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SAE TECHNICALPAPER SERIES 2001-01-0547

Diesel Engine Combustion Chamber Geometry

Optimization Using Genetic Algorithms

and Multi-Dimensional Spray

and Combustion Modeling

D. D. Wickman, P. K. Senecal and R. D. ReitzEngine Research Center, University of Wisconsin-Madison

Reprinted From: Advances in Combustion 2001(SP1574)

SAE 2001 World CongressDetroit, Michigan

March 5-8, 2001

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2001-01-0547

Diesel Engine Combustion Chamber GeometryOptimization Using Genetic Algorithms and Multi-

Dimensional Spray and Combustion Modeling

D. D. Wickman, P. K. Senecal, and R. D. ReitzEngine Research Center, University of Wisconsin-Madison

Copyright 2001 Society of Automotive Engineers, Inc

ABSTRACT

The recently developed KIVA-GA computer code wasused in the current study to optimize the combustionchamber geometry of a heavy-duty diesel truck engine

and a high-speed direct-injection (HSDI) small-borediesel engine. KIVA-GA performs engine simulationswithin the framework of a genetic algorithm (GA) global

optimization code. Design fitness was determined usinga modified version of the KIVA-3V code, whichcalculates the spray, combustion, and emissions

formation processes. The measure of design fitnessincludes NOx, unburned HC, and soot emissions, as wellas fuel consumption. The simultaneous minimization of

these factors was the ultimate goal.The KIVA-GA methodology was used to

optimize the engine performance using nine input

variables simultaneously. Three chamber geometryrelated variables were used along with six othervariables, which were thought to have significant

interaction with the chamber geometry. The inputvariables include the piston bowl radius, the piston bowldepth, the piston crown height, the start of injection

(SOI) timing, the percent of cooled exhaust gasrecirculation (EGR), the swirl ratio (SR) at intake valveclosure (IVC), the duration of injection (DOI), the fuel

injection nozzle hole size, and the angle of a fuel

injection plume with respect to the cylinder axis. Bothengines were optimized at a medium-speed, high-load

condition with a similar global equivalence ratio. Theresults show impressive reductions in both exhaustemissions and fuel consumption.

INTRODUCTION

Recently, much research effort and resources havefocused on promising new alternatives to interna

combustion (IC) engines (e.g., fuel cells). Theseadvanced concepts have potential as clean and efficientpowerplants of the future. However, in the much nearer

future, advances in combustion will lead to cleaner andmore efficient engines using practical fuels. It is theauthors opinion that there is significant room fo

improvement remaining with IC engines. The currenwork showcases a newly developed optimization tool forexploring the vast design space being opened up by

modern flexible electronically controlled engines.It is well known that the spray characteristics

must be well matched with the combustion chambe

geometry and air motion to achieve optimal performancein a direct injection (DI) diesel engine. Singal et al. [1]provide a review of the spray-air motion interaction in DI

diesels. The improvement of the chamber geometry hasbeen the focus of many previous studies. In the presentpaper, a brief review of modern DI diesel chamber

designs is given, followed by a review of previousexperimental and computational studies on the effect ofchamber geometry. The focus of this paper is the

optimization of the engine chamber geometry usingcomputer modeling techniques.

BACKGROUND

Most modern DI diesel designs can be categorized as

either an open chamber or a re-entrant chamber design.Most small-bore diesel engines use a small diameter,relatively deep, re-entrant type bowl. The fuel spray is

typically aimed at the bowl lip. This design has beenused for its high swirl and strong squish flows, which





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tend to promote sufficient mixing, especially at highengine speeds. Some researchers have found that

when modern high-pressure injection systems are usedalong with sufficiently small bowl throat diameterchambers, liquid impingement occurs on the piston at

certain operating conditions. They contend that thetraditional small diameter bowl may be inappropriatewhen used with modern high-pressure injection systems.

Larger heavy-duty engines have typically usedlarger diameter, open-type bowls. These systems relymore on the fuel spray than the air motion to provide the

mixing energy required. These engines generallyoperate at lower speeds, where the mixing rate requiredfor complete combustion is lower. The orientation of the

fuel spray varies from engine to engine. Some aim thefuel spray along the bottom surface of the bowl, othersdirect the fuel towards the squish region.

Middlemiss [2] performed an extensiveexperimental study on the effect of chamber geometry ina small-bore high-speed diesel engine. Many different

designs were tried. The designs included a baseline,open-type chamber with a small center crown and a hostof re-entrant designs, where the throat diameter and

angle of the re-entrant portion of the bowl were varied.One of the re-entrant designs included a center crown.Four bowl lip designs were tried along with a variety of

compression ratios in a parametric study. In general, itwas found that re-entrant chambers resulted in highermixing rates thereby allowing retarded injection timings

and higher speed operation. This resulted in low sootand NOx emissions with no degradation in fueleconomy.

Saito et al. [3] performed an experimental study

of bowl geometry in a small-bore diesel engine. Twoopen-type chambers were tried, one shallow and one

deep. A re-entrant chamber was also tried, with equalmaximum bowl diameter to the open chambers. Thethroat diameter of the re-entrant bowls was varied. It

was found that a 40 mm throat diameter was optimal.They found that the re-entrant chamber producedshorter ignition delays, lower fuel consumption, and

lower soot and NOx emissions when used with retardedinjection timings.

Sakata et al. [4] performed a combined

experimental and computational study of piston bowldesign in a small-bore diesel engine. They found that a

specially designed bump (so-called reflex edge) on there-entrant portion of the bowl increased fuel spray airentrainment and mixing. This resulted in increasedperformance and reduced hydrocarbon (HC) emissions.

An experimental study of the effects of the sprayorientation, injector hole size and number, compressionratio, and combustion chamber geometry was carried

out by Corcione et al. [5]. They used a small-bore air-cooled DI diesel. Two bowl shapes were tried, a parallelsided open chamber (so-called toroidal) and a re-entrant

chamber. In general, it was found that the toroidachamber performed better at low engine speeds and the

re-entrant bowl was better at high speeds.Zhang et al. [6] performed an experimental study

on the effect of chamber geometries on combustion

behavior. Three geometries were investigated, a right-circular-cylinder dish type open bowl, a flat bottom reentrant bowl, and the re-entrant bowl with a pronounced

center crown. They concluded that the re-entrant bowwith the center crown resulted in the fastest combustionThey also found it was important to achieve a good

fuel/flame distribution inside and outside the bowl toreduce soot emissions.

