Available online at www.sciencedirect.comProceedings

Proceedings of the Combustion Institute 32 (2009) 2751–2758

www.elsevier.com/locate/proci

of the

CombustionInstitute

Development of a time-scale interactioncombustion model and its application

to gasoline and diesel engines

Atsushi Teraji *, Yoshihiro Imaoka, Tsuyoshi Tsuda, Toru Noda,Masaaki Kubo, Shuji Kimura

Nissan Research Center, Nissan Motor Co., Ltd., 560-2, Okatsukoku, Atsugi-shi, Kanagawa 243-0192, Japan

Abstract

The combustion processes of both gasoline and diesel engines are becoming similar, as a result of theapplication of direct fuel injection to the former and the reduction of the compression ratio of the latter.A novel time-scale interaction (TI) combustion model has been developed for simulating combustion phe-nomena with high accuracy, ranging from premixed charge combustion to diffusion combustion. Thismodel is based on reasonable combustion regimes, taking into account the characteristic time scales ofthe chemical reactions and turbulence eddy break-up. The accuracy of the TI combustion model was val-idated by applying it to gasoline and diesel IC engines under a wide range of operating conditions. Com-parisons of measured and calculated heat release rate patterns and cylinder pressure histories showed goodagreement for both gasoline and diesel IC engines.� 2009 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

Keywords: Gasoline engine; Diesel engine; Combustion modeling

1. Introduction

There are strong demands today to improve theefficiency of internal combustion (IC) engines andto achieve cleaner exhaust emissions, as a result ofthe heightened awareness of environmental issuesin recent years, including global warming andenvironmental destruction. To accomplish that, itis essential to analyze the various phenomena thatoccur in the combustion chamber and to ascertainthe influence of different factors on IC engine per-formance, such as in-cylinder flows and the com-

1540-7489/$ - see front matter � 2009 The Combustion Institdoi:10.1016/j.proci.2008.06.009

* Corresponding author. Fax: +81 46 282 8903.E-mail address: teraji@mail.nissan.co.jp (A. Teraji).

bustion chamber geometry. Three-dimensionalsimulation techniques are being used extensivelyto obtain such information.

The models used in conducting three-dimen-sional simulations of combustion in IC enginescan be broadly classified into two types: a pre-mixed charge combustion model that is typicallyapplied to gasoline IC engines [1–4] and a diffu-sion combustion model that is generally appliedto diesel IC engines [5–7]. However, the combus-tion processes of gasoline and diesel IC enginesare gradually becoming more alike today, as typ-ified by stratified combustion induced throughdirect injection of the fuel into the cylinders ofgasoline IC engines and the lowering of the com-pression ratio of diesel IC engines. This trend has

ute. Published by Elsevier Inc. All rights reserved.

2752 A. Teraji et al. / Proceedings of the Combustion Institute 32 (2009) 2751–2758

made it more difficult to derive accurate solutionsby applying the combustion models traditionallyused exclusively either for gasoline or diesel ICengines. Therefore, in order to accommodate thetrends seen for both types of IC engines today,it has become necessary to develop a combustionmodel [8] that can reproduce combustion phe-nomena accurately, ranging from premixed chargecombustion to diffusion combustion.

In order for a combustion model to be able tosimulate such a wide range of combustion pro-cesses from premixed charge combustion to diffu-sion combustion, it must be developed on thebasis of a thorough understanding of actual com-bustion regimes. The authors previously devel-oped a Universal Coherent Flamelet Model(UCFM) [2,3] as a premixed charge combustionmodel capable of predicting the burning velocityin a gasoline IC engine under a wide range ofoperating conditions. In the present study, wecombined the UCFM with a characteristic time-scale combustion (CTC) model [6,7], which ismainly applied to diffusion combustion, todevelop a time-scale interaction (TI) combustionmodel. The TI combustion model applies thetwo different combustion models to suitablymatch the combustion regime in IC engines, byfactoring the characteristic time scales of thechemical reactions and turbulent mixing into thescope of application of each model. The accuracyof the TI combustion model was validated byapplying it to gasoline and diesel IC engines undera wide range of operating conditions.

2. Calculation model

2.1. Time-scale interaction combustion model

In gasoline combustion, the fuel and oxygenare premixed at a flammable mixture ratio. Thepremixed charge is burned in a turbulent combus-tion process in which it can be assumed that thecharacteristic time scale of the chemical reactionsis always smaller than that of turbulent mixing.The burning velocity in this process is dependenton turbulent mixing.

