Computational Optimization of Internal Combustion Engines

Computational Optimization of InternalCombustion Engines

Yu Shi • Hai-Wen Ge • Rolf D. Reitz

Computational Optimizationof Internal CombustionEngines

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Dr. Yu ShiDepartment of Chemical EngineeringMassachusetts Institute of TechnologyBldg. 66-26477 Massachusetts AvenueCambridge, MA 02139USAe-mail: [email protected]

Dr. Hai-Wen GeEngine Research CenterUniversity of Wisconsin-Madison1500 Engineering Dr.Madison, WI 53706USAe-mail: [email protected]

Prof. Rolf D. ReitzEngine Research CenterUniversity of Wisconsin-Madison1500 Engineering Dr.Madison, WI 53706USAe-mail: [email protected]

ISBN 978-0-85729-618-4 e-ISBN 978-0-85729-619-1

DOI 10.1007/978-0-85729-619-1

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Preface

Striking progress has been made in internal combustion engine design due to thedevelopment of computer models and optimization techniques. In this book westrive to document the state of the art in predictive IC engine modeling andoptimization. The fact that this is an important topic for research and developmentis emphasized by society’s reliance on IC engines for transportation, commerceand power generation. Indeed, the world as we know it would be a quite differentplace were it not for the remarkable internal combustion engine! It drives allmanner of utility devices (e.g., pumps, mowers, chain-saws, portable generators,etc.), as well as earth-moving equipment, tractors, propeller aircraft, ocean linersand ships, personal watercraft and motorcycles. However, its major application ispowering the 600 million passenger cars and other vehicles on our roads today.250 million vehicles (cars, buses, and trucks) were registered in 2008 in the UnitedStates alone. According to the International Organization of Motor VehicleManufacturers, about 50 million cars were made world-wide in 2009, compared to40 million in 2000. Much of this dramatic increase comes from increased pros-perity in China, which became the world’s second-largest car market in 2010. Athird of all cars are produced in the European Union, and about 50% of those arepowered by diesel engines. Thus, IC engine research spans both gasoline anddiesel powerplants.

The world’s economic expansion has been powered by cheap oil. It has beenargued that the increase in population from 1.9 billion in the 1920s to today’s 6.6billion has been made possible, in part, by fossil fuel combustion and by the Ha-ber–Bosch process to make crop fertilizer. 80% of the roughly 80 billion barrels ofcrude oil consumed annually world-wide is used in IC engines for transportation.In the United States, 10 million barrels of oil are used per day in automobiles andlight-duty trucks, and 4 million barrels per day are used in diesel engines, withtotal oil usage of about 2.5 gallons per day per person. Of this, 62% is imported oil,which at today’s $80/barrel, costs the US economy $1 billion/day. This cost iscertain to increase as more-and-more economic development drives increased de-mand for automotive fuels world-wide.

v

Associated with our massive oil use is the accompanying annual emission of 37billion tons of CO2 (6 tons each for each person in the world) and other pollutantemissions, including nitric oxides (NOx) and particulates (soot). Pollutant emis-sions have serious environmental and health implications, and thus most govern-ments have imposed stringent vehicle emissions regulations that are continuallybeing tightened further. In addition, CO2 emissions contribute to Green HouseGases (GHG), which some fear could lead to climate change with unpredictableconsequences. Drastic reductions in fuel usage will be required to make appre-ciable changes in GHG trends.

Today’s gasoline IC engine powered vehicle equipped with its 3-way catalystfor emission control converts only about 16% of the chemical energy in the fuel touseful work—the rest is lost to the environment. The modern automotive dieselengine is 20 to 40% more efficient than its gasoline counterpart. However, mea-sures introduced to meet emissions mandates, such as the use of non-optimal fuelinjection timings, large amounts of Exhaust Gas Recirculation (EGR) or ultra-highinjection pressures reduce diesel engine fuel efficiencies, and also increase engineexpense. Many diesel engine manufacturers have elected to use Selective CatalyticReduction (SCR) exhaust after-treatment for NOx reduction. However, with SCRthere is also a fuel penalty since a reducing agent such as urea (carbamide) must besprayed into the exhaust stream at rates (and cost) of about 1% of the fuel flow ratefor every 1 g/kWh of NOx reduction desired. Soot control is achieved using DieselParticulate Filters (DPF), which generally require periodic regeneration. This isachieved by adjusting the fuel-air mixture strength so as to increase exhausttemperatures to burn off the accumulated soot, which imposes as much as a 3%additional fuel penalty.

