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Reduction of Heavy Duty Diesel Engine Emission and Fuel

Economy with Multi-Objective Genetic Algorithm and

Phenomenological ModelT. Hiroyasu, M. Miki, M. Kim

Doshisha University

S. WatanabeNational Institute of Advanced Industrial Science and Technology

H. Hiroyasu, H. MiaoKinki University

Copyright c 2003 Society of Automotive Engineers, Inc.

ABSTRACT

In this paper, the system to perform parameter searchof heavy duty diesel engines is proposed. The pro-posed system consists of multi-objective genetic algo-rithm (MOGA) and phenomenological model. Usually, op-timization is performed to optimize only one objective. Onthe other hand, MOGA optimizes several objectives at thesame time. There is often trade off relations ship betweenobjects, to derive the Pareto optimum solutions that ex-press the relation ship between the objects is one of the

goals in this case. MOGA has strong search capability forPareto optimum solutions. However, MOGA needs a lot ofiterations. Therefore, for MOGA, diesel combustion sim-ulator that can express combustion precisely with smallcalculation cost. In the numerical experiments, fuel in-

jection shape, boost pressure, EGR rate, start angle ofinjection, duration angle of injection, and swirl ration arechosen as design variables. The values of these de-sign variables are optimized to reduce SFC, NOx, andSOOT. Through the experiments, the following five topicsare made clarified. First of all, the proposed system canfind the Pareto optimum solutions successfully. Secondly,MOGAs are very effective method to derive the solutions.

Thirdly, phenomenological model is very suitable for MO-GAs, since it can simulate precisely with small calculationcost. Fourthly, multi step injection shape can affect theamounts of SFC, NOx, and SOOT. Finally, parameter op-timization is essential for designing diesel engines.

INTRODUCTION

Diesel engines have considerable advantages in the as-pect of engine power, fuel economy and durability. Theyare widely applied in the area of transport and ship propul-sion and off-road applications, such as mining, construc-

tion and agriculture. In order to meet increasing environ-

mental concerns and more stringent emission regulations,currently researches are carried out aiming the reductionof soot and nitric oxide (NOx) emissions simultaneouslywhile maintaining reasonable fuel economy.

There are several techniques to design diesel enginesthat have small amounts of NOx and Soot while maintain-ing fuel efficiency, these being multiple injection, exhaustgas recirculation (EGR) and boost pressure. However, tocarry out parameter studies through experiments to findthe optimum parameters, huge expenses and huge time

are needed. For this reason, the optimization of param-eters with the aid of computer simulation is very usefulfor design purposes. Efforts were carried out to solve theoptimization problems related to diesel engines. To per-form engine design optimization by simulation, an opti-mizer (which determines the next searching point) and ananalyzer (which evaluates searching points) are needed.

These days, Genetic Algorithm (GA) is focused for op-timization method. GA is an algorithm that simulatesthe heredity and evolution of creatures[1]. At the sametime, GA is one of probabilistic and multi point search-ing methods. Therefore, GA can apply for not only con-

tinuous function but also discrete functions. In designingdiesel engines, normal combustion cannot be performedin some parts of design field. Thus, it is difficult to per-form parameter search with conventional methods suchas gradient methods. On the other hand, GA can applyeven in this situation. Therefore, GA is suitable for param-eter search in designing diesel engines.

The University of Wisconsin group has researched op-timization of diesel engine parameters. Montgomeryand Reitz are used response surface method foroptimization[2]. In the Reference [3] and [4], GAs are uti-

lized. Many cases are treated as single objective prob-lems. However, there are several points that should be

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optimized are existed in designing diesel engines; SFC,NOx, SOOT, and so on.

In this case, these several points are integrated into oneobject. Then, a single objective optimization method canapply to solve problem. However, it is very difficult to in-tegrate these points into one. In our former studies, wepointed out that it is better to treat as multi-objective op-timization problems[5, 6]. In multi-objective optimization

problems, several objectives are optimized at the sametime. For multi-objective optimization, it has also pointedout Neighborhood Cultivation GA (NCGA) and HIDECSare useful implementation.

In this paper, target engines are heavy duty diesel en-gines. For these engines, the following topics are dis-cussed. First of all, parameter optimization and multiplefuel injections are essential for designing diesel engines.Then, it is pointed out that multi-objective optimization ismuch useful than single objective optimization. Thirdly,GA is effective for multi-objective optimization problems.

