2003-01-1060

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2003-01-1060

A New Quasi-Three Dimensional Combustion Model forPrediction of DI Diesel Engines Performance and Pollutant

Emissions

E. G. Pariotis and D. T. HountalasMechanical Engineering Department, National Technical University of Athens

Copyright 2003 Society of Automotive Engineers, Inc.

ABSTRACT

The fundamental understanding of mixture formationand combustion process taking place in a DI dieselengine cylinder is an important parameter for engine

design since they affect engine performance andpollutant emissions. Multi-dimensional CFD models areused for detailed simulation of these processes, butsuffer from complexity and require significantcomputational time. The purpose of our work is todevelop a new quasi-dimensional 3D combustion modelcapable of describing the air fuel mixing, combustionand pollutant formation mechanisms, on an engine cycleby cycle basis, needing reasonably low computationaltime compared to CFD ones, while describing in a morefundamental way the various processes compared toexisting multi-zone phenomenological models. As aresult, a number of problems associated with the

application of multi-zone models are resolved. Thecombustion chamber is divided into a number ofcomputational cells and the equations of mass, energyand species conservation are solved to calculatetemperature and species concentration at each node.The gas flow field is estimated using a newly developedsemi-empirical gas motion model, based on theassumption that the in-cylinder pressure is uniform. Thefinite volume method is used for the solution of theconservation equations. The implicit temporal and hybridcentral upwind spatial differencing scheme is used forthe discretization of the conservation equations. Spraytrajectory, fuel vaporization and combustion aresimulated using simplified sub-models based on semi-empirical correlations. A first application of this newmodel is made on a high speed DI diesel engine. Theeffect of operating conditions on the combustion andpollutant formation mechanism is examined. Informationconcerning local air fuel ratio, temperature distributionand species concentrations is derived. To validate themodel experiments have been conducted at the authors'laboratory on a DI diesel engine. Comparingexperimental with calculated results, a relatively goodagreement is observed. This reveals that the proposedmodel produces qualitatively reliable predictions of thein-cylinder processes and engine performance at

reasonable computational time. Furthermore it appearsthat it can be used to study pollutant formation and theeffect of various engine design parameters on thecombustion mechanism, providing results that are acompromise between phenomenological models and

detailed CFD ones.

INTRODUCTION

Diesel engines have been widely used extensively inheavy-duty vehicles while lately are increasingly beingused for light-duty vehicles. The attractiveness of dieseengine lies on its high efficiency. On the other hand itsmain disadvantages compared to spark-ignition enginesare lower power density and higher particulate pollutanemission levels. To increase power density, turbo-charging systems can be used, while for the reduction ofpollutant emissions various strategies have been

proposed, focusing on the improvement of thecombustion mechanism or the use of after-treatmentechniques. With the anticipated extreme tightening ofNO and PM emission standards by year 2010, anintensive research is taking place nowadays aiming toreduce diesel engine emissions without affectingseriously its bsfc.

Some of the main strategies that have been proposedfor the optimization of the combustion mechanism areimproved combustion chamber design, use of advancedhigh-pressure fuel injection systems, and use of EGR [16]. The determination of the optimum strategy is very

difficult due to the complexity of the combustionmechanism, and the contribution of computer modelingto the fundamental understanding of these processes isessential.

Diesel engine computer simulation models are widelyused to predict the effect of various parameters onengine performance and emissions. In this way aconsiderable amount of time and effort is saved byreducing the number of experiment, while it is possibleto focus on the effect of individual parameters, which isdifficult using experimental techniques. There exisvarious computer models and the final choice depends

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on the purpose of the simulation and the level ofaccuracy required [7]. In the present work a new quasi-three dimensional combustion model for the prediction ofDI diesel engines performance and pollutant emissionshas been developed. The main scope of this model is todescribe the fuel air mixing mechanism and thecombustion process in a more fundamental waycompared to existing multi-zone phenomenologicalmodels, while being less time consuming andcomplicated compared to existing CFD models. Toachieve this, some of the basic features of thesophisticated multi-zone phenomenological models andthe multidimensional CFD ones have been combined.The cylinder is divided in finite volumes (cells) where themass, energy and species conservation equations arenumerically solved similarly to CFD models, while theflow field is estimated from a newly developedphenomenological model to avoid the solution of themomentum equation. On the other hand the fuelinjection, spray trajectory, ignition delay and pollutantemissions (NO and Soot) are simulated using existingsemi-empirical phenomenological models that areproperly modified. As a result the spatial distribution of

temperature, species concentration and pollutantemissions is derived at each crank angle. To validate themodel, experiments have been conducted at theauthors laboratory on a high speed DI diesel engine.Comparing experimental with calculated results at awide range of engines speeds (1500-2500 rpm) and atengine loads ranging from 20% to 80% of full engineload, it is revealed that the model predicts adequatelyengine performance and with a reasonable goodaccuracy the exhaust pollutant emissions (NO andSoot). This is quite encouraging considering thecomplexity of the proposed model and the fact that it hasbeen developed from scratch.

