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SAE TECHNICALPAPER SERIES 2000-01-0662

3-D CFD Analysis of the Combustion Process in aDI Diesel Engine using a Flamelet Model

H. Bensler, F. Bühren and E. SamsonVolkswagen AG

L. VervischINSA de Rouen & LMFN – CORIA / CNRS

Reprinted From: Multi-Dimensional Engine Modeling(SP–1512)

SAE 2000 World CongressDetroit, MichiganMarch 6–9, 2000

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1

2000-01-0662

3-D CFD Analysis of the Combustion Process in a DI DieselEngine using a Flamelet Model

H. Bensler, F. Bühren and E. SamsonVolkswagen AG

L. VervischINSA de Rouen & LMFN – CORIA / CNRS

Copyright © 2000 Society of Automotive Engineers, Inc.

ABSTRACT

A 3-dimensional numerical study has been conductedinvestigating the combustion process in a VW 1.9l TDIDiesel engine. Simulations were performed modeling thespray injection of a 5-hole Diesel injector in a pressurechamber. A graphical methodology was utilized to matchthe spray resulting from the widely used Discrete DropletSpray model to pressure chamber spray images.Satisfactory agreement has been obtained regarding thesimulated and experimental spray penetration and coneangles. Thereafter, the combustion process in the enginewas simulated. Using engine measurements to initializethe combustion chamber conditions, the compressionstroke, the spray injection and the combustion simulationwas performed. The novel RTZF two-zone flameletcombustion model was used for the combustionsimulation and was tested for partial load operatingconditions. An objective analysis of the model ispresented including the results of a numerical parameterstudy. A comparison of numerical and experimentalengine results was found to be encouraging and showpotential for the further development and implementationof the combustion model.

INTRODUCTION

Due to increasing market demands, there is a great needto design and develop cleaner and optimized Dieselengines in ever shorter time periods. Through the use of3-dimensional Computational Fluid Dynamics (CFD)simulations, the design process can be greatly speededup with minimal costs. The amount of manufacturing andtesting of prototypes can be reduced through the pre-optimization of engine processes via numericalsimulations. Of these engine processes, the 3-Dsimulation of the combustion process has one of thehighest levels of complexity. Here all the various aspectsand parameters of the combustion process need to bemodeled including the proper flow field (main flow and it’sassociated turbulence), the spray injection and the

combustion process itself. In direct-injection (DI) Dieselengines the complexity of the CFD simulation is evenhigher through the presence of partially mixedcombustion.

In this study, the Diesel combustion process wasinvestigated both numerically and experimentally in a VW1,9l TDI engine. The following sections will describe theexperimental and numerical setups utilized. A briefreview of turbulent combustion modeling will bepresented along with the theory behind the new RTZFcombustion model used for the simulations. Finally, theresults will be discussed and improvements to thecombustion model will be proposed.

COMBUSTION MODELING THEORY

Although non-premixed combustion is not the mostefficient way to burn, it is the most common regime foundin internal combustion engines. The modeling of non-premixed (and partially premixed) turbulent combustionrequires expressing the mean reaction rate, as a functionof chemistry and flow. As it is impossible to directlyaverage the reaction rate due to its highly non-linearity, itis necessary to propose other approaches to express themean reaction rate .

The different tools used to model turbulent combustioncan be listed as follows:

• the mean values method, where the mean reactionrate is calculated using the mean values of differentproperties [1]

• the geometric description method, where the flame isdescribed as a geometrical entity [2]

• the scalar dissipation method, where the reactionrate is calculated using the dissipation rate of ascalar field [3]

• the statistical description method, which uses astochastic approach to determine [4,5,6].

ω&

ω&

2

Some assumptions need to be made to simplifychemistry and transport. Depending on the conditions,several hypotheses can be made:

• infinitely fast chemistry

• finite rate chemistry, where diffusion and reaction arecoupled as in laminar flames (the laminar flameletassumption)

• finite rate chemistry, where diffusion and reaction aretreated separately, as in probability density function(pdf) methods.