Fourthly, phenomenological model is effective in optimiza-tion using GAs. Finally, the optimum results of heavy dutydiesel engines are discussed.

BACKGROUND

The system that is proposed in this paper consists ofsimulator and optimizer. Several types of the models ofdiesel combustion exist[7] and can be used as an ana-lyzer. Those models are roughly divided into three cate-gories: thermodynamic models, phenomenological mod-els and detailed multidimensional models. As the ther-modynamic model only predicts the heat release rate andthe calculation cost is considerably high to use detailedmulti-dimensional models. When parameter search isperformed by GAs, a lot of analyzer call is needed. There-fore, a model whose calculation cost is small and it cansimulate precisely. In this paper, the phenomenologicalmodel is chosen as an analyzer. Since response equa-tions are determined by the data that is derived by experi-ments, calculation cost is very small and it simulates com-bustion precisely. Phenomenological model is utilized assimulator and multi-objective genetic algorithm is chosenas optimizer. These two factors are described briefly.

PHENOMENOLOGICAL MODEL AND HIDECS In thepast 30 year, the most sophisticated phenomenologicalspray-combustion model, HIDECS has shown great po-tential as a predictive tool for both performance and emis-sions in a wide range of direct injection diesel engines.It was originally developed at the University of Hiroshimaand was named HIDECS recently. A detailed discussionof this model, and the examples of its successful applica-tions were given in references[8, 9, 10, 11, 12, 13, 14].Only a brief description of the model is provided in this ar-ticle. In HIDECS, the spray injected into the combustion

chamber from the injection nozzle is divided into manysmall packages of equal fuel mass as shown in figure1.

No intermixing among the packages is assumed. Thespray characteristics are defined by the empirical equa-tions of spray penetration. For example, the shaded re-gions shown in figure1 are the fuel packages injected atthe start of injection that constitute the spray tip duringpenetration. Air entrainment into a package is controlledby the conservation of momentum, that is, the amount ofentrained air is proportional to the decrease in packagevelocity. The fuel, which is mixed with the air, begins to

evaporate as drops, and ignition occurs after an ignition-delay period.

Breakup Length

Spray tip penetration

Package pf Spray P(L, M, N)

M

L

N

Injected at the start of injection

* No-intermixing among the package is assumed.

* Spray tip penetration is defined by the experimental equations

Figure 1: Schematic of the package distribution

The air-fuel mixing processes within each package are il-lustrated in figure 2. Each package, immediately after theinjection, involves many fine drops and a small amountof air. As a package moves away from the nozzle, airentrains into the package and the fuel drops evaporate.Thus, the package consists of liquid drops, vaporized fuel,and air. After a short period of time after the start of in-

jection, ignition occurs in the gaseous mixture, resultingin the rapid expansion of the package. Therefore, morefuel drops evaporate, and more fresh air entrains into thepackage. The vaporized fuel mixes with fresh air and com-bustion products as the spray continues to burn.

Air Entralnment Expansion & Air Entralnment

Injection Evaporation& Mixing

Fuel Ignition &Combustion

EvapolationMixing &Combustion

Mixing &Combustion

Figure 2: Schematic of the mass system during combus-tion

Figure 3 shows two possible combustion processes in-side each package. The Case (A) is called evaporation-rate-controlled combustion, while Case (B) is called theentrainment-rate-controlled combustion. When ignitionoccurs, the combustion mixture that is prepared before ig-nition burns in a small increment of time. The fuel-burningrate in each package is calculated by assuming stoichio-metric combustion. When there is enough air in the pack-age to burn all of the vaporized fuel, there are combustionproducts, liquid fuel and fresh air remaining in the pack-age after combustion. This process is shown in Figure3 as Case (A). In the next small increment of time, more

fuel drops evaporate and fresh air entrains into the pack-age. At this point, if the amount of air in the package is

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of the multi-objective GA[17, 18]. These algorithms of themulti-objective GA are roughly divided into two categories;those are the algorithms that treat the Pareto optimum so-lution implicitly or explicitly. The most of the latest meth-ods treat the Pareto optimum solution explicitly. Typicalalgorithms are SPEA2[19] and NSGA-II[20].