OUTLINE OF COMPUTATIONAL MODEL

A quasi-three dimensional combustion model has beendeveloped for four-stroke direct injection diesel engines.The cylinder is divided in finite volumes where theconservation equations for the fuel vapor, combustionproducts and mixture enthalpy are numerically solved bythe finite difference technique. The flow field is estimatedusing a revised method proposed by the authors in thepast [8], assuming that the in-cylinder pressure is almostuniform which is very close to reality [9]. In this way athree-dimensional vector of the velocity is estimated at

each computational cell, avoiding the solution of themomentum equation, as it happens in a pure CFD code[10-13]. Although the velocity field obtained by thismethod is only a rough estimation, it is more realisticthan the corresponding one used by existingphenomenological models. In this way the effect ofcombustion chamber geometry and operating conditionsis considered at least qualitatively.

As far as the spray model is concerned, the sprayconsists of many packages, each having its ownvelocity, which is computed using semi-empiricalequations. The rates of fuel vapor generation and the

resulting heat absorption are computed in each spraypackage and treated as source terms in theconservation equations at the computational cellslocated at each spray package neighborhood. Thecombustion model computes the ignition delay of themixture in each computational cell and the combustionproducts are treated as source terms in the speciesconservation equation. As a result the spatial distributionof enthalpy, fuel vapor, oxygen, combustion productsand temperature is obtained at each crank angle, andthe mean cylinder pressure, the heat release rate andpollutant emissions (NO, Soot) can be calculated. Themodel simulates only the closed part of the engine cycleusing initial conditions estimated at inlet valve closure.

COMPUTATIONAL DOMAIN

The engine treated in this study has a bowl in piston anda three-hole injector centered at the cylinder bore. Dueto symmetry, the computational domain is restricted toone third of the cylinder volume Fig.1, to savecomputational time. The area inside the cylinder isdivided into cylindrical computational cells as shown in

Fig.2a.

r direction

zdirection

direction

r directionPiston cavity

Cylinder walls

-r lane view

Injection

Direction

Fig.1 Computational domain

The number of cells in the r and direction is constantin contrast to the number of cells outside the piston bowin the z direction, which is variable depending on pistonposition. The number of cells inside the piston bowl in

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r

z

N

B

W

E

S

Fig.2a. Computational cell and coordinates

direction z is also constant. The grid follows the pistonmotion contracting and expanding [10,11,14]. The axialgrid velocity inside the piston bowl is equal to the pistonvelocity, in contrast to the axial velocity of the grid in thearea between the top of the piston and the cylinderhead, which is obtained from EQ(1). In the radialdirection the cylinder is divided into an annular and innervolume. Thus the number of nodes, referring to the r

direction, in the annular volume may differ from thecorresponding one in the inner volume.

>

=pistonpiston

piston

pistonpiston

grid

zzifwz

z

zzifw

w (1)

In the present study the grid used for all cases examinedhas in the r-direction, ten cells inside the piston bowl andten cells in the outer volume. In the axial direction, thereare ten cells inside the piston bowl and the number of

cells between the piston and the cylinder head rangefrom twelve to five, according to the piston position.Finally in the angular direction there are fourteen cells.The present resolution is found to give adequately grid-independent results, while it should be noticed that theresults are found to be more sensitive to the gridresolution in the angular direction, which is consistent towhat has been observed by other researchers [15].Moreover reducing the number of cells in the axialdirection during piston motion towards TDC a moreuniform grid is obtained, since the computational cells inthe piston bowl retain their shape in contrast to the onesoutside the bowl which contract and expand [14,15].

CONSERVATION EQUATION

The conservation equation for the species concentrationand gas enthalpy is described in terms of the cylindricalcoordinates, which expand and contract following thepiston motion EQ(2).

