) engines to mitigate knock. Therefore,along with other operating parameters, the effects of EGR onautoignition have been incorporated in the correlation toaddress the need for predicting ignition delay in SI enginesoperating with EGR. Unlike the ignition delay expressionsavailable in literature for primary reference fuel blends, thecorrelation developed in the present study can predict ignitiondelay for a TRF blend, a more realistic gasoline surrogate.

1. INTRODUCTIONTwo of the means to achieve the objective of improved fueleconomy in spark ignition (SI) engines are (a) improving thefuel conversion (thermal) efficiency by increasing thecompression ratio, and (b) increasing the specific output(brake power per unit displacement) through turbochargingand downsizing the engine. The ability to raise in-cylinderpeak pressures in either mechanism is, however, limited byknock. Accurate prediction of autoignition phasing is thuscritical in designing engines with improved efficiency.Clearly, such a prediction also is pertinent to thehomogeneous charge compression ignition (HCCI)technology, which relies on controlled autoignition throughcompression of the homogeneously mixed oxidizer-fuelmixture. Detailed chemical kinetic mechanisms can beemployed to predict autoignition. However, their sheercomplexity presents a serious challenge in terms of directlyincorporating them in engine simulation or computationalfluid dynamics (CFD) tools. Therefore, there is a need for acomputationally feasible autoignition model that accuratelycaptures the complexity of fuel oxidation in SI engines undervarying operating conditions and is easy to use. This need hasprompted the development of empirical autoignition models.A pressure-temperature correlation of the form

Ignition Delay Correlation for PredictingAutoignition of a Toluene Reference Fuel Blend inSpark Ignition Engines

2011-01-0338Published

04/12/2011

Asim IqbalOhio State Univ.

Ahmet SelametOhio State Univ

Ronald ReeseChrysler

Roger VickChrysler Powertrain Engrg

Copyright © 2011 SAE International

doi:10.4271/2011-01-0338

(1)

for predicting ignition delay in SI engines, which is based onempirical data and employs a global Arrhenius reaction ratewas first introduced by Livengood and Wu [1], In Eq. (1), τ isthe ignition delay; p and T are the in-cylinder pressure andtemperature, respectively; and A, B, and n are constants. Thederivation of Eq. (1) is based on the assumption that thefunctional relationship between the concentration ratio [M]/[M]c and time t is given by

(2)

where [M] is the concentration of products of the overallcombustion reaction, and [M]c the concentration at the timeof autoignition t = tc. This concept was further developed byRifkin et al. [2], Burwell and Olson [3], and Vermeer et al.[4]. Douaud and Eyzat [5] introduced a fuel dependent termin Eq. (1) by expressing the constant A as

(3)

where C1 and C2 are fit coefficients, and antiknock index AKI= 0.5×(RON + MON) is the average of the research octanenumber (RON) and motor octane number (MON). Effortshave been made to improve the ignition delay correlation [ofEq. (1)] by modifying the fit coefficients [6,7], andincorporating fuel concentration [8] and fuel-air equivalenceratio [9,10] in the ignition delay correlation. While modifiedversions of the Douaud and Eyzat [5] model are commonlyused in engine simulation tools, these models all assume thecombustion initiation point can be modeled with a singleglobal reaction rate. These empirical models do not capturethe cool flame phenomenon exhibited by saturatedhydrocarbons (or paraffins) of the form CnH2n+2 with n > 2[11] which is a consequence of the negative temperaturecoefficient (NTC) of reaction rate. Competition betweenchain branching and terminating steps results in decreasingreaction rates as temperature increases, hence the term“negative temperature coefficient”. This NTC behaviormanifests itself in paraffin oxidation as two-stage ignition.The termination of the first stage ignition is a result of theinhibited branching, also known as degenerate branching.This mechanism is commonly referred to as the lowtemperature kinetic scheme because of the modesttemperature rise associated with it. The chain terminatingsteps become dominant and prevent the mixture fromcompletely reacting to reach its adiabatic flame temperature.An induction time follows until branching again becomes

dominant, leading to the second stage or hot ignition wherethe majority of heat is released. Figure 1 illustratestemperature profiles for single and two-stage ignitiontypically observed in a constant volume reactor (CVR) for aTRF blend. It is evident from Fig. 1 that for two-stageignition, the oxidation reaction proceeds in two distinctphases and this phenomenon cannot be captured with a singleglobal reaction rate. As saturated hydrocarbons are asignificant constituent of automotive gasoline fuels, it isimperative that the autoignition models capture the details oftwo-stage ignition to provide accurate ignition delaypredictions.