In multi-objective GAs, the most remarkable feature com-pared to conventional GAs is setting fitness function. In

multi-objective GAs, the Pareto ranking is often used fordetermining the fitness value[21]. The Pareto ranking isdetermined in the following procedure. For each solution,the number of the solution that is dominant to the focusedsolution is counted. The Pareto ranking is this number +1. When the solution is non-dominant, the Pareto rankingbecomes 1. The concept of the Pareto ranking is shown infigure5. In this figureR denotes the Pareto ranking. Thefitness value of each individual is a reciprocal number ofthe Pareto ranking.

f1

f2

R=1

R=3

R=4

R=2

R=1

Figure 5: Pareto Ranking

PROPOSED SYSTEM

The overview of the system is illustrated in figure6.

Figure 6: System construction

In Figure6, the NCGA is used as an optimizer and theHIDECS is used as an analyzer. Between the optimizerand analyzer, text files are exchanged. Therefore, basi-cally several types of the GAs and analyzers can be usedin this system.

As it is described before, the HIDECS is an implemen-

tation code of phenomenological model that is originallydeveloped at the University of Hiroshima. It had pre-

viously demonstrated potential as a predictive tool forboth performance and emissions in several types of thedirect injection diesel engine. A detailed discussion ofthe HIDECS spray-combustion model and some exam-ples of its previous applications are given in Reference[8, 9, 10, 11, 12, 13, 14].

Neighborhood Cultivation Genetic Algorithm (NCGA) isone of multi-objective genetic algorithms. NCGA has the

searching mechanism that NSGA-II[20] and SPEA2 [19]have. At the same time, NCGA has another searchingmechanism that is called neighborhood crossover. Usu-ally, the parent individuals are chosen randomly. How-ever, in the neighborhood crossover, adjoining individu-als are chosen for parent individuals. This mechanismhelps to derive distributed solutions uniformly. The pre-cise procedures and validity of NCGA are explained in thereferences[5, 22].

The NCGA is a multi point search method. Therefore,several searching points are evaluated at the same time.

For this reason, this system is very suitable for parallelprocessing. The system is implemented as master slavemodel and performed on PC cluster system.

TARGET ENGINES

In this paper, our HIDECS-NCGA system is applied toheavy duty diesel engine. As mentioned in introduction,Reitz and his fellow researchers carried out GA optimiza-tion of diesel engine parameters in Reference[2]. It wouldbe very interesting to use the same engine as their re-searches by applying different GA methodology. There-fore, our investigation on treating the diesel engine designas a multi-objective problem is based on the same engineas theirs.

CATERPILLAR 3400 SERIES The target engine is asingle cylinder version of the Caterpillar 3400 series truckengine. The baseline engine operation condition wasused the same as that of Reference[2]. The specificationof this engine is summarized in table1.

Table 1: Specification of Caterpillar 3400 Series

Bore (m) 0.1372Stroke (m) 0.08255

Connecting Rod (m) 0.24

Cavity (m) 0.06

EPS Compress Ratio 15.6

Nozzle Number 6

Nozzle Diameter (m) 0.000214

Displacement (l) 2.44

In this paper, design starts from the baseline. The speci-fication of baseline is summarized in Table 2.

HIDECS is applied to simulate this engine. The calculatedand the measured in-cylinder pressure trace are com-

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Table 2: Operation conditions of baseline case

Engine Speed (rpm) 1737

Load (% of Maximum) 57

Start of Injection (ATDC) 3.5

Injection Duration (CA) 20.5

Fuel Rate (kg/hr) 6.97

Intake Temperature (Co) 32

Intake Pressure (kPa) 184

Exhaust Pressure (kPa) 181Exhaust Pressure (kPa) 181

EGR rate 0%

pared in figure 7 and show good agreements.

Crank angle

Cylinderpress

ure

-40 -20 0

12

10

8

6

4

2

020 40 60

Measured

HIDECS

Figure 7: Cylinder pressure of base line design

EXPERIMENTS

In this paper, three experiments are performed. Thedesign condition of the first experiment is the same asReference[2] and the second is the same as [3]. In theseexperiments, the target engine is the caterpillar engine.Two step injection is applied in these experiments. In thethird experiment, the caterpillar engine is also targeted,however, the three step injection is applied.