( ) ( ) ( )

piston

piston

Sz

z

r

r

1

r

r

r

r

1

z

w

v

r

1

r

ru

r

1

t

z

z

1

+

+

+

=

+

+

+

(2

In this study the combustion products are definedconsidering dissociation, using the chemical equilibrium

scheme proposed by Vickland et al. Thus in general ateach computational cell, apart from fuel vapor andpollutant emissions (NO, Soot), the following elevenspecies are considered to be present in chemicaequilibrium:

O2, N2, CO2, H2O, H, H2, N, NO, O, OH, CO

The velocities u, v, w are computed by the simplified gasmotion model which will be described later. Thediffusivity is defined by the following equation (4) andis assumed to be the same for all the dependenvariables .

pc

= (3

As far as the volumetric source rate S is concernedwhen the dependent variable is the enthalpy (=h) isdefined as follows:

onvaporizatipressureheath

h

SSSS

onVaporizatiFuel

byAbsorptionHeat

variation

pressure

toduePower

boundariescylinder

thethroughrate

ferHeat trans

S

++=

+

+

=

=

=

(4)

The heat transfer between cylinder walls and gascomputational cells is defined by:

( ) (

+

= 4cell

4wall

cell

cellwallheat TTc

V

TThAS ) (5

The convection heat transfer coefficient is obtained fromthe following correlation:

char

c3c21

l

kPrRech = (6

where:

lwRe charchar= (7

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k

cPr

p= (8)

and c1, c2, c3, c: constants. In this study c1=0.30,c2=0.80, c3=0.33, c=5.668E-8.

In the Reynolds number expression, lchar is thecharacteristic length and wchar is the characteristicvelocity. As far as the energy source rate due to

pressure changes is concerned, it is defined as:

t

PSpressure

= (9)

It is assumed that the gas is ideal which means that thepressure at each computational cell can be defined by,

TRP = (10)

The density of the gas at each computational cell iscalculated from the gas motion model described later on.

The source term Svaporization represents the energy that isabsorbed by each computational cell located in theregion where fuel vaporization occurs. It is calculated byweighting the distance between each fuel vapor packageand the computational cells that exist in itsneighborhood. Solving EQ(2), using the finite volumetechnique at each computational cell, the spatialdistribution of enthalpy is obtained and using the specificheat of the gaseous components the local temperatureis calculated at each crank angle. Consequently thelocal pressures can be computed from the perfect gasstate equation EQ(10). The calculation of the spatialdistribution of pressure is essential for the gas motionmodel, as explained later on.

When the dependent variable is the fuel vaporconcentration then in order to calculate the volumetricsource rate S, the rate of fuel vapor generationcalculated at each spray package is distributed to thecomputational cells that exist in its neighborhoodsimilarly to what is done for the calculation of Svaporization.In this way a coupling between the mesh generated tosolve the conservation equations and the fuel spraygeometry is achieved.

COMPUTATIONAL METHOD

The conservation equations are solved using the fullyimplicit finite volume method. For the spatial differencingthe hybrid-differencing scheme is used due to its abilityto exploit the advantages of the upwind and the centraldifferencing scheme. It switches to the upwinddifferencing when the central differencing producesinaccurate results at high Peclet numbers. The schemeis fully conservative and since the coefficients arealways positive it is unconditionally bounded [16]. As faras the temporal differencing is concerned the fullyimplicit method is used due to its unconditionally stablebehavior for any time step. However, the accuracy of the

scheme is only first-order in time, which is the reason forselecting a rather small time step. In this study the timeincrement is equivalent to 0.5 degree crank angle.

Discretising the energy equation results to a system olinear algebraic equations that are solved by the tri-diagonal matrix algorithm (TDMA), which is appliediteratively, in a line-by-line fashion. In this study the Top-Bottom sweep direction has been applied for the line-by-line solution of the system.

SIMPLIFIED GAS MOTION MODEL

The definition of the velocity field inside the cylinder isvery important given that in the conservation equationsthe convection term depends on the magnitude anddirection of the local velocity field. Multidimensionamodels use the momentum equation to calculate thevelocity and pressure at each computational cellHowever the solution of the momentum equation needsspecial treatment given that the convective termscontain non-linear quantities, and that the momentumequation (containing the local pressure) and thecontinuity equation are intricately coupled. Althoughthere have been proposed many computational fluiddynamic methods for the calculation of the velocity fieldinside the cylinder of an internal combustion engine [11-13,16], they all have in common that they arecomplicated and extremely time consuming. On theother hand they appear to be quite accurate.

