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1169 Proceedings of the Combustion Institute, Volume 28, 2000/pp. 1169–1175 HOT-SPOT AUTOIGNITION IN SPARK IGNITION ENGINES SHAHROKH HAJIREZA, 1 FABIAN MAUSS 2 and BENGT SUNDE ´ N 1 1 Division of Heat Transfer 2 Division of Combustion Physics Lund Institute of Technology PO Box 118, 221 00 Lund, Sweden The appearance of exothermic centers caused by inhomogeneities within the end-gas of spark ignition engines is investigated. A detailed chemical mechanism is adapted to calculate the autoignition of the primary reference fuels, n-heptane and iso-octane. The pressure history in the cylinder of the engine is obtained from a homogeneous two-zone model consisting of a burned gas zone and an unburned end-gas zone. The fraction of gases burned by the spark-ignited, propagating flame front is calculated from the Wiebe function. Within the end-gas zone, we introduce a one-dimensional coordinate, the distance from cylinder wall. Conservation equations for mass, momentum, energy, and species concentrations are solved instationary along this coordinate. The pressure is assumed to be homogeneously distributed. Gas inhom- ogeneities are modeled as sine waves in the initial temperature field. The development of the exothermic centers is investigated for amplitudes of the sine wave between 5 and 20 K. It is found that the gas near the exothermic center is prereacted. Products and intermediate products from low- and high-temperature reactions can be found. Thus, an apparent reaction front can propagate from the exothermic center with a velocity of several meters per second. The velocity increases with decreasing temperature gradients in the inhomogeneous mixture. Introduction Knock occurs basically due to spontaneous igni- tion in the end-gas of spark ignition (SI) engines. It results from the compression of the reactive gas mix- ture by the high-temperature burned gas behind the normal ignited flame front and the piston move- ment. Generally, the spontaneous ignition phenom- enon that can cause knock is governed by the tem- perature and pressure histories in the end-gas [1]. However, this spontaneous ignition does not occur in the whole gas volume at the same time. Inhom- ogeneities of temperature, pressure, or species con- centrations [2] result in one or more exothermic cen- ters [3,4]. These centers are also called hot spots. In knocking combustion, both thermochemical and gas dynamic effects are involved. Since the oc- currence of inhomogeneities in the gas is stochastic, the nature of the exothermic centers is stochastic [2]. After ignition, a reaction front starts to propagate from the hot spots into the surrounding gases. This leads to space and time-dependent processes gov- erned by the superposition of chemical kinetics, gas dynamics, and transport [5]. The type of the reaction front is strongly affected by the gradients of the in- homogeneities. Three different ignition cases may occur [6,7]. If the gradient is weak, a continuous thermal explosion is observed. Autoignition occurs in different loca- tions nearly at the same time, giving the appearance of a reaction front. This apparent reaction front moves so fast that transport processes play no role. The resulting pressure oscillations are moderate. If the gradients are steep, a deflagration is observed. This results in a weak pressure wave. For interme- diate gradients, if the gradient is smaller than a criti- cal value, a strong shock is created. The shock may be strong enough to initiate and sustain chemical reactions. This leads to a developing detonation. The appearance of exothermic centers has been investigated in Refs. [5,8–11]. The ignition process for fuels, such as H 2 , CH 4 ,C 2 H x , or C 3 H x is char- acterized by three phases: induction, excitation, and propagation. During induction, a sufficiently high temperature causes the formation of a radical pool. If the induction phase is sufficiently long, it is con- trolled by diffusion and heat conduction. When the radical pool has grown, the process enters the exci- tation phase, and all fuel and intermediate products are suddenly consumed and the heat is released. The excitation phase is controlled by chemical kinetics. The last phase is the propagation of a reaction front from the hot spot, as discussed in the previous sec- tion. For higher hydrocarbon fuels, such as C 7 and C 8 hydrocarbons, the induction phase becomes more complicated [12]. It is controlled by either low- or high-temperature consumption of the fuel. At low