EXPERIMENT 1

Experiment Setup and Design Condition In this experi-

ment, Caterpillar 3400 series Engine is applied that isexplained in the former section. The base line conditionis shown in table2. For this engine, fuel injection shape,boost pressure, and EGR are chosen as design variables.In this experiment, two step injection is performed. To ex-press fuel injection shape, duration angle, dwell betweeninjections, percent of fuel in the first part are used. This isshown in figure9.

In this experiment, dwell between injections and percentof fuel in the first part are design variables. This designsetting is same as Reference[2]. Therefore, there are four

types of design variables. The minimum and maximumvalues of each design variable are described in table3.

Rateo

finjection

Crank shaft angle

Percent of fuelin the first part

Dwell betweeninjections

Figure 9: Description of two step injection shape

Table 3: Range of design variables (Experiment 1)

Item Min Max bit for GA

Dwell between

injections (angle) 0 12 7Percentage offirst part (%) 50 84 7

Boost Pressure(kg/cm2) 1.62 1.83 5

EGR rate 0.0 0.50 5

For NCGA, 24 bits are used for expressing the total designvariables. These bits are explained in table3.

The used parameters for GAs are summarized in table4.

Table 4: GA parameters (Experiment 1)

Population Size 200

Crossover Rate 1.0

Mutation Rate 1/bit length

Terminal Generation 100

Trials 2

Results In figure8, the derived Pareto optimum solu-tions are illustrated. In this figure, the solutions are illus-

trated in three object space. At the same time, solutionsare projected on the surface of two objectives.

In these figures, point B indicates the base line design.Point A is the optimum solution that is derived in Refer-ence [2]. In this reference, the optimum solution is derivedby response surface method.

From these figures, it is obvious that there is trade off re-lation ship between SFC and NOx or Soot and SFC. Onthe other hand, there is no trade off relationship but lin-ear relation ship between SFC and SOOT. It is also fig-

ured out that the base line design is far from the Paretooptimum solution. At the same time, point A is one of

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B

A

B

A

B

A

Figure 8: Pareto Optimum Solutions (Experiment 1)

Pareto optimum solutions. Therefore, the value of NOxis very small. However, the values of NOx and Soot arenot so good. Since the solutions that have good valuesof NOx are weak Pareto optimum solutions in this case,the values of SFC are almost the same. In this condi-tion, to determine the weights that are used to integrateseveral objective functions into one object is very difficult.In Reference[2], the optimum solution is derived thorough

several steps. On the other hand, the Pareto optimum so-lutions are derived at once in this experiment. GAs havestrong search capability to find Pareto optimum solutions.However, GAs need many iterations. Phenomenologicalmodel is a simulator that need not high calculation cost.Thus, by using phenomenological model, GA can performseveral iterations.

In figures10, 11, and 12,fuel injection shapes that provideminimum values of SFC, SOOT, and NOx are illustrated.

Figure 10: Injection Shape that gives minimum SFC (Ex-periment 1)

Figure 11: Injection Shape that gives minimum NOx (Ex-periment 1)

From figure10, it is found that most of fuel should be in-jected at the first part to derive the minimum SFC. Thisis the same for the case where SOOT is minimized. To

Figure 12: Injection Shape that gives minimum SOOT (Ex-periment 1)

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derive the minimum NOx, uniform rate of fuel should beinjected during the injection duration.

Like this way, by solving multi-objective optimization prob-lems, several types of solutions are derived at the sametime. This information is very useful for diesel engine de-signers.

Calculation Time This experiment is performed on thePC cluster. Spec of PC cluster is shown in table5.

Table 5: Spec of PC Cluster

Number of CPUs 64

CPU type Pentium III 933 MHz

OS RedHat Linux 7.1

The total execution time to derive the Pareto optimumsolution is 6602 [s] and each HIDECS call takes 13.91[s]. This calculation time is very small compared to otherdiesel engine combustion simulators. This is a strongcharacteristic of phenomenological model and this featureis fit to GAs.

EXPERIMENT 2

Experiment Setup and Design Condition In this experi-ment, the design conditions are the same as experiment1, but start angle and duration angle of injections are cho-sen as design variables. The fuel injection shape is also

double step injection. The range of design variables issummarized in table6. In this table, the bit for GA to ex-press each design variable is shown. This design condi-tion is the same in Reference[3].