From these discussions it is clear that new technologies are urgently needed toimprove the efficiency of both gasoline and diesel engines. For further improve-ments, engines need to be optimized to balance emissions, fuel cost, and marketcompetitiveness. As described in this book, this task can be efficiently attackedusing state-of-the-art computational models and optimization methods. This hasbeen made possible, in part, by dramatic increases in computer speeds that haveincreased 10,000-fold in the past 15 years. Engine development is now greatlyfacilitated using multi-dimensional Computational Fluid Dynamic (CFD) tools andoptimization algorithms, supported by significantly reduced requirements for ex-perimental testing, which is extremely expensive.

An additional enabling factor for engine CFD modeling has been the devel-opment of predictive models for the physical processes occurring in the com-bustion chamber. Many of these models are reviewed in this book, together withdiscussion of strategies to reduce computational cost and numerical inaccuracies.Example applications are presented for the optimization of 2-stroke spark-ignitiongasoline and 4-stroke heavy- and light-duty diesel engines. The effects of designparameters including nozzle design, injection timing and pressure, swirl, EGR,engine size scaling, and piston bowl shape are considered, together with explo-ration of fuel effects for low temperature combustion strategies. It is also dem-onstrated how optimization results can be used in combination with regression

vi Preface

analysis to explore and explain the complex interactions between engine designparameters.

The present example applications also demonstrate that current multi-dimen-sional CFD tools are mature enough to guide the development of more efficientand cleaner internal combustion engines. New low temperature combustion con-cepts, such as Homogeneous Charge Compression Ignition (HCCI), PremixedCharge Compression Ignition (PCCI) and Reactivity Controlled CompressionIgnition (RCCI) offer the promise of dramatically improved engine efficiencies.For example, optimized dual fuel RCCI operation (port injection of gasolinetogether with optimized in-cylinder multiple diesel fuel injections) was discoveredwith computer simulations using the models and tools described in this book(Kokjohn et al. 2009). The computer simulations predicted high-efficiency, low-emissions operation with excellent combustion phasing control at high and lowengine loads without excessive rates of pressure rise. Subsequent engine experi-ments have confirmed the model predictions, and have demonstrated that US EPA2010 NOx and soot emissions mandates can be met in-cylinder without after-treatment, while achieving up to 57% gross indicated thermal efficiency (Kokjohnet al. 2011).

The adoption of RCCI combustion engines could improve fuel efficiencies byup to 20% over standard diesel operation, while also providing dramatic costreductions through the elimination of the need for exhaust after-treatment. RCCI isapplicable with a wide range of fuels, including conventional gasoline and diesel,as well as biofuels such as ethanol and biodiesel and their blends. The implicationsof such improvements in fuel efficiency are very significant. For example, if RCCIwere adopted to replace the relatively inefficient spark-ignition engine it is esti-mated that US transportation oil usage could be reduced by 34%, which equals100% of the current US oil imports from Persian Gulf. If these efficiencyimprovements were combined with electric hybrid technologies in the vehicle,even greater reductions in oil usage would be possible.

The ultimate goal of engine modeling is to guide designers to improve engineperformance and to reduce pollutant emissions. The goal of this book is to providean up-to-date reference to current developments and future directions in the fieldof engine modeling. We hope that you will think that we have achieved this goal.

Preface vii

Acknowledgments

This book expands on recent computational optimization studies of internal com-bustion engines performed at the Engine Research Center of the University ofWisconsin-Madison. The present work would not have been possible without thesolid research foundation that our ERC colleagues have built over the past dec-ades.We would like to express our sincere gratitude to them. During the preparation ofthis book, we also received valuable suggestions from our colleagues, Dr. ShiyouYang, Dr. Yuxin Zhang and Mr. Yue Wang, to whom we are indebted.