Figure 1. Single and two-stage ignition [Reactor: CVR;Fuel: TRF 91].

Yates and Viljoen [12] and Yates et al. [13] have developedan empirical ignition delay correlation that characterizes theeffects of the cool flame phenomenon by calculating theoverall ignition delay in two stages. This improvedcorrelation addresses the fundamental drawback ofautoignition models confined to a single global reaction rate.However, it is important to note that this correlation wasinitially calibrated for primary reference fuel (PRF) blends.Unlike PRF blends which are binary mixtures of the paraffinsn-heptane (C7H16) and iso-octane (C8H18), commercialgasoline is a complex blend of several different species whichcan be broadly classified into paraffins, olefins, aromatics,and naphthalenes (cycloparaffins) based on their molecularstructure. The presence of aromatics and olefins significantlyalters the chemical kinetics of the oxidation process, as unlikeparaffins, they do not exhibit NTC behavior. Leppard [14]has shown that the NTC behavior becomes more pronouncedwith decreasing pressures, increasing temperatures, anddecreased reaction times. These changes in operatingparameters are consistent with those encountered in movingfrom the RON test to the MON test conditions. As paraffinsexhibit NTC behavior, they are more resistant to autoignitionunder MON rating conditions compared to olefins and

aromatics. Therefore unlike a PRF blend for which the RONand MON ratings are identical, a fuel blend that includesaromatics and olefins will have a lower MON rating than itsRON rating. As gasoline blends are composed of severaldifferent species including aromatics and olefins they areoctane sensitive with different RON and MON ratings. Sincearomatic compounds are a major component (∼30%) ofgasoline [15,16], unlike PRF blends, fuel blends includingaromatic compounds can capture the fuel octane sensitivity ofgasoline fuels. Availability of well established detailedchemical kinetic mechanisms for toluene, an aromatic, makesit a suitable candidate for modeling the effect of aromatics ingasoline. Therefore, a TRF blend has been selected in thepresent study for the kinetic modeling.

The objective of this work is to develop an improvedempirical ignition delay correlation for a TRF 91 blend.Ignition delay predictions for operating conditions covering awide range of inlet pressures pin, inlet temperatures Tin, fuel-air equivalence ratios ϕ, and EGR rates obtained fromdetailed chemical kinetic simulations performed inCHEMKIN [17] are used to develop the correlation.

Section 2 briefly discusses the kinetic modeling performed inCHEMKIN and Section 3 describes in detail the developmentof the improved ignition delay correlation. Results anddiscussion are presented in Section 4, followed by concludingremarks in Section 5.

2. KINETIC MODELINGHydrocarbon oxidation is a complex chemical processinvolving a large number of different species and reactions.Most of the radicals and intermediates involved incombustion reactions are typically very short lived and areformed in small quantities. Consequently, their detection andmeasurement is difficult. This makes chemical kinetic modelsan indispensable tool for understanding the combustionmechanisms. Since knock is a fundamental problem in SIengines, one of the main objectives of kinetic modelingefforts has been to accurately capture the autoignition event.As the knocking tendency of the binary mixtures of n-heptaneand iso-octane in a Cooperative Fuel Research (CFR) engineis used to assign octane ratings to fuels, the oxidationchemistry of these two PRFs has been studied extensively,leading to the development of several reduced [18,19,20],skeletal [21], and global [22] kinetic mechanisms. Thecombustion chemistry group at the Lawrence LivermoreNational Laboratory (LLNL) has compiled a detailed kineticmechanism for PRF oxidation by combining n-heptane [23]and iso-octane [24] oxidation mechanisms. This mechanismis comprised of 1034 species and 4238 reactions, and isreferred to as PRF (LLNL). Toluene (C6H5CH3) is one of themore prominent aromatic components of gasoline fuels [16].This has prompted numerous experimental studies usingshock tubes, rapid compression machines (RCM), flow