In this work we estimate the velocity field using a revisedversion of a simplified gas motion model developed bythe authors [8]. The advantage of this method is that it issimple and describes the physical phenomenon of masstransfer between the computational cells in a realistic

way, based on the assumption that the in-cylindepressure must be practically uniform at each crankangle. The main improvement that has been made to theexisting gas motion model is that at present is able tohandle three-dimensional cases. The velocity isestimated at the boundaries of each computational cellby calculating the mass that should be transferredthrough each boundary to the neighboring cell toachieve a uniform pressure field inside the cylinder. Thevelocity field is obtained following an iterative procedureFirst, at each crank angle the energy conservationequation is solved, and a spatial distribution of thetemperature is obtained assuming that the velocity of the

gas relative to the grid is zero. Then the pressuredistribution is obtained using the perfect gas stateequation. Given that the pressure must practically beuniform, an amount of mass dmcell should betransferred to each computational cell through itsboundaries from the neighboring cells to eliminate thepressure difference and make its pressure practicallyequal to the mean pressure of the cylinder. The requiredmass is defined from,

cellcell

cellmeancell m

TR

VPdm

= (11)

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The total transferred mass dmcell for all computationalcells at each crank angle should be equal to zero, giventhat the total mass of the gas inside the cylinder isconstant. Thus the mean cylinder pressure can beestimated from,

=

kj,i, cell

cell

kj,i,

cell

mean

T

V

Rm

P (12)

In this way the amount of mass dmcell transferred toeach computational cell is estimated.

This amount of mass is taken from the neighboring cells.The amount of mass transferred from the neighboringcells depends on the local pressure differences. Forexample if the examined computational cell requires anamount of mass to be added in order to increase itspressure and make it equal to the mean cylinder one,this mass has to be taken from each of its neighboringcells through their common boundary. The proportion ofthe total mass dmcell that each of the neighboring cellswill offer is a function of its own pressure relative to thecalculated mean cylinder pressure. This means that if aneighboring cell has a pressure that exceeds the meancylinder pressure i.e DP>0 then its contribution to thetotal mass needed will be directly proportional to DP,otherwise this cell will not submit any mass. Theopposite occurs if the examined computational cellneeds to expel mass i.e. dmcell

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( ) ( ) ( )( ) t(M)t,Mt1ttd

P2.95MS b

0.5bb

0.5n

0.25

+

= (16)

where P is the pressure drop across the nozzle hole, land is the density of the liquid fuel and the ambientgas respectively, and dn the nozzle hole diameter. Thevelocity of each zone V(M) is derived from the temporaldifferentiation of EQ(15) and EQ(16). Since the break-uptime of the zones at the edge of the spray is shorter thanthe inner zones, the radial variation of the break-up timein the spray is incorporated as follows:

( )( ) NM

M1NM

Pc

d4.351Mt

0.5

2D

nlb

+= (17)

where NM is the number of zones in the radial directionof the spray, which in the present study is NM= 3.

The direction of each parcel (M) is computed from theempirical relation of the spray angle [24] as follows:

( )NM

M

Pd0.05M

0.25

2

2n

= (18)

In this study fuel spray impingement on the cylinderwalls is considered, according to the Hiroyasu et al.model [23]. After impingement on the cylinder walls thezones are assumed to penetrate radially from theimpingement point along the wall, retaining their width.Given that no zone mixing is allowed, if a zone near theedge of the spray has not yet reached the cylinder walls,but reaches inner zones that have already impinged andchanged their direction, then this zone follows the radial

direction too. Spray wall impingement affects thepenetrating velocity of each zone, which is given by thefollowing correlation:

( ) ( ) ( )( 0.25bb0.5n

0.25

Mt1ttd

P2.95MS +

= ) (19)

INJECTION RATE

To estimate the injection rate of fuel and the initialconditions at the nozzle exit, it is assumed that the flowthrough the nozzle hole is quasi-steady, one

dimensional and incompressible so the fuel mass flowrate is calculated by the following equation [7]:

P2Acm lnD=& (20)

where An is the nozzle hole area and P the localpressure difference. The fuel injection velocity at thenozzle tip is obtained from:

lD

P2cu

= (21)

FUEL VAPORIZATION

After break-up a group of drops is generated in eachzone. In this study the size of the drops is assumed tobe uniform and equal to the Sauter Mean Diametegiven by the following empirical correlation [24].

( ) ( ) ( ) 131.0f121.0135.0

32 VP9.23D = (22)

where Vf is the volume of fuel injected per fuel injectionin (mm

3). The number of droplets N within each zone is

calculated from the following expression (assuming thathe droplets are spherical):

l32

zone,lzone

D

m6N

= (23)

where ml,zone is the zone fuel mass. For evaporation themodel of Borman and Johnson [27] is followed. Afterbreak-up the fuel evaporation rate (dmfg/dt) and the heasupplied from the hot ambient gas to the liquid fue

droplets for vaporization is calculated using the followingexpressions:

dt

dm

dt

dmlfg = (24)

( )Sh1lnDDdt

dmMfOgOl

l += (25)

=

dt

dT

dT

d

6

D

dt

dm

D

2

dt

dD l

l

l3ll

l2l

l (26)