Hot-spot autoignition in spark ignition engines

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1169

Proceedings of the Combustion Institute, Volume 28, 2000/pp. 1169–1175

HOT-SPOT AUTOIGNITION IN SPARK IGNITION ENGINES

SHAHROKH HAJIREZA,1 FABIAN MAUSS2 and BENGT SUNDEN1

1Division of Heat Transfer2Division of Combustion Physics

Lund Institute of Technology

PO Box 118, 221 00 Lund, Sweden

The appearance of exothermic centers caused by inhomogeneities within the end-gas of spark ignitionengines is investigated. A detailed chemical mechanism is adapted to calculate the autoignition of theprimary reference fuels, n-heptane and iso-octane. The pressure history in the cylinder of the engine isobtained from a homogeneous two-zone model consisting of a burned gas zone and an unburned end-gaszone. The fraction of gases burned by the spark-ignited, propagating flame front is calculated from theWiebe function. Within the end-gas zone, we introduce a one-dimensional coordinate, the distance fromcylinder wall. Conservation equations for mass, momentum, energy, and species concentrations are solvedinstationary along this coordinate. The pressure is assumed to be homogeneously distributed. Gas inhom-ogeneities are modeled as sine waves in the initial temperature field. The development of the exothermiccenters is investigated for amplitudes of the sine wave between 5 and 20 K. It is found that the gas nearthe exothermic center is prereacted. Products and intermediate products from low- and high-temperaturereactions can be found. Thus, an apparent reaction front can propagate from the exothermic center witha velocity of several meters per second. The velocity increases with decreasing temperature gradients inthe inhomogeneous mixture.

Introduction

Knock occurs basically due to spontaneous igni-tion in the end-gas of spark ignition (SI) engines. Itresults from the compression of the reactive gas mix-ture by the high-temperature burned gas behind thenormal ignited flame front and the piston move-ment. Generally, the spontaneous ignition phenom-enon that can cause knock is governed by the tem-perature and pressure histories in the end-gas [1].However, this spontaneous ignition does not occurin the whole gas volume at the same time. Inhom-ogeneities of temperature, pressure, or species con-centrations [2] result in one or more exothermic cen-ters [3,4]. These centers are also called hot spots.

In knocking combustion, both thermochemicaland gas dynamic effects are involved. Since the oc-currence of inhomogeneities in the gas is stochastic,the nature of the exothermic centers is stochastic [2].After ignition, a reaction front starts to propagatefrom the hot spots into the surrounding gases. Thisleads to space and time-dependent processes gov-erned by the superposition of chemical kinetics, gasdynamics, and transport [5]. The type of the reactionfront is strongly affected by the gradients of the in-homogeneities.

Three different ignition cases may occur [6,7]. Ifthe gradient is weak, a continuous thermal explosionis observed. Autoignition occurs in different loca-

tions nearly at the same time, giving the appearanceof a reaction front. This apparent reaction frontmoves so fast that transport processes play no role.The resulting pressure oscillations are moderate. Ifthe gradients are steep, a deflagration is observed.This results in a weak pressure wave. For interme-diate gradients, if the gradient is smaller than a criti-cal value, a strong shock is created. The shock maybe strong enough to initiate and sustain chemicalreactions. This leads to a developing detonation.

The appearance of exothermic centers has beeninvestigated in Refs. [5,8–11]. The ignition processfor fuels, such as H2, CH4, C2Hx, or C3Hx is char-acterized by three phases: induction, excitation, andpropagation. During induction, a sufficiently hightemperature causes the formation of a radical pool.If the induction phase is sufficiently long, it is con-trolled by diffusion and heat conduction. When theradical pool has grown, the process enters the exci-tation phase, and all fuel and intermediate productsare suddenly consumed and the heat is released. Theexcitation phase is controlled by chemical kinetics.The last phase is the propagation of a reaction frontfrom the hot spot, as discussed in the previous sec-tion.

