SPECIAL ISSUE PAPER 41

Dual injection homogeneous charge compressionignition engine simulation using a stochastic reactormodelS Mosbach1, H Su1, M Kraft1*, A Bhave2, F Mauss3, Z Wang4, and J-X Wang4

1Department of Chemical Engineering, University of Cambridge, Cambridge, UK2Reaction Engineering Solutions, Cambridge, UK3Division of Combustion Physics, Lund Institute of Technology, Lund, Sweden4Department of Automotive Engineering, Tsinghua University, Beijing, People’s Republic of China

The manuscript was accepted after revision for publication on 16 August 2006.

DOI: 10.1243/14680874JER01806

Abstract: Multiple direct injection (MDI) is a promising strategy to enable fast-responseignition control as well as expansion of the homogeneous charge compression ignition (HCCI)engine operating window, thus realizing substantial reductions of soot and NO

xemissions.

The present paper extends a zero-dimensional-probability-density-function-based stochasticreactor model (SRM) for HCCI engines in order to incorporate MDI and an improved turbulentmixing model. For this, a simplistic spray model featuring injection, penetration, and evaporationsub-models is formulated, and mixing is described by the Euclidean minimal spanning tree(EMST) sub-model accounting for localness in composition space. The model is applied tosimulate a gasoline HCCI engine, and the in-cylinder pressure predictions for single anddual injection cases show a satisfactory agreement with measurements. From the parametricstudies carried out it is demonstrated that, as compared with single injection, the additionalsecond injection contributes to prolonged heat release and consequently helps to preventknock, thereby extending the operating range on the high load side. Tracking the phase spacetrajectories of individual stochastic particles provides significant insight into the influence oflocal charge stratification owing to direct injection on HCCI combustion.

Keywords: homogeneous charge compression ignition, dual injection, stochastic reactormodels

1 INTRODUCTION dictates the in-cylinder pressure, local temperatures,and local concentrations of the air–fuel–EGR mixture.Thus, direct fuel injection (DI) can influence theHomogeneous charge compression ignition (HCCI)stratification of composition and temperature, andcombustion, an advanced engine operation mode, isthereby control the auto-ignition timing and com-attracting significant attention from the combustionbustion duration. Individual single DI strategies suchresearch community on account of its intrinsicas early and late DI have been successfully used tobenefits in terms of high efficiency and ultra-lowdemonstrate HCCI or HCCI-like combustion modes.emissions for NO

xand soot, and owing to the need

However, single DI faces certain limitations, forto overcome technical obstacles such as difficulty ininstance, the problem with the soot–NO

xtrade-offcontrolling ignition timing and a narrow operation

persists with single late DI or high injection pressuresrange. Mixture formation in the combustion chamberfor diesel fuel, whereas late DI with gasoline canusing a fuel directly injected into compressed airresult in knock [1, 2]. Multiple direct injection (MDI)(or air mixed with exhaust gas recirculation (EGR))strategy has the potential for a robust, fast response

* Corresponding author: Department of Chemical Engineering, in ignition timing control and also for expandingUniversity of Cambridge, Pembroke Street, Cambridge CB2 3RA, the HCCI operating window over the load-speed

sweep [1].UK. email: mk306@cam.ac.uk

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42 S Mosbach, H Su, M Kraft, A Bhave, F Mauss, Z Wang, and J-X Wang

Experimental research involving MDI schemes for operation has been simulated using a 3D CFD codecontaining a hollow cone spray sub-model and aa range of conventional as well as alternative fuels has

been widely reported. In recent years, optical experi- combustion model based on the Shell auto-ignitionreaction and eddy dissipation concept (mean reactionmental studies of MDI strategies of diesel and other

synthetic fuels have been carried out, with the number rate), resulting in computational time of the order ofseven days on an SGI machine (400 MHz) [18]. In aof injection pulses as high as 9 within an engine

cycle [3–5]. In these studies, merits of MDI in terms brief study elsewhere, the influence of dual injectionon in-cylinder pressure in a diesel-fuelled PCCIof improving the homogeneity of the in-cylinder

mixture, increasing the combustion efficiency, and engine has been validated against experiments [19].Recently, the role of multi-pulse injections in con-lowering soot concentrations have been observed.