The work included in this book was supported financially by several govern-ment and industry research projects. We are grateful to the US Department ofEnergy, Caterpillar Inc., Ford Motor Company, General Motors, and DetroitDiesel Company for their long term support. We also thank Dr. David Wickman ofWisconsin Engine Research Consultants for allowing use of the Kwickgrid soft-ware. ESTECO provided access to optimization software (modeFRONTIER),which facilitated some of the assessment studies in this book.

We thank the Society of Automotive Engineers (SAE), American Society ofMechanical Engineers (ASME), American Chemical Society (ACS), SAGE Pub-lications Ltd., Elsevier, and Taylor & Francis for allowing us to use figures andother materials from previously published articles. We also thank Springer forinviting us to write and helping us to prepare this book.

Finally, we very much appreciate our families for their love, encouragement,support, and their understanding in our lives, in our research work, and in thepreparation of this book.

December 31, 2010 Yu ShiHai-Wen Ge

Rolf D. Reitz

ix

Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Roles of Internal Combustion Engines . . . . . . . . . . . . . . . . . . . 11.2 Modeling of Internal Combustion Engines . . . . . . . . . . . . . . . . 21.3 Computational Optimization of Internal Combustion Engines . . . 4

1.3.1 Engine Optimization with Parametric Studies . . . . . . . . . 41.3.2 Engine Optimization with Non-Evolutionary Methods . . . 71.3.3 Engine Optimization with Evolutionary Methods . . . . . . 9

2 Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.1 Optimization Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.1.1 Comparison of Different Optimization Algorithms . . . . . 152.1.2 Multi-Objective Genetic Algorithms . . . . . . . . . . . . . . . 222.1.3 Genetic Algorithm Source Code and Software . . . . . . . . 26

2.2 Engine Modeling with Computational Fluid Dynamics. . . . . . . . 272.2.1 Governing Equations . . . . . . . . . . . . . . . . . . . . . . . . . . 272.2.2 Physical Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322.2.3 Numerical Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 682.2.4 CFD Codes and Software for Engine Simulations . . . . . . 70

2.3 Regression Analysis Methods . . . . . . . . . . . . . . . . . . . . . . . . . 71

3 Acceleration of Multi-Dimensional Engine Simulationwith Detailed Chemistry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 753.1 Methods for Reducing Mesh- and Timestep-Dependency

in Engine CFD Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 753.2 Efficient Methods for Reaction Mechanism Reduction . . . . . . . . 79

3.2.1 Overview of Reaction Mechanism Reduction . . . . . . . . . 793.2.2 Automatic Mechanism Reduction of Hydrocarbon Fuels

for HCCI Engines Based on DRGEP and PCA Methodswith Error Control. . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

3.3 An Adaptive Multi-Grid Chemistry (AMC) Model . . . . . . . . . . 94

xi

3.3.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 943.3.2 Model Description. . . . . . . . . . . . . . . . . . . . . . . . . . . . 953.3.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . 100

3.4 An Extended Dynamic Adaptive Chemistry (EDAC) Scheme . . . 1053.4.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1053.4.2 Model Description. . . . . . . . . . . . . . . . . . . . . . . . . . . . 1063.4.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . 114

3.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

4 Assessment of Optimization and Regression Methodsfor Engine Optimization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1254.1 Assessment of Multi-Objective Genetic Algorithms . . . . . . . . . . 1254.2 Assessment of NSGA II: Niching Technique, Convergence

and Diversity Metrics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1324.2.1 Design- and Objective-Space Niching of NSGA II . . . . . 1324.2.2 Convergence and Diversity Metrics . . . . . . . . . . . . . . . . 1344.2.3 Assessment of Niching Strategies . . . . . . . . . . . . . . . . . 135

4.3 Assessment of Regression Methods for Replacing CFDEvaluations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

5 Scaling Laws for Diesel Combustion Systems . . . . . . . . . . . . . . . . 1475.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1475.2 Scaling Laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

5.2.1 Combustion Chamber Geometry . . . . . . . . . . . . . . . . . . 1495.2.2 Power Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1495.2.3 Spray Tip Penetration . . . . . . . . . . . . . . . . . . . . . . . . . 1495.2.4 Flame Lift-Off Length . . . . . . . . . . . . . . . . . . . . . . . . . 1505.2.5 Swirl Ratio. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1515.2.6 Summary of Scaling Laws . . . . . . . . . . . . . . . . . . . . . . 152