For higher hydrocarbon fuels, such as C7 and C8hydrocarbons, the induction phase becomes morecomplicated [12]. It is controlled by either low- orhigh-temperature consumption of the fuel. At low

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1170 COMBUSTION IN ENGINES

Fig. 1. Schematic illustration of the homogeneous two-zone model and the coordinate for the inhomogeneous cal-culations. The typical horseshoe geometry of the cylinderhead as introduced in Ref. [16] is also evident from thefigure.

temperature, fuel consumption occurs via oxygen-ated hydrocarbons. At high temperatures, the ther-mal decomposition of the fuel is faster. In the inter-mediate temperature regime, the reverse of theoxygenation reactions become important, and the ig-nition delay time increases with increasing tempera-ture. This regime is also called the negative tem-perature coefficient (NTC) regime. Here, ignitionoccurs in two or more stages. For the higher hydro-carbons, since the chemical processes after the firstinduction time are slow in the NTC regime, the in-teraction of heat conduction, diffusion, and chemicalreactions can be much more complex. In an SI en-gine, each of the three temperature regimes mayoccur while the end-gas is compressed and therebywarmed up.

Typical intermediate products, observed duringthe ignition of primary reference fuels (PRFs), areformaldehyde (CH2O) or ethene (C2H4). The for-mation of CH2O can be visualized by the use of pla-nar laser-induced fluorescence PLIF [2]. If autoig-nition occurs, CH2O is found to be smoothlydistributed in the end gas zone of the engine. In avery thin region close to the cylinder walls, no CH2Ois detected. The occurrence of exothermic centers isdetected by a very sudden consumption of CH2Oand leads to a zero LIF signal.

The smoothly distributed CH2O signal suggeststhat the gas conditions near the exothermic centerare close to the conditions before excitation. The re-action front from the spot will move through a highlyreactive gas mixture. This can develop a detonationthat may damage the engine.

Problem Statement

This paper concerns the one-dimensional model-ing of an inhomogeneous end-gas in an SI engine.

It is an extension of another category of models,namely, the zonal models [13–15]. The engine issubdivided into different zones, and each zone is as-sumed to be homogeneous with uniform tempera-ture and species concentrations. However, the zonein the end-gas close to the cylinder wall is assumedto be inhomogeneous, and the processes in this zoneare calculated in one spatial coordinate, the distancefrom the cylinder wall. This is shown schematicallyin Fig. 1.

We use the two-zone model from Ref. [13] to cal-culate the overall increase of the cylinder pressuredue to the piston movement and flame propagation.The flame propagation is calculated from the Wiebefunction. Adiabatic conditions, calculated by mini-mizing Gibbs free energy, are assumed behind theflame front in the burned gas.

The initial values, boundary conditions, general as-sumptions, and numerical procedures for the zero-dimensional and the one-dimensional calculationsare identical. The principal sketch of the wholemodel is shown in Fig. 1. The piston movement oc-curs perpendicular to the plane shown in Fig. 1. Thehorseshoe-formed cylinder extension is part of ajoint research project where in-cylinder measure-ments of the temperature distribution [16], chemicalmodeling [17], thermal analysis [13–15], and com-putational fluid dynamics (CFD) calculations aredone.

The chemical kinetic model for the PRF has beenvalidated for the system under consideration in Ref.[13]. The governing equations for continuity of mass,momentum, energy, and concentration of species,presented in the next section, are discretized andsolved by a fully implicit method for laminar, tran-sient, compressible, and reacting flows. The influ-ence of turbulence is not considered here. Since ig-nition delay is highly temperature dependent, theheat transport to the combustion chamber wall isvery important for the occurrence of knock. Con-sequently, either wall temperature or heat flux at thewall is implemented as the boundary condition. Thegas in the combustion chamber is assumed to followthe ideal gas law.

Governing Equations

As explained in the previous section, the overallpressure increase due to the compression by the pis-ton and flame front is calculated by the two-zonemodel as developed in Ref. [13]. In the following,we give the governing equations of this model.

