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Sedigheh Tolou Department of Mechanical Engineering, Michigan State University, 1497 Engineering Research CT, East Lansing, MI 48824 e-mail: [email protected] Ravi Teja Vedula Department of Mechanical Engineering, Michigan State University, 1497 Engineering Research CT, East Lansing, MI 48824 e-mail: [email protected] Harold Schock Department of Mechanical Engineering, Michigan State University, 1497 Engineering Research CT, East Lansing, MI 48824 e-mail: [email protected] Guoming Zhu Department of Mechanical Engineering, Michigan State University, 1497 Engineering Research CT, East Lansing, MI 48824 e-mail: [email protected] Yong Sun Tenneco Inc., 3901 Willis Road, Grass Lake, MI 49240 e-mail: [email protected] Adam Kotrba Tenneco Inc., 3901 Willis Road, Grass Lake, MI 49240 e-mail: [email protected] Combustion Model for a Homogeneous Turbocharged Gasoline Direct-Injection Engine Homogeneous charge is a preferred operation mode of gasoline direct-injection (GDI) engines. However, a limited amount of work exists in the literature for combustion models of this mode of engine operation. Current work describes a model developed to study combustion in a homogeneous charge GDI engine. The model was validated using experi- mental data from a 1.6 L Ford EcoBoost V R engine, tested at the U.S. EPA. The combustion heat release was approximated using a double-Wiebe function, to account for the rapid initial premixed combustion followed by a gradual diffusion-like state of combustion, as observed in this GDI engine. Variables of Wiebe correlations were adjusted into a semi- predictive combustion model. The effectiveness of semipredictive combustion model was tested in prediction of in-cylinder pressures. The root-mean-square (RMS) errors between experiments and numerical results were within 2.5% of in-cylinder peak pressures during combustion. The semipredictive combustion model was further studied to develop a pre- dictive combustion model. The performance of predictive combustion model was exam- ined by regenerating the experimental cumulative heat release. The heat release analysis developed for the GDI engine was further applied to a dual mode, turbulent jet ignition (DM-TJI) engine. DM-TJI is a distributed combustion technology with the potential to provide diesel-like efficiencies and minimal engine-out emissions for spark-ignition engines. The DM-TJI engine was observed to offer a faster burn rate and lower in-cylinder heat transfer compared to the GDI engine. [DOI: 10.1115/1.4039813] Introduction In recent years, a range of different technologies have been under consideration to improve the fuel economy of gasoline engines and reduce exhaust emissions. Among these, gasoline direct-injection (GDI) engines have a greater degree of feasibility for market acceptance [1,2]. Therefore, a large portion of light- duty vehicle developments lean toward achieving higher thermal efficiency and lower exhaust emissions in GDI engines. Signifi- cant developments include [3]: Higher compression ratio Charge dilution using exhaust gas recirculation (EGR) Tumble enhancement Higher ignition energy Late intake valve closure timing (Miller or Atkinson cycle) Direct injection of the fuel into the combustion chamber decreases the charge temperature, resulting in higher volumetric efficiency and less knock tendency at higher compression ratios. These characteristics lead to higher thermal efficiency and power output for GDI engines, which facilitates engine downsizing. GDI engines can be designed to operate in both homogenous and lean stratified modes of operation. Homogeneous charge is obtained through early intake injection of the fuel. Stratified charge, on the other hand, is attained as a result of a late fuel injection during compression stroke causing local fuel-rich mixture in the vicinity of spark plug surrounded by a globally fuel-lean mixture in the combustion chamber. At engine low-mid load operation, the homogeneous mode with its higher combustion stability lacks the advantage of lower pumping work compared to the lean strati- fied mode. Combustion stability is challenging to obtain in lean stratified mode due to high cycle-to-cycle variability of in-cylinder charge motion and quenching of the flame. The dual mode, turbulent jet ignition (DM-TJI) is an engine com- bustion technology wherein an auxiliary air supply apart from an auxiliary fuel injection, as seen in TJI systems, is provided into the prechamber [3,4]. Upon spark ignition in the prechamber, highly energetic chemically active turbulent jets enter the main chamber through a multi-orifice nozzle and ignite the lean air/fuel mixture inside the main chamber. DM-TJI ignition strategy extends the mixture flammability limits by igniting leaner mixtures compared to the traditional spark ignition approach [3]. Therefore, the DM- Contributed by the IC Engine Division of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received February 27, 2018; final manuscript received March 8, 2018; published online June 19, 2018. Editor: David Wisler. Journal of Engineering for Gas Turbines and Power OCTOBER 2018, Vol. 140 / 102804-1 Copyright V C 2018 by ASME Downloaded From: https://gasturbinespower.asmedigitalcollection.asme.org/ on 07/03/2018 Terms of Use: http://www.asme.org/about-asme/terms-of-use
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Page 1: Combustion Model for a Homogeneous Turbocharged Gasoline ... · Gasoline Direct-Injection Engine Homogeneous charge is a preferred operation mode of gasoline direct-injection (GDI)

Sedigheh TolouDepartment of Mechanical Engineering,

Michigan State University,

1497 Engineering Research CT,

East Lansing, MI 48824

e-mail: [email protected]

Ravi Teja VedulaDepartment of Mechanical Engineering,

Michigan State University,

1497 Engineering Research CT,

East Lansing, MI 48824

e-mail: [email protected]