reactors, and jet-stirred reactors to determine thecharacteristics of toluene oxidation. Lindstedt and Maurice[25] proposed one of the first detailed kinetic mechanisms fortoluene combustion. This mechanism has since been furtherdeveloped for a wide range of pressure and temperatureconditions [26,27,28,29]. Andrae et al. [30] have combined atoluene oxidation submechanism with the PRF (LLNL)mechanism to develop a detailed chemical kinetic scheme forthe autoignition of TRFs. Andrae [31] has developed adetailed kinetic mechanism for gasoline surrogate fuels bycombining his earlier mechanism [30] with submechanismsfor diisobutylene and ethanol. This mechanism is comprisedof 1121 species and 4961 reactions and will be hereafterreferred to as the Surrogate (Andrae). All predictions for theTRF 91 oxidation presented in this study were obtained usingthe Surrogate (Andrae) mechanism.

Simulating reaction systems with detailed chemical kineticmechanisms is computationally intensive as it requires thesolution of a large number of stiff differential equations.CHEMKIN, a computer software originally designed atSandia National Laboratories, facilitates the formulation,solution, and interpretation of a wide range of combustionproblems involving gas-phase and surface kinetics, and gastransport. It features a large variety of flame simulators, flowcomponents, and reactor models, including the closedhomogeneous constant volume reactor or CVR. Knock istypically observed in SI engines when the piston is near topdead center (TDC), at which point the volume of thecombustion chamber does not change very rapidly and thesurface area of the combustion chamber is at its minimum.Due to the relatively little change in volume of thecombustion chamber, reduced surface area for heat loss, andthe small time scales involved, autoignition may beapproximated as a constant volume adiabatic process. Thisapproximation allows the effects of various engine operationparameters to be studied qualitatively in a CVR. In addition, aCVR is analogous to the compressed volumes in rapidcompression machines and shock tubes, allowingcomparisons between CVR predictions and RCM/shock tubeexperiments. Since the CVR facilitates the study of acomplex problem like knock in a somewhat simplifiedmanner, it has been used for performing all simulations inthis work.

3. MODELING APPROACH ADOPTEDFOR DEVELOPING IMPROVEDIGNITION DELAY CORRELATIONThe ignition delay correlation proposed here builds upon themodel originally developed by Yates and Viljoen [12] andlater refined by Yates et al. [13] at the Sasol Advanced FuelLaboratory, or the Sasol model. As indicated in Section 1, theSasol model captures the cool flame effect by modeling theoverall ignition delay in two stages. For a two step process,

the conservation-of-delay principle [Eq. (2)] of Livengoodand Wu [1] can be rewritten as

(4)where t0 represents the start of the combustion process, t1 isthe time from the start of the reaction to the first stageignition which coincides with the appearance of the coolflames, and tAI is the overall ignition delay (see Fig. 2). In Eq.(4) τh,in and τh,CF represent the characteristic exothermicreaction delays evaluated at the initial and post cool flameconditions, respectively. The characteristic exothermicreaction delay can be described as the time from the start ofthe reaction to the ultimate heat release for a single stepprocess governed by a global reaction rate. Therefore, τh,inand τh,CF are essentially the time delays corresponding to twodifferent global reactions. Assuming constant pressure andtemperature during each stage and t0 = 0, Eq. (4) simplifies to

(5)

Equation (5) can be rearranged to obtain the overall ignitiondelay

(6)where

(7)

(8)and

(9)

In Eqs. (7,8,9) pin is the inlet pressure, Tin is the inlettemperature, pCF is the post cool flame pressure, ϕ is the fuel-air equivalence ratio, and ▵TCF is the temperature riseassociated with the first stage ignition and is defined as

(10)

Yates and Viljoen [12] have observed that as Tin increases thecool flame temperature rise ▵TCF decreases. As ▵TCF in Eq.(10) is a linear function of Tin, it can yield negative values for▵TCF at high Tin. Since negative values for ▵TCF arephysically not feasible, Yates and Viljoen [12] introduced thetermination function

(11)

to prevent ▵TCF from becoming negative. In Eqs.(7,8,9,10,11) β1, A1, n1, B1, βh, Ah, nh, Bh, X, ω, TEQ, κ, µ, σ,and C0 are coefficients determined from nonlinear leastsquares curve fits.

Figure 2. Description of the different terms associatedwith the Sasol model.