Dwell betweeninjections (angle) 0 12 7

Percentage of Dwellbetween first part (%) 50 80 7

Boost Pressure Dwellbetween (kg/cm2) 1.62 1.83 5

EGR rate 0.0 0.50 5

Start Angle -10.0 10.0 8

Duration Angle 20.5 29.0 5

Results The derived Pareto solutions are described infigure 13.

The tendency of the results is the same as experiment 1.There is trade off relation ship between SFC and NOx.

The fuel injection shapes that give the minimum values ofSFC, NOX, and SOOT are shown in figures 14,15,16.


Figure 15: Injection Shape that gives minimum NOx (Ex-periment 2)

The tendency of the results is also the same as Experi-ment 1. Most of fuel should be injected at the first partto derive the minimum SFC. To derive the minimum NOx,uniform rate of fuel should be injected during the injectionduration.

EXPERIMENT 3

Experiment Setup and Design Condition In this experi-ment, three step injection that is illustrated in figure17 isapplied.

Figure 16: Injection Shape that gives minimum SOOT (Ex-periment 2)

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B

A

B

A

B

A

Figure 13: Pareto Optimum Solutions (Experiment 2)

Rateofinjection

Crank shaft angle

duration angle

rate 1

rate 2

duration 1

duration 2

dwell 1dwell2

Figure 17: Description of three step injection shape

To express this shape, seven parameters are needed. Notonly fuel injection shape but also boost pressure, EGRrate, start angle, duration angle, and swirl ratio are cho-sen as design variables. When the number of designvariables is increased, the search space becomes bigger.This means that users have huge space to design but itis difficult to search optimum solutions. Each range of de-sign variables are summarized in Table7.

Results In figures 18, the derived Pareto optimum solu-tions are described. The tendency of the results is almostsame as experiment 1 and 2. There is trade off relationship between SFC and NOx. There is a linear relationship between SFC and SOOT.

Figure 19,20 and 21illustrate the optimization resultswhich provide the minimum SFC, NOx emission and sootemission respectively. Although three step injection shapeis used as the design parameter, these results suggest

that two step injection may be good enough for the dieselengine economy and emissions optimization.



Duration ofFirst Injection Step 2 5 5

Duration ofSecond Injection Step 6 5

Duration of

Third Injection Step 2 10 5Amount of EachInjection Step (%) 5 5

Amount of Each0.5 degree (%) 8 5

Boost Pressure(kg/cm2) 1.62 1.83 5

EGR rate 0.0 0.50 5

Start Angle -10.0 10.0 8

Duration Angle 20.5 29.0 5

Swirl Ratio 0.0 6.4 5

CONCLUSIONS

In this paper, multi-objective genetic algorithm (MOGA)and phenomenological model are applied for parameter


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REFERENCES

[1] Goldberg, D. E., Genetic Algorithms in search, op-timization and machine learning. Addison-Wesly,1989.

[2] Montgomery, D. T. and Reitz, R. D., Optimizationof Heavy-Duty Diesel Engine Operating ParametersUsing A Response Surface Method, SAE Paper

2000-01-1962, 2000.

[3] Senecal, P.K. and Reitz, R. D., SimultaneousReduction of Diesel Engine Emissions and FuelConsumption using Genetic Algorithms and Multi-Dimensional Spray and Combustion Modeling, SAEPaper 2000-01-1890, 2000.

[4] Yun, H. and Reitz, R. D., An Experimnetal Study onEmissions Optimization Using Micro-Genetic Algo-rithms in a HSDL Diesel Engine, SAE Paper 2003-01-0347, 2003.

[5] Hiroyasu, T., Miki, M., Kamiura, J., Watanabe, S. andHiroyasu, H., Multi-Objective Optimization of DieselEngine Emissions and Fuel Economy Using GeneticAlgorithms and Phenomenological Model, SAE pa-per 2002-01-2778, 2002.

[6] Hiroyasu, H., Miao, H., Hiroyasu, T., Miki, M, KamiuraJ. and Watanabe, S., Genetic Algorithms Optimiza-tion of Diesel Engine Emissions and Fuel Efficiencywith Air Swirl, EGR, Injection Timing and Multiple In-

jections, SAE paper 2003-01-1853, 2003.