Zolver et al. [7] performed a computational study

on piston bowl shapes in a small-bore diesel engine.Injection characteristics were found to have a firstorder control of the combustion process, followed by the

piston bowl shape. It was found that the intake stroke isimportant to generate a good mean velocity pattern atBDC, both in terms of its magnitude and structure. For a

given internal geometry, the flow field controls theturbulence and its dissipation rate at the end ofcompression. The bowl design and volume balance

(between the bowl and squish regions) were found toplay an important role in defining the flow near TDC.Raising the swirl level and turbulence or destroying swirl

to create turbulence were found to be productiveapproaches. NOx emissions were reduced throughchamber-geometry-generated turbulence. An interesting

configuration with individual pockets for each sprayplume was investigated, with favorable results.

De Risi et al. [8] performed a combined

experimental and computational study on the effects of

chamber geometry and engine speed on emissions in asmall-bore diesel. The basic chamber shape

investigated was a Mexican hat-type bowl. Five differenvariations of this shape were tried, one of which was anopen-type bowl. They also tried a bowl with a reflex

edge, similar to that of Sakata et al. [4]. They found theeffect of bowl geometry more prevalent at low enginespeeds. At higher engine speeds a smoother bowl lip

resulted in lower soot and higher NOx. The highly reentrant bowl was found to have performance moreindependent of engine speed, however the spray angle

and injection timing became more critical. The besresults were found when aiming the fuel spray at the

bottom of the bowl.Bianchi et al. [9] performed a computationastudy on the use of a larger diameter, less re-entrantbowl configuration along with high pressure common rail

fuel injection and low swirl in a small-bore diesel engineThe concept was to use a bowl design more well suitedto the modern injection system, thereby eliminating

spray-wall impingement and the need for high swirlThis would increase the volumetric efficiency andpossibly allow for simultaneous reductions in exhaus





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emissions and fuel consumption. The spray angle andnumber of injector holes was also changed. It was found

that the high-pressure common rail injection systemprovided sufficient mixing without a highly re-entrantbowl and high swirl. They were able to reduce soot and

NOx emissions, while paying only a small indicatedmean effective pressure (imep) penalty.

Boulouchos [10] outlined possible future

strategies for combustion, which included homogeneouscharge external ignition (HCEI), stratified charge externalignition (SCEI), stratified charge compression ignition

(SCCI), and homogeneous charge compression ignition(HCCI). The present paper focuses on the optimizationof traditional diesel combustion (so-called SCCI).

Ultimately, clean and efficient SCCI combustion may beachieved when operation takes place within the elusivewindow described by Boulouchos [10], where mixing

takes place fast enough to avoid stagnant soot-producing fuel rich zones and hot burned gases arequenched to global temperatures on time scales shorter

than those required for significant NOx production.

SCOPE OF PRESENT STUDY

The current work demonstrates the use of the newlydeveloped design methodology of Senecal and Reitz

[11, 12] (KIVA-GA). KIVA-GA performs enginesimulations (using the KIVA code) within the frameworkof a genetic algorithm (GA) global optimization code.

Genetic algorithms can be used as an efficient methodof optimization in a large search space. Senecal andReitz successfully demonstrated the use of a GA in

optimization of a heavy-duty diesel engine with split

injection capability. In their study, boost, % EGR,injection duration, injection timing, % mass in the first

injection pulse, and the dwell between injection pulseswere allowed to vary within a predefined range. Theresults showed soot emissions at half the baseline level,

NOx emissions at one-third of the baseline, and a 15%reduction in fuel consumption.

The goal of the current study is the same as that

of the work of Senecal and Reitz [11, 12] i.e., thereduction of emissions and fuel consumption, subject tocertain predefined constraints. However, the parameters

varied are different. In total 9parameters were used, 3geometric and 6 other parameters with significant

interaction. The 3 parameters related to chambergeometry are the bowl diameter, the bowl depth (as a %of the maximum bowl depth), and the central crownheight of the piston (as a % of the bowl depth).

Chamber geometry optimization seems to be anexcellent application for KIVA-GA, since an extensiveexperimental study would require many different pistons

to be manufactured. In this study, only open-typeMexican hat shaped chambers were considered.

Figure 1 shows examples of possible chambeshapes within the search space and the three geometric

parameters varied. Grid generation was automatedusing the program PKSgrid. The squish height isadjusted automatically in each case to preserve the

compression ratio. The 6 other parameters are theinjection duration, the injector hole size (as a % of themaximum hole size), the injection angle (with respect to

the cylinder axis), the start of injection timing (SOI), theswirl ratio (SR), and the % of cooled exhaust gasrecirculated (EGR). Table 1 lists these parameters, the

ranges through which they were allowed to vary, and theresolution of each parameter (# of steps allowed withineach parameter). Using these parameters and

resolutions results in a search space containing about7x10

10possible designs. The hole size is given as % of

maximum hole size, which is a function of injection

duration, such that the injection pressure ranges fromapproximately 1000 to 2000 bar.

Figure 1. Examples of chamber geometries within thesearch space. The present geometric parameters

included in the optimization studies are illustrated.





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Table 1. Design parameters, ranges, and resolutions.

Parameter Range Resolution

bowl diam. 2 37 cm (small-bore)511.7 cm (large-bore)

16

bowl depth 5090 % max. 16

crown height 2090 % max. 16DOI 12.9528 deg. 16

hole size frac 0100 % max. 16injection angle 2080 deg. 32

SOI -155 deg. atdc 16swirl ratio 04 8

EGR 050 % 16

The actual hole size used in the simulation is calculatedfrom the hole size fraction by

Anozdiameter

*4

=(1)

where

( )[ ] minminmax* AAAfracAnoz += (2)

TinjVholesnum

injmassCA

fuel min***_

_*max 1

= (3)

TinjVholesnum

injmassCA

fuel max***_

_*min

1

= (4)

and frac is the nozzle hole fraction taken from the GAcode. Num_holes is the number of holes per nozzle.Vmin and Vmax are the minimum and maximuminjection velocities, respectively, based on the range of

injection pressure used. Tinj is the time duration ofinjection. C1 is a constant that accounts for the deviationfrom a square rate shape of injection, which is assumed

in equations 1-4. This method allows the injectionduration to vary, independent of the injection pressure.