Harold SchockDepartment of Mechanical Engineering,

Michigan State University,

1497 Engineering Research CT,

East Lansing, MI 48824

e-mail: [email protected]

Guoming ZhuDepartment of Mechanical Engineering,

Michigan State University,

1497 Engineering Research CT,

East Lansing, MI 48824

e-mail: [email protected]

Yong SunTenneco Inc.,

3901 Willis Road,

Grass Lake, MI 49240

e-mail: [email protected]

Adam KotrbaTenneco Inc.,

3901 Willis Road,

Grass Lake, MI 49240

e-mail: [email protected]

Combustion Model for aHomogeneous TurbochargedGasoline Direct-Injection EngineHomogeneous charge is a preferred operation mode of gasoline direct-injection (GDI)engines. However, a limited amount of work exists in the literature for combustion modelsof this mode of engine operation. Current work describes a model developed to studycombustion in a homogeneous charge GDI engine. The model was validated using experi-mental data from a 1.6 L Ford EcoBoostV

R

engine, tested at the U.S. EPA. The combustionheat release was approximated using a double-Wiebe function, to account for the rapidinitial premixed combustion followed by a gradual diffusion-like state of combustion, asobserved in this GDI engine. Variables of Wiebe correlations were adjusted into a semi-predictive combustion model. The effectiveness of semipredictive combustion model wastested in prediction of in-cylinder pressures. The root-mean-square (RMS) errors betweenexperiments and numerical results were within 2.5% of in-cylinder peak pressures duringcombustion. The semipredictive combustion model was further studied to develop a pre-dictive combustion model. The performance of predictive combustion model was exam-ined by regenerating the experimental cumulative heat release. The heat release analysisdeveloped for the GDI engine was further applied to a dual mode, turbulent jet ignition(DM-TJI) engine. DM-TJI is a distributed combustion technology with the potentialto provide diesel-like efficiencies and minimal engine-out emissions for spark-ignitionengines. The DM-TJI engine was observed to offer a faster burn rate and lowerin-cylinder heat transfer compared to the GDI engine. [DOI: 10.1115/1.4039813]

Introduction

In recent years, a range of different technologies have beenunder consideration to improve the fuel economy of gasolineengines and reduce exhaust emissions. Among these, gasolinedirect-injection (GDI) engines have a greater degree of feasibilityfor market acceptance [1,2]. Therefore, a large portion of light-duty vehicle developments lean toward achieving higher thermalefficiency and lower exhaust emissions in GDI engines. Signifi-cant developments include [3]:

� Higher compression ratio� Charge dilution using exhaust gas recirculation (EGR)� Tumble enhancement� Higher ignition energy� Late intake valve closure timing (Miller or Atkinson cycle)

Direct injection of the fuel into the combustion chamberdecreases the charge temperature, resulting in higher volumetricefficiency and less knock tendency at higher compression ratios.

These characteristics lead to higher thermal efficiency and poweroutput for GDI engines, which facilitates engine downsizing. GDIengines can be designed to operate in both homogenous and leanstratified modes of operation. Homogeneous charge is obtainedthrough early intake injection of the fuel. Stratified charge, on theother hand, is attained as a result of a late fuel injection duringcompression stroke causing local fuel-rich mixture in the vicinityof spark plug surrounded by a globally fuel-lean mixture in thecombustion chamber. At engine low-mid load operation, thehomogeneous mode with its higher combustion stability lacksthe advantage of lower pumping work compared to the lean strati-fied mode. Combustion stability is challenging to obtain inlean stratified mode due to high cycle-to-cycle variability ofin-cylinder charge motion and quenching of the flame.

The dual mode, turbulent jet ignition (DM-TJI) is an engine com-bustion technology wherein an auxiliary air supply apart from anauxiliary fuel injection, as seen in TJI systems, is provided into theprechamber [3,4]. Upon spark ignition in the prechamber, highlyenergetic chemically active turbulent jets enter the main chamberthrough a multi-orifice nozzle and ignite the lean air/fuel mixtureinside the main chamber. DM-TJI ignition strategy extends themixture flammability limits by igniting leaner mixtures comparedto the traditional spark ignition approach [3]. Therefore, the DM-

Contributed by the IC Engine Division of ASME for publication in the JOURNAL

OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received February 27,2018; final manuscript received March 8, 2018; published online June 19, 2018.Editor: David Wisler.

Journal of Engineering for Gas Turbines and Power OCTOBER 2018, Vol. 140 / 102804-1Copyright VC 2018 by ASME

Downloaded From: https://gasturbinespower.asmedigitalcollection.asme.org/ on 07/03/2018 Terms of Use: http://www.asme.org/about-asme/terms-of-use

Page 2: Combustion Model for a Homogeneous Turbocharged Gasoline ... · Gasoline Direct-Injection Engine Homogeneous charge is a preferred operation mode of gasoline direct-injection (GDI)

TJI combustion system is a promising combustion technology toachieve higher fuel economy. Vedula et al. reported a net thermalefficiency of 45.5 6 0.5% for both lean and near-stoichiometricoperations of a gasoline-powered DM-TJI engine [3].