[7] Hiroyasu, H., Diesel Engine Combustion and itsModeling, International Symposium on Diagnostics

and Modeling of Combustion in Reciprocating En-gines. Pp.53-75, 1985.

[8] Hiroyasu, H. and Kadota, T., Models for Combustionand Formation of Nitric Oxide and Soot in Direct In-

jection Diesel Engines, SAE Paper 760129, 1976.

[9] Hiroyasu, H., Kadota, T. and Arai, M., Developmentand Use of a Spray Combustion Modeling to Pre-dict Diesel Engine Efficiency and Pollutant Emissions(Part 1, Combustion Modeling), Bulletin of the JSME,Vol.26, No.214, April, 1983.

[10] Hiroyasu, H., Kadota, T. and Arai, M., Developmentand Use of a Spray Combustion Modeling to Pre-dict Diesel Engine Efficiency and Pollutant Emissions(Part 2, Computational Procedure and ParametricStudy), Bulletin of the JSME, Vol.26, No.214, April,1983.

[11] Kuo, T. W., Evaluation of a PhenomenologicalSpray-Combustion Model for Two Open-ChamberDiesel Engines, SAE Paper 872057, 1987.

[12] Nishida, K. and Hiroyasu, H., Simplified Three-Dimensional Modeling of Mixture Formation and

Combustion in a D.I. Diesel Engine, SAE Paper890269, 1989.

[13] Yoshizaki, T.Ishida, K. and Hiroyasu, H. Approachto Low NOx and Smoke Emission Engines by UsingPhenomenological Simulation, SAE Paper 930612,1993.

[14] Imanishi, H. Yoshizaki, T and Hiroyasu, H., Simula-tion Study of Effects of Injection Rate Profile and AirEntrainment Characteristics on D.I. Diesel Engine,SAE Paper 962059, 1996.

[15] Steuer, R. E., Multiple Criteria Optimization: The-ory, Computation, and Application, Wiley, New York,1986.

[16] Ringuest, J. L., Multiobjective Optimization: Be-havioral and Computational Considerations, Kluwer,Boston, 1992.

[17] Cantu-Paz, E., A survey of parallel genetic algo-rithms., Calculateurs Paralleles, 10(2), 1998.

[18] Coello, C. A., Handling preferences in evolution-ary multiobjective optimization: A survey., In 2000

Congress on Evolutionary Computation, volume 1,pages 3037, 2000.

[19] Zitzler, E., Laumanns, M. and Thiele., L. Spea2: Im-proving the performance of the strength Pareto evo-lutionary algorithm., In Technical Report 103, Com-puter Engineering and Communication NetworksLab (TIK), Swiss Federal Institute of Technology(ETH) Zurich, 2001.

[20] Pratab, A., Deb, K., Agrawal, S. and Meyarivan, T., Afast elitist non-dominated sorting genetic algorithmfor multi-objective optimization: NSGA-II., In Kan-

GAL report 200001, Indian Institute of Technology,Kanpur, India, 2000.

[21] Fonseca. C.M, and Fleming, P. J., An Overview ofEvolutionary Algorithms in Multiobjecctive Optimiza-tion, Evolutionary Computation, Vol. 3, No. 1, pp.1-16, 1995.

[22] Watanabe, S., Hiroyasu, T., and Miki, M., Multi-Objective Rectangular Packing Problem and Its Ap-plications,Proceedings of Second International Con-ference on Evolutionary Multi-Criterion Optimization(EMO 03), pp.565-577,2003.

APPENDIX A: PHENOMENOLOGICAL MODEL:HIDECS

In the past 30 years, the most sophisticated phenomeno-logical spray-combustion model, HIDECS has showngreat potential as a predictive tool for both performanceand emissions in a wide range of direct injection dieselengines. It was originally developed at the University ofHiroshima and was named eHIDECSf recently. HIDECSis based on phenomenological model that is explained in

section hoge. In this appendix, some examples of its suc-cessful applications are given in this APPENDEX.

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The code, HIDECS has been validated against wideranges of engine rig experiments. Both the in-cylinderpressure, the emissions formation and the detailed infor-mation of the diesel spray were obtained. Some of themare discussed below.