The bowl depth is calculated from the bowl

depth fraction by

= 2**_ tdcVol

fracdepthbowl (5)

where frac is the bowl depth fraction, Voltdc is the volume

at TDC, and is the bowl radius.A small-bore direct injection diesel engine and a

heavy-duty direct injection diesel engine are considered

in the current study. The small-bore diesel is a singlecylinder version of a Fiat automotive diesel (Corgard and

Reitz [13]). Engine specifications are given in Table 2.The heavy-duty diesel considered is a single cylinder

version of the 3400 series Caterpillar diese(Montgomery [14]). Engine specifications are given inTable 3. Note that, with the exception of bowl diameter,

all parameters and resolutions are identical for the largeand small-bore engines (see Table 1). However, theminimum and maximum bowl diameters used for the two

engines represent 35% and 85% of their respective boresizes.

Table 2. Small-bore Automotive Engine Specifications.

Engine Type 4 valve DI diesel

Bore x Stroke 82.0 x 90.4 mm

Compression Ratio 18.79:1

Displacement 477 cm3

Piston Geometry reentrant bowl

Intake Ports 1 swirl, 1 tumble

Spray included half angle (deg.) 72.5

Swirl ratio (at IVC) 1.83

Boost pressure (bar) 1.96

Bowl dia. 2(mm) 46Bowl depth frac 1.0Crown height frac 0.07DOI (deg.) 18.3

Hole size frac 1.0 (0.160 mm)

EGR 0 %

IVO 10 BTDCIVC 38 ABDCEVO 38 BBDCEVC 8.5 ATDC

Table 3. Heavy-duty Engine Specifications.

Engine Type 4 valve DI diesel

Bore x Stroke 137.2 x 165.1 mm

Compression Ratio 16.1:1

Displacement 2440 cm3

Piston Geometry Mexican Hat

Combustion Chamber Quiescent

Spray included half angle (deg.) 62.5

Swirl ratio (at IVC) 1.0

Boost pressure (bar) 1.62

Bowl dia. 2 mm 98

Bowl de th frac 0.9

Crown hei ht frac 0.22DOI (deg.) 21

Hole size frac 0.4 (0.188 mm)

EGR 0 %

IVO 32 BTDCIVC 33 ABDCEVO 46 BBDCEVC 29 ATDC





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For both engines an operating condition waschosen that had experimental data available for baseline

validation. For the small-bore diesel the operatingcondition is 1757 rev/min and full load. This operatingcondition has a global equivalence ratio of about 0.72.

For the heavy-duty engine the operating condition is 993rev/min and 75% load. This operating condition resultsin a similar overall equivalence ratio of about 0.77.

These operating conditions were chosen since they areboth high load, near the middle of their respectiveengines speed range (near the torque peak), and have

similar global equivalence ratios. This allows for ameaningful comparison of results between the 2 enginesizes. It is important to note that the optimization is only

at this load and speed and that other loads and speedsmay have different optimums. In the future, as computerspeeds increase, more than one operating condition will

be considered for each function evaluation (i.e., morethan one KIVA-GA run), with appropriate weighting givento each condition.

NUMERICAL MODELS

CFD CODE - The multi-dimensional model used in thepresent study is a modified version of the KIVA-3Vcomputer code [15]. KIVA3V solves for unsteady,

compressible, turbulentreacting flows on finitevolumegrids. With the addition and modification of manysubmodels, this code is now being widely applied and

validated for engine combustion simulations [16]. Thesemodels have been adequately described in the literatureand are only briefly described here.

Turbulent flow within the combustion chamber is

modeled using the RNG k model, modified forvariabledensity engine flows [17], and an improved

temperature wall function model is used to predictgas/wall convective heat transfer. This model accountsfor the effect of thermodynamic variations of gas density

and the increase of the turbulent Prandtl number in theboundary layer [18].

The nozzle flow model of Sarre et al. [19] was

implemented to provide initial conditions for the spraymodel. The model takes into account the nozzlepassage inlet configuration, flow losses and cavitation,

the injection pressure and instantaneous combustionchamber conditions [19]. The injector discharge

coefficient, effective injection velocity and injected liquidblob sizes at the injector exit are calculateddynamically throughout the entire injection event.

The KHRT (KelvinHelmholtz and Rayleigh

Taylor) model is used to model the spray breakup. Thismodel assumes that aerodynamic instabilities (i.e., KHwaves) are responsible for liquid breakup within the

dense core region, and that both aerodynamic and RTaccelerative instabilities form droplets beyond a breakuplength defined by

0

2

1 dCL

=

(6

where 1 and 2 are the liquid and gas densities

respectively, and d0

is the diameter of the injected liquidblob. Furthermore, C is a model constant, which canbe shown to be related to the KH model breakup time

constant [16].The spray model also considers the effects o

drop distortion on the drag coefficient of the drops. The

drops drag coefficient is allowed to change dynamicallybetween that of a sphere (in the case of no distortion)and that of a disk (in the case of maximum distortion)

depending on the conditions surrounding the dropDetails of this and other models are described byRutland et al. [20].

To model diesel engine ignition delay, a multistep kinetics model (Shell model) is used. In the Shel

model [21], eight generic reactions are used to representfuel, intermediate species, and products. The premise of

the Shell model is that degenerate branching plays animportant role in determining the cool flame and the twostage ignition phenomena that are observed during the

autoignition of hydrocarbon fuels. A chain propagationcycle is formulated to describe the history of thebranching agent together with one initiation and two

termination reactions [22]. Diesel spray combustion ismodeled with a characteristic time model, which isexplained in detail by Kong et al. [22].

Soot formation is computed with the model ofHiroyasu and Kadota [23] and soot oxidation is

determined with the Nagle and StricklandConstablemodel [24]. In addition, NOx is modeled with theextended Zeldovich mechanism [25]. A detaileddescription of the implementation of these models is

presented by Patterson et al. [26].The one-dimensional gas dynamics code of Zhu

and Reitz [27] was used to model the gas exchange

processes and provide the initial (IVC) conditions for themulti-dimensional code.

OPTIMIZATION - Although a multidimensional CFDmodel provides a tool for simulating both conventionaand unconventional engine design concepts (e.g., [28],

[29]), an efficient design process must be based on amathematical or statistical scheme which searches aconstraintlimited objective function surface for an

optimum [30]. In this context, the CFD model becomesa function evaluator that calculates the objective functionf(X) to be optimized. Thus, if X is the vector o

parameters, or control factors, to be varied (e.g.injection and/or geometric parameters), the presenoptimization problem can be stated as:





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For an objective function f(X), find X=(X1,X2,X3,...,Xk)which maximizes f(X) subject to possible constraints on

the system.