The mass of burned gas mb in the cylinder is cal-culated by the Wiebe function in dependence on thecrank angle degree (CAD) h:

n�1h � h0

m � m 1 � exp �b (1)b total � � � � ��Dh

h0 is the timing of ignition and Dh is the duration

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HOT-SPOT AUTOIGNITION IN SI ENGINES 1171

time. According to Refs. [1,18], curves of burnedmass fraction have been fitted with b � 5 and n �2. For comparison with the experimental data, theparameters b and n have been adjusted in Ref. [14].The time-dependent cylinder volume Vtotal is cal-culated from the engine geometry [1]

2pBV � V � (l � c � s) (2)total c 4

where the distance between the crank angle axis andthe piston pin axis s is obtained by

2 2 2 1/2s � c cos h � (l � c sin h) (3)

The clearance volume Vc, the bore diameter B, theconnecting rod length l, and the crank radius c aregiven by the engine geometry. The mass balanceequations for each species j in the burned gas (indexb) is

NrdYj,bq � W m xb j,b � j,k k

dt k�1

mb� q (Y � Y ) (4)b j,f j,b

mb

Here, q is the density of the gas, t is the time, Yj arethe species mass fractions, Wj is the respective mo-lecular weight, mj,k is the stoichiometric coefficientof species j in reaction k, and xk is the reaction ve-locity. Nf is the number of chemical reactions in thesystem.

As a result of the thermal analyses in Ref. [13], thegoverning equations for the burned gas (equations 4and 5) are those of a compressed perfectly stirredreactor. The first term on the right-hand side is thechemical source term. The last term accounts for thedifference of the species mass fraction directly be-hind the flame front (index f ) and the mean speciesmass fraction in the burned gas. Adiabatic conditionsare assumed in the flame front. The temperature andspecies concentrations directly behind the flamefront are calculated by minimizing the Gibbs freeenergy.

The heat balance equation for the burned gasreads

N Ns rdT dpbq c � � h W m xb p,b � j,b j,b � j,k k

dt dt j�1 k�1

Nsmb 4� q Y (h � h ) � reT (5)b � j,f j,f j,b bm j�1b

Here, cp is the heat capacity at constant pressure p,T is the temperature, and h is the enthalpy. Theterms on the right-hand side of equation are the vol-ume work, the heat released from the chemical re-actions, the influx from the flame front into theburned gas, and the radiation heat losses in the limitof optical thin gases, respectively. The Stefan–Boltz-mann constant r is equal to 5.67 � 10�8 W/m2K4,

and the gas emissivity e is the average emissivity forCO2 and H2O. Radiation heat losses are found to beof minor importance.

The species balance equation of the unburned gas(index u) is

NrdYj,uq � W m x (6)u j,u � j,k k

dt k�1

and the heat balance for the unburned gas is givenby

N Ns rdT dpuq C � � h W m xu p,u � j j,u � j,k k

dt dt j�1 k�1

Aw� � (T � T ) (7)w u

Vu

Equations 6 and 7 are the governing equations ofa compressed plug flow reactor with heat loss. Inequation 7, the radiation heat losses are neglecteddue to the lower temperature compared to theburned gas. The cylinder pressure is calculated byusing the equation of state as the mean weightedpressure between the burned and unburned zones.

The model, described by equations 1 to 7, is usedto calculate the pressure history needed in the one-dimensional model in the spatial coordinate x. Thegoverning equations for conservation of mass, mo-mentum, energy, and species concentrations, givenbelow, are solved for the near wall region.

Mass:

�q �(qu)� � 0 (8)

�t �x

where u is the velocity of the gas in direction of x.

Momentum:2�(qu) �(qu ) �q 4 � �u

� � � � l (9)� ��t �x �x 3 �x �x

Since pressure waves are not taken into account inthis paper, �p/�x � 0, and l is the dynamic viscosityof the gas.

Energy:

�T �T �q � �Tqc � quc � � kp p � ��t �x �t �x �x

N Ns r

� h W m x (10)� j j � j,k kj�1 k�1

It is assumed that viscous dissipation is negligible. kis the thermal conductivity of the gas.

Species:Nr�Y �Y �j j

q �qu � (qY m )�W m x (11)j j j � j,k k�t �x �x k�1

vj are the diffusion velocities of the gas components.