Modeling combustion in DI diesel engines requires totake into account the possibility to burn under differentregimes: premixed, non-premixed and partially premixed,due to the inhomogeneous mixing of the reactants.Models have to represent those phenomena accurately.This approach is the one of pdf-generator modeling [5].Other ways can be followed, using a more empiricalformulation such as in the mean values and geometricaldescription methods.

RTZF COMBUSTION MODEL

A combination of these two methods is the novel RicardoTwo Zone Flamelet (RTZF) combustion model [7]investigated by this study. In this model, a semi-empiricalapproach is adopted where the turbulent burning velocityand the burning rate are estimated based on fractalgeometry and basic dimensional analysis of turbulentflames. In this way, difficulties such as the description ofthe flame front area can be avoided. In addition, there is asimple and clear relationship between the turbulence andburning velocity, which can be easily compared withmeasurements. A fractal-based model provides limitedphysical insight, but it quickly provides the burning rate,which is a major requirement for combustion modeling.

The proper description of the effects of chemistry is anessential of combustion modeling. A large amount ofcomputing resources is required for the simulation of fullchemical reaction schemes; however, as an engineeringtool, this approach is too costly and complex. On theother hand, simplified reduced reaction schemes havebeen developed for a few particular fuel types. These are,however, lacking in generality and can be over simplified.An example of this is the previously mentionedMagnussen model [1], which uses an over-simplifiedscheme, based on a one-step reaction of burning at astoichiometric air/fuel ratio. Important effects such as theincomplete combustion of fuel-rich mixture burning areignored with this method. Moreover, informationconcerning the chemical composition of the combustionproducts is also not provided thus emissions formationcannot be determined.

The current model uses a chemical equilibrium approachfor the chemistry modeling. Since the reactions, whichare responsible for the heat release, are alwaysperformed at fast rates, they can therefore be treated atequilibrium conditions. The chemical species

concentrations and thermal properties are calculated fora given mixture composition, pressure and temperature.The mixture compositions consist of the mass fractions ofair, unburned fuel, burned air and burned fuel. There are11 chemical species making up the combustion products:

, , , , , , , , , and .These represent the major chemical species in both thecomplete and incomplete combustion products. Thesechemical species concentrations are then used for thedetermination of the emissions, which are calculatedseparately. Their formation reactions have much slowerrates and make a small contribution to the total energybalance.

SPECIES SCHEME – The computational cells arenotionally divided by the flame front into two zones: anunburned zone and a burned zone. Air, fuel vapor andresidual gases are found in the unburned zone andcombustion products are in the burned zone. Theunburned region is further divided into two regions: asegregated and a fully mixed region. In the segregatedregion, the air and fuel are not mixed at a molecular leveland are therefore not ready to react chemically. In theother region, the air, fuel and residuals are fully mixed.

The segregated region increases in mass from newlyevaporated fuel from a fuel spray or from the flow from aninlet boundary. The fluid flow and molecular diffusionconvert segregated reactants to fully mixed reactants;combustion then consumes the fully mixed reactants andconverts them into combustion products. The mixturecomponents in the unburned zone have effectively threemass fractions: a segregated, a fully mixed and an overallmass fraction; only two of these are howeverindependent. The segregated and overall mass fractionsare solved for and the fully mixed mass fraction isobtained from the other two.

The species concentrations of the combustion productsare determined from the initial air/fuel ratio beforecombustion. Thus the mass fractions of both the burnedair and fuel are used rather than the total mass fraction ofthe combustible products in the burned zone. In a similarmanner, the separate mass fractions of the residual airand fuel are also used.

Figure 1. Schematic of the RTZF Combustion model.

CO 2CO H 2H OH 2 2N NO O 2O OH N

3

MIXING AND FLAME PROPAGATION – The differentcomponents in the segregated region are converted tothe fully mixed mass fraction by turbulent mixing. Theturbulent mixing is based on the large-eddy scale andhas a mixing rate of:

(1)

where is the mixing constant ranging from a value of2 to 32 (a value of 20 is the recommended default value

for ).

Reactants, which are fully mixed, are consumed by thecombustion. Low temperature reactions occur for auto-ignition and high-temperature reactions occur for theflame propagation. High-temperature reactions alwaysfollow after auto-ignition. Thereafter, the combustiblescan be consumed by either more auto-ignition or bynormal flame propagation. For the normal flamepropagation, the burning rate is determined by:

(2)

where the effective unstretched laminar burning velocity is derived from measured maximum laminar burning

velocity where the effects of the reference condition, fuel-air equivalence ratio and residuals are taken intoaccount.