Another study involving two-stage injection in a trolling premixed mixture preparation was modelledduring the closed-volume part of the cycle in apartially premixed charge compression ignition (PCCI)

engine demonstrated the role of reduced wall-wetting, dodecane-fuelled engine, using a commercial 3DCFD code [20]. For an earlier DI timing, the pulsehigher peak heat release rate after first injection, and

better evaporation even early in the compression width showed a strong impact on evaporation andmixing, whereas for late DI, a short dwell time wasstroke on improvements in thermal efficiency and

lowering of NOx

and soot emissions [6]. A second found to promote charge uniformity. However, theinfluence of combustion in evaluating the mixinginjection has been used as an ignition-trigger and

control mechanism in a diesel-fuelled DI HCCI process was not accounted for. Inclusion of a detaileddescription of chemical kinetics – vital for HCCIengine. For optimized conditions, sufficient torque

was generated under low NOx

and soot emissions [7]. combustion – within the CFD model framework wouldput an additional demand on the computationalIn the case of gasoline-fuelled engines, a dual-

injection strategy has been proposed, in which a power. This expense can be significantly reducedusing integrated engine cycle models while maintain-homogeneous lean air–fuel mixture (from first early

DI during intake stroke) compressed close to con- ing the reduced predictive power within an acceptablerange. The single- and multi-zone-based full-cycleditions favourable for HCCI combustion, was ignited

using the second-stage injection (stratified charge) [2]. simulators have only been implemented for early DIHCCI simulations.This strategy is further assisted with spark discharge

by reducing the cyclic fluctuations in combustion The purpose of the current paper is to presenta zero-dimensional PDF-based stochastic reactor[8, 9]. Utilizing the thermal energy of the hot trapped

EGR combined with dual injection in a 6-stroke modelling (SRM) approach to account for MDI, whichcan be easily incorporated in an engine cycle codegasoline direct injection (GDI) engine has been

introduced [10]. Another MDI strategy consisting of without major modifications. The SRM approach, withits inherent benefits in terms of detailed chemicalinjecting a portion of fuel into the trapped internal

EGR during negative valve overlap and injecting the kinetics and ability to account for inhomogeneitiesas demonstrated in previous work by the presentremaining fuel in the intake stroke has also been pro-

posed. The first-stage injection enabled fuel reforming authors for single early DI [14] and port-injectedHCCI combustion [21], is extended by formulatingand improving the ignitability of the fuel, and this

dual injection scheme expanded the lean limit of and incorporating a simplistic spray model. Thismodel, rather than taking into account the detailedHCCI combustion without increase in NO

xemissions

[11]. Optimizing a set of injection parameters and physics of sprays, combines the physical attributesinto a small number of parameters, namely anintake temperature to obtain significant reduction in

fuel consumption and emissions for a dual injection evaporation constant, the Sauter mean diameter(SMD), and a constant governing penetration. How-HCCI engine has also been reported [12].

Compared with experimental MDI HCCI studies, ever, in spite of these simplifications, this model iscapable of capturing the experimentally observedcomputational modelling investigations have been

limited. In general, for simulating single early DI spreading of heat release. It should be noted that itis a non-trivial insight that the prolonging of com-HCCI combustion, a range of tools such as single-

zone, multi-zone, and probability density function bustion duration owing to charge stratification canbe reproduced with such a strongly simplified model.(PDF)-based engine cycle simulators as well as three-

dimensional (3D) computational fluid dynamics Furthermore, the present model is sufficiently simpleand computationally cheap so that extensive studies(CFD) models have been implemented [13–17]. How-

ever, for MDI operation, only studies involving CFD of parameter dependencies and sensitivities canbe performed within reasonable time spans. Suchmodels have been reported. A dual-stage DI HCCI

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43Dual injection HCCI engine simulation

studies can be relevant for practical applications and the mass density, cV

the specific heat capacity atconstant volume, m the total mass, and V theare not feasible using complex CFD models for

instance. instantaneous cylinder volume. This function G will bemodified in the following subsection to incorporateThe current paper is structured as follows. In sec-

tion 2, the numerical model is presented and the a simplistic spray model.For the description of turbulent mixing we use thespray sub-model and its implementation in the SRM

framework is explained. In section 4, results are pre- Euclidean minimal spanning tree (EMST) model [24].We elaborate in detail on the role of mixing below.sented of numerical simulations in which the model

is applied to simulate a dual injection HCCI engineand is validated against measurements. A discussion 2.2 Spray modelon stratification in composition space, and para-

The spray model employed consists of three parts:metric investigations related to DI are included.an injection, a penetration, and an evaporationFinally, in section 5, conclusions are presented andsub-model. The shape of the spray (the dropletopen questions for future work and development arecloud) remains unspecified, i.e. account is not takenidentified.of geometrical information such as the spray-tippenetration or the cone angle. However, under certainassumptions these quantities could be related to one