The importance of GDI engines in current and future markets isidentified, and it is worthwhile to develop predictive combustionmodels that allow the engine developers to find optimal operatingconditions. There have been several numerical and experimentalinvestigations on GDI engines. Fuel economy and exhaustemissions were numerically and/or experimentally studied underdifferent injection strategies and advanced injection systems inRef. [5–8]. Berni et al. examined the effects of water/methanolinjection as knock suppressor on a downsized GDI engine [9].Simulations of in-cylinder charge motion, spray development, andwall impingement in GDI engines were performed by Lucchiniet al. [10] and Fatouraie et al. [11]. Cho et al. investigated the com-bustion and heat transfer behavior in a single-cylinder GDI engine[12]. These studies cover a wide variety of subjects. However, thecurrent authors did not find any in-depth investigation on the zero-dimensional (0D) combustion model of a GDI engine.

Burnt and Platts [13] and Egnell [14] conducted single-zone heatrelease analysis on direct-injection (DI) diesel engines. Dowellet al. meticulously studied heat release models for modern high-speed diesel engines [15]. Lindstr€om et al. reported an empiricalcombustion model for a port fuel injection (PFI) spark ignitionengine [16]. Hellstr€om et al. [17,18] have done studies on the com-bustion model of spark-assisted compression ignition engines.Spicher et al. showed GDI development potentialities and com-pared the heat release behavior of a PFI and GDI engine [19]. Hue-gel et al. investigated the heat transfer of a single-cylinder GDIengine with a side study on the heat release behavior of the enginein both homogeneous and stratified modes of operations [20].Results obtained in the current study well agree with the worksdone by Spicher and Huegel describing heat release behavior andconsequently the combustion model of a GDI engine.

There are two goals behind the work done here: (1) develop a0D combustion model, which can be used toward the whole-cyclesimulation of a GDI engine (2) perform a preliminary heat releaseanalysis of the DM-TJI engine and compare the results obtainedwith those of the GDI engine. The work addresses the combustionbehavior of a GDI engine using experimental data from a FordEcoBoost

VR

1.6 L engine (model year 2013). The heat releasebehavior of the DM-TJI engine was examined using the samesingle-zone analysis as the GDI engine.

The paper is organized as follows: The experimental arrange-ment is first described. After that, the numerical approach andmodel development are explained followed by the section provid-ing the numerical results using experimental data and the discus-sion of the results. A separate section covers the preliminaryresults for the heat release behavior of a DM-TJI engine and com-pares the combustion characteristics of current homogeneous tur-bocharged GDI engine with that of DM-TJI engine. Conclusionsare drawn in the last section.

Experimental Arrangement

Experimental Setup. Experimental data were collected from a2013 Ford Escape 1.6 L EcoBoost turbocharged GDI engine. Tomake use of the stock engine and vehicle controllers, the enginewas tethered to its vehicle located outside the test cell. Details ofthe test site, vehicle tether information, engine setup, engine sys-tems including intake/exhaust, charge air cooling, cooling system,oil system, and front end accessory drive (FEAD) can be found inRef. [21]. Engine specifications are listed in Table 1.

Data Set Definition. The data logged included engine torque,fuel flow rate, air flow rate, pressures, temperatures, in-cylinderpressure, and on-board diagnostics/extended proportional–integral–derivative controller area network data.

Data Collection Procedure. Two data acquisition systemswere used. The first was an A&D Technology iTest Test SystemAutomation Platform for low-frequency data at a rate of 10 Hz.The second was an A&D Technology Combustion Analysis Sys-tem (CAS) for high-frequency data acquisition. CAS was sampledat 0.1 crank angles resolution and transmitted to iTest at 10 Hzrate. The engine with its associated engine control unit operatesunder original equipment manufacturer (OEM) specific protectionmodes. These protection modes limit the engine operation in a testcell, especially at higher loads as engine temperatures reach thesafety thresholds. To obtain experimental data, two test proce-dures were used to compensate for the protection modes.

The first procedure was used for the loads below �70% of themaximum rated torques at which the engine temperatures remainwithin the safety thresholds. During this procedure, a set ofselected parameters was used as stability criteria. These parame-ters included fuel flow, torque, and turbine inlet temperature. Thesettling time ranged from 20 s to 30 s at different loads andspeeds.

The second procedure was used to obtain high-load data, whichgo beyond OEM safety thresholds. It should be noted that in real-world driving, the engine does not remain at high-load operatingconditions for more than a few seconds. Thus, the quasi-steady-state values were of interest for the high-load operating pointsbeyond the OEM safety thresholds. This second procedure startedwith the engine being set to the desired speed and a load of10 N�m. The data logger was triggered on and the load stepped tothe desired value. The data were logged for 20 s in total before theengine was brought back to the cool-down mode of 1500 rpm and10 N�m.

Details of these test procedures can be found in Ref. [21]. Atotal of 50 cycles were used for the current study at each operatingcondition. Table 2 shows all the cases studied here. It should benoted that the engine was always operated at stoichiometriccondition.