In diesel combustion, the fuel discharged fromthe fuel injector mixes with the surrounding airduring the ignition delay interval. The fuel–airmixture formed during this interval then beginsto burn, consuming the oxygen in the fuel jet.After all the oxygen in the fuel jet is used up,the fuel is subsequently consumed by diffusioncombustion in the region where the fuel jet surfacemixes with the surrounding air. This process wasmade clear by Dec [12] in visualization experi-ments using laser-sheet imaging. The laminarburning velocity in the initial combustion phaseis extremely slow because the interior of the fueljet is fuel-rich, and thus combustion cannot be

sustained by the flame. Consequently, the charac-teristic time scale of the chemical reactions skin isgreater than that of turbulent mixing st, i.e., awell-stirred reactor regime is formed locally inwhich the nondimensional Damkohler numberDa, representing the ratio of the two time scales,is less than 1. Therefore, we applied the CTCmodel to the reaction-rate-controlled combustionregion where the time characteristic scale of thechemical reactions is dominant owing to the influ-ence of a fuel-rich or -lean mixture. The CTCmodel determines the fuel consumption rate basedon the characteristic time scale of the chemicalreactions. Dec reported that light emission fromOH radicals was observed in the vicinity of thefuel jet and that the fuel and air were partially pre-mixed in that region at an equivalence ratio rang-ing from 0.78 to 2.02 [12]. Because the combustionreaction zone in this region is extremely thin, itcan be treated as an agglomeration of laminarflamelets [9,10]. Accordingly, in the TI combus-tion model, we applied the UCFM premixedcharge combustion model to combustion in theregion where the fuel and air are premixed suchthat the characteristic time scale of the chemicalreactions is smaller than that of turbulent mixing.

2.2. Combustion model in premixed and partiallypremixed charge region

In the combustion process in the premixedcharge region, it is assumed that the characteristictime scale of the chemical reactions is smaller thanthat of turbulent mixing and that the burningvelocity is rate-controlled by the characteristictime scale of turbulent mixing. Accordingly, theUCFM [3] premixed charge combustion modelwas applied to the premixed charge region in theTI combustion model.

In the UCFM, the flame area is expressed mac-roscopically in terms of the flame area density R.Flame propagation is expressed by solving thetransport equation of R, which is expressed as

oRotþ ouiR

oxi¼ o

oxi

mt

rc

oRoxi

� �þ S þ D ð1Þ

where mt is the coefficient of turbulent viscosity, rc

is the turbulent Schmidt number, S is the sourceterm and D is the extinction term. A model ofthe source term S was newly created for theUCFM, and the model proposed by Bouldieret al. [11] was used for the extinction term D.

The source term S in the equation above wasmodeled as shown below using the flame areagrowth ST attributed to turbulent combustionand the growth SL attributed to laminarcombustion.

S ¼ ST þ SL ð2Þ

A. Teraji et al. / Proceedings of the Combustion Institute 32 (2009) 2751–2758 2753

The turbulent combustion source term ST is ex-pressed in the UCFM as

ST ¼ a0

ffiffiffiffiffiffiffiRetp e

kCR ð3Þ

where a0 is a model constant, k, e and Ret indicatethe turbulent energy, the turbulence dissipationrate and the turbulent Reynolds number, respec-tively, and C denotes the intermittent turbulencenet flame stretch (ITNFS) model [13], which ex-presses the stretching and quenching of the flamefront by turbulence.

The source term SL attributed to laminar com-bustion is expressed as shown in the followingequation using the ratio of the combustion gastemperature T b to the unburned gas temperatureT u and its product with the laminar burning veloc-ity U L, as well as the attenuation functionexpressed as the Karlovitz number and taking intoaccount the Kilmov–Williams criterion [14].

S ¼ b0 expð�b1KaÞ T b

T uU LR

2 ð4Þ

where b0 and b1 are model constants. In theUCFM, the fuel consumption rate xF UCFM is de-rived as

xF UCFM ¼ minðY F ; Y O2=fstÞquU LR ð5Þusing the unburned mixture density qu, the hypo-thetical fuel mass fraction Y TF and the hypotheti-cal oxygen mass fraction Y T 02, both of which willbe explained later, the laminar burning velocityUL and the flame area density R. Here, the nota-tion fst is the ratio of the oxygen mass fractionto the fuel mass fraction relative to a stoichiome-tric mixture ratio.

