A Control-Oriented Jet Ignition Combustion Model for an SI ... · gies become necessary for jet ignition systems and a precise control-oriented jet ignition combustion model is the

A CONTROL-ORIENTED JET IGNITION COMBUSTION MODEL FOR AN SI ENGINE

Ruitao Song, Gerald Gentz, Guoming Zhu, Elisa Toulson, and Harold SchockDepartment of Mechanical Engineering

Michigan State UniversityEast Lansing, MI 48824 USA

ABSTRACTA turbulent jet ignition system of a spark ignited (SI) en-

gine consists of pre-combustion and main-combustion cham-bers, where the combustion in the main-combustion chamberis initiated by turbulent jets of reacting products from the pre-combustion chamber. If the gas exchange and combustion pro-cesses are accurately controlled, the highly distributed ignitionwill enable very fast combustion and improve combustion stabil-ity under lean operations, which leads to high thermal efficiency,knock limit extension, and near zero NOx emissions. For model-based control, a precise combustion model is a necessity. Thispaper presents a control-oriented jet ignition combustion model,which is developed based on simplified fluid dynamics and ther-modynamics, and implemented into a dSPACE based real-timehardware-in-the-loop (HIL) simulation environment. The two-zone combustion model is developed to simulate the combustionprocess in two combustion chambers. Correspondingly, the gasflowing through the orifices between two combustion chambers isdivided into burned and unburned gases during the combustionprocess. The pressure traces measured from a rapid compres-sion machine (RCM), equipped with a jet igniter, are used forinitial model validation. The HIL simulation results show a goodagreement with the experimental data.

INTRODUCTIONIn the recent years, various alternative combustion technolo-

gies have been investigated for improving combustion thermalefficiency and meeting the increasingly strict emission regula-tions. Lean burn technologies, such as jet ignition combustion [1]

and homogeneous charge compression ignition (HCCI) combus-tion [2, 3], provide promising means to achieve these goals. Theengine thermal efficiency is improved by increasing the specificheat ratio due to the introduction of additional air. The low leancombustion temperature leads to a significant reduction of NOxemissions, especially when the relative air-to-fuel ratio λ is be-yond the lean limit (e.g., at λ > 1.4) [1]. However, the appli-cation of lean burn technologies to a conventional spark ignition(SI) engine is limited by the poor combustion stability and de-creased effectiveness of the three-way catalyst under lean opera-tion conditions.

The HCCI combustion, one of the lean burn technologiesthat have been widely studied in recent years, is initiated by theauto-ignition of the in-cylinder air-fuel mixture, which is similarto the operation of compression ignition (CI) engines. The heatreleasing at multiple sites within the combustion chamber resultsin a very fast rate of combustion, which improves the thermalefficiency. However, the combustion phase control and SI-HCCIcombustion mode transition control are two of the key challengesof the HCCI combustion [3,4]. Regulating the charge air temper-ature is often used to control the start of combustion. However,this technology needs to be further improved for practical appli-cations.

The jet ignition system consists of a main-combustion cham-ber and a small-volume pre-combustion chamber filled with arelatively rich air-fuel mixture. It has two fuel delivering sys-tems: one for the pre-combustion chamber and the other for themain-combustion chamber. The two combustion chambers areconnected by a few small orifices. The combustion process isinitiated by a spark inside the pre-combustion chamber, and the

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turbulent jets of the reacting mixture from the pre-combustionchamber cause the combustion of the lean air-fuel mixture in themain-combustion chamber.

In 1918, Harry R. Ricardo developed and patented the 2-stroke Ricardo Dolphin engine that first used the jet ignition sys-tem [5]. In the 1970s, as strict emission standards appeared, sig-nificant amount of research was devoted to the development ofjet ignition systems. In 1976, Toyota developed a jet ignitionengine with no auxiliary fueling system for the pre-combustionchamber [6]. Similar engines were also developed by Ford [7],Volkswagen [8], etc. The compound vortex controlled combus-tion (CVCC) system developed by Honda is usually consideredto be the most successful example of jet ignition technology [9].It was able to meet the 1975 emission standards without a cat-alytic converter.