Affes et al. [31] developed a methodology for IC

engine intake port design utilizing CFD calculations anda numerical calculusbased, or local, optimizationtechnique. Local search techniques are typically highly

dependent on the initial design point and tend to betightly coupled to the solution domain. This tightcoupling enables such methods to take advantage of

solution space characteristics, resulting in relatively fastconvergence to a local optimum. However, constraintssuch as solution continuity and differentiability can

restrict the range of problems that can be optimized withsuch methods.

On the other hand, global search methods place

few constraints on the solution domain and are thusmuch more robust for illbehaved solution spaces. Inaddition, these techniques tend to converge to a global

optimum for multimodal functions with many localextrema. Genetic algorithms are global searchtechniques based on the mechanics of natural selection

which combine a survival of the fittest approach withsome randomization and/or mutation. The SimpleGenetic Algorithm (SGA) can be summarized as

follows [32]:

Individuals are generated through randomselection of the parameter space for each controlfactor, and a population is then produced from theset of individuals.

A model (which may be empirical or multidimensional) is used to evaluate the fitness of eachindividual.

The fittest individuals are allowed to reproduce,resulting in a new generation through combiningthe characteristics from two sets of individuals.Mutations are also allowed through random

changes to a small portion of the population.

The fitness criteria thins out the population by killingoff less suitable solutions. The characteristics of the

individuals tend to converge to the most fit solution

over successive generations.

Genetic algorithms have been successfully applied to

design problems ranging from laser systems [33] toreinforced concrete beams [34] and have also beenused for engine design. Edwards et al. [35] constructed

statistical models from a set of factorial experiments andused a genetic algorithm to optimize these models. Withthis methodology, the responses of emissions, fuel

consumption and combustion noise to control factorssuch as boost pressure, swirl ratio and injection pressure

were assessed over a wide range of engine operatingconditions.

While previous studies (e.g., [35]) used Genetic

Algorithms to optimize empirical models constructedfrom experimental results, the present study uses a

MicroGenetic Algorithm (GA) to automaticallydetermine what designs to simulate and hence drive thenumerical experiments to the optimum. Like the SGA

outlined above, the GA operates on a family, opopulation, of designs. However unlike the SGA, the

mechanics of the GA allow for a very small populationsize, npop. For SGAs, npoptypically ranges from 30 to

200, while the GA of Krishnakumar [36] uses apopulation size of five. As a result, a GA is a muchmore feasible tool for use with multidimensiona

modeling. The GA used in the present study is basedon the GA code of Carroll [37] and can be outlined as

follows:

1. A population of five designs is generated fourare determined randomly and one is the presen

baseline design.

2. The fitness of each design is determined and thefittest individual is carried to the next generation

(elitist strategy).

3. The parents of the remaining four individuals aredetermined using a tournament selection strategy. In

this strategy, designs are paired randomly andadjacent pairs compete to become parents of theremaining four individuals in the following generation

[15].

4. Convergence of the population is checked. If thepopulation is converged, go to step 1 keeping the

current fittest individual as the new baseline. If thepopulation has not converged, go to step 2.

Note that mutations are not applied in the GA sinceenough diversity is introduced after convergence of a population. In addition, Krishnakumar [36] andCarroll [37] have shown that GAs reach the optimum in

fewer function evaluations compared to an SGA for theirtest functions.

OPTIMIZATION METHODOLOGY

This section summarizes the key elements incorporatedin the present design methodology including the baseline

design, constraints, the objective function and itsevaluation, and the search technique.





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BASELINE DESIGNS - The baseline combustionchamber geometry for the small-bore engine is shown in

Fig. 2. The baseline design is a re-entrant type bowlwith a pronounced center crown. For computationalefficiency, a sixty-degree sector of the combustion

chamber was modeled. This is afforded by the six-foldsymmetry inherent with the six-hole fuel injection nozzleand axi-symetric chamber geometry. A baseline

simulation was performed and compared to theexperimental data of Corgard and Reitz [13]. As seen inFigure 3, there is good agreement between the

computed and measured cylinder pressure.The automated mesh generation program used

in the current study was not designed to consider such a

complicated geometry. Therefore, a baseline Mexican-hat geometry starting point for the optimization wasconfigured to match as close as possible the actual

engines bowl radius and crown height.

Figure 2. Small-bore diesel engine baseline

computational mesh used for model validation.

-40 -30 -20 -10 0 10 20 30 40 50 60

0

2

4

6

8

10

12

14

Measured

Predicted

Pressure

(MPa

)

crank angle (deg. ATDC)

Figure 3. Comparison of computed and measuredcylinder pressure for the small-bore diesel baseline

geometry shown in Figure 2.

The baseline combustion chamber geometry forthe heavy-duty engine is shown in figure 4. The

baseline design is an open-type chamber featuring aMexican-hat shape. Again, a baseline simulation wasperformed and compared to experimenta

measurements (Montgomery and Reitz [14, 30]). Figure5 shows the computed and measured cylinder pressurewith good agreement between the two. The successfu

comparisons shown here, along with previous results(not shown, Senecal and Reitz [11, 12]) provideconfidence in the model predictions.

Figure 4. Heavy-duty diesel engine baseline

computational mesh.

-40 -30 -20 -10 0 10 20 30 40 50 60

0

2

4

6

8

10

12

Measured

Predicted

Pressure(MPa)

crank angle (deg. atdc)

Figure 5. Comparison of computed and measuredcylinder pressure for the heavy-duty diesel baselinecase.

OBJECTIVE FUNCTION AND ITS EVALUATION Since the goal of the present optimization process is to

reduce emissions without sacrificing fuel economy, theobjective, or merit, function should contain engineoutNOx, Hydrocarbon (HC) and soot emissions levels, as

well as fuel consumption. In this study, the proposedmerit function of Montgomery and Reitz [14, 30], whichha s also been used by Senecal and Reitz [11, 12], is

used and is given by





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3

2

2

2

1

1000)(

RRRf

++=X

(7)

where

( )01

1HCNOx

HCNOx

++

=WR(8)

02

2PM

PM

WR =

(9)

0

3BSFC

BSFC=R

(10)

and the parameter vector X is defined in Table 1.For the small-bore engine the (NOx + HC)o and

PMo values are 6.015 and 1.481 g/kg-fuel, respectively.