Numerical Approach and Model Development

Heat Release Analysis. The single-zone analysis applied in thecurrent work considered the change in sensible internal energy(first term on the right-hand side of Eq. (1)), work done by the pis-ton motion (second term); and heat transfer from in-cylinder gas

Table 1 Engine specifications

Vehicle (model year, make, model) 2013 Ford EscapeEngine (displacement, name) 1.6 L EcoBoostRated torque 240 N�m at 1600–5000 rpmRated power 180 hp at 5700 rpmCompression ratio 10:1No. of cylinders 4Firing order 1-3-4-2Fuel injection Common railFuel type LEV III regular gasoline

Table 2 Loads, speeds, and corresponding case numbers

Load (N�m)

60 120 180

Speed (rpm)

1500 1 2 32000 4 5 62500 7 8 93000 10 11 123500 13 14 154000 16 17 —4500 18 19 —

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to the walls (Qh:t). The effects of blow-by and crevice losses wereassumed to be negligible. The energy equation is written as[22,23]

dQch

dt¼ 1

c� 1V

dp

dtþ c

c� 1p

dV

dtþ dQh:t

dt(1)

Net Heat Release. The summation of change in sensible inter-nal energy and work done by the piston is commonly called netheat release. Having the in-cylinder pressure and volume, net heatrelease can be calculated if the dependency of specific heat ratio,or gamma, on temperature is well defined. In general, gamma is afunction of both temperature and mixture composition. However,as Chang et al. showed in Ref. [24], ignoring the gamma depend-ency on mixture composition leads to a negligible error. Theyreported a third-order polynomial gamma dependency on temper-ature as a result of curve fitting at a median air/fuel ratio. Thispolynomial was used in the current work

c ¼ �9:97� 10�12T3 þ 6:21� 10�8T2 � 1:44� 10�4T þ 1:40

(2)

Average in-cylinder temperature was determined from theideal gas law using the total mass trapped in the cylinder at theintake/exhaust valve closing (IVC/EVC), the in-cylinder pressureat each crank angle, and the corresponding in-cylinder volume.This temperature was believed to be close to the mass-averagedcylinder temperature during combustion, since the molecularweights of burned and unburned mixtures are basically the same[22]. Trapped in-cylinder mass can be calculated as a summationof trapped air, fuel, internal EGR, and external EGR in the com-bustion chamber. There was no external EGR for all the casesunder study. Thus, the term was set to zero.

Internal EGR was calculated using the Yun and Mirsky correla-tion [25]. An iterative algorithm was used to find gamma andin-cylinder temperature at IVC. In-cylinder temperature at IVCcan be calculated as a weighted average of intake temperature andexhaust temperature at intake pressure [16]

T�exh ¼ Texh

pint

pexh

� �ðc�1Þ=c(3)

xr ¼VEVC

VEVO

PEVC

PEVO

� �1=c

(4)

T ¼ 1� xrð ÞTint þ xrT�exh (5)

Heat Transfer Model. The GT-POWER WoschniGT heat trans-fer model was used to simulate the heat transfer term in the energyequation of the heat release analysis. WoschniGT closely matchesthe classical Woschni correlation without swirl. The most impor-tant difference lies in the treatment of heat transfer coefficientswhen the intake and exhaust valves are open, where intake inflowvelocities and exhaust backflow velocities increase the in-cylinderheat transfer

hcWoschni ¼K1p0:8w0:8

B0:2TK2(6)

where k1 ¼ 3:01 and k2 ¼ 0:50

w ¼ C1Sp þC2 VdTrð Þ

PrVrp� pmð Þ (7)

where

C1¼2:28þ3:90

�minnet mass flow into cylinder from valves

trapped mass�engine frequency;1

� �

C2¼0 during cylinder gas exchange and compression

3:24�10�3 during combustion and expansion

(

After calculation of the heat transfer coefficient using Wosch-niGT formulation, the rate of in-cylinder heat transfer can becalculated as below, Eq. (8). Since there was no temperature dataavailable for the piston, head, and liner of this Ford EcoBoostengine, the temperature profiles were extracted from the work byHuegel et al. on a single-cylinder GDI engine [20]. A heat transfermultiplier (HTM) was used to adjust the heat transfer term,assuming the combustion efficiency as 99.9% with no blow-by orcrevice losses

dQh:t

dt¼ HTM�hc �

Apiston � T � Twall;pistonð ÞþAhead � T � Twall;headð ÞþAliner � T � Twall;linerð Þ

0B@

1CA (8)

Start of Combustion. Several approaches can be found in theliterature to define start of combustion (SOC). Reddy et al. studieddetermination of SOC based on first and second derivatives ofin-cylinder pressure [26]. Hariyanto et al. applied the waveletanalysis to define SOC of a diesel engine [27]. Shen et al. andBitar et al. defined SOC as the start for the dynamic stage of com-bustion, which corresponds to the transition between compressionand expansion process, using a pressure–volume (P–V) diagram[28,29]. Katra�snik et al. developed a new criterion to determineSOC in Ref. [30]. Their study mathematically demonstrated thedelay in SOC prediction using first and second derivatives of in-cylinder pressure. They proposed a SOC criterion based on thelocal maximum of third derivative of in-cylinder pressure withrespect to crank angle. Determination of SOC using wavelet anal-ysis requires the engine vibration data, which was not available.Additionally, Hariyanto et al. showed a high degree of correlationbetween the results from their wavelet analysis and the SOC crite-rion of Katra�snik group. The accuracy of SOC determinationmethods based on P–V diagram depends on a level of judgment indefining SOC as the point where the straight portion of compres-sion stroke deviates from its averaged path.