The effect of strain on flame burning velocity isrepresented by the flame stretch factor . Withincreasing strain, the propagating flame will be partiallyquenched and can even be extinguished. For theturbulent flame, the ratio of flame surface area to theprojected transverse area ( ) is determined fromfractal geometry:

(3)

Here is the integral length scale and is theKolmogorov scale. When considering the transition fromlaminar to turbulent regime, the fractal dimension iscorrelated as a function of the ratio of turbulence intensityto laminar burning velocity:

(4)

The flame projected transverse area per unit volume( ) is a shape function, and is defined as

(5)

where is the regress variable and is defined as thesum of mass fractions of unburned air, unburned fuel and

residuals ( ). Before the start ofcombustion, the regress variable for a given cell is equalto 1; it has a value of 0 after the completion ofcombustion. The characteristic cell length is evaluated by

the cubic root of the cell volume ( ) and thecoefficient has an approximate value of 4.

For the case of non-premixed flames, the ratio of the fullymixed reactant volume to the total volume ( ) isestimated for the degree of segregation. The segregatedair/fuel mixture causes holes in the flame front. Thus thenon-premixed burning rate is slower than a pre-mixedrate.

AUTO-IGNITION MODEL – Since low temperaturereactions are responsible for auto-ignition and high-temperature reactions for the normal flame, these tworeactions are treated separately. Low-temperaturereactions for the auto-ignition are considered as alumped one-step reaction of a generic intermediate

ignition species , which is inversely proportional to the

ignition time ( ). The ignition probability, , is

determined via the integral:

(6)

The ignition delay is a function of temperature andpressure given by:

(7)

where the coefficients , and (activationtemperature) are determined from experimental ignitiondelay measurements. A transport equation for the ignitionprobability is solved and auto-ignition occurs when has reached a value of unity. The contribution of heatfrom the low-temperature reactions is considerednegligible.

COMMENTS – The mixing rate is built in the same wayas the Eddy Break-Up model [8], using a linear relaxationmodel. Only the effect of turbulence is taken into account.Reaction takes place in a thin zone between burned andunburned gas, assimilated to a set of laminar flames. Itsformulation seems to be a mix between the BML modelmodified by Bray et al. [9] and the approach of Gouldin etal. [10]. The BML model supposes that a point of the flowis either in the burned or in the unburned zones,separated by the reaction area. The reaction rate is thenproportional to the pass frequency of the flame front.

segmixmix Yk

c αα ρε

ω =

mixc

mixc

volT

Lrf rA

AIS Σ= ρω

LS

I

AAT /

2−

=

D

k

IT

l

l

A

A

Il kl

D

′+−

+= LS

u

eD1ln/5,0

75,02

VA /=Σ

( )cL

ccg −=Σ 1

c

RFRAFA YYYYc +++=

3cc VL =

g

volr

igY

igigY τ/1= igp

∫=ig

igdt

pτ

)/( TTnig

AeAP −=τ

A n AT

igp

4

Those models are formulated in terms of flame density.The first one, with reference of equation (5) for theformulation of the flame density, makes the flame densityto be proportional to the crossing frequency of the flamefront. In the other one, the flame density is expressed asa fractal surface and gives an expression quite analog to(3).

The RTZF model uses the approach of Bray et al. [9] forthe reaction rate, the fractal formulation being used forthe calculation of the surface area of the flame. Themodel enables to simulate both non-premixed andpremixed combustion. For non-premixed combustion,reactants are first mixed locally, in each cell, and are thenburned. For pre-mixed combustion, only the second stepis required. For more RTZF model details see [7].

EXPERIMENTATION

There were two experiments involved for the validation ofthe numerical results: a pressure chamber for the spraymodeling and a TDI Diesel engine. Their respectivesetups will be discussed in the sections below.