The Sasol model was first developed for PRF blends withoctane number (ON) ranging from 0 to 100 [12] and lateraugmented to predict ignition delay for blends of PRFs withmethanol [12] and ethanol [13]. In current work, the basicstructure of the Sasol model has been retained with the focuson developing an ignition delay correlation for a TRF 91blend (53.8% i-C8H18, 13.7% n-C7H16, and 32.5% C6H5CH3by liquid volume) that also accounts for the effect of EGR onautoignition. In addition to controlling NOX, EGR isincreasingly used to control combustion phasing and mitigateknock in contemporary SI engines. It is imperative that aneffective knock prediction tool capture the effect of EGR onautoignition. The ignition delay correlation proposed here hasbeen developed to address this need and captures the effectsof EGR on autoignition in addition to pin, Tin, and ϕ. Todevelop the correlation for TRF 91, ignition delay predictionswere obtained from CVR simulations for 1710 distinct cases,including 3 different inlet pressures pin = 12, 25, and 40 bar;19 different inlet temperatures over the range 650 ≤ Tin ≤1200 K; 5 different fuel-air equivalence ratios covering the

range 0.8 ≤ ϕ ≤ 1.2 in 0.1 increments; and 6 different exhaustgas recirculation (EGR) rates spanning the range 0 ≤ EGR ≤25% in 5% increments.

The present work models EGR as a mixture of CO2, H2O,and N2 (the products of complete combustion of the fuel) andintroduces it into the CVR at the same pin and Tin as the fuel-air mixture. In order to incorporate EGR in the ignition delaycorrelation, the effect of EGR on t1, ▵TCF, and tAI wasexamined. It was observed with increasing EGR, t1 and tAIincrease for all pin, as depicted in Fig. 3 (both in linear andlogarithmic scales for ignition delay) by colored open andsolid symbols, respectively. At a given Tin, the cool flametemperature rise ▵TCF decreases with increasing EGR for allpin, as illustrated in Fig. 4. Also, due to the lower heat releaseduring the first stage ignition with increasing EGR, theinduction time between the first and second stage ignition,tInduction = tAI - t1, increases (open black symbols in Fig. 3).The EGR term was introduced in the correlation in a mannerthat resembles the equivalence ratio term. Thus, the first stageignition delay t1 was proposed here to be of the form

(12)

Similarly, the two characteristic exothermic reaction delaysτh,in and τh,CF were defined as

(13)

and

(14)

Finally, the cool flame temperature rise ▵TCF in Eq. (14) isexpressed as

(15)

The form of the proposed EGR term as ensuredthat it contributed to increasing t1 and tAI and decreasing▵TCF for EGR > 0%. Therefore, the new correlation is

comprised of Eq. (6) along with Eqs. (11,12,13,14,15) insteadof Eqs. (7,8,9,10,11).

In order to obtain the overall ignition delay from Eq. (6), thefit coefficients associated with Eqs. (11,12,13,14,15) need tobe ascertained. These coefficients are obtained fromnonlinear least squares curve fits to ignition delay predictionsobtained from CHEMKIN for individual pin as a function ofTin. The curve fitting process involves three steps:

STEP 1: FIRST STAGE IGNITIONDELAYAs discussed in Section 1, the cool flame phenomenon isassociated with the competition between chain branching andterminating steps. Therefore at high Tin, where the chainbranching steps dominate, the cool flame phenomenon wasnot observed. To determine the coefficients for Eq. (12), theinitial delay time t1 was first ascertained from CHEMKINsimulations, for the cases where first stage ignition isobserved, as the time from the start of the reaction to thepoint of maximum temperature rise gradient. Next Eq. (12) isexpressed as a linear relation

(16)

and fit to the t1 values obtained from CHEMKIN for aspecific ϕ and EGR combination, as illustrated in Fig. 5.While Eq. (16) is linear in nature, t1 varies non-linearly athigh temperatures (Tin > 750 K) in Fig. 5. As Tin increases,high temperature kinetics start dominating and the reactionsystem starts shifting from the two-stage to the single-stageignition regime. The first stage ignition becomes difficult todetect and the cool flame temperature rise approaches zero,resulting in the non-linear variation of t1 with increasing Tin.Thus, to avoid inclusion of cases in which the occurrence ofthe first stage ignition is questionable, the curve fits areobtained only for the region where t1 varies linearly with inlettemperature, Tin ≤ 750 K in this case, to provide the valuesfor the coefficients β1, A1, n1, B1, and r1.