2 EXTENSION OF THE SRM TO DIRECT of the parameters used in the current model.INJECTION INCLUDING SPRAY Concerning injection, it is assumed that the popu-

lation of droplets entering the cylinder possesses a2.1 Summary of the stochastic reactor model user-specified SMD. Recall that the SMD is defined

such that a fictitious population of identical dropletsSome fundamentals of the SRM successfully employed

each with a diameter equal to SMD possesses theearlier [21] are briefly recalled in order to describe

same total volume and surface area as the actualin the next subsection the inclusion of the DI and

population considered. Since the surface area of thespray model. The SRM is presented in detail in

droplets is the relevant quantity as far as evaporationreference [22], which will therefore not be repeated

is concerned, it can safely be assumed for this purposehere. Readers unfamiliar with PDF methods in

that the diameter of every droplet equals SMD. Forcombustion are strongly recommended to consult

diesel fuels, an empirical expression has been pro-reference [23]. The output of the current model

posed [25, 26] and used to develop a zero-dimensionalconsists of (distributions of) the species mass

spray model [27]. Similar work for gasoline has notfractions Y

jand temperature T, combined into a

yet been carried out to the knowledge of the presentvector y=(Y

1, … , Y

S, T ) for notational convenience,

authors.where S denotes the number of chemical species.

In the penetration sub-model it is assumed thatThe source terms generating the time evolution of the

the inflowing fuel is distributed at a constant ratePDF represent the various physical processes taken

such that no fluid parcel receives fuel at more thaninto account by the model, i.e. chemical kinetics,

one instant in time. More quantitatively, in a timeturbulent mixing, piston movement, and convective

step Dt, the mass of cylinder charge that is to beheat transfer. The chemical reactions and their heat

endowed with fuel droplets is given by aDt, where arelease including temperature change owing to

is a model parameter. Physically, larger a correspondscompression and expansion are summarized in the

to more evenly spread fuel, i.e. greater cone anglefunction G defined by

or tip penetration. Contrariwise, smaller a impliesstronger charge stratification.

Gj(y)=

Mjvj

r, j=1, … , S The mass flowrate for the evaporation of a single

droplet can be calculated from elementary consider-ations [28] (mass conservation). In the current case,

GS+1

(y)=−1

cVr∑S+1

i=1eiMivi−

p

cV

m

dV

dt this leads to an equation describing the time evolutionof the liquid fuel mass of the entire population

(1)

mliq=−3

2levapAp6 rliqNdB2/3m1/3liqwhich generates the time evolution of the mass

fractions and the temperature. Here, Mj

denotes themolar mass, v

jthe molar production rate, and e

jthe where l

evapis an evaporation constant and r

liqis the

mass density of the liquid fuel. The number Nd

ofspecific internal energy of the jth species. r denotes

JER01806 © IMechE 2007 Int. J. Engine Res. Vol. 8

44 S Mosbach, H Su, M Kraft, A Bhave, F Mauss, Z Wang, and J-X Wang

droplets in the population is given by Nd=6m

liq(0)/ with zero, and the mass fractions are normalized as

usual, i.e. Wj

Y (i)j=1. For convenience, the numberpr

liqSMD3, which follows from the assumption that

all droplets are spherical with diameter SMD. The of droplets N(i)d

is also associated with each particlefor the purpose of implementation, but this is notsolution of the preceding differential equation is

given by an additional scalar and hence neither appearsexplicitly in y nor in the PDF transport equation.

Since in the present work there is no in-/outflowmliq(t)=Cmliq(t0)2/3−Ap6 rliqNdB2/3levap×(t−t0)D3/2 of stochastic particles, and the injection by con-struction does not affect the particle number at all,(2)there is no need for down-sampling (reduction of thenumber of particles whilst conserving the PDF asNote that by setting t

0=0, t=t

evap, and m

liq(t

evap)=0

well as possible), in contrast to reference [14].the expression tevap=SMD2/l

evapcan be derived for

However, this becomes necessary again as soon asthe evaporation time tevap

, i.e. the time it takes for athe method considered here is incorporated into adroplet to evaporate. A physical interpretation of l

evap full-cycle simulation, which is easily achieved.is the change of surface area of a single droplet perThe following model parameters are required asunit time.

input: the mass density rliq

of the liquid fuel, theThe PDF transport equation is extended to includemass flowrate m

fuelof the injected fuel, the SMD,this model simply by appending the scalar m

liqto y,

the evaporation constant levap

, and the constant ai.e. y=(Y1, … , Y

S, T , m

liq). The time evolution of m

liq measuring the spray penetration. The mass flowrateis then described bym

fuelis also assumed constant during the injection

process. Note that the constant parameters SMD,GS+2

(y)=−3

2levapAp6 rliqNdB2/3y1/3S+2 (3)

levap

, and a can be replaced by sub-models calcu-lating them based on physical properties of the

Apart from that, the equation for the SRM remains fuel and geometrical information of the injector,unaltered. thereby leaving room for future developments and

The current authors are aware that this model lacks improvements.several physical attributes commonly associated with The only modification made to the SRM sourcesprays such as heat of evaporation, droplet Weber code is one additional splitting step, which accountsnumber effects, etc., which in the present model are for combined injection and penetration, and one forsimply lumped into a small number of parameters. evaporation. If the current crank angle lies betweenHowever, in exchange for the lack of detail, with the SOI

2and EOI

2then the following splitting step for

current model it is possible to study the influence and injection and penetration is performed.sensitivity of the parameters easily and extensively.