PRESSURE CHAMBER – The pressure chamber is acylindrical chamber equipped with small windows, whichenable to take pictures of the inside-phenomena. Fig. 2shows a schematic of the pressure chamber. A lightsource is used to illuminate the spray and a digital videocamera then records the images. A high-pressurecompressor and a heat exchanger allow the pressureand temperature in the chamber to be adjusted. In thisstudy, the chamber pressure was set to 20 bar with aconstant temperature of 293K. The Diesel fuel wasinjected with a 5-hole injector and had a temperature of303K and an injection pressure of 400 bar. Pictures weretaken through the bottom window of the chamber each50 µs for a duration of 2 ms.

Figure 2. Schematic of pressure chamber.

TDI ENGINE – The experimental engine used was a VWTDI 1.9l direct injection Diesel engine. The enginecharacteristics are found in Table 1 below.

The engine was mounted on a standard VW test bed.Important engine parameters were measured includingthe injected mass of the fuel, the cylinder pressure, andemissions such as NOx, Soot, Hydrocarbons, , and . Air and exhaust temperatures were measuredusing thermal resistance sensors at 8 different locationsranging from the air filter to the exhaust pipe. For thenumerical simulations conducted in this study, themeasured intake manifold temperature was of primeimportance.

In order to determine the time-dependent fuel injectionrate for a given injector, measurements were madeseparately on a hydraulic injector test bed. Here the fuelis injected into a tube filled with the same fuel. Timedependent pressure waves are measured, whose integralis proportional to the injected mass of fuel. In thismanner, an accurate injection law can be determined forany type of injector. This methodology provides anaccurate description of the time dependent injected fuelmass flow rate law.

Engine measurements for this study were made for partload operating conditions with an engine speed of 1000RPM, a Pmep of 1 bar and with 6 mg of injected fuel. Thefuel was injected with a pressure of 400 bar in twophases: a pre- and a main-injection. The mass of theinjected fuel equaled 1.6 mg and 4.4 mg, respectively.The corresponding injection law can be seen in Fig. 3.

L ightS our ce

L ightS our ce

K am era

Calculat ion

D at a

S av ing

10° 10°

20°20°

40° 40°

60°60°

K-EFAMVOLKSWAGEN

D U T

F uel-pres s ure

E lect r ical

D at aA quis it ion

P ow er U nit

S ignal-cont roller

H igh-P r es s ure-com pres s or

H eat -exchanger

Opt r ical

D at aA quis it ion

Table 1. Engine Characteristics.

TDI 1,9 liter

Type 4 in-line-cylinder

Injection Direct

Arrangement Row

Timing 1 overhead camshaft (belt)

Valves 2 per cylinder

Capacity

Bore x stroke

Compression ratio 17,8

Connecting Rod

Turbocharger Garrett VNT15

Engine speed

31896cm

mmmm 5,95 5,79 ×

mm 144

rpm 1000

CO 2CO

2O

5

Figure 3. Measured injection rate.

NUMERICAL ANALYSIS

The 3-dimensional simulations were performed using thefinite-volume CFD code VECTIS [11]. The CFD solverprovides 3-D time-dependent, compressible orincompressible solution of the continuity, Navier-Stokes,and energy equations. The turbulence model used is thestandard model [12] based on the assumption oflocal isotropic turbulence at high Reynolds numbers.Equations are solved fully-implicitly with couplingbetween variables and non-linear effects using iterativeor predictor-corrector methods. An orthogonal structuredCartesian mesh is used with wall cell volume and facearea adaptation. The computational meshes aregenerated using a fully automatic mesh generator. Localmesh refinement is utilized for the resolution of small-scale flow structures near boundaries and in regions ofhigh gradients. The standard logarithmic “law of the wall”is used for the evaluation of the wall boundary layer.

SPRAY MODELLING – The fuel injection simulation isdone using a Lagrangian stochastic spray model ofdiscrete droplets [7]. The spray is modelled as adispersed liquid phase which interacts and penetratesthe surrounding continuous gas phase. The spray isdescribed by an ensemble of discrete droplets parcels,where each parcel contains a quantity of droplets with theidentical velocity, temperature and size. Both the dropletparcels and the gas phase interact with each otherthrough drag forces and heat and mass transfer.Differential equations for the droplet mass, momentumand temperature are solved. In addition, other sprayphenomena such as droplet-coalescence, -turbulenceinteraction, -wall interaction and –breakup are alsomodelled. The droplet-breakup model used for this studyis that of Patterson and Reitz [13].