( ) ( )Nu1lnTTKDqT

TlggOl

+= (27)

+=

dt

dmLq

Cm

1

dt

dT l

pll

l (28)

The mean temperature at the interface between the gasand liquid phase of the droplet, is estimated by thefollowing expression:

3

T2T

T

lg

erfaceint,m

+

= (29)

COMBUSTION MODEL

IGNITION

In each computational cell combustion initiates after anignition delay period tign calculated from the locapressure and temperature using the following relation[28]:

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( ) 1ePc

1ign

g0 T465019.1ign

=

(30)

where P is the mean cylinder pressure and cign is aconstant. After ignition, evaporated fuel (which in thisstudy is assumed to be normal dodecane) and air reactat a rate give by the following Arrehnious type equation[7]:

)T

Eexp(YYAR

g

nox

mfv

2mixfv = (31)

where mix is the local density of the mixture, A is thefrequency factor, E the reduced activation energy, m, nconstants, and Yfv, Yox are the local fuel vapor andoxygen mass concentrations respectively.

POLLUTANT EMISSION FORMATION

Nitric Oxide Formation

In order to calculate the formation of nitric oxide insideeach computational cell the chemical equilibriumscheme proposed by Vicland et al. [29] is used tocalculate the concentration of each of the followingeleven species.

O2, N2, CO2, H2O, H, H2, N, NO, O, OH, CO

The formation of nitric oxide is controlled by chemicalkinetics [7]. In the present work, the extended Zeldovichmechanism is used to calculate the NO concentration ateach computational cell. According to the extendedZeldovich mechanism the principal reactions that govern

the formation of NO are:

( )10

3f

62f2

101f2

10x2.4kHNOOHN

T/3125expT10x4.6kONOON

10x6.1kONNON

=++

=++

=++

(32)

The variation of [NO] concentration in eachcomputational cell is expressed as follows:

[ ]( ) ( )

++

=

32

1

12

cell

cell

RR

R1

R12

dt

VNOd

V

1(33)

where

[ ] [ ][ ] [ ]

[ ] [ ] OHNkR

ONkR

NONkR

eef33

e2ef22

eef11

=

==

(34)

where b=[NO]/[NO]e and Vcell is the volume of eachcomputational cell. In the previous relations, index edenotes equilibrium. Integrating the previous differentiaequation, we obtain the NO concentration in eachcomputational cell.

Soot Formation and Oxidation

As far as the soot formation is concerned, the semiempirical two-rate equation model proposed by Hiroyasuet al [24] is used. Although the detailed mechanism osoot formation in internal combustion engines is not fullyunderstood, it is well established that the net sooformation is primarily affected by pressure, temperatureand equivalence ratio. Based on this model the net sooformation rate is given by:

dt

dm

dt

dm

dt

dm sbsfs = (35)

where dmsf/dt, dmsb/dt are the soot formation andoxidation rates respectively defined by the following

equations:

([ TR/EexpPmAdt

dmmolsf

5.0ev,ff

sf = )] (36)

([ TR/EexpPP

PmA

dt

dmmolsb

8.1O

sbsb 2

= )] (37)

where mev is the mass of evaporated fuel inside thecomputational cell and PO2 is the partial pressure ooxygen. The activation energies of soot formation andcombustion Esf and Esb, are 1.25x10

4kcal/kmol and

1.40x104 kcal/kmol respectively while Af and Ab areconstants.

RESULTS AND DISCUSSION

TEST ENGINE SPECIFICATIONS

To validate the model, it has been applied on a naturallyaspirated air-cooled four stroke DI Diesel engine, with abowl-in-piston combustion chamber and a three-holeinjector nozzle located at the center of the cylinder bore

The main engine specifications are given in Table 1.

MODEL CALIBRATION

A single operating point, which lies in the middle of theengine speed range (2000 rpm) and at 80% of fulengine load, has been selected as the reference pointfor model calibration. Once the constants of the model

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Table 1. Engine Specifications

Type Single Cylinder,4-Stroke,DI

Bore 85.73mmStroke 82.55mmConnecting RodLength

148.59mm

Compression Ratio 18Inlet Valve Opening 15oCA before

TDCInlet Valve Closure 41

oCA after BDC

Exhaust ValveOpening

41oCA before

BDCExhaust ValveClosure

15oCA after TDC

are determined, they retain their value during the entirerange of the operating conditions examined. Modelcalibration is based on the proper estimation of the

cylinder pressure diagram and the prediction of theignition delay period and the Soot tailpipe value.