Jet ignition combustion possesses all the advantages of thelean burn technology mentioned at the beginning of this section.Besides, the distributed ignition source enables a very fast rateif combustion, which is similar to the HCCI combustion. It iscapable of up to 18% fuel economy improvement relative to SIengines [1]. The enhanced ignition provided by the turbulentjets results in a significant improvement of combustion stabil-ity under lean operation conditions. Stable combustion can beachieved when λ is up to 1.8, approaching elimination of NOxemissions [10]. In addition, a jet ignition system makes it easy tocontrol the combustion phase, compared with the HCCI combus-tion, due to the simple control of the start of combustion throughthe spark plug in the pre-combustion chamber.

However, the higher heat losses due to the additional surfacearea of the pre-combustion chamber along with the poor mix-ture propagation within the small pre-combustion chamber cav-ity may somewhat compromise thermal efficiency [11]. The gasexchange and combustion processes within the pre-combustionchamber need to be precisely controlled to provide an opti-mal turbulent intensity. Therefore, model-based control strate-gies become necessary for jet ignition systems and a precisecontrol-oriented jet ignition combustion model is the foundationof model-based control of the jet ignition system. The simulationtools, such as GT-Power and WAVE, are widely used in the au-tomotive industry due to their high fidelity and accuracy [12].However, they can only be used for offline simulations. Formodel-based control, a simplified model with sufficient accu-racy is required for real-time hardware-in-the-loop (HIL) sim-ulations [2, 13].

In this article, a crank-based one-zone gas exchange modelis constructed to simulate the gas exchange process in the pre-combustion chamber. It is based on the assumption that the air,fuel, and residual gas are uniformly mixed in the pre-combustionchamber before ignition. After ignition, the chamber is dividedinto two zones: the burned and unburned zones. Correspond-ingly, the gas flowing through the orifices connecting the twocombustion chambers is also divided into burned gas and un-

FIGURE 1. BASIC STRUCTURE OF A JET IGNITION SYSTEM.

burned gas. The gas in the pre-combustion chamber is assumedto be an ideal gas. The pressure and temperature within thepre-combustion chamber are calculated based on mass and en-ergy conservation principles and the mass fraction burned (MFB)Wiebe function. The main-combustion chamber is modeled in asimilar way. However, the ignition time and burn rate of themixture in the main-combustion chamber are influenced by thecombustion condition in the pre-combustion chamber.

The main contribution of this article is the formulation anddevelopment of the control-oriented jet ignition system model,the implementation of the developed model into a dSPACE real-time HIL engine simulation environment for model-based con-trol development and validation. The simulation results are vali-dated using the experimental data from a rapid compression ma-chine (RCM).

This paper is organized as follows. The next section brieflydescribes the jet ignition system and modeling framework andthe following section provides the governing equations of gasexchange and combustion processes. The developed model wasvalidated using the experimental data from the RCM, and finally,conclusions are drawn at the last section.

SYSTEM DESCRIPTION AND MODELING FRAME-WORKSystem Working Principle

Figure 1 shows the basic cylinder architecture of a jet igni-tion system modeled in this paper. The jet ignition engine modelwas developed for a four-cylinder engine with a pre-combustionchamber of 2.3 cm3 located in each cylinder head. The pre-combustion chamber has an auxiliary fuel system that injects theair-fuel mixture directly into the pre-combustion chamber. Thetwo combustion chambers are connected by a few small orifices.

The working process of the jet ignition system can be il-lustrated by Fig. 2. The valve timing of the system is similarto a conventional SI engine. During the intake stroke, a leanfresh charge flows into the main-combustion chamber until theintake valve closes near bottom dead center. Then, the pressureincreases in the main-combustion chamber in the compressionstroke. At the same time, premixed fresh charge is injected into



180 270 450 5400

10

20

30

40

50

Pre

ssur

e (b

ar)

Crank position (deg)

EVO

IVC

Intake Compression

Expansion ExhaustSpark→

TDC0

3

6

9

12

15

Mas

s flo

w r

ate

(g/s

)

Pre−chamber pressureMain−chamber pressureFuel Injection

FIGURE 2. JET IGNITION SYSTEM WORKING PROCESS.

the pre-combustion chamber, which pushes the residual gas out,increases the pressure in the pre-combustion chamber, and thusreduces back-flow from the main-combustion chamber to makeair-fuel ratio (AFR) control possible. When the piston movesclose to the top dead center (TDC), the spark plug ignites the rel-atively rich air-fuel mixture within the pre-combustion chamber.The released heat from chemical reaction quickly increases thepressure and temperature in the pre-combustion chamber. Thegreat pressure gradient and small orifice size produce high in-tense turbulent jets of the reacting mixture that ignite the leanmixture in the main-combustion chamber.