The current work used the SOC criterion of Katra�snik et al. Sig-nal preparation for in-cylinder pressures was done using a MATLAB

filtering algorithm called “filtfilt.” This algorithm performs zero-phase forward and reverse filtration. Design specifications wereset to a third-order Butterworth filter with a 0.15 normalized cut-off frequency for the 3 dB point, corresponding to 450–1350 Hzfor different speeds. Ignition delay was defined as the differencebetween spark timing and calculated SOC for the range of speedsand loads studied.

Combustion Model. Ivan Wiebe was one of the pioneers toconnect the rate of combustion to chain chemical reactions in aninternal combustion engine [17,31]. In real combustion systems,chain reactions progress sequentially and in parallel with reactionsinvolved in the formation of intermediate species called “activecenters” [31]. Active centers, which were referred to as effectivecenters by Wiebe, initiate effective reactions, which result in theformation of combustion products. The well-known Wiebe func-tion was developed over the basis of this concept [31].

Current work demonstrates a two-stage heat release phenom-enon for the studied GDI engine. Thus, a single Wiebe function isnot suitable to capture the heat release characteristics ofthe engine wherein premixed combustion is followed by a

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diffusion-like combustion. “Diffusion-like” combustion here ischaracterized with the slow-rate combustion as a result of eithermixture inhomogeneity or wall impingement. The mixture inho-mogeneity can arise due to locally fuel-rich regions, thereby lead-ing to a slow-rate combustion. The wall impingement, on theother hand, can result from fuel film deposition or flame hittingthe wall. The deposited fuel film can evaporate in the course ofcombustion, resulting in the second stage of heat release. Also,the heat losses when the flame reaches the chamber walls wouldslow down the rate of combustion.

The current study used a double-Wiebe function to fit theresults of heat release calculation, see the below equation:

xb hð Þ ¼ alpha � 1� exp �ah� h0

Dh1

� �m1þ1" #( )

þ 1� alphað Þ � 1� exp �ah� h0

Dh2

� �m2þ1" #( )

(9)

where a ¼ �ln 0:001 ¼ 6:9.

Semipredictive Combustion Model. The double-Wiebe functionincludes six unknown variables, a, m1, m2, Dh1, Dh2, and the SOC(h0). The first five variables were determined based on a nonlinearleast-squares optimization using MATLAB Curve Fitting Tool-boxTM. The SOC was determined using Katra�snik et al. criterionas mentioned earlier. A total of six look-up tables, one for eachvariable, were built for different loads and speeds. These look-uptables were used in the GT-POWER model as discussed next.

GT-POWER Model. The effectiveness of the semipredictivecombustion model was tested by comparing the experimentalin-cylinder pressures with results obtained from a model builtusing the 0D/one-dimensional engine simulation tool, GT-POWER (Gamma Technologies, Westmont, IL). The six variablesof the double-Wiebe function, used to model the two-stage com-bustion behavior of the GDI engine, were defined in GT-POWERby importing the look-up tables built from semipredictive com-bustion model. The GT-POWER model simulates the engine com-ponents from intercooler outlet to turbine inlet. Components’characteristics were set based on experimentally measured dataand three-dimensional computer-aided design models including:valve geometries, timings, lift profiles, and discharge coefficients;in-cylinder and port geometries; injection timings and durations,and air/fuel ratio. The engine induction and exhaust system werebuilt to a close approximation, as there was no computer-aideddesign model available. Intake manifold throttle angle was con-trolled using a proportional-integral controller with brake-mean-effective-pressure as its input value. The in-cylinder heat transfermodel was set to WoschniGT with the same in-cylinder tempera-tures and heat transfer multiplier of heat release analysis describedearlier. The combustion model was imposed based on resultsobtained from the semipredictive combustion model.

Predictive Combustion Model. The semipredictive combustionmodel, verified using the GT-POWER simulation, was furtherstudied to find correlations for each of the six variables of thedouble-Wiebe function. The corresponding combustion modelcalled as “predictive combustion model” can correlate the com-bustion behavior of the GDI engine to a set of engine parameters.The predictor parameters (x1 to x4) chosen for each of these varia-bles are listed in Table 3. The linear correlations, as shown inexpression 10, were found to well predict the six variables. Thefirst four variables, h0, a, Dh1, and Dh2, were predicted using themanifold temperature, internal EGR, engine speed, and ignitiontiming. However, the behavior of last two variables, m1 and m2,was best captured by using Dh1 and Dh2, respectively, along withiEGR and Speed as model predictor parameters (see Table 3).Thus, the same linear correlation shown in expression 10 wasused for m1 and m2, excluding the x4 parameter. A variety of

parameters were examined to define these dependencies. Itseemed that the engine in-cylinder characteristics at differentloads and speeds could be well captured by current predictorparameters. The combination of manifold temperature and frac-tion of internal EGR was believed to act as an indicator of theboundary temperature. The speed parameter could play a role incapturing the in-cylinder turbulence. The ignition timing alongwith three other parameters could represent the effect of flame ini-tiation on the combustion behavior

a0 þ a1x1 þ a2x2 þ a3x3 þ a4x4 (10)

A least-squares optimization was performed using the MATLAB

algorithm “LinearModel.fit” to minimize the RMS error in theprediction of each variable. The linear correlations found herewere validated by regenerating the experimental cumulative heatrelease as discussed later.