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1172 COMBUSTION IN ENGINES

TABLE 1Engine data

Parameter Value

Bore, B 96 mmStroke 87 mmDisplaced volume 630 cm2

Compression ratio 5.9:1RPS 25Timing of ignition, h0 �10 CADDuration, Dh 50 CADEquivalence fuel/air ratio 1.0RON 40Wall temperature 750 K

Fig. 2. The pressure history as calculated from the two-zone model.

Fig. 3. Calculated profiles of the temperature (uppergraph) and of the mole fraction of n-heptane (lower graph)as functions of the distance from the wall and the time.The amplitude of the sine wave in the initial temperatureprofile is 20 K.

Fig. 4. Calculated profiles of the temperature as func-tion of the distance from the wall and the time. The am-plitude of the sine wave in the initial temperature profileis 20 K.

The mean pressure is calculated by the equation ofstate under assumption of the ideal gas law.

At the wall, Dirichlet boundary conditions areused for the temperature and the velocity, and it isassumed that radicals are recombined. Neumannboundary conditions were assumed for all the vari-ables at the open end.

Sample Calculations

The chemical kinetic mechanism involving 510chemical reactions and 75 species has been dis-cussed and validated in Refs. [13,17] using shocktube experiments from Ref. [19]. The mechanism issuch that the research octane number (RON) of thefuel is a free input parameter.

Engine data and boundary conditions are given inTable 1. The horseshoe geometry of the combustionchamber, shown in Fig. 1, is the same as in the testengine used for temperature and pressure measure-ments in Ref. [16]. The low compression ratio of thistest engine is caused by an optical cylinder extensionused for end-gas temperature measurements with

dual-broadband rotational coherent anti-Stokes Ra-man spectroscopy (CARS). The parameters b and nin the Wiebe function, equation 1, were adjusted forthis engine in Ref.[14].

The sample calculations have been made to inves-tigate the effect of temperature inhomogeneities.The pressure history, calculated from the two-zone

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HOT-SPOT AUTOIGNITION IN SI ENGINES 1173

Fig. 5. Calculated profiles of the mole fractions of CO(left graph) and CH2O (right graph) as function of the dis-tance from the wall and the time. The amplitude of thesine wave in the initial temperature profile is 20 K. Thesymbols used in the figure are explained in Figs. 3 and 4.

Fig. 6. Calculated profiles within an exothermic centeras function of the time. Profiles of the temperature and themole fractions of n-heptane and iso-octane (upper graph)and CO and CH2O (lower graph) are shown. The ampli-tude of the sine wave in the initial temperature profile is20 K.

model, is shown in Fig. 2. The initial conditions andthe engine data are given in Table 1. The followingsine wave defines the inhomogeneous initial condi-tions of the temperature in the one-dimensional cal-culation:

T(x, t � 0) � 750 K � T sin (x: mm)0

The mean temperature is equal to the tempera-ture in the homogeneous two-zone model. T0 hasbeen set to 20 K, 10 K, and 5 K, respectively. Thewall temperature is kept constant with TW � 750 K.Species concentrations are assumed to be homoge-neous. The initial conditions are arbitrary, and themodel is not restricted to these. The pressure is as-sumed to be uniform in space.

Results and Discussion

The one-dimensional inhomogeneous and time-dependent model, as described above, is used to cal-culate autoignition of an n-heptane, iso-octane mix-ture with RON 40, under engine-relevantconditions. The amplitude of the sine wave, whichdisturbs the initial temperature profile, is first set toT0 � 20 K. Time t � 0 ms corresponds with h ��42.3 CAD. Calculated profiles of the temperature,the fuel components and the intermediate products,CO and CH2O, are shown in Figs. 3 through 6 asfunctions of the distance from the cylinder wall andthe time. The pressure history for this case as cal-culated from the two-zone model is shown in Fig. 2.