STEP 2: FIRST STAGE IGNITIONTEMPERATURE RISEIn this work ▵TCF was defined as the difference between thetemperature at the midpoint of the induction period after thefirst stage ignition and Tin. As the first stage ignition was notobserved at high Tin, ▵TCF values can be determined fromCHEMKIN simulations only for the cases where the firststage ignition is discernable. Equation (15) was fit to the▵TCF values obtained from CHEMKIN as illustrated in Fig. 6to determine the coefficients ω, TEQ, κ, µ, σ, and rCF.

Figure 3. Effect of EGR on t1, tAI, and tAI - t1 for different inlet pressures: (a) pin = 12 bar, and ϕ = 1.0; (b) pin = 25 bar and ϕ =1.0; and (c) pin = 40 bar and ϕ =1.0.

Figure 4. - First stage temperature rise [Reactor: CVR;Fuel: TRF 91; ϕ = 1.0].

Figure 5. First stage ignition delay t1 [Reactor: CVR;Fuel: TRF 91; ϕ =1.0; EGR = 0%].

Figure 6. First stage ignition temperature rise ▵TCF[Reactor: CVR; Fuel: TRF 91; ϕ =1.0; EGR = 0%].

STEP 3: OVERALL IGNITION DELAYThe coefficients obtained in Steps 1 and 2 were substituted inEqs. (12) and (15) to obtain t1 and ▵TCF for the temperaturerange 650 ≤ Tin ≤ 1200 K. These t1 and ▵TCF values alongwith Eqs. (11), (13), and (14) were substituted in Eq. (6)which was then fit to the tAI values obtained from CHEMKINsimulations as illustrated in Fig. 7. The overall ignition delaycurve fits yield the remaining 7 coefficients βh, Ah, nh, Bh, X,C0, and rh.

Figure 7. Overall ignition delay tAI [Reactor: CVR;Fuel: TRF 91; ϕ =1.0; EGR = 0%].

Steps 1-3 provide the 18 fit coefficients for a specific inletpressure. These steps were repeated for the differentcombinations of pin, ϕ, and EGR over the temperature range650 ≤ Tin ≤ 1200 K to yield 90 distinct sets of coefficients.Note that during the nonlinear least squares fitting procedure,all the coefficients were treated as fit parameters to minimizethe constraints on the equation being fitted. To determine aunique set of coefficients for a single ignition delaycorrelation that can capture the autoignition characteristics ofTRF 91 over the wide range of pin, Tjn, ϕ, and EGR rates,different coefficient sets were compared in order to identifysimple patterns in trends. These comparisons revealed thatwhile, β1, r1, ω, TEQ, κ, σ, rCF, nh, and rh could be treated asconstants, A1, B1, n1, µ, Ah, Bh, X, C0, and βh can beexpressed as linear functions of pin over the entire range ofoperating parameters. This condensed set of coefficients willbe referred to as the “TRF 91” correlation. Comparison ofcurve fits corresponding to specific pin (solid lines) withthose obtained from the “TRF 91” correlation (dashed lines)in Fig. 8 reveals that the overall ignition delay correlation fitsthe CHEMKIN tAI predictions.

Figure 8. Overall ignition delay curve fits [Reactor:CVR; Fuel: TRF 91; ϕ = 1.0; EGR = 0%].

4. DISCUSSION4.1. IGNITION DELAY CORRELATIONFOR TRF 91To examine the ability of a single ignition delay correlation(represented here by the “TRF 91” correlation) to predictautoignition effectively over the entire range of operatingconditions, curve fits from the new correlation were matchedwith CHEMKIN predictions. Figures 9 (a)-(f) depict samplecomparisons between the CHEMKIN ignition delaypredictions and the “TRF 91” correlation curve fits for aselected subset of the operating conditions examined in thisstudy. In Figs. 9 (a)-(f) the symbols represent CHEMKINpredictions. The lines correspond to “TRF 91” fits, and colorsindicate different pin. Considering that the “TRF 91” ignitiondelay correlation developed here covers a wide range ofoperating conditions and has four independent variables, pinTin, ϕ, and EGR, it was able to match the CHEMKINpredictions well. Note that the ability to effectively capturethe coupled effects of varying ϕ and EGR on autoignitionsimultaneously is unique to the “TRF 91” correlationdeveloped here.