Results and Discussion

The following discussion for the GDI engine was divided intothree parts. The first part covered the results obtained for the heatrelease analysis including the ignition delays at different loadsand speeds. The second part discussed the semipredictive combus-tion model results followed by a comparison between the experi-mental and model regeneration of engine heat release in the thirdpart.

Heat Release Analysis. The results obtained from the heatrelease analysis demonstrated rapid initial premixed combustion(stage 1) followed by a gradual diffusion-like state of combustion(stage 2) for all the loads and speeds studied in this homogenouscharge GDI engine. Figure 1 shows the heat release rate for theloads of 60, 120, and 180 N�m at 2000 rpm. Premixed and

Table 3 Double-Wiebe variables and associated predictorparameters

Variables x1 x2 x3 x4

h0 TMan iEGR Speed hign

a TMan iEGR Speed hign

Dh1 TMan iEGR Speed hign

Dh2 TMan iEGR Speed hign

m1 Dh1 iEGR Speed �m2 Dh2 iEGR Speed �

Fig. 1 In-cylinder heat release rate at 2000 rpm/120 N�m. Theplots for 120 and 180 N�m were shifted to the left.

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diffusion-like phases of combustion are clearly noticeable in thisfigure. To highlight the two stages of combustion in the figure, therate of combustion at 120 and 180 N�m were shifted to the leftwith an offset of 6 and 19 crank angle degrees, respectively, tomatch their SOCs with that of 60 N�m load. The end point for thepremixed combustion is the start point of the diffusion-like phaseof combustion, which continues up to nearly exhaust valve open-ing (EVO). The switch point from premixed to diffusion-likephases of combustion was determined as the point where thedouble-Wiebe function shifts from the first Wiebe function to thesecond Wiebe function, the crank angle degree corresponding tothe a value. In this work, 0CA deg corresponds to firing top deadcenter. Cumulative heat release results obtained for 120 N�m at2000 rpm are displayed in Fig. 2. In this figure, the peak of theresulting apparent heat release curve was matched to the totalchemically released energy (energy from burned fuel) using aver-aged heat transfer calibrations. These calibrations were attainedby adjusting the values for HTM. The blow-by and crevice losseswere assumed negligible, and a value of 99.9% was used for thecombustion efficiency of all the cases studied.

The SOCs were determined from filtered cycle-averaged cylin-der pressure measurements, based on the local maximum of thirdderivative with respect to crank. Accordingly, the correspondingignition delays are shown in Fig. 3. The reported ignition delayswere not used in the current engine model development.

Nevertheless, they are reported as they can be of interest to thereaders. The ignition delay, in general, increased with an increasein the engine speed. However, the ignition delay first decreasedwith the increase in engine load and then slightly increased withfurther load increase from 120 N�m to 180 N�m. Assanis et al.reported the same trends for the ignition delay of a direct-injection diesel engine [32]. However, their results were limited to100 N�m of load for a speed range of 900 rpm to 2100 rpm. Itshould be noted that the signal preparation for all the in-cylinderpressures was performed using a third-order Butterworth filterwith a 0.15 normalized cutoff frequency for the 3 dB point, corre-sponding to 450–1350 Hz for different speeds. This may result insome seemingly inaccurate ignition delays for the operating con-ditions at lower speeds. However, the matter is inevitable withoutenough information regarding the nature of signal noise at eachoperating condition.

Semipredictive Combustion Model. The validity of the semi-predictive combustion model was tested using GT-POWER simu-lation. Figure 4 shows the comparison between experiments andnumerical predictions for three loads of 60, 120, and 180 N�m at2000 rpm. It should be noted that the plots in Figs. 4–7 start atSOC. The RMS errors between the measured and predicted in-cylinder pressures ranged from 0.4–1.2 bar, which corresponds to1.2–2.2% of the peak cylinder pressures.

It was observed that the model predicts higher air mass flowrate through the system. The model over-predictions of air massflow rate ranged from 3–6%, resulting in 0.6–3.4 bar higher com-pression pressures. In addition, there were slight differences inpressure traces at EVO. The model predicts lower pressures,within 0.5 bar, for the exhaust stroke, leading to a lower pumping-mean-effective-pressure, within 0.2 bar, compared to that duringexperiments. It should be recalled that the wall temperatures forthe heat transfer model were extracted from the work by Huegelet al. [20]. For their single-cylinder GDI engine, the heat transfermodels were reported to underpredict during the discharge(intake/exhaust) strokes and early compression. These underpre-dictions could be the reason behind the discrepancies seen inFig. 4. During the early and late stage of combustion, the heattransfer term is the dominant term in the heat release calculation.Any underpredictions of this term would result in lower predictedin-cylinder temperatures and pressures. This causes the engine totake in more air, leading to higher modeling intake air flow ratesand thus higher pressures. Additionally, Ford EcoBoost isdesigned to be a tumble engine. It may not be suitable to use the

Fig. 2 Cumulative heat release results at 2000 rpm/120 N�m

Fig. 3 Engine ignition delay—all cases studiedFig. 4 Cylinder pressures, experiments versus numerical pre-dictions at 2000 rpm

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Woschni heat transfer model for tumble motion engines. Furtherstudies are required to verify this inference.