These fuel specific emissions targets were derived fromthe EPA tier II 2004 automotive diesel mandates

(Krieger et al. [38]) using the vehicle road powerrequirements of Stodolsky et al. [39] and an assumptionof 40% brake thermal engine efficiency (approximately

60 miles/gallon diesel fuel). The baseline fuelconsumption BSFCo is taken as 210 g/kW-hr (i.e., 40%brake thermal efficiency). NO emissions were used in

the small-bore optimization.For the heavy-duty engine, the (NOx + HC)o and

PMo values are the EPA mandated on-highway

emissions levels (3.35 and 0.13 g/kWhr, respectively)for 2002/2004 and BSFC0 is a baseline fuel consumption(215 g/kWhr in the present work, obtained form the

experiments of Montgomery [14]). The weightingconstants W1 and W2 are set to 1.0 in the present studyfor both engines. Note that hydrocarbon emissions are

determined from the predicted amount of unburned fuelat the end of each simulation. The brake power in eachcase was calculated using the calculated gross indicated

power and subtracting a baseline pumping and frictionalpower. No correction to the frictional power was madefor changes in the imep.

CONSTRAINTS - As described by Montgomery [14],physical constraints on the heavy-duty engine include a

maximum exhaust temperature of 1023 K and a peak

combustion pressure of approximately 15 MPa. Thepenalty method technique of Senecal [11,12] is used to

inhibit convergence to an unphysical solution (i.e., onethat violates the present constraints). The maximumcylinder pressure limit is taken as 14 MPa for the small-

bore engine. The small-bore exhaust temperature limitwas set equal to that of the heavy -duty engine (i.e., 1023K). The exhaust temperature change during blow-down

was estimated by an isentropic expansion from the

cylinder pressure at exhaust valve opening (EVO) to the

exhaust manifold pressure, assuming a (ratio ospecific heats) of 1.2.

SEARCH TECHNIQUE - The final, and perhaps mosimportant, element of the KIVAGA methodology is the

GA optimization technique described above. TheKIVAGA code is completely automated to simulate aGA generation (i.e., five designs) in parallel. Once thefive simulations are completed, the genetic operatorsproduce a new population and the process is repeated.In this study 80 generations were run (i.e., 400 KIVA

simulations). Representative run times were 2-4 weekson an SGI Origin 2000 supercomputer.

RESULTS AND DISCUSSION

The results from the small-bore optimization are

presented first, followed by the large-bore, and finally a

comparison of results between the two engine sizes ispresented.

SMALL-BORE OPTIMIZATION- Figure 6 presents themaximum merit function curve for the small-bore engine

This curve shows the maximum merit value of eachsuccessive generation. As seen in the figure, theoptimum design at generation eighty has a significantly

higher merit value when compared to the optimizationstarting point. Notice that the predicted optimum did notchange between generations 50 and 80, indicating

convergence. However, convergence is not guaranteed,since the true global optimum is not known a prioriFigure 6 also presents the chamber geometries and

spray included angles corresponding to major merivalue changes. It is interesting to note the evolution ofthe chamber geometry through the optimization process

which started with a small diameter deep bowl, moved toa Mexican hat type geometry, and finally arrived at amore toroidal like geometry with a low center piston

crown. It is important to note that many othegeometries were included in the optimization processand only goemetries associated with maximum merit

changes are shown here. The spray orientation angle ofthe optimum case is shown in Table 4, along with thevalues of all parameters for the optimum designs fo

both engines. As shown in Figure 6, this spray angle

directs the fuel towards the far bottom corner of thebowl.

Figure 7 presents the best design of eachgeneration for six of the parameters, along with themaximum merit curve, for reference. Figure 7 a, b, c, d

e, and f show the bowl diameter, bowl depth fraction,piston crown fraction, injection duration, start of injectiontiming, and spray included half-angle, respectively. The

bowl diameter was initially small, to best match the





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baseline engine geometry. It then moved to a large bowldiameter, dipped back to a slightly smaller diameter,

then finished with a relatively large diameter. The bowldepth fraction moved to a large value early in theoptimization and stayed large to the end.

Interestingly, the piston crown fraction startedlow (high center piston crown height) and moved to alarge value (low center crown height) between

generations 30 and 40. The convergence to a relativelylarge diameter shallow bowl shape is an indication thatthe high injection pressure is sufficient for good mixing

and does not require strong swirl and squish flows.However, it is important to note that this is a mediumspeed operating condition and at high engine speed

more air motion may be required for clean and efficientcombustion.

Up to about generation 50 the injection duration

was shorter than that of the baseline case, however theinjection duration then moved to a larger value (longerinjection duration) where it remained until the end of the

optimization. The spray orientation angle progressivelymoved from smaller to larger values, i.e., moving

towards spraying into the squish volume.Figure 8 presents the best design of each

generation for the remaining three parameters, along

with the maximum merit curve, for reference. Figure 8 ab, and c shows swirl ratio, EGR fraction, and nozzle holediameter, respectively. The swirl ratio was initialized at

approximately 1.8, dipped to 0.0, and converged to 1.1.The reduced swirl, when compared to the baseline, is anindication of a reduced reliance on air motion for mixing.

This can be attributed to the higher injection velocity, aswell as the larger bowl diameter, which has less swirlintensification near TDC. The EGR fraction, which was

initially 0.0 (from the baseline case), converged to 0.23.The nozzle hole diameter, initially 0.16 mm, convergedto 0.11 mm. The final (converged) values for all nine

parameters are shown in Table 4.

0 10 20 30 40 50 60 70 80

150

200

250

300

350

400

450

500

Maximummeritvalue

Generation number

Figure 6: Maximum merit function curve for the small-bore engine optimization study. Also shown are the chamber

geometries corresponding to the major merit value changes.





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0 10 20 30 40 50 60 70 803.0

3.5

4.0

4.5

5.0

5.5

6.0

6.5

7.0

Bowldiameter(cm)

Generation number

0

50

100

150

200

250

300

350

400

450

500

Maximu

mmeritvalue

(a)

0 10 20 30 40 50 60 70 800.5

0.6

0.7

0.8

0.9

1.0

Bowldepth

fraction

Generation number

0

50

100

150

200250

300

350

400

450

500

Maximummeritvalue

(b)

0 10 20 30 40 50 60 70 800.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Pistoncrownfraction

Generation number

0

50

100

150

200

250

300

350

400

450

500

Maximummeritvalue

(c)

0 10 20 30 40 50 60 70 8012

14

16

18

20

22

24

26

28

Injectionduration(CAdeg.)

Generation number

0

50

100

150

200

250

300

350

400

450

500

Maximummeritvalue

(d)

0 10 20 30 40 50 60 70 80-16-14

-12

-10

-8

-6

-4

-2

0

2

4

6

Star

tofinjectiontiming(CAdeg.ATDC)

Generation number

050

100

150

200

250

300

350

400

450

500

Maximummeritvalue

(e)

0 10 20 30 40 50 60 70 8020

30

40

50

60

70

80

Sprayincludedhalf-angle(deg.)