Modeling FrameworkAs shown in Fig. 3, the jet ignition engine model mainly

consists of four subsystem models: piston and crank dynam-ics model, exhaust gas recirculation (EGR) model, manifoldmodel, and combustion model. The combustion model includestwo parts: main-combustion chamber model and pre-combustionchamber model. A two-zone combustion model was developedfor the main-combustion chamber. The mass fraction burnedis calculated based upon the Wiebe function. The coefficientsof the Wiebe function are determined by the gas properties inthe pre-combustion chamber. For the pre-combustion chamber,a two-zone combustion model is developed. There is gas ex-change through the orifices connecting two combustion cham-bers. Crank-based combustion related variables are updated ev-ery crank degree. The other subsystem models provide the com-bustion model with crank position, manifold pressures, and othervariables. The details of these models can be found in [2, 3].

JET IGNITION SYSTEM MODELINGPre-Combustion Chamber Model

In compression stroke, an air-fuel charge is injected into thepre-combustion chamber. The pressure of the charge is assumedto be larger than that of the residual gas within the chamber.Then, the injected air-fuel mixture flow rate can be calculated

FIGURE 3. MODELING FRAMEWORK.

by the one-dimensional compressible flow equation [14].

min j =Cd1Av1Pin j√RTin j

ψ

(Ppre

Pin j

),Pin j > Ppre (1)

where

ψ (x) =

√κ

(2

κ +1

)(κ+1)/(κ−1)

x <(

2κ +1

)κ/(κ−1)

x1/κ

√2κ

κ−1(1− x(κ−1)/κ

)x≥

(2

κ +1

)κ/(κ−1)

(2)The coefficient Cd1 can be determined by experiments, Av1 is

the area of the fuel injector orifice, κ is the ratio of specific heats,Pin j and Tin j are the charge pressure and temperature, respec-tively, and Ppre is the residual gas pressure in the pre-combustionchamber. The gas exchange between the two combustion cham-bers is modeled similarly. However, the gas pressure in the pre-combustion chamber can be either larger or smaller than that inthe main-combustion chamber. The pre-combustion chamber isconsidered as a control volume with mass and energy exchange.In this paper, heat transfer through the walls is not consideredduring the intake and compression stroke. The following equa-tions can be used for solving the gas pressure and temperature inthe pre-combustion chamber during these two strokes.

dmpre

dt= min j− mtur

dUpre

dt= Hin j− Htur

(3)

where mpre and Upre are the mass and internal energy of the gas inthe pre-combustion chamber, respectively, and H is the enthalpyflow.

Assuming that the gas can be considered as an ideal gas, thetwo equations can be coupled by the ideal gas law.



FIGURE 4. TWO-ZONE COMBUSTION MODEL

P ·V = m ·R ·T (4)

Substituting Eqn. (4) into Eqn. (3), the following two equa-tions are obtained to calculate the gas pressure and temperature.

dPpre

dt=

cpRV cv

[min jTin j− mturTtur]

dTpre

dt=

TpreRPpreV cv

[cpmin jTin j− cpmturTtur− cv (min j− mtur)Tpre]

(5)

where cp and cv are the specific heat at constant pressure and thatat constant volume, V is the pre-combustion chamber volume,and

Ttur =

{Tpre mtur > 0Tmain mtur ≤ 0

(6)

where Tpre and Tmain are the temperatures in the pre-combustionand main-combustion chamber, respectively.

To improve the model accuracy, the pre-combustion cham-ber is divided into two zones after ignition. Both the burned andunburned zones can be regarded as control volumes. Besides themass, enthalpy, and work exchange between these two controlvolumes, there are also mass and enthalpy exchange through theorifices to the main-combustion chamber, shown in Fig. 4. More-over, the mass flow can be positive, where the gas flows from pre-combustion to main-combustion chamber, or negative, where thegas flows backwards. In the case of positive mass flow, the gasflow is divided into burned gas and unburned gas. The energybalance equation of the burned zone is shown in Eqn. (7). To

make the equations concise, the variables in the following equa-tions in this subsection are for the pre-combustion chamber, ifnot specified.

cvd(mbTb)

dt+P

dVb

dt+ xb

dQht

dt=

dQch

dt+

mu

1− xb

dxb

dtcpTu− mtur−bcpTb

(7)

The energy balance equation of the unburned zone is repre-sented by

cvd(muTu)

dt+P

dVu

dt+(1− xb)

dQht

dt=

− mu

1− xb

dxb

dtcpTu− mtur−ucpTu

(8)