1. Pick particles randomly according to statisticalThis requires a considerable number of simulationweight such that the sum of the masses of theruns, which is for example not practicable with CFDparticles does not exceed aDt and that no particlesimulations within an acceptable amount of centralthat has been chosen previously is picked again.processing unit (CPU)-time. In addition, as shownAssign to each of the chosen particles a value ofbelow, it turns out that the level of detail in the currentm(i)

liqproportional to the statistical weight such thatmodel suffices to reproduce some experimental

the total injected mass Wm(i)liq

per time step Dtobservations.equals m

fuelDt, i.e.

m(i)liq=W (i)

WW (j)mfuelDt3 EXTENSION OF THE ALGORITHM

where the sum ranges over the indices of theThe extended SRM (the PDF transport equationchosen particles.together with equation (3)) is solved as previously [21]

2. Calculate the droplet numbers according toby an operator-splitting technique combined with aMonte Carlo method, in which the PDF is approxi-

N(i)d =6m(i)liq

prliqSMD3Yiµ{1, … , Npar}mated by a notional ensemble of N

parstochastic

particles. Now, however, each particle carries S+2scalars, namely not only the mass fractions and After the second injection has started, if there is

still liquid fuel left, the following splitting step fortemperature, but also the liquid fuel mass, i.e.y(i)(Y (i)

1, … , Y (i)

S, T (i), m(i)

liq). All m(i)

liqare initialized evaporation is performed.

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45Dual injection HCCI engine simulation

1. Update the liquid fuel mass of all particles, i.e. for n-heptane (mass fraction 0.141), which correspondsto an octane number of roughly 86 (experiment:each iµ{1, … , N

par} set m(i)

liq. m(i)

liq, where

RON=90.6, MON=81). As a computational surrogatenecessarily has to be used, with no means ofm(i)liq=C(m(i)liq)2/3−Ap6 rliqN(i)d B2/3lDtD3/2 accurately representing RON and MON, the roadoctane number RdON=(RON+MON)/2#86 is used.or set m(i)

liq(and N(i)

d) to zero if the expression in

The chemical mechanism describing the kineticssquare brackets is non-positive.contains 157 species and 1552 reversible reactions2. Update the statistical weights according to(see explanation and references in [22]).

W (i).W (i)+m(i)liq−m(i)liq7W (i) As the present study focuses mainly on the secondinjection (at−40 crank angle degree (CAD) after topfor all iµ{1, … , N

par}.

dead centre (ATDC)), simulations are restricted to the3. Update the (gaseous) species mass fractionsclosed-volume part of cycle (i.e. from intake valveaccording toclosing (IVC) to exhaust valve opening (EVO)), so forthe time being the gas exchange during the engineY (i)

j.Y (i)

jW (i)

W (i)7Y (i)

jYj≠fuel

breathing process is neglected. The start of the firstinjection SOI

1is timed shortly after intake valve

Y (i)fuel. 1− ∑S

j=1, j≠fuelY (i)j opening (IVO) close to TDC (see Table 1). As a con-

sequence of the rapid turbulent mixing during thefor all iµ{1, … , N

par}, where ‘fuel’ denotes the intake process, it is assumed as initial condition at

indices of all fuel species. IVC that the cylinder charge is homogeneous intemperature as well as in composition.

A central feature of DI is the charge stratification4 NUMERICAL STUDY it gives rise to, which underlines the importance of

accurate modelling of the turbulent mixing process,4.1 Model calibration i.e. the precise representation of the interaction of

fluid parcels in phase space. The current authorsThe implementation of the model was built uponfound this aspect of mixing in their simulations toa version used in previous work [21]. The newbe of greater significance than the choice of mixingsub-models discussed in the previous section weretimes. The simplest mixing model is the interactionintegrated into this existing code. All simulationsby exchange with the mean (IEM) model, in whichwere carried out on AMD Athlon 3000+Linux PCsall scalars relax exponentially to their mean value.running at 2.16 GHz.One (out of several) unphysical aspects of this modelFor the calibration and validation of the currentis that every particle can mix with any other particlemodel, experimental data obtained previously [9] werein phase space. Using IEM in the current simulationsused. The experiments were carried out on a two-results in too rapid dilution of the injected fuel, evencylinder in-line four-stroke DI gasoline engine, whichfor slow mixing (i.e. large turbulent mixing times t).was operated on a single cylinder only and naturallyMuch more suitable for current purposes is the EMSTaspirated. Main engine and operating parametersmodel [24], in which particles to be mixed are chosenare listed in Table 1. The fuel is modelled as beingbased on proximity in phase space.composed of iso-octane (mass fraction 0.859) and