4.2. EFFECT OF FUEL-AIREQUIVALENCE RATIO ONAUTOIGNITION As indicated in Section 3, to develop the ignition delaycorrelation, autoignition predictions were obtained for fivedifferent equivalence ratios spanning the range 0.8 ≤ ϕ ≤ 1.2in 0.1 increments. Figure 10 illustrates the ignition delaypredictions (both in linear and logarithmic scales) obtainedfrom CHEMKIN for ϕ = 0.8, 1.0, and 1.2 and no EGR. Thefirst stage ignition delay t1, the overall ignition delay tAI, andthe induction period between first and second stage ignitiontInduction decreased as the intake charge becomes fuel rich.Also, the rate at which tAI decreases slows down as ϕincreases. This trend became more evident in Fig. 11 whichdepicts the overall ignition delay predictions as a function ofϕ for a selected inlet temperature Tin = 750 K. Halstead et al.[32] observed experimentally a similar reduction in the rate atwhich tAI decreases with increasing ϕ for PRF 90.Comparison of ▵TCF values obtained from CHEMKINsimulations in Fig. 12 shows that the temperature riseassociated with the first stage ignition increased with ϕ. Thehigher energy release from richer mixtures during the firststage ignition speeds up the reactions leading up to thesecond stage ignition, resulting in shorter overall ignitiondelay times. Sjöberg and Dec [33] observed experimentallyan increase in cool flame activity with increasing ϕ for PRF60 and PRF 80, and Little et al. [34] demonstratedcomputationally an increase in first stage heat release withricher fuel-air mixtures for PRF 20. The ability of the ignitiondelay predictions for varying ϕ to replicate the trendsobserved experimentally in the literature lends credence tothe methodology adopted in this study in terms ofincorporating the effects of equivalence ratio into the “TRF91” ignition delay correlation.

Figure 9. Overall ignition delay tAI curve fits for pin = 12, 25, and 40 bar, 650 ≤ Tin ≤ 1200 K and different ϕ and EGRcombinations: (a) ϕ = 0.8 and EGR = 0%; (b) ϕ = 0.8 and EGR = 25%; (c) ϕ = 1.0 and EGR = 0%; (d) ϕ =1.0 and EGR = 25%;

(e) ϕ = 1.2 and EGR = 0%; and (f) ϕ = 1.2 and EGR = 25%.

Figure 10. Effect of ϕ on t1, tAI, and tAI - t1 for different inlet pressures: (a) pin = 12 bar and EGR = 0%; (b) pin= 25 bar andEGR = 0%; and (c) pin = 40 bar and EGR = 0%.

Figure 11. Effect of ϕ on overall ignition delay for Tin =750 K [Reactor: CVR; Fuel: TRF 91; EGR = 0%].

Figure 12. Effect of ϕ on first stage temperature rise▵TCF [Reactor: CVR; Fuel: TRF 91; EGR = 0%].

4.3. EFFECT OF EXHAUST GASRECIRCULATION ON AUTOIGNITIONAs elaborated in Section 3, increasing EGR increases t1, tAI,and tInduction while decreasing ▵TCF The lower heat releaseduring the first stage ignition slows down the reactionsleading up to the second stage ignition, resulting in longeroverall ignition delays. Introduction of EGR in the intakecharge significantly retards the oxidation process asillustrated in Fig. 13 for a specific case of ϕ = 1.0 and Tin =750 K. Increasing the EGR rate from 0 to 25 % significantlyincreases the ignition delay time for all three pin examined. Intheir engine experiments for a 95 RON unleaded fuel,Grandin et al. [35] observed that adding increasing amountsof EGR decreases combustion rates and suppresses thetemperature increase of the cylinder charge, which isexpected to result in longer ignition delays therefore

promoting mitigation of knock. Sjöberg and Dec [36] havedemonstrated experimentally that the addition of completestoichiometric products of combustion CO2, H2O, and N2,which predominantly constitute EGR, suppresses the heatrelease associated with first stage ignition, making EGR aneffective means for controlling combustion phasing thereforeknock. The consistency of the trends exhibited by the ignitiondelay predictions for varying amounts of EGR withexperimental observations in the literature lends evidence tothe fact that the new ignition delay correlation developed herecan effectively capture the changes in combustion chemistrydue to the introduction of EGR.