The masses of the burned zone and unburned zone are ob-tained based on the mass conservation law.

dmb

dt=−mtur−b +

mu

1− xb

dxb

dtdmu

dt=−mtur−u−

mu

1− xb

dxb

dt

(9)

The subscripts b and u represent burned zone and unburnedzone. Qht is the heat transfer to the chamber wall. Qch is thechemical energy released by the combustion. xb is the mass frac-tion burned. mtur−b and mtur−u represent the mass flow ratesfrom burned and unburned zones to the main-combustion cham-ber. They are calculated by

mtur−b = αbCd2Av2Ppre√RTb

ψ

(Pmain

Ppre

)mtur−u = (1−αb)Cd2Av2

Ppre√RTu

ψ

(Pmain

Ppre

) (10)

The coefficient αb is chosen according to xb, shown in Fig. 5.At the start of combustion, because the burned zone is far fromthe orifices to the main-combustion chamber, αb is much smallerthan xb. As the mass fraction of the unburned zone decreases dur-ing combustion, αb gets close to or even greater than xb. How-ever, αb is bounded by 1. The precise value of αb is experimen-tally determined.

The case of negative mass flow, where the gas flows frommain-combustion to pre-combustion chamber, is also considered.



0 0.5 10

0.2

0.4

0.6

0.8

1

α b

Pre−chamber xb

Ppre>Pmain

0 0.5 10

0.2

0.4

0.6

0.8

1

Main−chamber xb

Ppre<Pmain

FIGURE 5. THE VALUE OF αb USED IN THE SIMULATION.

Before ignition in the main-combustion chamber, all the gas fromthe main-combustion chamber enters the unburned zone in thepre-combustion chamber. After ignition of the main-combustionchamber, the orifices to the pre-combustion chamber will soon besurrounded by the burned gas in the main-combustion chamber.As a result, most of the gas entering the pre-combustion chamberis assumed to be the burned gas and enters the burned zone in thepre-combustion chamber.

Applying the principle of mass conservation, the instantmass of fuel in the pre-combustion chamber can be obtained by

dmpre− f uel

dt=−

mpre− f uel

1− xb

dxb

dt− mtur−u

(1

λ (A/F)s +1

)(11)

where λ is the relative AFR, and (A/F)s is the stoichiometricAFR. Only the fuel from the unburned zone is considered.

From Eqn. (10) and Eqn. (11), the following conclusioncan be made. The total amount of fuel burned inside the pre-combustion chamber is highly influenced by αb. If αb is small,the total amount of fuel flowing out of the pre-combustion cham-ber is large, and correspondingly, the total chemical energy re-leased inside the pre-combustion chamber is small and morereleased chemical energy is trapped inside the pre-combustionchamber.

The rate of chemical energy release can be obtained by thefollowing equation.

dQch

dt= ηpreQLHV

mpre− f uel

1− xb

dxb

dt(12)

where the combustion efficiency ηpre is experimentally deter-mined, and QLHV is the lower heating value of the fuel.

The heat transfer to the chamber wall can be modeled by thefollowing relationship [15].

dQht

dt= Aprehc (Tpre−Tw) (13)

where Apre is the pre-combustion chamber surface area, Tw isthe mean wall temperature, and hc is the heat-transfer coefficientcalibrated by the experiment.

The mass fraction burned is obtained from the Wiebe func-tion [16].

xb = 1− exp

[−a(

θ −θign

∆θd

)m+1]

(14)

The coefficient a and m are chosen to be 6.908 and 2 respec-tively, θign is the start of ignition, and ∆θd is the burn durationin crank angles, which is calibrated by spark timing and AFRbefore ignition.

Main-Combustion Chamber ModelAfter the ignition in the pre-combustion chamber, the com-

bustion in the main-combustion chamber will not be initiated un-til the generation of the turbulent jet from the pre-combustionchamber. During this period, the mass flow from the burned zonein the pre-combustion chamber to the main-combustion chamberis neglected. The unburned gas from the pre-combustion cham-ber is assumed to be well mixed with the mixture in the main-combustion chamber. As a result, an additional amount of fuel isadded into the main-combustion chamber.

dmmain− f uel

dt= mtur−u

(1

λpre(A/F)s +1

)(15)

where mmain− f uel is the fuel mass in the main-combustion cham-ber.