2.3. Combustion model in reaction-rate-controlledregion

In the region of reaction-rate-controlled com-bustion, it is hypothesized that there are variousfields where the characteristic time scale of turbu-lent mixing is greater than that of the chemicalreactions, including a high-turbulence field andfuel-rich or -lean fields, among others. For dieselcombustion in particular, a fuel-rich field ismainly hypothesized, making it necessary to con-sider the mixing time of the unreacted fuel andoxygen when determining the chemical reactiontime. In addition, because the characteristic timescale of the chemical reactions increases due tothe low oxygen concentration, it is necessary toconsider both characteristic time scales in thesame way. Therefore, it was decided to derivethe fuel consumption rate in the reaction-rate-controlled region using a characteristic time-scalecombustion (CTC) model [6,7] that determines thefuel consumption rate on the basis of chemicalkinetics and turbulent mixing.

The fuel consumption rate xFctc in the CTCmodel can be expressed as shown below usingthe equilibrium concentration Y �i and characteris-tic time scale sc in relation to the mass fraction Y i

of each species.

xF CTC ¼Y i � Y �i

scð6Þ

Using the characteristic time scales of the chemi-cal reactions skin and of turbulence st, sc can be ex-pressed as

sc ¼ skin þ f st ð7ÞThe notation f pertaining to the characteristictime scale of turbulence is a function determinedby the physical properties of the combustion fieldand has a value from 0 to 1. It can be expressed asshown below using the oxygen concentration Y 02

and the hypothetical oxygen concentration Y T 02,which will be explained later.

f ¼ 1� e�r

0:632ð8Þ

r ¼ 1� Y O2

Y TO2

ð9Þ

The rate of progress of the chemical reactions ofthe fuel per unit time can be expressed as shownbelow using an Arrhenius function as the reactionrate of a single-stage overall reaction.

d½Fuel�dt

¼ A½Fuel�0:25½O2�1:5 exp�EA

RT

� �ð10Þ

Here, A and EA=R denote a model constant andthe activation temperature, respectively. Valuesof A ¼ 4:6� 1011 and EA=R ¼ 15098 K [15] wereused for the gasoline IC engine based on the reac-tion rate for iso-octane, and A ¼ 7:68� 109 andEA=R ¼ 9300 K, as determined by Kong et al.[7], were used for the diesel IC engine. Accord-ingly, assuming the reaction of a quiescent fieldprior to the onset of combustion, the characteris-tic time scale of the chemical reactions skin can bederived as

skin ¼ A�1½Fuel�0:75½O2��1:5 expEA

RT

� �ð11Þ

Based on the foregoing discussion, the fuel con-sumption rate in the TI combustion model is de-rived with Eq. (5) in the premixed charge regionand with Eq.(6) in the reaction-rate-controlledregion.

2.4. Mass fraction conservation equations

The mass fraction conservation equation foreach species is solved to calculate the combustiongas temperature T b and unburned gas temperatureT u, which are needed to find the laminar burning

2754 A. Teraji et al. / Proceedings of the Combustion Institute 32 (2009) 2751–2758

velocity and to solve each model functions. Themass fraction conservation equation for the fuelis given as

oqY F

otþ oquiY F

oxi¼ o

oxi

qmt

rc

oY F

oxi

� �þ xF evap

� xF UCFM � xF CTC ð12Þ

where xF evap is the amount of increase in the fueldue to evaporation of the fuel spray.

The UCFM developed in this research alsosolves conservation equations for transportedhypothetical unburned physical quantities fromburned physical quantities (i.e., velocity, tempera-ture and pressure). As a result, the unburnedphysical quantities of the burned fields areobtained which are needed in order to derive thefuel consumption rates xF UCFM and xF CTC dueto each combustion regime and the laminar burn-ing velocity U L. The transport equation of thehypothetical unburned fuel mass fraction Y TF isexpressed as

oqY TF

otþ oquiY TF

oxi¼ o

oxi

qmt

rc

oY TF

oxi

� �þ xFevap ð13Þ

Y TF is a variable that varies only due to fuel trans-port and does not change due to combustion.Hence, Y TF ¼ Y F in the unburned state andY TF > Y F in the burned region. Conservationequations are also solved for hypothetical oxygenY TO2, hypothetical combustion products Y TCO2 andT TH2O, and hypothetical enthalpy hu.