As for the choice of the turbulent mixing time t, itis found that, in order to reproduce experimental

Table 1 Engine specification and operating condition measurements, intensified mixing (i.e. a shortermixing time) is necessary during the injection period.Bore×stroke 95×115 mm2

Displaced volume 815 cm3 Reduced mixing times during injection have beenConnecting rod length 210 mm observed previously in CFD simulations (see forCompression ratio (CR) 11Speed 1400 r/min example Fig. 7 in reference [15]). In all current simu-Air/fuel equiv. ratio 1.6 lations, t=0.5 ms was used during injection andEGR (internal+external) 20%

t=4 ms otherwise: values which are very similar toInlet temperature (after heater+ext. EGR) 433 KInlet valve opening (IVO) 350 CAD ATDC those found in reference [15]. The mixing time para-Inlet valve closing (IVC) 150 CAD BTDC meter determines how long any charge stratificationExh. valve opening (EVO) 120 CAD ATDC

is maintained, or in other words how quickly locallyExh. valve closing (EVC) 370 CAD ATDCStart of 1st inj. (SOI

1) 340 CAD BTDC rich conditions are diluted. Too rapid mixing would

Start of 2nd inj. (SOI2) 40 CAD BTDC

result in a relatively homogeneous charge at the time

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46 S Mosbach, H Su, M Kraft, A Bhave, F Mauss, Z Wang, and J-X Wang

of ignition, similar to a single early injection or even stants of levap=0.6 mm2/s and a=20 were used. The

number of stochastic particles was chosen Npar=100port injection.

For all dual injection simulations a split ratio of 6 : 1 unless indicated otherwise.Under these particular conditions, the dual injectionwas used, as in the experiments (ratio of fuel masses

injected into the cylinder during the first and second is seen to have very little effect on the shape of thepressure profile, experimentally as well as numerically.injection). With a total injected fuel mass of 21.6 mg,

the fuel injected during second injection constitutes The difference in ignition timing is found to be theresult of different temperatures at IVC (by about 4 K).of order 0.1 per cent of the total mass inside the

cylinder. Therefore, the simplifying assumption was The remainder of this paper focuses on exhibitingunder which circumstances the pressure profiles aremade that the temperature of the charge is not

affected by the second injection. affected by a second injection and how.It should be noted that it is a common andThe SMD has been chosen as follows. The fuel

injector used in the experiments was designed to accepted strategy in engine modelling, irrespectiveof what model is used (CFD, multi-zone, etc.), to firstproduce droplet distributions with SMD=15 mm for

injection into atmospheric ambient pressure. How- tune model parameters to a particular engine andthen predict trends resulting from parameter variation.ever, at the conditions of the second injection

(−40 CAD) the ambient in-cylinder pressure is Such an approach is usually necessary, owing to theinherent difficulties in ICE modelling, such as verymuch larger (about 7 bar), which tends to lead to

significantly bigger droplets [26]. Typical values for large experimental uncertainties and the fact thatmany crucial quantities are unknown or inaccessiblediesel fuel lie roughly in the range between 25 and

75 mm [26], but for gasoline smaller values are to measurements.expected [29] partly owing to the lower viscosity,which is consistent with the design specification 4.2 Results and discussionof the employed injector. Based on these consider-

Figure 2 depicts the time evolution of the totalations, SMD=27 mm was somewhat arbitrarily chosen

in-cylinder liquid fuel mass for various values ofthroughout. Reasonable estimates for l

evapyield

the evaporation constant levap

. Recall that largevalues of order 1 mm2/s, which for an SMD of 27 mm

values of levap

correspond to short evaporation timescorrespond to an evaporation time of t

evap#0.73 ms

(via tevap=SMD2/l

evap). The start (at −40 CAD) and

(or 6.1 CAD at 1400 r/min).the end (at −37 CAD) of the second injection are

Before the model can be applied to investigativereadily discernible, as are the different evaporation

studies, several model parameters need to be cali-time scales.

brated. Some results of this tuning process are shownin Fig. 1. For the dual injection case evaporation con-

Fig. 2 Time evolution of the total in-cylinder liquid fuelmass for various values of the evaporation con-

Fig. 1 Experimental and simulated in-cylinder pressure stant levap

(start of second injection SOI2=−40

CAD, end of second injection EOI2=−37.4 CAD)profiles for single and dual injection