Experiments and numerical predictions for all other cases understudy are shown in Fig. 5. The results achieved a reasonabledegree of accuracy with an RMS error ranging from 1.1% to 2.4%of the peak cylinder pressures. The model was able to capture thepeak pressure at all the loads and speeds except for 3500 rpm and180 N�m (case #15). At this operating condition, the experimentaldata reveal a relatively low coolant temperature (marked witharrow in Fig. 8), which can be the response to the abnormally highin-cylinder temperature (see case #15 in Fig. 9). The loadand speed associated with each of these case numbers, listed inFigs. 8–10, can be found in Table 2. This abnormality wasaccounted for the larger deviation of experimental and numericalpeak pressures. Additionally, higher pressures were observed for

all the cases during the early compression and late expansion. Thereason behind these discrepancies has been identified while dis-cussing Fig. 4.

Predictive Combustion Model. The predicting correlationswere found for the six variables of the double-Wiebe functionfrom the results obtained for the semipredictive combustion modelusing linear regressions. The comparisons between direct calcula-tions of double-Wiebe function variables and those of linearlydeveloped model predictions are shown in Fig. 10. Results dem-onstrate a good prediction for all the variables except for Dh1.However, even the linear model for Dh1 with a low R-squaredvalue of 0.51 predicts a general trend close to the experiments. Itis shown in this figure that the major discrepancy happens at case#15 (speed/load of 3500 rpm/180 N�m), in which the abnormalbehavior of this operating condition has been already discussed.

Cumulative heat release can be regenerated using linear corre-lations found for the six variables of the double-Wiebe function.Figure 6 compares the cumulative normalized apparent heatrelease obtained from direct calculations with those from thedeveloped linear model predictions for the loads of 60, 120, and180 N�m at 2000 rpm. The RMS errors between direct calculationsand model predictions ranged from 0.5% to 3.5%. The resultsobtained for all other loads and speeds can be found in Fig. 7.Overall, the comparison of direct calculations and model predic-tions showed a RMS error within 3.5%. Therefore, the developedpredictive combustion model is believed to well predict in-cylinder heat release characteristics. The model accuracy can beimproved further by employing nonlinear regression models,which were avoided in this work for the sake of model simplicity.

Heat Release Analysis of a Dual Mode, Turbulent Jet

Ignition Engine

As mentioned earlier, this study was performed to set theground for future works where the combustion behavior of aproduction-based GDI engine would be compared to that of aDM-TJI engine. Single-zone heat release analysis cannot accountfor the mass and energy transfer between DM-TJI pre- and mainchambers. Therefore, a more detailed two-zone analysis such as

Fig. 5 Cylinder pressures, experiments versus numerical predictions—all cases studied; solid and dashed line represent theexperiments and numerical prediction, respectively. In subplots for speeds from 1500 rpm to 3000 rpm, traces with low,medium, and high peak pressures represent loads of 60 N�m, 120 N�m, and 180 N�m, respectively. Traces for 3500 rpm do notfollow the general trend as others and the pressure traces for 180 N�m have peak pressures slightly lower than 120 N�m. Sub-plots for 4000 rpm and 4500 rpm represent loads of 60 N�m and 120 N�m with the low and high peak pressures, respectively.

Fig. 6 Cumulative normalized apparent heat release, directcalculations versus developed linear model predictions at2000 rpm

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the work by Song et al. [4] should be done to study the complexityof the problem. However, single-zone analysis should be able toproduce reliable simplified results since the prechamber volumein a DM-TJI engine is as small as 3% of volume at top dead center[3].

Single-zone heat release analysis has been performed on theexperimental data obtained from a gasoline-powered single-cylinder DM-TJI engine at Michigan State University. Enginespecifications can be found in Table 4. Engine was operated at1500 rpm for all the cases studied here. Details of the engine setupand experimental procedure can be found in Ref. [3]. Figure 11compares the normalized apparent heat release for the DM-TJIengine for a range of gross indicated-mean-effective-pressure(IMEPg) values below 6.5 bar with that of the Ford EcoBoost GDIengine at 1500 rpm and a load of 60 N�m (IMEPg: 5.8 bar).

The different behaviors of normalized apparent heat release forDM-TJI and GDI engine are evident in Figs. 11 and 12. InFig. 11, the DM-TJI combustion system is shown to benefit froma rapid pressure rise similar to that in the GDI engine. However,DM-TJI engine operation retains the fast burn rate until the end ofcombustion, while GDI engine operation entails a slow-paceddiffusion-like phase of combustion after approximately 10 CAdeg. Additionally, for a given load, lean burn combustion in theDM-TJI engine showed a lower percentage of in-cylinder heattransfer (see Fig. 12) compared to a GDI engine, as a result oflower in-cylinder temperatures. Recall that the GDI engine wasrun at stoichiometry with throttled intake to attain IMEPg of5.8 bar. These predictions made by current single zone analysiswill be further verified by employing a two-zone analysis on theDM-TJI engine. In addition, the corresponding combustion model

Fig. 8 Intercooler, intake manifold, coolant, and exhaust manifold temperature—all casesstudied. The load and speed associated with each of these case numbers can be found inTable 2.

Fig. 7 Cumulative normalized apparent heat release, direct calculations versus developed linear model predictions—allcases studied; solid and dashed line represent the experiments and numerical predictions, respectively. In each subplot, thetraces for the cumulative heat release gradually shift to the right, as loads increase.

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of the DM-TJI engine will be studied and published in a separatepaper.