DISCUSSION AND RESULTS

PRESSURE CHAMBER – The two main parametersconsidered for the correlation of the simulated andphotographed spray images were the spray cone angleand the penetration. Several calculations were needed toget an acceptable match with the pressure chamberimages. The procedure was to begin with an estimatedvalue of the cone angle of 8 degrees resulting fromcorrelations existing in the literature [14]. The simulationwas conducted and the width of the spray angle and thepenetration were visually compared to the experimentalimages. If a poor correlation was obtained, an iterativeprocess was used either increasing or decreasing the oldvalue of the cone angle. Once a suitable cone angle wasobtained, the other parameters such as droplet sizedistribution and droplet interaction models were tested.

Results showed that a cone angle of 10 degreescorresponded well with the experimental images. Anexample of the computational mesh and thecorresponding spray are seen in Fig. 4. Each of the 5holes was modeled identically which resulted in 5 verysimilar jets. Note that the mesh in the area near theinjector is twice as fine as in the area of the spray jets.This was done to increase the numerical accuracy of thespray modeling. The mesh density used for the pressurechamber simulations was also used later for modeling thespray and combustion in the TDI engine. It should befurther noted that the only the main injection described inFig. 3 was modeled in the pressure chamber since nophotographs were available for the pre-injection.

Figure 4. Pressure chamber computational mesh and spray simulation.

ε−k

6

Figure 5. Comparison of simulated and pressure chamber spray penetration: Pchamber = 20 bar, Tchamber = 293 K, Prail=400bar and Trail=303K.

A comparison of the simulated and photographed sprayresults can be seen in Fig. 5. A total of six pairs of imagesare presented showing the cone angle and penetrationfor one representative jet of the spray. Both the simulatedand photographic images were directly comparablethrough the use of a 10-mm square reference grid. Aspray image is shown every 250 microseconds. The linesat the tip and sides of the sprays had identicaldimensions for both the simulated and photographicimages. One can see that although the slightly non-symmetric nature of the photographed spray was notfound in simulated spray, general good agreement wasfound with regards to both the spray cone angle andpenetration.

TDI ENGINE – The engine numerical simulations weredone from –40° CA BTDC until 40° ATDC. Thecalculations were initialized with measured swirl ratio of2.2 from another study done on a transparent VW TDIengine [15]. The initial conditions in the combustion weretaken from engine measurements where the pressureand temperature equaled 9.2 bar and 735K, respectively.The species in the chamber were initialized to take intoaccount the 30% EGR set up on the experimentalengine. The injection parameters used for the simulationswere the same as those for the engine measurementsmentioned in the Experimentation section.

A view of the computational mesh used for the enginesimulations can be seen in Fig. 6. Note that in the area ofthe injector, local mesh refinement is used to improve theaccuracy of the spray modeling. The cell size in the bowlwas 1mm square that resulted in an average mesh sizeof 100000 internal cells. The calculation time on a single-processor workstation which included the compression,spray and combustion simulation equaled about 40hours.

Figure 6. Cross-sectional view of the computational mesh at 10°CA ATDC.

A comparison of the simulated and measured in-cylinderpressure can be seen in Fig. 7 based on the defaultvalues of the combustion model constants. Themeasured pressure curve has a maximum value of about43 bar. Thereafter, two pressure peaks are found at 5 and17° ATDC, which indicate combustion occurring after thepre- and main injections. When considering the simulatedpressure curve, very good agreement is observed from –

7

40 to –5° CA BTDC. The simulations also show twopeaks smaller in magnitude, however both beginning veryclose to the measured start of combustion.

Figure 7. Comparison of simulated and measured in-cylinder pressure using the default values of the combustion model constants(Cmix=20, RSF=1, ISF=1).

Figure 8. Measured and simulated in-cylinder pressure with and without combustion with default values of the combustion model constants (zoom of Fig.7).