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47Dual injection HCCI engine simulation

Figure 3 displays the average mass fraction ofgaseous iso-octane in the cylinder as function of thecrank angle for a=20. Until SOI

2=−40 CAD the

iso-octane mass fraction stays constant because fuelconsumption (pyrolysis, thermal decomposition, OHradical attack) has not yet set in. After the secondinjection has begun, the mass of iso-octane risesas expected. Again, the effect of different l

evapcan

clearly be seen. Roughly at the same time the gaseousfuel starts to be consumed (and low-temperaturereactions commence). The consumption of iso-octanewas studied for different levels of stratification, i.e.different values of a: it was consumed more rapidlyfor stronger stratification (smaller a), although thiseffect was small.

Figures 4, 5, and 6 illustrate the effect of varying thespray model parameters a and l

evapon the pressure

profile. Figure 4 demonstrates the influence of varyingFig. 4 Pressure profiles for various levels of chargethe level of charge stratification, i.e. choosing different

stratification at levap=1.2 mm2/s (short evapor-values of a. For all the curves l

evap=1.22 mm2/s

ation time) compared with experiment(short evaporation time). For the case of mediumevaporation time the curves turn out very similar tothose shown. However, for long evaporation time allcurves basically coincide with each other, which influence. For a=20, the case of strongest stratifi-means that the effect of charge stratification is no cation, the combustion duration is prolonged com-longer visible. A possible explanation for this is that pared with the other cases by more than 2 CAD,in the latter case too little fuel is released into the and the pressure profile agrees much better with thegas phase per unit time, so that there is enough time experimental one.to dilute it. In particular, the mixture might be overall Figure 5 shows again the influence of the stratifi-too dilute so that the stratification has virtually no cation level for medium evaporation constant l

evap=

0.6 mm2/s and higher resolution, which corroborates

Fig. 3 Time evolution of the average mass fraction of(gaseous) iso-octane for various values of the

Fig. 5 Pressure profiles for various levels of chargeevaporation constant levap

at a=20 (start ofsecond injection SOI

2=−40 CAD, end of second stratification at higher resolution and l

evap=

0.6 mm2/s compared with experimentinjection EOI2=−37.4 CAD)

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48 S Mosbach, H Su, M Kraft, A Bhave, F Mauss, Z Wang, and J-X Wang

the trend exhibited in Fig. 4, namely the higher thelevel of stratification the longer the combustionduration. The number of stochastic particles deter-mines the resolution of the model, i.e. the maximumattainable stratification. For a given particle numberN

par, the maximal stratification which can be resolved

by the model is reached if precisely one particlereceives liquid fuel per time step. For example, atN

par=100 this limit of resolution is attained for a=20

roughly. Higher levels of stratification, i.e. smallervalues of a, can be reached for larger N

par. Note that

this is merely a limit of numerical resolution in thesame way as the grid spacing limits the smallestresolvable turbulence scale in a CFD simulation. Thepredictions of the model are of course (asymptotically)independent of numerical parameters. Extensive testsof this and other numerical properties of an earlierversion of the code, identical with the one used here

Fig. 6 Pressure profiles for various evaporation con-except for the spray and mixing model, can be found stants at a=20 compared with experimentin reference [14]. In Fig. 5, for each N

par, a has been

chosen such that only one particle receives fuel pertime step. Note that it is not possible to pick a fixednumber of particles to be endowed with liquid fuel,because then predictions of the model would dependon the numerical parameter N

par. This is a main

reason for introducing a, a physical parameter,because the stratification is then independent of N

par(at least asymptotically for large particle numbers).The simulation for N

par=100, a=20 required a CPU-

time of 50 min, which is also the typical CPU-timefor most of the other runs performed in the presentwork. The run for N

par=200, a=10 took 1 h 50 min,

and the one for Npar=500, a=4 required 5 h 30 min

of computation.Figure 6 illustrates the impact of varying l

evapon the

pressure profile for maximum stratification (a=20). Itis recognized that shorter evaporation times promotestratification and therefore the spreading of heatrelease, which can be explained as follows. If the fuel Fig. 7 Local history of temperature and iso-octane mass

fraction, for single particles (‘fuel’ and ‘lean’)evaporates rapidly then it will be relatively stronglyand in-cylinder average (‘mean’)located at where the liquid fuel was. In case of slower

evaporation, turbulent mixing has sufficient time todilute locally higher concentrations. For lower strati-fication levels (greater a), all considered pressure pro- particle that does not. The cylinder average is labelledfiles exhibit large pressure rise rates at ignition (short ‘mean’. The effects of evaporation (until about −30combustion duration) with virtually no dependence CAD ATDC) and the chemical kinetics of the gaseouson the evaporation time. iso-octane (until TDC) of the fuel particle demonstrate