oqhu

otþ oquihu

oxi¼ o

oxi

qmt

rc

ohu

oxi

� �þ q

qu

o

oxiqui

þ qqu

opotþ ui

o

oxip

� �þ qe ð14Þ

Table 2Specifications of experimental gasoline engine

Engine type 4-Stroke, 4-valve, single-cylinder

3. Calculation method

In this study, calculations were performed withthe STAR-CD general-purpose CFD analysiscode for the purpose of validating the newlydeveloped TI combustion model. The physicalmodels used here are listed in Table 1. TheKelvin–Hemholtz/Rayleigh–Taylor (KH–RT) hy-

Table 1Configuration of 3-D combustion simulation

Engine Gasoline Diesel

Combustionmodel

TI combustion

Burned gasdissociation

Post chemistry

Ignition model ERC spark SHELLIgnition [19] Autoignition [17]

Spray model – KH-RT [16]Turbulence model Standard k � e RNG k � e [18]

brid model [16] was used in the simulation of die-sel IC engine combustion, and a shell model [17]was used for judging the low-temperature oxida-tion mechanism below 1100 K and autoignition.As the turbulence model, the standard k � emodel was used in the gasoline IC engine combus-tion simulation and the Renormalization Group(RNG) k � e model [18], which is generallyregarded as having high accuracy in swirl flowsimulations, was used in the diesel IC engine com-bustion simulation.

4. Model validation for gasoline IC engine

The fuels used in gasoline and diesel IC enginesboth have a flammable region where combustionof a premixed charge takes place. Because repro-duction of premixed charge combustion wasregarded as being important in this respect, theTI combustion model was first applied to combus-tion of a flammable premixed charge in the gaso-line IC engine. A multi-point injection (MPI) fuelsupply system was used in the experiments as theobject of comparison.

A single-cylinder 4-valve engine having thespecifications shown in Table 2 and a compressionratio of 10:1 was used in the investigation of theburning velocity in premixed charge combustion.Experiments were conducted under various enginespeeds and a wide-open-throttle (WOT) load asshown in Table 3. The simulation model used inthe calculations for validation in comparison withthe experimental data was composed of approxi-mately 250,000 cells at top dead center (TDC),including the intake and exhaust port.

4.1. Investigation of combustion regimes in pre-mixed charge combustion fields in gasoline ICengine

In order to make the TI combustion modelapplicable to gasoline IC engines under a wide

Combustion chamber Pentroof typeBore � Stroke 86 mm � 86 mmDisplacement 488� 10�6 m3

Compression ratio 10:1Fuel Gasoline (RON 100)

Table 3Engine operating conditions

Case 1 Case 2 Case 3 Case 4

Engine speed (rpm) 800 1600 2400 3200Engine load WOT Air fuel ratio 12.5

A. Teraji et al. / Proceedings of the Combustion Institute 32 (2009) 2751–2758 2755

range of operating conditions, we considered thatit was essential to set the model constants on thebasis of a thorough understanding of the combus-tion regimes in an actual engine. Toward that end,the calculated results were used to investigate thecombustion regimes in the premixed charge com-bustion fields of the experimental gasoline ICengine. In Fig. 1, the results calculated for the foursets of operating conditions in Table 3 are plottedin the diagram of turbulent combustion proposedby Peters [20]. It is seen that in-cylinder turbulencebecame stronger as the engine speed increased andthat the combustion regime changed from wrin-kled flamelets to thickened-wrinkled flamelets.

Figure 2 shows averaged turbulent Reynoldsnumber Ret, Karlovitz number Ka and Damkoh-ler number Da at TDC under various engine oper-ating conditions. The combustion regime of

Fig. 1. Location of various engine operating conditionsin Peters’ diagram of turbulent combustion at TDC.

Fig. 2. Averaged Ret, Ka and Da under various engineoperating conditions at TDC.

gasoline IC engine was characterized by wrinkledflamelets under low engine speeds and loads andthickened-wrinkled flamelets under high enginespeeds and loads. The in-cylinder distributionscalculated for Ka and Da at TDC at an enginespeed of 2400 rpm are shown in Fig. 3. The resultsshow that both Ka and Da increased in the centerof the cylinder and decreased near the wall, indi-cating that the combustion regimes differedbetween the two locations. The combustionregime at the cylinder center was characterizedby thickened-wrinkled flamelets and that nearthe cylinder wall by wrinkled flamelets.