5.3 Validation of Scaling Laws on a Light-Duty and aHeavy-Duty Diesel Engine . . . . . . . . . . . . . . . . . . . . . . . . . . . 1535.3.1 Engine Specifications . . . . . . . . . . . . . . . . . . . . . . . . . 1535.3.2 Numerical Models. . . . . . . . . . . . . . . . . . . . . . . . . . . . 1545.3.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . 155

5.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175

6 Applications. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1776.1 Engine Optimization with Simple Combustion Models. . . . . . . . 177

6.1.1 Optimization of a 2-stroke Direct-InjectionSpark-Ignited Engine . . . . . . . . . . . . . . . . . . . . . . . . . . 178

6.1.2 Optimization of a Caterpillar Heavy-DutyDiesel Engine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189

6.1.3 Optimization of a DDC Heavy-Duty Diesel Engine. . . . . 210

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6.1.4 Optimization of a High-Speed Direct-InjectionDiesel Engine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218

6.2 Engine Optimization with Advanced Combustion Models . . . . . 2336.2.1 Optimization of a Heavy-Duty Compression-Ignition

Engine Fueled with Diesel and Gasoline-Like Fuels . . . . 2346.3 Strategies for Simultaneous Optimization of Multiple Engine

Operating Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2596.3.1 A Two-Step Method for Simultaneous Optimization

of Multiple Operating Conditions . . . . . . . . . . . . . . . . . 2596.3.2 A Consistent Method for Simultaneous Optimization

of Multiple Operating Conditions . . . . . . . . . . . . . . . . . 2706.4 Coupling of Scaling Laws with Computational Optimization . . . 271

6.4.1 Downsizing of a HSDI Diesel Engine . . . . . . . . . . . . . . 2726.4.2 Optimization of Downsized Engine . . . . . . . . . . . . . . . . 274

6.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280

7 Epilogue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305

Contents xiii

Abbreviations, Nomenclature

AbbreviationsAFR Air-fuel ratioALE Arbitrary Lagrangian–EulerianAMC Adaptive multi-grid chemistryARMOGA Adaptive range multi-objective genetic algorithmATDC After top dead centerBFGS Broyden–Fletcher–Goldfarb–ShannoBML Bray-Moss-LibbyBTDC Before top dead centerCA Crank angleCFL Courant–Friedrichs–LewyCHA ChalmersCI Compression ignitionCDM Continuous droplet modelCFD Computational fluid dynamicsCFM Continuous formulation modelCMC Conditional moment closureCOSSO Component selection and smoothing operatorCSP Computational singular perturbationCTC Characteristic time combustionDAC Dynamic adaptive chemistryDDB Droplet deformation and breakupDDF Droplet distribution functionDDM Discrete-droplet modelDFS Depth first searchDI Direct injectionDICI Direct injection compression ignitionDISC Direct injection stratified chargeDMZ Dynamic multi-zoneDNS Direct numerical simulation

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DOI Duration of injectionDPF Diesel particulate filterDPIK Discrete particle ignition kernelDRG Directed relation graphDRGEP Directed relation graph with error propagationEDAC Extended dynamic adaptive chemistryEGR Exhaust gas recirculationEOI End of injectionEPA Environmental Protection AgencyEPFM Eulerian particle flamelet modelEPO Exhaust port openERC Engine Research CenterEVO Exhaust valve openingFTP Federal test procedureGDI Gasoline direct injectionGISFC Gross indicated specific fuel consumptionHCCI Homogeneous charge compression ignitionHSDI High speed direct injectionHTC High throughput computingHRR Heat release rateILDM Intrinsic low-dimensional manifoldsIMEP Indicated mean effective pressureISFC Indicated specific fuel consumptionIVC Intake valve closureKH Kelvin-HelmholtzKN K-nearest neighborsKR KrigingLDEF Lagrangian-Drop Eulerian-FluidLES Large-eddy simulationLHF Locally homogeneous flowLISA Linearized instability sheet atomizationLLNL Lawrence Livermore National LaboratoryMD Methyl decanoateMDDNPS Mean deviation of the distance between neighbor Pareto solutionsMDEPF Mean distance between extreme Pareto solutionsMDPF Mean distance to the Pareto frontMMF Maximum merit functionMOC Method of characteristicsMOEA Multi-objective evolutionary algorithmsMOGA Multi-objective genetic algorithmMOP Multi-objective optimization problemsNMHC Non-methane hydrocarbonNN Neural networksNPR Non-parametric regressionNPS Number of Pareto solutions