Figure 7 gives some insight into the local evolution a faster depletion of iso-octane compared with thatof temperature and gaseous iso-octane mass fraction for the lean particle and the mean iso-octane level.of fluid parcels inside the cylinder. The curves labelled The fuel particle ignites about 3 CAD earlier than the‘fuel’ belong to a single stochastic particle, which lean one and its local peak temperature exceedsreceives liquid fuel during the second injection, the average by almost 500 K. Finally, it is noted that

none of the observed qualitative trends are sensitivewhereas the curves referred to as ‘lean’ belong to a

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49Dual injection HCCI engine simulation

towards small variations in timing of the second REFERENCESinjection.

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2 Marriott, C. D. and Reitz, R. D. ExperimentalDual injection in a gasoline HCCI engine is studied investigation of direct injection gasoline for premixedusing a zero-dimensional PDF-based stochastic compression-ignited combustion-phasing control.reactor modelling approach. The model includes SAE paper 2002-01-0418, 2002.detailed chemical kinetics and accounts for inhomo- 3 Delebinski, T., Eckert, P., and Merker, G. P. Optical

investigation of HCCI two-stage ignition usinggeneities in composition and temperature on accountmultiple injection of synthetic fuels. In Proceedingsof turbulent mixing, convective heat transfer, andof ICEF2005, 2005 Fall Technical Conference ofdirect injection. A simplistic spray model describingthe ASME Internal Combustion Engine Division,injection, penetration, and evaporation sub-processesOttawa, ON, Canada, 2005, ICEF2005-1282 (ASME,

is developed. For mixing, the EMST model whichNew York).

accounts for localness in composition space is 4 Mueller, C. J., Martin, G. C., Briggs, T. E., andemployed. Duffy, K. P. An experimental investigation of in-

The predicted ignition timing and peak pressure cylinder processes under dual-injection conditionsagreed satisfactorily with measurements, for both in a DI Diesel engine. SAE paper 2004-01-1843, 2004.

5 Pottker, S., Eckert, P., Delebinski, T., Baumgarten, C.,single- and dual-injection cases. Systematic para-Oehlert, K., Merker, G. P., Wagner, U., and Spicher, U.metric studies related to spray penetration, charac-Investigations of HCCI combustion using multi-teristic evaporation lag, and level of stratificationstage direct-injection with synthetic fuels. SAE paperdemonstrate the role of increased charge stratifi-2004-01-2946, 2004.

cation induced by DI in prolonging the combustion 6 Ogawa, H., Miyamoto, N., Sakai, A., and Akao, K.duration and increasing the rate of iso-octane Combustion in a two-stage injection PCCI engineconsumption. with lower-distillation-temperature fuels. SAE paper

Tracing the evolution of individual stochastic 2004-01-1914, 2004.7 Hasegawa, R. and Yanagihara, H. HCCI combustionparticles in phase space revealed that the particles

in DI diesel engine. SAE paper 2003-01-0745, 2003.receiving fresh fuel from the second injection experi-8 Yoshizawa, K., Teraji, A., Miyakubo, H.,enced advanced auto-ignition compared with the lean

Yamaguchi, K., and Urushihara, T. Study of high loadparticles not exposed to fresh fuel. This observationoperation limit expansion for gasoline compressionfurther substantiates the role of dual injection inignition engines. In Proceedings of ICES2003, 2003

widening the heat release, thereby increasing the Spring Technical Conference of the ASME InternalHCCI operating limit to higher loads. Combustion Engine Division, Salzburg, Austria,

The focus of the present work has been on gaining 2003, ICES2003-543 (ASME, New York).insight into the influence of dual injection on com- 9 Wang, Z., Wang, J.-X., Shuai, S.-J., and Ma, Q.-J.

Effects of spark ignition and stratified charge onbustion parameters on local and global levels. Thegasoline HCCI combustion with direct injection. SAEmain advantage of this approach is that the influencepaper 2005-01-0137, 2005.and the sensitivities of the parameters can easily be

10 Yamamoto, S., Satou, T., and Ikuta, M. Feasibilitystudied in a large number of simulations within astudy of two-stage hybrid combustion in gasoline

reasonable amount of computing time, in sharp con- direct injection engines. SAE paper 2002-01-0113,trast to complex CFD models for instance. Improving 2002.the spray model by including sub-models for the 11 Urushihara, T., Hiraya, K., Kakuhou, A., and Itoh, T.parameters, full-cycle simulations, and studying Expansion of HCCI operating region by the com-in detail the influence of multiple injections on bination of direct fuel injection, negative valve

overlap and internal fuel reformation. SAE paperemissions form the scope of future work.2003-01-0749, 2003.