Generation number

050

100

150

200

250

300

350

400

450

500

Maximummeritvalue

(f)Figure 7: Merit and parameter values for the best design of each generation of the small-bore optimization study. Shown

here are (a) bowl diameter, (b) bowl depth fraction, (c) piston crown fraction, (d) injection duration, (e) start of injectiontiming, and (f) spray included half-angle.





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0 10 20 30 40 50 60 70 80-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Swirlratio

Generation number

0

50

100

150

200

250

300

350

400

450

500

Maxi

mummeritvalue

(a)

0 10 20 30 40 50 60 70 800.0

0.1

0.2

0.3

0.4

0.5

EGRfraction

Generation number

0

50

100

150

200

250

300

350

400450

500

Maximummeritvalue

(b)

0 10 20 30 40 50 60 70 800.10

0.12

0.14

0.16

0.18

0.20

Nozzleholediameter(mm)

Generation number

0

50

100

150

200

250

300

350

400

450

500

Maximummeritvalue

(c)

Figure 8: Merit and parameter values for the bestdesign of each generation of the small-bore optimizationstudy. Shown here are (a) swirl ratio, (b) EGR fraction,

and (c) nozzle hole diameter.

0 2 4 6 8 10 12 14 16 18 20

0

1

2

3

4

soot(g/kg-fuel)

NOx+HC (g/kg-fuel)

Optimization start point

Optimum

Low BSFC case

Figure 9: Soot vs. NOx+HC data from the present small-

bore optimization study (not all points are shown due toscaling) including the optimization start point, optimumand low BSFC cases.

0 2 4 6 8 10 12 1 4 16 1 8 20

190

200

210

220

230

240

BSFC

(g/kW-hr)

NOx+HC (g/kg-fuel)

Optimization start point

Optimum

Low BSFC case

Figure 10: BSFC vs. NOx+HC data from the presensmall-bore optimization study (not all points are showndue to scaling) including the optimization start point

optimum, and low BSFC cases.

has higher TKE prior to injection due to swir

amplification and strong squish flows. After fuel injectioncommences, the optimum and high crown cases TKEraises to a level significantly higher than that of the

baseline case. This is mainly due to the much higherinjection pressure of the optimum and high crowndesigns (2000 bar vs. 1100 bar). In the optimum and

high crown cases it is apparent that the TKE producedfrom the high injection pressure dominates thaproduced from the in-cylinder air motion (i.e., swirl andsquish flows).





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Figure 11. Fuel vapor concentration for the optimumgeometry (top) and high center crown (bottom) in g/cm

3.

-40 -30 -20 -10 0 10 20 30 40 50 60

0

2

4

6

8

10

12

Optimum

High Crown

Pressure(MPa)


Figure 12: Comparison of predicted in-cylinder pressurefor the optimum and high crown cases.

-10 0 10 20 30 40 50 60

0

20

40

60

80

100

Optimum

High Crown

Heatreleaserate(J/deg.)


Figure 13: Comparison of predicted heat release rate forthe optimum and high crown cases.

0 20 40 60 80 100 120 140 160

0

10

20

30

40

50

60

Baseline (Measured)

Baseline (Predicted)

Optimum

High Crown

NOx(g/kg-fuel)


Figure 14: Comparison of predicted NOx for theoptimum, high crown and baseline cases. Circle shows

the measured engine-out NOx for the baseline engine[13].





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0 20 40 60 80 100 120 140 160

0

2

4

6

8

10

12

14

Baseline (Measured)

Baseline (Predicted)

Optimum

High Crown

soot(g/kg-fuel)


Figure 15: Comparison of predicted soot for theoptimum, high crown and baseline cases. Circle shows

the measured engine-out soot for the baseline engine[13].

Figure 16. Soot concentration for the baseline enginegeometry at 13 degrees ATDC (top) and 23 degrees

ATDC (bottom) in g/cm3.

Figure 17. Gas velocity magnitude contours at 28

degrees ATDC in cm/s.

-10 0 10 20 30 40 50

0.0

2.0x105

4.0x105

6.0x105

8.0x105

1.0x106

1.2x106

1.4x106

OptimumHigh Crown

Baseline

TKE(cm

2/s

2)


Figure 18. Turbulent kinetic energy vs. crank angle forthe optimum, high center crown, and baseline designs.

LARGE-BORE OPTIMIZATION - Figure 19 presents themaximum merit function curve for the large-bore engine

optimization study. As shown in the figure, the optimumdesign has a significantly higher merit value compared tothe present optimization start point, which features the

actual test engine geometry. Notice that the merifunction remains constant from about generation 65onward, indicating convergence of the optimization.

Figure 19 also presents the chamber geometriesand spray included angles corresponding to the major

merit value changes (the baseline geometry and angleare shown for reference). Interestingly, designs withlarge geometric differences are produced during theevolution process (note that many other geometries

were tried in the optimization and only thosecorresponding to the maximum merit are shown, as inFigure 6). During the first 6 generations, deep bowl, low

piston crown designs are favored, while a shallow bowlwith a large radius is the most fit design for generations





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7 through 16. The bowl diameter next decreases alongwith an increase in bowl depth.

Interestingly, the final best geometry (shown inthe upper right of the figure), which remains unchangedafter generation 20, is somewhat similar to the baseline

geometry, however, it includes a slightly wider bowl withless depth and a lower piston crown. The reducedvolume in the bowl is evident in the larger squish height

compared to the baseline geometry. Recall that thecompression ratio was held constant for all geometriesconsidered. The spray included angles for the best-so-

far designs are also shown in Fig. 19 (see arrows). Aswith the geometric parameters, the optimal spray angleremains the same after generation 20 at 68.4 degrees,

which should be compared to the baseline engines 62.5degrees (see table 3).