These results make it clear that the combustionregimes in the gasoline IC engine were mostly tur-bulence-controlled combustion. Based on thisinvestigation and former results [2] which wereobtained by application of UCFM to combustionin constant volume vessel, the values of the modelconstants a0 ¼ 0:012, b0 ¼ 8:5 and b1 ¼ 1:4 of theUCFM used in the TI combustion model for thepremixed charge combustion region were deter-mined, and combustion calculations were per-formed under each set of operating conditions.

4.2. Study of burning velocity

Because the burning velocity is a critical factorin predicting combustion in the premixed chargeregion, we first validated the accuracy of theUCFM for predicting the burning velocity. Figure4 compares the experimental and calculated cylin-der pressure histories and heat release rate histo-ries obtained for the four cases in Table 3. Inorder to compare the calculated and experimentalresults, the measured data shown in the figurewere averaged for 400 cycles. It is seen that thecalculated results reproduce the measured datawell under each set of engine operating condi-tions. This suggests that the model constants a0,b0 and b1, which were uniquely determined bymodeling the source term of the flame area densityR on the basis of physical quantities like Ret andKa, are capable of accommodating a wide rangeof operating conditions.

In view of these results, we concluded that thenewly developed TI combustion model can predictthe burning velocity in the premixed charge com-bustion region with sufficient accuracy. As the nextstep, the model was applied to a diesel IC engine.

Fig. 3. Ka and Da distributions at TDC under WOT at2400 rpm.

Fig. 4. Comparisons of pressure histories and heatrelease rates under the various engine operating condi-tions shown in Table 3.

Table 5Specifications of experimental diesel engine

Engine type 4-Stroke, 4-valve,single-cylinder

Fig. 5. Analysis of visualized results for spray combus-tion at 2.0 ms after start of injection.

2756 A. Teraji et al. / Proceedings of the Combustion Institute 32 (2009) 2751–2758

5. Model validation for diesel IC engine

5.1. Study of spray combustion

Combustion in a diesel IC engine takes place ina spray combustion in which burning beginsbefore the fuel injected directly into the cylinderfrom the fuel injector mixes completely with thesurrounding air to form a premixed charge.Accordingly, the TI combustion model was firstapplied to spray combustion in a constant volumevessel under the conditions shown in Table 4 toinvestigate the combustion regime.

The heat release rates calculated with the TIcombustion model in a partially premixed chargeregion and in a fuel-rich region are shown inFig. 5 along with the Damkohler number Da, tem-perature and equivalence ratio. As noted earlier,Dec’s visualization measurements of spray com-bustion [12] showed light emission from OH rad-icals around the fuel jet in the region of anequivalence ratio of 0.78–2.02. The heat releaseregion found with the premixed charge combus-tion model was distributed around the fuel jet,and the results indicate that the UCFM expressedthe heat release rate in this partially premixedcharge region.

Table 4Calculation condition

Ambient pressure 2.7 MPaAmbient temperature 930 KInjection pressure 55 MPaInjector nozzle diameter 0.15 mm

The region upstream of the fuel jet is the areawhere air is introduced. A fuel-rich region occursnear the liquid phase of the fuel spray tip, and theoxygen in the fuel jet is consumed by reaction-rate-controlled combustion. In this region whereDa < 1:0, the heat release rate was expressed bythe CTC model which was used as a reaction-rate-controlled combustion model. These resultssubstantiate the diesel combustion concepthypothesized by Dec. Based on this study, it wasconcluded that the TI combustion model is capa-ble of reproducing combustion both in the pre-mixed charge region and in the fuel-rich region.

Performance tests were then conducted with asingle-cylinder diesel engine that was used in theexperimental validation. A comparison was madeof the experimental and calculated results to vali-date the accuracy of the TI combustion model.Table 5 shows the specifications of the single-cyl-inder direct-injection (DI) diesel engine used inthis comparison.

Combustion chamber Re-entrantBore � stroke 108 mm� 115 mmDisplacement 1050� 10�6 m3

Compression ratio 18.6:1Swirl ratio 2.2Number of nozzle orifices 6Fuel JIS #2 diesel fuel

(CN 61)

A. Teraji et al. / Proceedings of the Combustion Institute 32 (2009) 2751–2758 2757

5.2. Experimental diesel IC engine

The calculation grid used the sector shape forone injector nozzle orifice which was configuredsuch that the calculation cells did not move inthe direction of fuel injection. Table 6 shows theengine operating conditions used in the calcula-tions. The fuel injection quantity and the injectiontiming were used as the parameters in this experi-mental validation of the TI combustion model.