After ignition in the main-combustion chamber, the burnedzone is created. Different from the two-zone combustion modelin a conventional SI engine, the combustion model of the main-combustion chamber needs to consider the gas flowing throughthe orifices into the pre-combustion chamber. The burned gas andunburned gas from pre-combustion (main-combustion) chamberare assumed to enter the burned zone and unburned zone in themain-combustion (pre-combustion) chamber, respectively. Themass and energy conservation equations for burned and unburnedzones are very similar to those of the pre-combustion chambermodel presented in the above subsection and is omitted in thispaper. The major difference is that the total volume of the main-combustion chamber is varying. The mass fraction burned inthe main-combustion chamber is also calculated by the Wiebefunction.

In a jet ignition system, the combustion in the main-combustion chamber is initiated by the turbulent jets generated



FIGURE 6. HIL SIMULATION PLATFORM.

from the pre-combustion chamber. The burn rate is highly de-pendent on the characteristics of the turbulent jets, which aremainly determined by AFR and total mass of the air-fuel mix-ture in the pre-combustion chamber right before ignition. Asa result, the ignition timing θign and burn duration ∆θd in theWiebe function of the main-combustion chamber are chosen asfunctions of spark timing, AFR, and the mass of air-fuel mixturein the pre-combustion chamber before ignition. These functionsare realized by lookup tables and experimentally calibrated.

The details of the gas exchange model for the main-combustion chamber can be found in [13].

SIMULATION RESULTS AND EXPERIMENTAL VALIDA-TION

The simulation of the jet ignition system model was per-formed using the HIL simulation environment shown in Fig. 6.The dSPACE based real-time engine simulator interacts with ahost computer, which is used for displaying the simulation re-sults and setting the simulation parameters [13]. A breakout boxconnects to the dSPACE simulator and an oscilloscope is usedfor displaying the simulation results.

The jet ignition engine modeled in this paper is for a 2.0-Lfour-cylinder engine equipped with turbulent jet igniters for eachcylinder. The detailed engine parameters are given in Tab. 1.

Since the experimental metal engine has not been set up yet,the RCM jet ignition experimental data were used to validate thedeveloped model. Fig. 7 shows the basic structure of the RCM atMichigan State University [17].

At the beginning of the experiment, the two combustionchambers were filled with air-fuel mixture with a known AFR.The piston in the RCM rapidly compressed the mixture in themain-combustion chamber. At the same time, fuel was injectedinto the pre-combustion chamber. At the end of compression, thepiston kept still; and, thus, the volume in the main-combustionchamber remained constant. After about 3 ms, the spark is initi-ated through the spark plug inside the pre-combustion chamberand then the reacting products from the pre-combustion cham-

TABLE 1. ENGINE SPECIFICATIONS.

Parameter Value

bore/stroke 86 mm / 86 mm

connecting-rod length 143.6 mm

compression ratio 9.8:1

pre-combustion chamber volume 2.3 cm3

pre-combustion chamber orifice diameter 1.25 mm

FIGURE 7. RAPID COMPRESSION MACHINE.

−10 −5 0 5 10 15

0

10

20

30

40

50

Time (ms)

Pre

ssur

e (b

ar)

Main−chamberPre−chamber

FIGURE 8. MEASURED PRESSURES IN THE RCM.

ber ignited the mixture in the main-combustion chamber. Thepressures in the combustion chambers were measured by Kistlerpressure sensors.

Figure 8 shows the measured pressure traces in the RCMwith the main-combustion chamber λ = 1.75. These data cannotbe used directly for the model validation since the RCM combus-tion occurs with a constant volume. To make the experimentaldata and the simulation results comparable, the following methodwas used.

Assuming the piston is moving the same way as in a realengine, there would be an additional pressure drop in the main-combustion chamber due to the chamber volume increasing. Thepressure after considering the pressure drop can be calculated



TABLE 2. RCM SPECIFICATIONS.

Parameter Value

bore/stroke 50.8 mm / 20.2 mm

compression ratio 8.5:1

pre-combustion chamber volume 2.3 cm3

pre-combustion chamber orifice diameter 1.25 mm

according to the adiabatic process equation.

Pmain−c = Pmain−r

(Vmain−r

Vmain−c

)γ

(16)

where Pmain−c is the converted pressure after considering the vol-ume change, Pmain−r and Vmain−r are the pressure and volume ofthe RCM main-combustion chamber, respectively, Vmain−c is thechamber volume of the engine, and γ is the specific heat ratio,which is considered to be a constant value. Note that only thepressure trace after the RCM piston reached the end of its strokelength is converted.