12 Canakci, M., Hruby, E., and Reitz, R. D. Assessingdouble injection and intake air temperature effectsACKNOWLEDGEMENTSon gasoline HCCI engine performance and emissionsusing fully automated experiments and micro-

This work was partially funded by the Engineering genetic algorithms. In Proceedings of ICES2002, 2002and Physical Sciences Research Council (EPSRC) Spring Technical Conference of the ASME Internal(grant number GR/R85662/01). The authors are Combustion Engine Division, April 2002, Rockford,

Illinois, USA, 2002, ICES2002-459 (ASME, New York).grateful for some helpful comments of the reviewers.

JER01806 © IMechE 2007 Int. J. Engine Res. Vol. 8

50 S Mosbach, H Su, M Kraft, A Bhave, F Mauss, Z Wang, and J-X Wang

13 Narayanaswamy, K. and Rutland, C. J. Cycle simu- Combustion Engine Division, Long Beach, California,USA, 2004, ICEF2004-927 (ASME, New York).lation Diesel HCCI modeling studies and control.

21 Bhave, A., Kraft, M., Mauss, F., Oakley, A., andSAE paper 2004-01-2997, 2004.Zhao, H. Evaluating the EGR-AFR operating range14 Su, H., Vikhansky, A., Mosbach, S., Kraft, M.,of a HCCI engine. SAE paper 2005-01-0161, 2005.Bhave, A., Mauss, F., and Kim, K.-O. A new com-

22 Bhave, A., Kraft, M., Montorsi, L., and Mauss, F.putational model for simulating direct injectionModelling a dual-fuelled multi-cylinder HCCI engineHCCI engines. Technical Report 31, Cambridgeusing a PDF-based engine cycle simulator. SAECentre for Computational Chemical Engineeringpaper 2004-01-0561, 2004.Preprint-Series, 2005, submitted for publication.

23 Pope, S. B. PDF methods for turbulent reactive15 Jhavar, R. and Rutland, C. J. Effects of mixingflows. Prog. Energy Combust. Sci., 1985, 11, 119–192.on early injection diesel combustion. SAE paper

24 Subramaniam, S. and Pope, S. B. A mixing model2005-01-0154, 2005.for turbulent reactive flows based on Euclidean16 Kong, S.-C., Patel, A., Yin, Q., and Reitz, R. D.minimum spanning trees. Combust. Flame, 1998,Numerical modelling of Diesel engine combustion115, 487–514.and emissions under HCCI-like conditions with high

25 Hiroyasu, H., Kadota, T., and Arai, M. DevelopmentEGR levels. SAE paper 2003-01-1087, 2003.and use of a spray combustion modeling to predict17 Cao, L., Zhao, H., Jiang, X., and Kalian, N.Diesel engine efficiency and pollutant emissionsNumerical study of effects of fuel injection timings(part 1 combustion modeling). Bull. JSME, 1983,on CAI/HCCI combustion in a four-stroke GDI 26(214), 569–575.

engine. SAE paper 2005-01-0144, 2005. 26 Heywood, J. B. Internal combustion engine funda-18 Sun, Y., Shuai, S.-J., Wang, J.-X., and Wang, Y.-J. mentals, 1988 (McGraw-Hill, New York).

Numerical simulation of mixture formation and 27 Jaine, T., Benkenida, A., Menegazzi, P., andcombustion of gasoline engines with multistage Higelin, P. Zero dimensional computation of Dieseldirect injection compression ignition (DICI). SAE spray – comparison with experiments and 3Dpaper 2003-01-1091, 2003. model. 6th International Conference on Engines for

19 Kong, S.-C., Ra, Y., and Reitz, R. D. Performance of automobile, Capri, Italy, 2003.multi-dimensional models for simulating Diesel 28 Crowe, C. T., Sommerfeld, M., and Tsuji, Y.premixed charge compression ignition engine com- Multiphase flows with droplets and particles, 1997bustion using low-and high-pressure injectors. Int. (CRC Press, London).J. Engine Res., 2005, 6(5), 475–486. 29 Takagi, M. and Moriyoshi, Y. Numerical simu-

20 Su, W., Zhang, X., Lin, T., Pei, Y., and Zhao, H. lations of spray formation process in high and lowStudy of pulse spray, heat release, emissions and ambient pressures using a swirl-type injector. In Theefficiencies in a compound Diesel HCCI com- Fifth International Symposium on Diagnostics andbustion engine. In Proceedings of ICEF2004, 2004 modeling of combustion in internal combustion

engines (COMODIA 2001), Nagoya, 2001.Fall Technical Conference of the ASME Internal

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