The initial temperatures vary between 730 and770 K at �42.3 CAD, and the maximum tempera-ture occurs two times, at 1.6 mm and at 7.9 mm. InFig. 3, the consumption of n-heptane is shown to-gether with the corresponding temperature profiles.The compression of the end-gas causes the tem-perature in the end-gas to rise. After 4.8 ms, themean temperature reaches about 900 K. Since up to

this time the temperature passes through the NTCrange, fuel consumption is initially observed at po-sitions with lower temperatures, near to the wall, andbetween the temperature maximums. Further com-pression causes the gas to leave the NTC range, andafter 6.0 ms fastest fuel consumption is noticed atthe places of maximum temperature. At furthertimes, the fuel is consumed via the high-temperaturereaction path. At about 7.013 ms (Fig. 4), the induc-tion phase is over and the heat is suddenly released.At 7.087, two temperature peaks appear at the placeof the exothermic centers. After excitation, propa-gation of apparent reaction fronts is observed. Thepropagation is caused by thermal expansion of thegases in the exothermic center and final ignition ofthe gases near to the exothermic center. The calcu-lated velocity of the apparently propagating reactionfront is around 15.4 m/s.

During ignition, the pressure rises within the hotspot [8]. Depending on this pressure rise, the ab-solute pressure, and the conditions of the surround-ing gases, a deflagration, a thermal explosion, or atransition to detonation [20–22] might occur. Sincewe assumed the pressure to be constant in space,these phenomena cannot be discussed in this paper.

Profiles of the intermediate products CH2O andCO are shown in Fig. 5. It is evident from the figurethat CH2O results from both kinetic pathways, lowand high-temperature kinetic. Hence, CH2O cannot

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1174 COMBUSTION IN ENGINES

trace the history of the ignition process. CH2O isconstantly produced during the induction phase andsuddenly consumed during excitation. The produc-tion of CO during the induction phase is low. Duringthe excitation phase the CO concentration rises sud-denly. At the end of the excitation phase, CO is con-sumed until it finally reaches equilibrium concentra-tions. Due to this behavior, CO marks the positionof current excitation sharply. The low concentrationof formaldehyde, as calculated near the cylinderwall, is also found in PLIF measurements [2].

In Fig. 6, the time-dependent profiles of the tem-perature, the fuel components, and the intermediateproducts CH2O and CO are shown at the positionof the hot spot. After an induction time, a radicalpool is produced that is enough to start the low tem-perature oxidation of n-heptane. This chain pro-duces further radicals, which are partially used toconsume iso-octane. At about 6 ms, when the inter-mediate C4 and C2 hydrocarbons are consumed toproduce CH2O and CO, the consumption of n-hep-tane becomes slower. After 6.6 ms, n-heptane is al-most completely consumed. At this time, the rate ofconsumption of iso-octane slows down. In between,the chemical reaction path changes from low-tem-perature to high-temperature kinetics. A constantrise of temperature is caused by the compression ofthe end-gas. The heat released from the chemicalreactions is low. However, two significant stages canbe observed in the temperature profile. This is inagreement with temperature measurements in theengine [16]. After another induction time, the inter-mediate products are consumed very suddenly. At7.4 ms, the heat is released and the temperaturepeak appears.

In Fig. 7, calculations are shown for amplitudes ofthe sine wave in the initial temperature profiles of10 K and 5 K. Temperature profiles as functions of

the distance from the cylinder wall and the time areshown in the figure. The lower maximum tempera-tures cause a longer ignition delay at the position ofthe hot spot. After the appearance of the first igni-tion, the lower initial temperature gradients causethe gas near to the exothermic center to ignite withshorter time delays. We calculate a velocity of theapparent reaction front, propagating from the hotspot, with 23.7 m/s for h� 10 K and with 55 m/sfor h � 5 K.