Although the three parameters defining the bowl

geometry and the spray included half-angle remainconstant after generation 20 for the best-so-far design,

changes in the other 5 parameters result in increases inmerit beyond this point. Figures 20 and 21 present the 9

parameter values for the best design of each generation,along with the corresponding merit curve for reference.Figures 20(a), (b), (c) and (f) illustrate the relatively fast

convergence of the chamber geometry and sprayincluded half-angle. In addition, the swirl ratio convergesvery quickly, as shown in Fig. 21(a). This relatively low

value of about 1.1 is similar to the baseline swirl value of1.0. With the geometry, spray angle and swirl ratioconverged, the remaining generations increased to the

highest merit by looking at different combinations oinjection duration, SOI, EGR and nozzle hole diameter.The final values of the 9 parameters are presented in

Table 4. Note that the optimum design features 10%EGR and a 2000 bar injection pressure with a 0.18 mmnozzle hole diameter

0 10 20 30 40 50 60 70 80

0

50

100

150

200

250

300

Maximummeritvalue

Generation number

Baseline geometry

Figure 19: Maximum merit function curve for the large-bore engine optimization study. Also shown are the chambergeometries and spray included angles corresponding to the major merit value changes.





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0 10 20 30 40 50 60 70 805

6

7

8

9

10

11

12

Bowldiameter(cm)

Generation number

0

50

100

150

200

250

300

Maximum

meritvalue

0 10 20 30 40 50 60 70 800.5

0.6

0.7

0.8

0.9

1.0

Bowldepthfraction

Generation number

0

50

100

150

200

250

300

Maximummeritvalue

0 10 20 30 40 50 60 70 800.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Pistoncrownfraction

Generation number

0

50

100

150

200

250

300

Maximummeritvalue

0 10 20 30 40 50 60 70 8012

14

16

18

20

22

24

26

28

30

Maximummeritvalue

Injectionduration(CAdeg

.)

Generation number

0

50

100

150

200

250

300

0 10 20 30 40 50 60 70 80

-16

-14

-12

-10

-8

-6

-4

-2

0

2

46

Startofinjectiontiming(CAdeg.ATDC)

Generation number

0

50

100

150

200

250

300

Maximummeritvalue

0 10 20 30 40 50 60 70 80

20

30

40

50

60

70

80

Sprayincludedhalf-angle(deg.)

Generation number

0

50

100

150

200

250

300

Maximummeritvalue

Figure 20. Merit and parameter values for the best design for each generation of the large-bore optimization study.

Shown here are the (a) bowl diameter, (b) bowl depth fraction, (c) piston crown fraction, (d) injection duration, (e) start ofinjection timing, and (f) spray included half-angle.





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0 10 20 30 40 50 60 70 800.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Swirlratio

Generation number

0

50

100

150

200

250

300

Maximum

meritvalue

0 10 20 30 40 50 60 70 800.0

0.1

0.2

0.3

0.4

0.5

EGRfraction

Generation number

0

50

100

150

200

250

300

M

aximummeritvalue

0 10 20 30 40 50 60 70 800.16

0.18

0.20

0.22

0.24

0.26

0.28

Nozzleholediameter(mm)

Generation number

0

50

100

150

200

250

300

Maximummeritvalue

Figure 21. Merit and parameter values for the bestdesign for each generation of the large-bore optimization

study. Shown here are the (a) swirl ratio, (b) EGRfraction, and (c) nozzle hole diameter.

Figures 22 and 23 present soot vs. NOx+HC and BSFCvs. NOx+HC, respectively, for the simulation casesperformed in the large-bore optimization study. Also

shown in the figures are target value boxes representingthe mandated emissions and baseline fuel consumption

levels presented above. Figures 22 and 23 also includethe optimization start point and optimum cases (see

arrows). As shown, the optimum case has significantlylower NOx+HC emissions with a slightly lower engineout soot level. In addition, while the optimums BSFC is

higher than the optimization start points value, it is still

well within the target level of 215 g/kW-hr.While the optimum case meets the target levelsof soot and BSFC, it does not meet the 2002/2004mandated NOx+HC levels. On the other hand, theoptimum of Senecal et al. [12] for this engine and

operating condition (0.038 g/kW-hr soot and 2.04 g/kWhr NOx+HC) was well within the mandated emissionslevels. This difference in optima is attributed to the fac

that both boost pressure and split injections wereincluded in the previous optimization study of Senecal etal. [12], but were not included here due to the addition of

the geometric parameters, spray included half-angleswirl ratio and nozzle hole diameter. As shown in Table4, the optimal EGR level is 10% for the present study.

One would expect that more EGR would result in evenlower NOx+HC, but with a penalty in soot. The use ofincreased boost pressure (211 kPa compared to 162

kPa in the present study) and a split injection strategy inthe previous optimization study allowed for reduced NOxwith a higher EGR level of about 17%, with very low soot

emissions. A comparison of the previous and presentoptimization studies indicates the significant influence ofboost pressure (i.e., global air-fuel ratio control) in

meeting future mandated emissions levels.

0 2 4 6 8 10 12 14 16 18 20

0.0

0.2

0.4

0.6

0.8

1.0

soot(g/kW-hr)

NOx+HC (g/kW-hr)

Optimization start pointOptimum

Low emissions case

High ex. temp. cases

Figure 22: Soot vs. NOx+HC data from the presentlarge-bore optimization study (not all points are showndue to scaling) including the optimization start point

optimum, and low emissions cases.





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-10 0 10 20 30 40 50 60

0

5

10

15

20

25

30

Optimum

Optimum with baseline geometry

NOx

(g/kg-fue

l)


Figure 26: Comparison of predicted NOx for the large-bore optimum and optimum with baseline (i.e.,production engine) geometry cases.

0 20 40 60 80 100 120 140

0

1

2

3

4

5

6

Optimum

Optimum with baseline geometry

soo

t(g/kg-fue

l)

crank angle (deg. ATDC) Figure 27: Comparison of predicted soot for the large-bore optimum and optimum with baseline (i.e.,

production engine) geometry cases.

COMPARISON OF RESULTS It is interesting to note

from Figures 6 and 19 that the predicted optima for thesmall and large bore engine geometries are remarkablysimi lar (see also Table 4). Both engines favor relatively

large diameter shallow bowls. This is consistent with thehigh injection pressures (2000 bar) found for bothengines optimum designs, where spray induced mixingis favored over swirl-flow induced mixing. Again, athigher engine speeds, higher air motion induced mixingmay be required to maintain good performance. Table 5

presents the predicted optimum values of soot, NOx+HCemissions, and BSFC, all in g/kW-hr, for the small-boreand large bore engines. The small-bore emissions were

converted to g/kW-hr using the BSFC of the optimum.As shown, the large-bore engines optimum has lower

BSFC and soot emissions, but has higher NOx+HCemissions. The higher NOx+HC emissions of the large

bore engine may be attributed to its lower EGR level(i.e., 10% vs. 23%). The convergence to a lower EGRlevel for the large-bore engine may be due to the poorer

air utilization inherent with the large-bore engine, i.e., itmay be more difficult to mix the air and fuel in the largebore engine using one centrally located fuel injector

However, it is also likely due to the target values oemissions chosen. The present small-bore and largebore emission targets are shown again in Table 6. The

small-bore targets were converted to g/kW-hr using theBSFC from the optimum design. As shown, the smallbore targets place more emphasis on NOx+HC

emissions, while the large-bore targets place moreemphasis on soot emissions. The NOx+HC targets forthe large-bore engine are 25 times the soot targets

while the NOx+HC targets are only about 4 times thesoot targets for the small-bore engine. This explainswhy the large-bore engine achieved lower soo

emissions and BSFC than the small-bore engine.