Conclusion

A combustion model was developed and validated for a homo-geneous turbocharged GDI engine operated at a wide range ofloads and speeds. Unlike that in a PFI engine, the combustion sys-tem of a homogeneous DI engine incurred initial rapid burn pre-mixed combustion followed by a slow diffusion-like phase ofcombustion. Based on this observation, a double-Wiebe functionwas employed to model the heat release behavior of the GDIengine. Double-Wiebe variables were further studied to develop apredictive combustion model by using a set of engine parameters.The validity of the predictive combustion model was tested in

Fig. 9 In-cylinder temperature at spark timing for all the cases.The load and speed associated with each of these case num-bers can be found in Table 2.

Fig. 10 Double-Wiebe variables, direct calculations versus linear models predictions; solid and dashed line represent thedirect calculations and models predictions, respectively. The load and speed associated with each of these case numbers canbe found in Table 2.

Fig. 11 Normalized apparent heat release, homogeneous tur-bocharged GDI engine versus DM-TJI; speed of 1500 rpm andIMEPg�6 bar

Table 4 Dual mode, turbulent jet ignition engine specifications

Bore 95 mmStroke 100 mmConnecting rod length 190 mmCompression ratio 12:1Prechamber volume 2700 mm3 (�0.4% of displacement volume)Main chamber volume 0.709 LFuel injection High-pressure injectors for both chambersFuel type EPA LEV-II liquid gasoline (both chambers)

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repeat study of the heat release characteristics of the current GDIengine.

� The semipredictive combustion model reasonably demon-strated the combustion behavior of this GDI engine in repro-ducing the in-cylinder pressure traces. The RMS errorsbetween experiments and numerical pressure traces werewithin 2.4% of peak in-cylinder pressures.

� The predictive combustion model was able to capture twophases of combustion for the GDI engine with a maximumRMS error of 3.4% in reproduction of the results obtainedfrom the direct semipredictive model.

This study is believed to act as a strong foundation for futureworks to compare the combustion behavior of a production-basedGDI engine with that of a DM-TJI engine. The DM-TJI combus-tion system offers several benefits in improving the performanceof spark ignition engines. Here, a preliminary study was con-ducted to compare the heat release and heat transfer characteris-tics of the GDI engine to those of a single-cylinder DM-TJIengine. The DM-TJI engine appears to benefit from a fasterenergy release and lower heat transfer compared to the GDIengine at the same load and speed. Future works will involve atwo-zone heat release analysis to account for the mass/energytransfer between pre- and main chambers of the DM-TJI engine.This heat release analysis can be used in further development of apredictive combustion model for such engines. Additionally, theheat transfer model of GDI engines should be further investigatedin order to extend the model prediction to the entire engine cycle.

Acknowledgment

The authors would like to thank Dr. Matt Brusstar and Mr.Mark Stuhldreher of EPA for their valuable technicalcontributions.

Funding Data

� U.S. EPA (RC105248 - Award No. 83589201).� Tenneco Inc. (RC106007 - Award No. APP 145466).� The State of Michigan (RC105712 - Award No. 139794).

Nomenclature

Mathematical Symbols

B ¼ cylinder bore, mC1 and C2 ¼ constants given

hc ¼ cylinder heat transfer coefficient, W=m2KK1 and K2 ¼ constant given

m1 ¼ combustion mode parameter (Wiebe exponent) forfirst Wiebe function

m2 ¼ combustion mode parameter (Wiebe exponent) forsecond Wiebe function

p ¼ cylinder pressure, kPapm ¼ motoring pressure, kPapr ¼ working fluid pressure prior to combustion, kPa

Qch ¼ apparent total heat release, kJQh:t ¼ heat transfer to the walls, kJ

Sp ¼ mean piston speed, m=st ¼ time, s

T ¼ cylinder temperature, KT�exh ¼ exhaust temperature at intake pressure, K

Tr ¼ working fluid temperature prior to combustion, KV ¼ cylinder volume, m3

Vd ¼ displacement volume, m3

Vr ¼ working fluid volume prior to combustion, m3

w ¼ average cylinder gas velocity, m=sxr ¼ internal residual gas fraction

Greek Symbols

a ¼ switch point from first Wiebe function to secondc ¼ specific heat ratio

Dh1 ¼ total burn duration for first Wiebe functionDh2 ¼ total burn duration for second Wiebe functionh0 ¼ start of combustion

hign ¼ ignition timing

Subscripts

c ¼ coefficientch ¼ chamberd ¼ displacement

exh ¼ exhausth:t ¼ heat transferint ¼ intakem ¼ motoring

Man ¼ manifoldp ¼ pistonr ¼ prior to combustion

Abbreviations

CAS ¼ combustion analysis systemDM-TJI ¼ dual mode, turbulent jet ignition

EGR ¼ exhaust gas recirculationEPA ¼ Environmental Protection Agency

Err ¼ errorEVC ¼ exhaust valve closingEVO ¼ exhaust valve opening

FEAD ¼ front end accessory driveGDI ¼ gasoline direct-injection

HTM ¼ heat transfer multiplierIMEP ¼ indicated mean effective pressure

IVC ¼ intake valve closingMax ¼ maximumMin ¼ minimum

OEM ¼ original equipment manufacturerPFI ¼ port fuel injection

RMS ¼ root-mean-squareSOC ¼ start of combustion

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