xvi Abbreviations, Nomenclature

NSGA Non-dominated sorting genetic algorithmNVO Negative valve overlapODE Ordinary differential equationPAH Polycyclic aromatic hydrocarbonPCA Principal component analysisPDF Probability density functionPFA Path flux analysisPM Particulate matterPPC Partially premixed combustionPPRR Peak pressure rise ratePRF Primary reference fuelPSO Particle swarm optimizationPSR Perfectly stirred reactorQSOU Quasi-second-order upwindQSS Quasi-steady-stateRANS Reynolds-averaged Navier-StokesRBF Radial basis functionsRBFS R-value-based breadth-first searchRIF Representative interaction flameletRNG Renormalization groupROI Radius-of-influenceRSM Reynolds stress modelRT Rayleigh-TaylorSCRE Single-cylinder research engineSF Separated flowSGS Subgrid-scaleSI Spark ignitionSIMPLE Semi-implicit method for pressure-linked equationsSMD Sauter mean diameterSMR Sauter mean radiusSOC Start of combustionSOGA Single-objective genetic algorithmSOI Start of injectionSR Swirl ratioSS-ANOVA Smoothing spline analysis of varianceTAB Taylor analogy breakupTDC Top dead centerUHC Unburnt hydrocarbonWHEAT Wall heat transferWSR Well stirred reactor

NomenclatureA Pre-exponential constant in Arrhenius equation; areaa Speed of sound

Abbreviations, Nomenclature xvii

ad Drop accelerationB0, B1 Model constants in KH modelBm Spalding mass transfer numberbcr Critical impact parameterC Consumption rate of species in chemical reactionCl, Ce,1, Ce,2 Model constants in k-e modelCs, C3 Discharge coefficientCd Drag coefficientCd, sphere Drag coefficient of the spherical dropCs, CRT Model constants in RT modelCl Liquid specific heatCp Constant pressure heat capacityc Progress variablecps Model constant in dispersion modelD Diffusion coefficient; internal diameter of nozzle; distance

between two dropsDd Drag functiond Diameter; nozzle diameterE Activation energye Specific internal energyF Fitness valueF Forcef Drop distribution function; delay coefficient; friction factor;

response functionf* Discrete drop distribution functionfE Fraction of energy dissipationg Gravity forceH Thickness; lift-off lengthH0 Enthalpy of formationh Specific enthalpyI0 Stretch factor; modified Bessel function of the first kindI1 Modified Bessel function of the first kindJ Roughness of the response function; heat fluxK Heat conductivity coefficient; entrainment constantK0, K1 Modified Bessel function of the second kindKf Rate of forward reactionKr Rate of reverse reactionKc Equilibrium constantk Turbulence kinetic energy; wave number; thermal conductivityL Nozzle length; latent heat; lengthlF Laminar flame thicknesslt Turbulence length scaleM Massm massN Number; engine speed

xviii Abbreviations, Nomenclature

Nu Nusselt numbern Number densityn Unit normal vector_P Momentum source term in wall film modelPe Peclet numberPr Prandtl numberPk Production term for turbulence kinetic energyp Pressure; production rate of species in chemical reactionpatm Atmosphere pressurepv Equilibrium fuel vapor pressure_Q Source terms in energy equation rate of heat conductionQi Energy flux from inside the drop to the surfaceQd Energy flux at the drop surfaceq Rate of progress of the elementary reactionqw Wall heat fluxR Universal gas constant; response function in gas-jet modelRs Swirl ratioRe Reynolds numberr Radius; mass fraction ratio of products to reactantsr32 Sauter mean radiusS0 Entropy of formationSc Schmidt numberSh Sherwood numberSt Stokes numbers propagation flame speed; spray tip penetrationsL

0 Laminar flame speedT TemperatureT Taylor numbert Timetc Time scale in CTC modeltsc Turbulence time scale in CTC model

tper Turbulence persistence timetturb Turbulence correlation timeU Velocityu Fluctuating velocityu* Shear speed in heat transfer modelV Velocity on the sample space (particle velocity)V VolumeVcell Volume of computational cellVcol Collision volumeW Molecular weight_W Source term in turbulence kinetic energy equation