Figure 13. Effect of EGR on overall ignition delay forTin = 750 K [Reactor: CVR; Fuel: TRF 91; ϕ = 1.0].

4.4. OCTANE SENSITIVITY OF TRF 91As discussed earlier, aromatics do not exhibit NTC behaviorand consequently their presence in fuel blends significantlyalters the chemical kinetics of the oxidation process. Toexamine the impact of aromatics (toluene) on autoignition,overall ignition delay predictions from CHEMKIN werecompared in Fig. 14(a) for PRF 91 and TRF 91 over thetemperature range 650 ≤ Tin ≤ 1200 K. The two differentpressures have been selected to illustrate the effect of fueloctane sensitivity. For the PRF 91 blend RON = MON =91,and for the TRF 91 blend RON = 92.9 and MON = 89.23.The ignition delay predictions for PRF 91 exhibited a morepronounced NTC behavior than TRF 91 for pin = 12 barwhich manifests itself in the form of the increased time delaydifference between the two fuels in the NTC region. Thesignificant increase in the ignition delay times for PRF 91relative to TRF 91 with pin = 12 bar can be better observed inFig. 14(b) which depicts the ignition delays for the two fuelsin the NTC region on a linear scale. This behavior can beexplained on the basis of the difference in the MON rating ofthe two fuels. Leppard [14] has observed that the NTCbehavior is more pronounced at lower pressures, higher

temperatures, and shorter reaction times, conditions that aremore typical of the MON rating method rather than those ofthe RON rating method. In the NTC region reaction ratesdecrease with increasing temperature, therefore a morepronounced NTC behavior of a fuel indicates greaterresistance to autoignition. In Fig. 14, the lower pressure pin =12 bar corresponds to operating conditions more typical ofthe MON test and consequently the MON rating of the twofuels dictates their combustion chemistry. As MONPRF 91 >MONTRF 91, the resistance of PRF 91 to autoignition wasenhanced in the NTC region for pin = 12 bar, leading tolonger ignition delay times. The higher pressure in Fig. 14 ismore typical of the RON test and therefore the NTC behaviorof PRF 91 is suppressed for pin = 40 bar, resulting in a muchsmaller difference in the ignition delays of the two fuels. It isinteresting to note that even though the two fuel blends havean identical AKI, the TRF 91 blend was more prone toautoignition at low-to-mid Tin, with the PRF 91 blendshowing slightly greater propensity for knock at high Tin. Thedifferences between ignition delay predictions for PRF 91and TRF 91 suggest that knock prediction models based onPRF blends are likely to over-predict ignition delay undermost operating conditions. Figure 14 effectively demonstratesthat the autoignition characteristics of a TRF blend are quitedifferent from those of a PRF blend with the same AKI due tothe octane sensitivity of toluene.

Figure 14 (a). Comparison of overall ignition delay forPRF 91 and TRF 91 blends [Reactor: CVR; ϕ = 1.0;

EGR = 0%].

Figure 14 (b). Comparison of overall ignition delay forPRF 91 and TRF 91 blends in the NTC region [Reactor:

CVR; ϕ = 1.0; EGR = 0%].

4.5. IMPLEMENTATION OF THE “TRF91” IGNITON DELAY CORRELATIONIN ENGINE SIMULATION CODESAs described in Section 3, the “TRF 91” ignition delaycorrelation has been developed based on autoignitionpredictions obtained from CVR simulations in CHEMKIN.However, unlike in a CVR, the temperature, and pressure arechanging continuously in an engine. Livengood and Wu [1]have demonstrated that the constants A, B, and n of Eq. (1)determined for a particular fuel based on RCM experiments,can be used to explain the occurrence of knock in an enginefor the same fuel. They accomplished this by computing theintegral of Eq. (2) with the experimentally determined valuesof time varying pressure p(t) and temperature T(t) of the endgas and comparing the time tc at which the integral reaches avalue of 1 with the observed time of knock in the enginecycle. If a CVR can be used to approximate the kinetics in anRCM, it follows by extension that the method adopted byLivengood and Wu [1] can be applied to predict knock in anengine by integrating an ignition delay correlation developedusing CVR predictions. Note that the knock integral for theoverall ignition delay given by Eq. (4) has two parts on theleft side. In order to evaluate the first part, the timing of thefirst stage ignition needs to be determined. This is done byevaluating Eq. (12) at each discrete time step for theinstantaneous temperature and pressure in the engine until thefirst stage ignition delay integral attains a value of unity