The area of combustion in Fig. 7 from 0 to 20 °CA isshown in more detail in Fig. 8. Here it can be seen thatthere is a general under-prediction of the calculatedpressure curve except in a region between 10° and 12°CA ATDC. Moreover, one can see that there is adifference of about 0.4 bar (approximately 1%) betweenthe measured pressure curves with and withoutcombustion where the unfired pressure curve is lower inmagnitude. An explanation for this discrepancy is that thecombustion chamber gas temperature and pressurecould be influenced by wall heating effects since a unfiredengine would have lower wall temperatures than a firedengine. In addition, since the fired engine was run with an

EGR level of 30%, the chemical composition of thechamber gases would be in effect different compared tothe unfired engine.

The simulation results based on the default values of thecombustion model constants already showed anencouraging correlation compared to the measuredpressure curve. However, in order to further test themodel, a parameter study was conducted by changingthe mixing coefficient (Cmix), the Reaction Scaling Factor(RSF) and the Ignition Scaling Factor (ISF). The mixingcoefficient is a real constant in the model and directlycontrols the rate of mixing of the species, i.e. theirconversion from a segregated to a mixed condition. Inaddition, Cmix has a strong influence on the overallcombustion reaction rate. The other two parametersinvestigated are used for fine-tuning of the model. TheRSF controls the burning velocity and thus the overallreaction rate. Finally, the ISF tunes the auto-ignition pdf,effecting the rate of the low-temperature reactions thatlead to auto ignition. The default values for theparameters are Cmix=20, RSF=1, and ISF=1.

In order to investigate the effects of varying Cmix, threesimulations were performed with Cmix set at 10, 20 and32; the values of RSF and ISF were left at their defaultvalues of 1. Fig. 9 shows the percentage differencebetween the simulated and the measured cylinderpressure curves as a function of °CA. It can be seen thatcombustion begins at about 3° CA ATDC for all the threeCmix values. For Cmix=10, the pressure is always moreunder-predicted than for the case of the other two Cmixvalues and has a mean difference of –3.0 %. WhenCmix=32, the mean difference equals –2.2% and has ahigher value of the pressure over the entire 25°CA. Thedefault value of Cmix=20 is very similar to Cmix=32 witha mean difference of -2.5%. Thus the higher the value ofCmix, the smaller was the mean difference between thesimulated and measured pressure.

Figure 9. Percent difference between simulated and measured combustion chamber pressure for varying mixing coefficient as a function of crank angle (RSF=1, ISF=1).

8

The variation of RSF is shown in Fig. 10. As the RSFvalue decreased, the percent difference increased from amean difference of –2.5% at RSF=1 to –3.1% atRSF=0.5. Once again the point of combustion begin at5°CA ATDC was not affected. Thus the default value ofRSF=1 showed the better fit to the experimental pressurecurve.

Figure 10. Percent difference between simulated and measured combustion chamber pressure for varying reaction scaling factor as a function of crank angle (CMIX=20, ISF=1).

As expected, by changing the ISF, the point of ignitionbegin was influenced. The ISF was simulated at threedifferent values: 0.5, 0.75 and 1.0. In Fig. 11, it can beclearly seen that the time of ignition begin occursprogressively later as ISF is decreased; moreover, themagnitude of the initial pressure peak also becomesprogressively smaller. After the initial point of pre-injection combustion, the effect of changing ISF becomessmaller with increasing °CA.

Figure 11. Measured and simulated in-cylinder pressure with and without combustion as a function of crank angle for varying ISF values(CMIX=20, RSF=1).

In Fig. 12, it is shown that the percent difference in thepressure for the different ISF values becomes relativelysimilar with increasing °CA where the mean differenceranges from –2.5 to -2.7%.

Figure 12. Percent difference between simulated and measured combustion chamber pressure for varying ignition scaling factor as a function of crank angle (CMIX=20, RSF=1).

In order to better understand the RTZF model and toprovide ways in which the model could be improved, datafrom the literature were analyzed. Direct NumericalSimulation (DNS) studies [16,17,18] have reported thatthe time evolution of the mixture during auto-ignitionstrongly depends on the time evolution of the mixturefraction dissipation rate itself. The mixture fractiondissipation rate is one of the key quantities of non-premixed turbulent combustion, where the extent ofmixing between evaporated fuel and oxidiser is usuallymeasured using a mixture fraction [19]. The controlparameters of a reaction-diffusion layer are: a diffusivetime measured from the diffusive flux of mixture fraction,used to define the inverse of the scalar dissipation rate,and a chemical time. Both are retained to build aDamkohler number useful for characterising variouscombustion regimes [20].