We Weber numberw Width

Abbreviations, Nomenclature xix

X Molar fractionx Spatial locationY Mass fractionYY Random numbery Distortion from sphericityZ Ohnesorge numberZst Stoichiometric mixture fractionz0 Proportion of fuel oxygen to fuel carbona Liquid surface tension coefficientaT Thermal conductivityv Symbol of speciesDt Time stepd Tensorial Kronecker symbolde Unsteady equilibrium thickness of thermal boundary layere Dissipation rate of turbulence kinetic energy/ Progress equivalence ratiog Wave amplitude; compressibility factor for isentropic flowj Model constant in heat transfer modelK Wavelength of the fastest growing wavek Heat conductivity; wave length; smoothness parameterl Viscosityv Stoichiometric coefficientv0 Forward molar stoichiometric coefficientv00 Reverse molar stoichiometric coefficientvl Liquid kinematic viscosityh Liquid volume fractionq Densityql0

Liquid macroscopic denistyR Flame surface densityrw Wall stress tensorr Surface tensionrk, re Model constants in k-e models Viscous stress tensorsv Response time scale in gas-jet modelX Frequency of the fastest growing wavex Chemical reaction rate; complex growth rate of disturbance; rate

of progress of the reaction

Superscript. Time rate of change~ Favre averaged- Time averaged+ Non-dimensional parameters in heat transfer model0 Fluctuating term in time averaging

xx Abbreviations, Nomenclature

00 Fluctuating term in favre averagingb Body forcen Time steps Spray

Subscript0 Standard conditiona Axialacc Accelerationair Airax Axialb Burnt; backward; breakupbu Breakupc Child; convectionch Chemistrycoll Collisioncrit Criticald Droplet; downstreameff Efficienteq Eqivalentexp Expansionf Forward; film; frictiongroup Group in AMC modelh Thickness of liquid sheeti Inertiaimp Impingementinj InjectionKH KH modelk SpeciesL Ligamentl Liquid; laminarlp Less populousmp More populousn Normal direction to the surfacenoz Nozzlep Pressure; piston; parcelplasma Plasmaprec PrecursorRT RT modelr Reaction; reverse; piston ringrel Relativerst Rate-of-strain tensors Species; soot; surface; oil resistancesf Soot formation

Abbreviations, Nomenclature xxi

so Soot oxidationsp Sprayspk SparkT Turbulencet Turbulence; tangent direction to the surfacetot Totalu Unburned; upstreamvap Vaporizationvena Vena contractaw Walls Turbulence? Outer boundary

xxii Abbreviations, Nomenclature

Chapter 1Introduction

The internal combustion (IC) engine is one the greatest inventions since theindustrial revolution. The computer marked the advent of the informational rev-olution. The use of computer models in IC engine design and optimization hassignificantly improved engine efficiency and reduced engine pollutant emissionsover the past decades. In the foreseeable future, computer-aided engine optimi-zation will continue to strengthen the vitality and the role of IC engines in moderntransportation. The present chapter reviews the important role of IC engines andthe challenges that IC engines are facing in terms of sustainability, and theirimpact on the environment is emphasized. We also briefly summarize the currentstatus of engine modeling and review recent progress on computational optimi-zation of IC engines in this chapter.

1.1 Roles of Internal Combustion Engines

Internal combustion (IC) engines have dominated the transportation sector for acentury. The high thermal efficiency and high power output-to-volume ratio aretwo major features that maintain the viability of IC engines as the primary powersource in vehicles. But increasing fuel prices and depleting petroleum reserveshave endangered this viability. Emerging technologies, such as the use of elec-tromotors with high energy density batteries or fuel cells, are expected to playincreasing roles in the transportation sector. Moreover, the US EnvironmentalProtection Agency (EPA) ranks transportation as the second major greenhouse gascontributing sector after power generation (EPA 2010). And IC engines are blamedfor contributing approximately one fourth of the total greenhouse gases that areemitted annually in the US. IC engines are also well-known contributors of nitricoxide and particulate matter emissions. However, the primary role of IC engines isnot expected to be completely replaced by any of these technologies in the nextfew decades. In other words, means have to be sought to improve current IC

Y. Shi et al., Computational Optimization of Internal Combustion Engines,DOI: 10.1007/978-0-85729-619-1_1, � Springer-Verlag London Limited 2011

1

engine designs in order to alleviate ever-increasing energy demands and to reduceharmful pollutant emissions.