The pressure in the pre-combustion chamber is mainly in-fluenced by combustion and the gas flow through the orifices be-tween the two combustion chambers. As a result, the pressuretrace in the pre-combustion chamber is converted by consideringthe difference between the mass flow rates through these orificesbefore and after conversion, as shown in Eqn. (17), where it isassumed that the temperatures of the gas flows before and afterconversion are the same.

dPpre−c

dt=

dPpre−r

dt+

cpRTtur

Vprecv(mtur−r− mtur−c) (17)

where the subscripts c and r denote the converted and originalproperties, respectively. Ttur is calculated by the calibrated RCMmodel which will be discussed later.

Table 2 provides the RCM parameters. The engine modelparameters were chosen accordingly to make the simulation re-sults comparable to the RCM experimental data.

The engine speed was chosen as follows. Considering thesimulation and experimental results of jet-ignition systems in[18, 19], the main-combustion chamber burn duration of our jetignition system was estimated to be around 20 crank degrees withλ = 1.75. From the RCM experimental data shown in Fig. 8, the

280 300 320 340 360 380 400 420

0

10

20

30

40

50

Crank position (deg)

Pre

ssur

e (b

ar)

Main experimentMain two−zonePre experimentPre two−zonePre one−zone

FIGURE 9. COMPARISON OF SIMULATION AND CONVERTEDEXPERIMENTAL RESULTS.

burn duration is about 3.6 ms. Therefore, the corresponding en-gine speed is about 900 rpm.

In this paper, the combustion process in the pre-combustionchamber is simulated by a two-zone combustion model. To ana-lyze the benefit of using the two-zone combustion model over theone-zone one, another jet ignition system model with one-zonecombustion model for the pre-combustion chamber was also de-veloped. In the one-zone model, the gas in the pre-combustionchamber is assumed to be homogeneous all the time. So, the gasflowing to the main-combustion chamber is also homogeneous.However, since main-combustion chamber model is unchangedthe gas flowing from the main-combustion chamber is still di-vided into burned and unburned gas.

In Fig. 9, the simulation results of the developed jet ig-nition system models are compared with the RCM data whenthe pre-combustion chamber relative AFR is 1.1 and the main-combustion chamber relative AFR is 1.75. The model simulationresults and converted RCM experimental data show a fairly goodmatch. Moreover, the two-zone model is more accurate than theone-zone model because the two-zone model is able to capturedetailed characteristics of the gas exchange process between thetwo combustion chambers.

Converting the RCM experimental pressure traces inevitablycauses additional errors. As a result, we used another methodto further validate the jet ignition system model. Since the ma-jor difference between the jet ignition engine and the RCM isthe piston movement, an RCM model can be developed by onlychanging the piston movement feature of the jet ignition systemmodel. Once the RCM model is validated by the experimentaldata, the corresponding jet ignition system model is also indi-rectly validated. The simulation results of the developed RCMmodel were compared with the experimental data from the RCMin Fig. 10. The simulation results match the experimental datafairly well, so the jet ignition system model is further validated.The relatively large simulation error occurs at the beginning ofthe combustion in the main-combustion chamber. One possible



−10 −5 0 5 10 15

0

10

20

30

40

50

Time (ms)

Pre

ssur

e (b

ar)

Main experimentMain two−zonePre experimentPre two−zonePre one−zone

FIGURE 10. COMPARISON OF SIMULATION AND EXPERI-MENTAL RESULTS.

reason is that utilizing Eqn. (10) could cause large error whenthe pressure difference between the pre-combustion and main-combustion chambers is small, which was discussed in [14]. Andagain, the two-zone model is more accurate than the one-zonemodel.

CONCLUSIONA control-oriented jet ignition system model is presented in

this paper, and the model was implemented into a dSPACE basedHIL (hardware-in-the-loop) engine simulation environment. Thesimulation results were compared with the RCM (rapid compres-sion machine) experimental data and show a fairly good match,indicating the developed control-oriented model is able to ac-curately capture the jet ignition system dynamics. This showsthat the developed model has the potential to be used for model-based control. The future work is to further validate and calibratethe developed model using actual engine data and to developedmodel-based combustion control strategies.

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A Control-Oriented Jet Ignition Combustion Model for an SI ... · gies become necessary for jet ignition systems and a precise control-oriented jet ignition combustion model is the