Conclusions

The effect of gas inhomogeneities on the autoig-nition of a mixture of n-heptane and iso-octane hasbeen investigated numerically under engine relevantconditions. This was realized by combining a ho-mogeneous two-zone model with a one-dimensionalmodel for a region near the cylinder wall. The two-zone model allows the calculation of the mean pres-sure history. Pressure waves have not been takeninto account in this study, and the investigation endsshortly after the excitation phase of the ignition pro-cess. Since the compressed end-gas passes, duringthe autoignition process, through the temperaturerange from 800 to 1100 K, low-temperature andhigh-temperature kinetic reactions can be observed.For all investigated temperature inhomogeneities,the occurrence of an exothermic center is observed.The velocity of the apparent reaction front, propa-gating from the hot spot, rises with decreasing tem-perature inhomogeneities. In future investigationswith the model we will include the pressure waves.

Acknowledgments

Financial support from the former National SwedishBoard for Industrial and Technical Development and theNational Swedish Energy Authority is kindly acknowl-edged.

REFERENCES

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Fig. 7. Calculated profiles of the temperature as func-tion of the distance from the wall and the time. The am-plitude of the sine wave in the initial temperature profileis 10 K (left graph) and 5 K (right graph). The symbolsused in the figure are explained in Figs. 3 and 4.

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HOT-SPOT AUTOIGNITION IN SI ENGINES 1175

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COMMENTS

Frederick L. Dryer, Princeton University, USA. Yourpresentation raises numerous questions, the most impor-tant being related to the practical situation of autoignitionin spark ignition engines. Turbulent mixing will never al-low gradients to be established on the length scales com-parable to those in your calculations. Furthermore, thethree-dimensional nature of actual thermal centers alsointroduces divergence/coalescence issues totally missed bythe configuration of your model. What do you believe tobe the practical relevance and implications of your find-ings?

Author’s Reply. In the past, kinetic processes in the endgas of spark ignition engine were often analyzed by the helpof simple homogeneous models. Of course those modelscould not explain the influence of turbulence on autoigni-tion or the influence of three-dimensional effects. Howeverthese models were used to gain important insight into thekinetics of the autoignition process under engine-relevantpressures and temperatures. They were also used to de-velop and validate reduced mechanisms for later usage inthree-dimensional numerical codes including turbulence.The model presented is thought as an expansion of the purehomogeneous models. The motivation for this expansion isto study how small inhomogeneities influence the ignitionprocess of higher hydrocarbons under engine-relevanttemperature and pressure conditions. It was found thatchemical processes were first observed at low temperaturewhen the system passes the negative temperature coeffi-cient (ntc) region. However, the time needed to rise thetemperature in the end gas due to compression, leadingthe system to undergo final excitation in the high-tempera-ture regime, was shorter than the time needed by the low-temperature kinetics to reach the excitation phase. Thisfinding is relevant for engines, independent of the gradi-ents that might appear. The gradients that will appear in

an engine depend on the turbulent mixing time and thetime needed for excitation. The latter time is found to beabout 0.03 ms. Gradients observed in experiments analyz-ing the LIF-signal of formaldehyde near to exothermiccenters are steep.

John Griffiths, University of Leeds, UK. For the tem-perature at which you have started the simulation shownin Fig. 3, the chemistry will pass through the negative tem-perature coefficient (ntc) region. This means that the tem-perature difference in the initial sinusoidal profile muststart to be smoothed out. Did you have any evidence forthis? This effect would not necessarily destroy the activezone (the “hot spot”) because, unless the calculation in-cluded fast mixing, a spatial inhomogeneity in concentra-tion of reactive intermediates would develop as a result ofthe differing extents of reaction that will have taken place.There should be some evidence of this in your concentra-tion profiles if the ntc chemistry is captured correctly inyour model.

Author’s Reply. It is right that the chemical systempasses first the negative temperature coefficient (ntc) re-gion, and this can be seen in the Figs. 3–5. This effectdecreases indeed the difference between highest and low-est temperature. In our example, modeling the inhomo-geneities in the temperature profiles as sine waves, we ob-serve something like a phase doubling of the wave.However we observe increased inhomogeneities in the pro-files of the oxygenated higher hydrocarbon species. Thiscould not be shown in the paper due to the space limita-tions. But one can state that chemistry increases inhomo-geneities for higher hydrocarbon fuels.