(17)

In Eq. (17), t1 corresponds to the first stage ignition delay ofEq. (12) and tFirst stage represents the time from the start ofthe reaction to the cool flame heat release in an engineenvironment. Equation (13) and the first part of Eq. (4) whichcorresponds to the first stage ignition are evaluated from thestart of the engine cycle till Eq. (17) is satisfied. Next, themagnitude of ▵TCF is determined from Eqs. (15) and (11) forthe instantaneous temperature and pressure in the cylinder atthe instant of first stage ignition. Following the cool flametemperature rise, ▵TCF is substituted into Eq. (14) which isthen evaluated along with Eq. (4) for subsequent time steps ofthe engine cycle. Autoignition occurs when the integral ofEq. (4) reaches unity.

5. SUMMARY AND CONCLUSIONSA new ignition delay correlation has been developed topredict knock in SI engines for a TRF blend. This correlationcaptures the two-stage ignition associated with gasoline fuelsas well as the effects of EGR on autoignition along withvarying pin, Tin, and ϕ. CHEMKIN was used forcomputations in constant volume reactor in combination withthe detailed chemical kinetic mechanism developed byAndrae [31]. To determine the fit coefficients for the ignitiondelay correlation, autoignition predictions were obtained for awide range of pin, Tin, ϕ, and EGR. The “TRF 91” correlationthus developed has been shown to accurately match ignitiondelay predictions from CHEMKIN over the entire range ofoperating conditions investigated. The following representsthe significant benefits of the new correlation:

• Commercially available gasoline blends exhibit fuel octanesensitivity. As TRF blends exhibit sensitivity due to thepresence of toluene, they are more realistic gasolinesurrogates than PRF blends with zero sensitivity. Unlike theempirical ignition delay expressions in literature, the newcorrelation developed here can predict autoignition for a TRFblend.

• Overall ignition delay increases with decreasing pin, Tin, andϕ, and increasing EGR. The ignition delay correlationdeveloped here captures these inherent effects of varying pin,Tin, ϕ, and EGR. It is the first ignition delay correlation tocapture the coupled effects of ϕ and EGR on autoignition.

• The ability to implement the new ignition delay correlationin engine simulation codes makes it an effective tool topredict knock that captures the complex chemistry associatedwith autoignition while avoiding the prohibitivecomputational cost of detailed kinetic calculations.

Future work will involve conducting engine experiments tovalidate and calibrate new correlations. Additionalcorrelations will be developed for other TRF blends and morecomplex gasoline surrogates involving olefins and alcohols inaddition to toluene, n-heptane, and iso-octane.

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CONTACT INFORMATIONCorresponding Author:

Prof. Ahmet SelametDepartment of Mechanical EngineeringThe Ohio State UniversityE 509 Peter L. and Clara M. Scott Laboratory201 West 19th AvenueColumbus, OH 43210-1142 USAselamet.1@osu.eduPh: 1-614-292-4143Fax: 1-614-688-4111

DEFINITIONS/ABBREVIATIONSAKI

Antiknock index

CFDComputational fluid dynamics

CFRCooperative fuel research

CVRConstant volume reactor

▵TCFCool flame temperature rise

EGRExhaust gas recirculation

HCCIHomogeneous charge compression ignition

LLNLLawrence Livermore National Laboratory

[M]Concentration of products of the overall combustionreaction

[M]cConcentration of products of the overall combustionreaction at the time of autoignition

MONMotor octane number

NTCNegative temperature coefficient

ONOctane number

ϕFuel-air equivalence ratio

pIn-cylinder pressure

pCFPost cool flame pressure

pinInlet pressure

PRFPrimary reference fuel

RCMRapid compression machine

RONResearch octane number

SISpark ignition

τIgnition delay

τ,h,inCharacteristic exothermic reaction delay at the initialconditions

τ,h,CFCharacteristic exothermic reaction delay at the postcool flame conditions

TTime

t0Time at the start of the combustion process

t1First stage ignition delay

tAIOverall ignition delay

tcTime of autoignition

tFirst stageTime from the start of the reaction to the cool flameheat release in an engine environment

tInductionTime delay between first and second stage ignition

TIn-cylinder temperature

TDCTop dead center

TinInlet temperature

TRFToluene reference fuel

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