MODEL VALIDATION

Performance

A wide range of operating conditions is selected tovalidate the models ability to predict engineperformance. In Figs. 3a-d the predicted cylinderpressure traces are compared with the experimentalones at 2000 and 2500 rpm engine speed only for thesake of space, for 40% and 80% of full engine load.

40 60 80 100 120 140 160 180 200 220 240 260 280

Crank Angle (degree)

0

10

20

30

40

50

60

70

80

CylinderPressure(Bar)

Cylinder Pressure2000 rpm, 40% Load

Calculated

Experimental

Fig. 3a. Comparison of predicted and measured cylinder pressure

traces at 2000 rpm engine speed, 40% load.

40 60 80 100 120 140 160 180 200 220 240 260 280


0

10

20

30

40

50

60

70

80

C

ylinderPressure(Bar)


Calculated

Experimental

Fig. 3b. Comparison of predicted and measured cylinder pressure


40 60 80 100 120 140 160 180 200 220 240 260 280


0

10

20

30

40

50

60

70

80



Calculated

Experimental

Fig. 3c. Comparison of predicted and measured cylinder pressure


40 60 80 100 120 140 160 180 200 220 240 260 280


0

10

20

30

40

50

60

70

80



Calculated

Experimental

Fig. 3d. Comparison of predicted and measured cylinder pressure


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At all operating conditions examined a good agreementbetween calculated and experimental values is observedduring the whole part of the closed engine cycle, whichmeans that the model is able to describe the effect ofengine speed and load on engine performance. Theprevious finding is enhanced comparing the predictedand measured values of peak cylinder pressure for allcases examined i.e. 1500, 2000 and 2500 rpm enginespeed and 20% to 80% engine load (Fig. 4). Themaximum cylinder pressure is well-predicted at alloperating conditions. The highest differences betweencalculated and measured values are observed at partload, being always lower than 5% of the maximumcylinder pressure.

20 40 60 80

Engine Load (% of full Engine Load)

50

60

70

80

50

60

70

80

50

60

70

80

Max.


Calculated Max. Cyl. Pressure

Experimental Max. Cyl. Pressure

1500 rpm

2000 rpm

2500 rpm

Fig. 4. Comparison of predicted and measured maximum cylinder

pressure at 1500, 2000, 2500 rpm engine speed and 20%, 40%, 60%,

80% load.

To validate the models ability to describe thecombustion mechanism, the predicted heat release ratesfor 2000 rpm engine speed and at 40% and 80% engineload are compared with the corresponding experimentalones (Fig. 5a,b). It should be stated that the heat releaserate derived from the measured cylinder pressure is thenet one, whereas the calculated one is the apparentgross, thus only a qualitative comparison is madebetween them.

Examining Figs. 5a,b it is obvious that the model

predicts adequately at both engine loads examined, theinitiation of combustion and moreover the duration of thepremixed and mixing controlled phases. The highestdifferences between measured and predicted heatrelease rates occur during the premixed combustionphase, due to the high heat transfer rate through thecylinder walls (since the calculated one is the grosswhile the experimental is the net one). The ability of themodel to predict the cylinder pressure and heat releaserate at various operating conditions shown above, is astrong indicator that the various sub-models describeadequately the fuel spray trajectory, fuel evaporation,air-fuel mixing and combustion mechanisms.

160 170 180 190 200 210 220 230 240 250 260


0

10

20

30

40

50

60

70

Heat

ReleaseRate(Joule/deg)

Heat Release Rate2000 rpm, 40% Load

Calculated Apparent HRR

Experimental Net HRR

Fig. 5a. Comparison of heat release rates at 2000 rpm engine speed

and 40% load.

160 170 180 190 200 210 220 230 240 250 260


0

10

20

30

40

50

60

70

HeatReleaseRate(Joule/de

g)

Heat Release Rate2000 rpm, 80% Load

Calculated Apparent HRR

Experimental Net HRR

Fig. 5b. Comparison of heat release rates at 2000 rpm engine speed

and 80% load.

Pollutant Emissions

As far as the pollutant emissions are concerned, in Figs6a-c the calculated concentrations of NO and Sooemissions at the engine exhaust are compared with themeasured ones, at all test cases examined. The effect ofengine speed and load on pollutant emissions is welpredicted and the predicted values of emission (NOSoot) concentrations are close to the measured ones. A

better agreement between calculated and measuredvalues is observed as far as the NO and Sooconcentrations is concerned, at 2000 rpm which is theengine speed selected for model calibration, while at2500 rpm occur the highest differences. In general itseems that, the NO emission model gives more accuratepredictions compared to the soot emission modelHowever taking into account that no adjustment of thecalibration constants is made with the variation of enginespeed and load, the calculated results are promising andindicate that the pollutant formation

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20 40 60 80


100

300

500

700

900

1100

1300

1500

1700

NOx(ppm

)

1500 rpm Engine Speed

Calculated

Experimental

0

50

100

150

200

250

300

350

400

Soot(mgr/m3)

Fig. 6a. Comparison of predicted and measured NOx and Soot

concentrations at 1500 rpm engine speed, 20%, 40%, 60% and 80%

engine load.