Reproducing the heat release rate pattern accu-rately is an important factor in predicting the per-formance of a diesel IC engine. For that reason, acomparison was first made of the experimentaland calculated heat release rate patterns and cylin-der pressure histories when the fuel injectionquantity was used as the parameter. Figure 6 com-pares the experimental and calculated results at aconstant engine speed of 1280 rpm. It is seen thatwhat is generally referred to as the premixedcharge combustion fraction and the diffusioncombustion fraction as well as the total heatrelease rate all changed depending on the fuelinjection quantity. The results indicate that thenewly developed TI combustion model repro-duced the qualitative tendencies seen for the pre-mixed charge combustion fraction and diffusion

Table 6Experimental conditions

Engine load Low Medium HighEngine speed 1280 rpm Fuel injectionamount

10 mm3/st 30 mm3/st 60 mm3/st

Injectiontiming

TDC TDC, 5 deg.ATDC

TDC

Boost +25 kPa

Fig. 6. Comparisons of pressure histories and heatrelease rates under different injection amounts.

combustion fraction when the fuel injection quan-tity was used as the parameter.

A comparison was then made of the experi-mental and calculated heat release rate patternsand cylinder pressure histories that were obtainedusing the fuel injection timing as the parameter.Figure 7 compares the experimental and calcu-lated results obtained with a fuel injection quan-tity of 30 mm3/st. The total heat release rate wasalmost identical in both cases and was the condi-tion for the change in the premixed charge com-bustion and diffusion combustion fractions.When the injection timing was advanced, the heatrelease rate waveforms showed an initial peakattributed to premixed charge combustion and asecond peak attributed to diffusion combustion.Retarding the injection timing produced a distinc-tive heat release rate pattern with only one heatrelease rate peak. The results calculated with theTI combustion model coincided reasonably wellwith the experimental data.

As explained above, the heat release rate calcu-lated with the TI combustion model for the exper-imental engine showed good agreement with the

Fig. 7. Comparisons of pressure histories and heatrelease rates under different injection timings.

Fig. 8. Analysis of heat release distribution in cylinderat 6 deg. ATDC (Medium load, Ne = 1280 rpm, Injec-tion timing = TDC).

2758 A. Teraji et al. / Proceedings of the Combustion Institute 32 (2009) 2751–2758

measured data. Since this indicated that the modelcan be used to analyze combustion in actual engine,it was then used to examine diesel combustionmodes. the heat release distributions calculatedfor reaction rate-controlled combustion and turbu-lence rate-controlled combustion in the cylinder areshown in Fig. 8. Heat release from partially pre-mixed combustion, in which turbulence is therate-controlling parameter, is distributed aroundthe fuel jet in which there is mixing of the fuel andair even in an ambient field with swirl flow. Heatrelease due to reaction rate-controlled combustionis distributed inside the fuel jet downstream of theregion where air is introduced.

Based on the foregoing results, it was con-cluded that the TI combustion model is capableof reproducing the heat release rate pattern of adiesel IC engine with good accuracy over a widerange of operating conditions.

6. Conclusions

This paper has described a time-scale interac-tion (TI) combustion model that has been devel-oped to predict the respective combustionperformance of gasoline and diesel IC engines.This TI combustion model applies two differentcombustion models matching the combustionregimes in IC engines, taking into account a suit-able range of application for each one based onthe characteristic time scales of the chemical reac-tions and turbulent mixing. The following resultswere obtained when the TI combustion modelwas applied to experimental gasoline and dieselIC engines under various operating conditions.

(1) The TI combustion model was able to predictthe burning velocities of both the gasolineand diesel IC engines without optimizingthe model constants for each engine.

(2) The TI combustion model applies a pre-mixed charge combustion model and achemical-reaction-rate-controlled combus-tion model, based on the characteristic timescales of the chemical reactions and turbu-lent mixing. The results obtained when theTI combustion model was applied to spraycombustion showed the same tendencies asin Dec’s proposed diesel combustion con-cept with respect to the heat release ratesin the partially premixed charge regionand in the fuel-rich region.

(3) The calculated results obtained with the TIcombustion model reproduced the heatrelease rate spike of initial (premixed charge)combustion and the subsequent heat releaserate of diffusion combustion, which are char-acteristic features of diesel engine combus-tion. It is concluded therefore that the TIcombustion model can predict the heatrelease rate not only of gasoline IC enginesbut also of diesel IC engines under a widerange of operating conditions.

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