Table 5. Soot, NOx+HC, and BSFC for the optimum

designs, all in g/kW-hr.

Parameter Large-bore Small-bore

Soot 0.115 0.223

NOx+HC 5.0 1.06

BSFC 204 216

Table 6. Soot and NOx+HC emissions targets in g/kWhr.

Parameter Large-bore Small-bore

Soot 0.13 0.32

NOx+HC 3.35 1.3

It is interesting to compare the values of the nineparameters for each engine, from Table 4. The bowgeometries are quite similar, with the small-bore engine

having a slightly larger and deeper bowl, with respect tothe bore. The optimum injection duration, sprayorientation angle, and swirl ratio were found to be the

same for both engines, which may be attributed to thevery similar operating conditions. For the large-boreengine, the start of injection timing is more advanced

and the EGR level is lower, as mentioned above. Thiscan be attributed to the large-bore emission targets

emphasis on low soot emissions.





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CONCLUSIONS

Chamber geometry optimization is an excellentapplication of KIVA-GA since KIVA features 3-Dspatial resolution and thus allows for many designs

to be investigated without actually manufacturing

many different engine components (e.g., pistons,cylinder heads, etc.).

KIVA-GA is an efficient tool for optimizingcombustion systems within the vast search spaceavailable to modern flexible electronically controlled

engines.

Both the small-bore and heavy-duty diesel enginesconsidered favored relatively large diameter shallowpiston bowls, long injection durations at highpressure through small holes, and moderate swirl, at

the operating conditions investigated (i.e., mediumspeed, high load).

The optimum start of injection timing and EGR levelare very sensitive to the NOx target value chosen.

Precise control over the global air / fuel ratio is veryimportant for achieving simultaneous emissions andfuel consumption reductions.

The optimum combustion chamber designs found inthe current study were able to keep the soot awayfrom the combustion chamber walls, where it could

contaminate the lubricating oil and threaten enginelongevity.

ACKNOWLEDGMENTS

The authors would like to thank the following

organizations for their generous support during thecourse of this work: Ford Research Center in Aachen-Germany (FFA), the Army Research Office, Caterpillar

Inc., and DOE / Sandia National Laboratories.

REFERENCES

1.) Singal, S. K., Pundir, B. P., Mehta, P. S., FuelSpray-Air Motion Interaction in DI Diesel Engines: A

Review, SAE 930604, 1993.2.) Middlemiss, I. D., Characteristics of the Perkins

Squish Lip Direct Injection Combustion System,

SAE 780113, 1978.3.) Saito, T., Yasuhiro, D., Uchida, N., Ikeya, N.,

Effects of Combustion Chamber Geometry on

Diesel Combustion, SAE 861186, 1986.4.) Sakata, I., Ishisaka, K., Yanagihara, H., Sami, H.,

Nagaoka, M., Ohsawa, K., Development of

TOYOTA Reflex Burn (TRB) System in DI Diesel,SAE 900658, 1990.

5.) Corcione, F. E., Prati, M. V., Vaglieco, B. M.Valentino, G., Improvement of Combustion Systemof a Small D. I. Diesel Engine for Low Exhaus

Emissions, SAE 910481, 1991.6.) Zhang, L., Ueda, T., Takatsuki, T., Yokota, K., A

Study of the Effects of Chamber Geometries on

Flame Behavior in a DI Diesel Engine, SAE952515, 1995.

7.) Zolver, M., Griard, S., Henriot, S., 3D Modeling

Applied to the Development of a DI Diesel Engine:Effect of Piston Bowl Shape, SAE 971599, 1997.

8.) De Risi, A., Manieri, D., and Laforgia, D., "A

Theoretical Investigation on the Effects oCombustion Chamber Geometry and Engine Speedon Soot and NOx Emissions", ASME-ICE, vol. 33-1

pp. 51-59, Book No. G1127A, 1999.9.) Bianchi, G. M., Pelloni, P., Corcione, F. E.

Mattarelli, E., Luppino Bertoni, F., Numerical Study

of the Combustion Chamber Shape for CommonRail H.S.D.I. Diesel Engines, SAE 2000-01-11792000.

10.) Boulouchos, K., Strategies for Future EngineCombustion Systems Homogeneous or StratifiedCharge ?, SAE 2000-01-0650, 2000.

11.) Senecal, P. K., Reitz, R. D., SimultaneousReduction of Engine Emissions and FueConsumption Using Genetic Algorithms and Multi

Dimensional Spray and Combustion Modeling, SAE2000-01-1890, 2000.

12.) Senecal, P. K., Montgomery, D. T., Reitz, R. D.,

Diesel Engine Optimization Using Multi-Dimensiona

Modeling and Genetic Algorithms Applied to aMedium Speed, High Load Operating Condition

ASME-ICED 2000 Fall Technical Conference, 2000.13.) Corgard, D., Reitz, R. D., Effects of Alternative

Fuels and Intake Port Geometry on HSDI Diese

Engine Performance and Emissions, submitted fopublication, SAE 2000 Congress, 2000.

14.) Montgomery, D. T., Ph.D. Thesis, An Investigation

into Optimization of Heavy-Duty Diesel OperatingParameters when Using Multiple Injections andEGR, University of Wisconsin-Madison, 2000.

15.) Amsden, A. A., KIVA-3V: A Block-Structured KIVAProgram for Engines with Vertical or Canted Valves,

Los Alamos National Laboratory Report NO. LA13313-MS, 1997.16.) Senecal, P. K., Development of a Methodology for

Internal Combustion Engine Design Using Multi

Dimensional Modeling with Validation ThroughExperiments, Ph.D. Thesis, University of WisconsinMadison, 2000.

17.) Han, Z and Reitz, R. D., Turbulence Modeling oInternal Combustion Engines Using k-? Models,Combust. Sci. and Tech., 106, 267, 1995.





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2001-01-0547