20 40 60 80Engine Load (% of full Engine Load)

100

300

500

700

900

1100

1300

1500

1700

NOx(ppm)


Calculated

Experimental

0

50

100

150

200

250

300

350

400

Soot(mgr/m

3)

Fig. 6b. Comparison of predicted and measured NOx and Soot


engine load.

20 40 60 80


100

300

500

700

900

1100

1300

1500

1700

NOx(ppm)


Calculated

Experimental

0

50

100

150

200

250

300

350

400

Soot(mgr/m3)

Fig. 6c. Comparison of predicted and measured NOx and Soot


engine load.

mechanism is simulated reliably, since trends arepredicted with good accuracy.

Spatial Distribution of Temperature

Detailed information on the pollutant formation andcombustion mechanism can be derived from the spatiadistribution of temperature inside the combustionchamber, predicted by the proposed model. Thepredicted temperature distribution is presented for thecase of 2000 rpm engine speed and 80% load, at certaintime instants after injection. Even though noexperimental data are available to validate the predicteddistributions, qualitative annotations can be made.

30350

400

450

500

550

600

650

700

750

800

850

0

Fig. 7a. Temperature in a vertical plane through the center of the fuel

spray at -12 CA degrees ATDC, 2000 rpm engine speed, 80% load.

In Fig. 7a the predicted in-cylinder temperature field at 12 CA degrees ATDC in a vertical plane through thecenter of the fuel spray is presented. As observed, thereis a cold region near the nozzle exit, which is attributedto fuel evaporation. Gas temperatures near the cylinder

boundaries are lower compared to the ones towards thecenter of the cylinder due to the heat transfer throughthe cylinder walls.

400

600

800

1000

1200

1400

1600

1800

2000

2200

2400

2600

Fig. 7b. Temperature field in a vertical plane through the center of the

fuel spray, at 10 CA degrees ATDC, 2000 rpm, 80% load.

In Fig.7b is given the temperature field at 10 CA degreesATDC in a vertical plane through the center of the fuespray. It is obvious that higher temperatures lie in theregions where combustion has initiated, whereas in theregions where no combustible fuel-air mixture exists lowtemperatures are prevalent. Moreover it is shown tha

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combustion takes place mainly inside the piston bowl, asit is expected [7].

Fuel-Air Equivalence Ratio Spatial Distribution

In Fig. 8 the local fuel-air equivalence ratio is shown at10 CA degrees ATDC in a vertical plane through thecenter of the fuel spray. As observed the main portion ofthe fuel vapour is restricted inside the piston bowl.Moreover comparing Fig. 8 with Fig. 7b, the highesttemperatures are observed in regions where the fuel-airequivalence ratio is near the stoichiometric value.

0.

0.4

0.8

1.2

1.6

2.0

2.4

2.8

3.2

3.6

4.0

0

Fig. 8. Fuel-air equivalence ratio distribution in a vertical plane throughthe center of the fuel spray at 10 CA degrees ATDC, 2000 rpm engine

speed, 80% load.

Spatial Distribution of NO and Soot Concentration

As far as in-cylinder local pollutant emissionconcentrations are concerned, in Figs 9a,b thedistribution of NO and Soot at 10 CA degrees ATDC in avertical plane through the center of the fuel spray is

shown. As revealed NO formation is predominant inregions where high temperatures are observed (Fig. 7b)and the gas mixture is stoichiometric to lean (Fig. 8),whereas soot concentration is higher in regions wherefuel vapour concentration is higher and temperature isrelatively high. Thus the model achieves to describeadequately the controversial mechanism of NO and Sootformation (i.e. formed in different areas), which is themain reason why it is difficult to find techniques thatwould reduce both of them.

Min

Max

Fig. 9a. NO in-cylinder distribution in a vertical plane through the center

of the fuel spray at 10 CA degrees ATDC, 2000 rpm engine speed,

80% load.

Min

Max

Fig. 9b. Soot in-cylinder distribution in a vertical plane through the

center of the fuel spray at 10 CA degrees ATDC, 2000 rpm engine

speed, 80% load.