Traditionally, spark-ignition (SI) gasoline engines and compression-ignition(CI) diesel engines are employed for light-duty and heavy-duty applications,respectively. The design of an SI gasoline engine is usually lighter and morecompact than that of a CI diesel engine and they also operate quieter, which is ademanding feature of passenger cars. In contrast, diesel engines are more powerfuland consume less fuel per power output than that of gasoline engines, which isdesirable for trucks and off-highway engineering applications. Recent progress indiesel engine downsizing has made diesel engines potential power plants forpassenger cars with better fuel economy and lower pollutant emissions. Dieselengines now share more than 50% of the passenger car market in Europe, and thispercentage is expected to further increase. Recently Gasoline Direct-Injection(GDI) engines have also shown much improved fuel economy and emissionscompared to conventional intake charge SI gasoline engines. This drives the trendthat more new passenger car models are being equipped with GDI engines in theUS market. On the other hand, emerging engine combustion techniques, such asHomogeneous Charge Compression Ignition (HCCI) and Partially PremixedCombustion (PPC), enable more flexible choices of fuels in IC engines. Forexample, Kalghatgi et al. (2007) conducted an experimental study of a heavy-dutycompression-ignition engine fueled with gasoline and diesel and operated at PPCmode. They showed that the gasoline CI engine has better fuel economy and loweremissions than the diesel CI engine. Due to the limited reserve of petroleum fuels,sustainable fuels, such as bio-fuels, are gradually becoming alternative energysources for IC engines. Gasoline with 10% blended ethanol is now a standardpump fuel in many states of the US. It is anticipated that the amount of alternativefuel usage in transportation sector will keep increasing, which will require mod-ifications of current engine designs. In the foreseeable future, new generation ICengines will directly benefit from better engine downsizing approaches, improveddirect-injection systems, advanced in-cylinder combustion techniques, and alter-native fuels. As a result, the future IC engine combustion system will become morecomplicated. Therefore, this book particularly focuses on describing enginecombustion system optimization using state-of-the-art modeling tools with sys-tematic optimization and regression methods.

1.2 Modeling of Internal Combustion Engines

The advent of computers has created a new branch of scientific and engineeringresearch, namely, numerical simulation. The gas exchange and combustion pro-cesses of IC engines are characterized by complex heat transfer, gas dynamics,multi-phase flows, and turbulence-chemistry interactions. IC engine combustionspans multiple regimes that include premixed flame propagation, mixing-con-trolled burning, and chemical-kinetics-controlled processes, which may occur

2 1 Introduction

simultaneously within a single device (Haworth 2005). The task of modeling ICengines is to completely or partly describe these physical and chemical processesusing mathematical models with stable and accurate numerical schemes so that theoutput of the modeling can reveal desirable information about engine cycles.

Early IC modeling studies can be traced back to 1950s when the computingcapability of computers only allowed for efficient calculation of simple mathe-matical formulae. For example, the best known empirical engine model is theWiebe function (Wiebe 1956, 1962), which is used to predict the burn fraction andburn rate. The Wiebe function and its derivatives, such as double Wiebe functions,have since been widely applied in zero-dimensional engine modeling tools. Thehistoric aspects of the Wiebe function were recently reviewed by Ghojel (2010).Progress in engine heat transfer modeling was also made by Woschni (1967) whoproposed the famous Woschni model for engine convective heat transfer calcu-lation. The model formulae and constants were empirically based on many engineexperiments and fundamental heat transfer physics. Such empirical heat transfermodels were reviewed by Finol and Robinson (2006). Studies of that age showedthat the combination of these empirically-based combustion and wall heat releasemodels with well tuned model variables was able to match the pressure traces ofengine experimental measurements satisfactorily.