EXAMPLE 1 YANMAR NFD 170 The in-cylinder pro-cesses of a four-stroke diesel engine, whose details are

shown in table 8, were calculated. The in-cylinder pres-sure was measured under the operation condition in table9. As shown in figure22, the calculated in-cylinder pres-sure via time trace matches well with the measured re-sults.

Table 8: Engine Dimensions

Bore 0.102 m

Stroke 0.105 m

Connecting Rod Length 0.11 m

Cavity Diameter 0.041 m

Number of Nozzle Hole 4

Nozzle Diameter 2.9E-4 m

Table 9: Engine Operation Condition

Intake Air Pressure 101.3 KPa

Intake Air Temperature 298 K

Engine Speed 1800 rpm

Swirl Ratio 2.2

Injection Timing -5 degree

Injection Duration 18

Mass of Injected Fuel 70 mg/stroke

Timing of Intake Valve Close -160 degree ATDCTiming of Exhaust Valve Open 145 degree ATDC

Figure 22: Comparison of the calculated and the measurein-cylinder pressure trace

*: For engine details and the measured results, pleaserefer to SAE paper 1999-01-1502, Effect of High SquishCombustion Chamber on Simultaneous Reduction of NOxand Particulate from a Direct-Injection Diesel Engine, byKidoguchi, Y., Yang, C. and Miwa, K.

EXAMPLE 2 BORE OF 0.135M The in-cylinder pro-cesses of a four-stroke diesel engine, whose details are

shown in table10, were calculated. The in-cylinder pres-sure was measured under the operation condition in

tablereftab:app2-1. As shown in figurefig:app2-1, the cal-culated in-cylinder pressure via time trace matches wellwith the measured results. Figurefig:app2-2 shows thatthe NOx and soot emissions are also well predicted. (Theoriginal data was reported in the SAE paper 930612, Ap-proach to low NOx and smoke emission engines by usingphenomenological simulation, by Takuo Yoshizaki, KeiyaNishida and Hiroyuki Hiroyasu.)

Table 10: Engine Dimensions

Bore 0.135 m

Stroke 0.13 m

Connecting Rod Length 0.15 m

Cavity Diameter 0.09 m


Nozzle Diameter 1.8E-4 m

Table 11: Engine Operation Condition

Intake Air Pressure 101.3 KPa

Intake Air Temperature 298 KEngine Speed 1500 rpm

Swirl Ratio 1

Injection Timing -7 degree ATDC



Timing of Intake Valve Close -145 degree ATDC

Timing of Exhaust Valve Open 145 degree ATDC

Figure 23: Comparison of the calculated and the mea-sured Pressure and heat release

EXAMPLE 3 CATERPILLAR 3400 SERIES The target

engine is a single cylinder version of the Caterpillar 3400series truck engine. The baseline engine operation con-dition was used the same as that of [SAE paper 2000-01-1962, Optimization of Heavy-Duty Diesel Engine Op-erating Parameters Using A Response Surface Method,by Montgomery, D. T. and Reitz, R. D.]. Engine detailsare shown in table12. The in-cylinder pressure was mea-sured under the operation condition in table13. Both thebaseline case and the optimization case of this paper arecalculated by HIDECS. The calculated and the measuredin-cylinder pressure trace are compared in figure25 andshow good agreements.

*: For details please refer to SAE paper 2000-01-1962.

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Table 15: Operating Conditions

Engine Speed 2000 rpm

Load: 4/4

Swirl Ratio 2.6

Injection Timing -9.5 degree ATDC



Timing of Intake Valve Close -150 degree ATDC

Timing of Exhaust Valve Open 130 degree ATDC

Figure 26: Comparison of the calculated and the measurein-cylinder pressure trace

Table 16: Measured Result Calculated ResultMeasured Calculated

Result Result

Power (kW/cylinder) 305.5 305.2

S.F.C. (g/kWh) 185 186

Thermal Efficiency (%) 45.6 42.1

NOx (ppm) 1000 1711

Soot (BSU) 0.2 0.219

Table 17: Engine Specifications

Bore m 0.260

Stroke m 0.385

Connecting Rod Length m 0.705

Cavity Diameter m 0.208

Compression Ratio 15.1


Hole Diameter 10-4 m 0.55

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