CONCLUSIONS

Under the present work a new quasi-three dimensionacombustion model has been developed. The mainobjective of the proposed model is to simulate in asimple and reliable way the air-fuel mixing, combustion

and pollutant formation mechanism and the spatiadistribution of the in-cylinder temperature and gasmixture concentration, in a reasonable computationatime. In this model the basic features of multi-zonephenomenological models are embodied in thecomputational procedure followed by CFD modelsThus, although the results may be less detailed thanthose that a pure CFD model would give, it seems thatthe newly proposed model can be used to investigatethe parameters affecting the fuel-air mixing andcombustion mechanism and provide results on a cyclebasis.

To validate the model an extended experimentainvestigation is conducted at the authors laboratory on ahigh speed DI Diesel engine. Cylinder pressure andpollutant emissions are measured at various enginespeeds and loads covering the entire engine operatingrange. Comparing measured and predicted values ofcylinder pressure traces a good agreement is observedfor all operating conditions examined without the need tovary the model constants. Similar results are observedfor pollutant emissions (NO and Soot). The proposedmodel predicts the effect of operating parameters on NOand Soot quite well, which is the most important role ofmodelling, although differences between calculated and

experimental emission concentrations have beenobserved when comparing absolute values.

Moreover the predicted in-cylinder spatial distribution oftemperature, fuel-air equivalence ratio and pollutantemission (NO, Soot) concentrations seems to be reliableand in accordance to the existing conceptual models fothe fuel spray trajectory, fuel evaporation, combustionand pollutant emission formation [7, 30]. Examining thekey features of the model, it manages to describe in amore reliable way the air-fuel mixing mechanismcompared to existing multi-zone models, where the aientrainment into each zone is estimated only based on

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empirical relations. Moreover in the proposed model thein-cylinder local conditions (temperature and fuelequivalence ratio), that affect combustion mechanism,are better estimated compared to multi-zone models,thus the effect of operating conditions on engineperformance and pollutant emissions is simulated in amore detailed and fundamental way.

Concluding, the proposed model manages to describereliably the various processes taking place inside thecylinder during the close part of the engine cycle, in amore fundamental way, compared to existing multi-zonemodels while being less time consuming andcomplicated compared to existing CFD models.

NOMENCLATURE

A :AreaAn :Nozzle hole areaBM :Transfer number for massBT :Transfer number for heatcD :Nozzle Discharge coefficientcp :Specific heat of the gasdmcell :Mass which need to be transferred to a

computational cell in order to have a pressureequal to the mean pressure

dn :Nozzle hole diameterD32 :Sauter mean DiameterDfO :Diffusivity of fuel vapor at the interface between

gas and liquidDl :Droplet diameterh :Specific enthalpy of the gask :Conduction heat transfer coefficientlchar :Characteristic lengthL :Heat of evaporationmcell :Mass of the gas which is contained in a

computational cellmfg :Mass of fuel vaporml :Liquid droplet massNM :Number of zones in the radial direction of the

fuel sprayP :PressurePmean :Mean pressure of the gas in the cylinderq :Convective heat transfer from the hot gas to

liquid fuel dropletsr :Radial directionR :Gas constantRmol :Universal gas constant

S :Volumetric source rate

Sconvection:Volumetric source rate due to heat transferthrough the cylinder walls

Spressure :Volumetric source rate due to the change of thepressure with respect to time

Svaporization:Volumetric source rate due to heat absorptionfor liquid fuel evaporation

S(M) :Penetration of fuel spray package Mt :Timetb :Spray Break-up timeT :Gas TemperatureTcell :Gas Temperature of a computational cellTl :Droplet TemperatureTwall :Temperature of the cylinder boundaries

u :Radial component of gas velocityv :Circumferential component of gas velocityVcell :Volume of a computational cellVf :Volume of fuel injected per fuel injectionw :Axial component of gas velocitywchar :Characteristic velocitywgrid :Axial velocity of grid lineswpiston :Axial velocity of the pistonY :Mass concentrationz :Axial directionzpiston :Distance between the gas face of the cylinde

head and the piston top

GREEK SYMBOLS

:Diffusion coefficient :Circumferential direction :Dynamic viscocity :Density :Crank angle degree :Spray Angle

:Angular crankshaft speed

SUBSCRIPTS

:Ambient gas mixturefv :Fuel vaporgO :Interface between gas and liquidl :Liquidmix :Mixtureox :Oxygens :Sootsf :Soot formationsb :Soot burnt

DIMENSIONLESS GROUPS

Re :Reynolds numberPe :Peclet numberPr :Prandtl number

ABBREVIATIONS

ATDC :After Top Dead Centrebsfc :Brake Specific Fuel ConsumptionCA :Crank Angle

DI :Direct InjectionNO :Nitric Oxideppm :Parts per million (volume)TDC :Top Dead Centre

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