DNS results suggest that one important point toreproduce auto-ignition is to capture the time history ofthe mean mixture fraction dissipation rate evaluatedunder stoichiometric conditions. Practically speaking,when all the local characteristic micro-mixing times(inverse of the scalar dissipation rate) are much smallerthan the local ignition times of the stoichiometric mixture(or of the most reactive mixture), ignition is more or lessuniformly distributed. Accordingly, when local turbulentmicro-mixing leads to possibilities of non-uniformignition, edge-flame combustion involving partiallypremixed flames will control the development of the heatrelease rate.

9

In the light of these DNS observations, one possibility toimprove the combustion model, and to mimic theseimportant features of auto-ignition, would consist ofmodifying the calculation of the probability of findingignition. Following the work of Ravet and Vervisch [5],based on an idea first proposed by Borghi [4], a tablelook up of ignition time delay could be constructed. Theresulting ignition times would be a function of the meantemperature, mean species mass fraction and position inmixture fraction space. Introducing the probability densitydistribution of micro-mixing time, the probability of findingignition for each possible instantaneous value of themixture fraction is then measured from the probability ofhaving micro-mixing times greater than the ignition time.A presumed beta-pdf for the mixture fraction could beused to average over the range of variation of mixturefraction. The existence of characteristic mixing timessmaller than ignition delay would prevent auto-ignitionand then combustion. However, when ignition prevailsover micro-mixing, combustion would occur. Thismodification of the model would lead to a more accuratedescription of the first stage of combustion in the engine.Finally, the ignition table look-up could be implementedusing a detailed chemical mechanism; this would allowfor better accuracy in the determination of the burningrate.

CONCLUSION

A numerical and experimental study was conductedinvestigating the combustion process in a 1.9L TDI Dieselengine. Simulations and measurements were conductedin both for the case of a pressure chamber and theengine. A graphical methodology was used whichmatched the simulated spray well with the spray imagestaken in the pressure chamber. The novel RTZF flameletmodel was used for the combustion simulations. Acomparison of the calculated and measured in-cylinderpressure indicated good agreement at partial loadoperating conditions with a mean difference between thesimulation and measurement pressure equalling 3%.Furthermore, suggestions based on Direct NumericalSimulations from the literature have been proposed howto improve the auto-ignition model utilized. In conclusion,this study has shown that the RTZF flamelet model testedshows encouraging results and thus merits furtherdevelopment and investigation at other engine operatingconditions.

ACKNOWLEDGMENTS

The authors would like to thank Arno Homburg andReinhard Schulz for their help concerning the pressurechamber measurements and diagrams. Finally, thanksare given to Dr. H.-J. Oberg for his useful discussionsduring the course of this study.

REFERENCES

1. Magnussen B. and Mjertager B., “On mathematicalmodelling of turbulent combustion”, 16th InternationalSymposium on Combustion, pp. 719-727, TheCombustion Institute, 1976.

2. Marble F. and Broadwell J., “The coherent flamemodel of non-premixed turbulent combustion”,Project Squid TRW-9-PU, Project SquidHeadquarters, Chaffee Hall, Purdue University, 1977.

3. Bilger R.W., “The structure of diffusion flames”,Combustion Science Technology, Vol. 13, pp. 155-170, 1976.

4. Borghi R., “Turbulent combustion modelling”, Prog.Energy Combust. Sci., Vol. 14, pp. 245-292, 1988.

5. Ravet F. and Vervisch L., “Modelling non-premixedturbulent combustion in aeronautical engines usingpdf-generator”, 36th Aerospace Sciences Meetingand Exhibit AIAA, paper 98-1027, Reno, Nevada,USA, 1998.

6. Pope, S.B., “Pdf method for turbulent reacting flows”,Prog. Energy Combust. Sci., Vol. 11, pp. 119-195,1985.

7. VECTIS Theory Manual, Version 3.4, RicardoConsulting Engineers Ltd, December, 1999.

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