The infancy of Computational Fluid Dynamics (CFD) in-cylinder enginemodeling started from the 1970s. However, until the 1980s, engine CFD modelingwas not generally applied in engine development due to two facts: first, thecomputer capacity was still a limiting factor; second, general engine CFD code orsoftware was not available. Instead, engine modeling with phenomenologicalmodels was the main stream in this period. For instance, coupling of phenome-nological quasi-steady spray models (Hiroyasu et al. 1978) and soot and NOformation models (Heywood 1976; Hiroyasu and Kodota 1976) largely extendedthe capability of engine modeling tools compared to zero-dimensional simulations.Details of engine phenomenological models of different physical processes havebeen reviewed by Lakshminarayanan and Aghav (2010).

In 1985, a group at the Los Alamos National Laboratory developed an open-source code called KIVA (Amsden et al. 1985) that integrated different compo-nents of engine CFD modeling, including moving meshes, compressible flows,spray and droplet evaporation, and fuel combustion chemistry. KIVA provides anopen source CFD modeling tool for engine reactive flow simulations, which hassignificantly stimulated the development of engine physical and chemical modelssince then. Reitz and Rutland (1995) reviewed various advanced diesel engine sub-models within the framework of KIVA 3 (Amsden 1993) and concluded that theCFD modeling tool was able to match experimental engine pressure traces andheat release well over investigated conditions and good quantitative agreements inNOx and soot emissions were also attainable. With the rapid increase of compu-tational power of personal computers and demands for better simulating advancedengine combustion techniques, detailed fuel chemistry solvers have also become astandard part of many engine CFD tools since 2001 (Kong et al. 2001). Also,flexible mesh generation techniques are found in many commercial engine CFD

1.2 Modeling of Internal Combustion Engines 3

software nowadays, which significantly expedites the complex mesh generationprocess and thus speeds-up the overall engine simulation cycle.

Despite the fact that even the state-of-the-art engine modeling tools normallyhave larger quantitative uncertainties than engine experiments, engine simulationshave some significant advantages over experimental measurements in enginedevelopment and optimization. These advantages include low cost, the ability tostudy a wide range of parametric space, separated physical and chemical pro-cesses, and detailed in-cylinder information, which is normally not available or isinaccessible in experiments. Continuous efforts in the research fields of meshgeneration techniques, numerical methods, heat transfer, turbulence, chemicalkinetics, and multi-phase flows will further improve the predictability of IC enginemodeling tools. Hence, the quantitative prediction capability of the next generationof IC modeling tools should be even better. Chapter 2 reviews current physical andchemical IC engine models in more detail.

1.3 Computational Optimization of InternalCombustion Engines

Engine CFD simulations provide insights about the engine working cycle andpollutant formation. The ultimate goal of engine modeling is to directly guidedesigners to improve engine performance and to reduce pollutant emissions.Computational optimization of IC engines has become more accepted in assistingpractical engine designs. The task of computational optimization of IC engines isto identify optimal combinations of design variables that can achieve minimum ormaximum objective functions of interest. This section reviews recent progress incomputational optimization of IC engines. Representative research from severalrelevant research areas are reviewed, and salient features of these studies aredescribed in three categories as follows.

1.3.1 Engine Optimization with Parametric Studies

Systematic optimization methods are not required for computational optimizationof IC engines. Indeed, optimal solutions can be found through parametric studiesthat extend over the practical range of design variables using modeling tools. Inparametric studies, the number of evaluations needed to achieve the optimalsolutions significantly increases with the number of design variables, which limitstheir applications in complex design problems. The experience and intuition ofengine designers are critically important to efficiently perform such parametricstudies for engine optimization. The interaction of data analysis and experimentalmeasurements can also expedite the exploration of the parametric space in order tolocate optimal designs.

4 1 Introduction

In the study of Sher and Bar-Kohany (2002), a computer program MICE(Modeling Internal Combustion Engines), which featured a semi-empirical gasexchange model, was employed to study the effects of variable valve timings(VVT) on the torque and fuel consumption of a gasoline SI engine. Three designvariables, including the exhaust valve opening, intake valve opening, and intakevalve closing times, were parameterized. Because the evaluation of engine per-formance used a simple modeling tool which was fast, the parametric study wasable to find the optimal combination of valve timings for different engine operatingconditions. They concluded that the optimal timing of each valve depends linearlyon the engine load and speed. Also, when the VVT strategy was applied, themaximum torque at any engine load was shifted towards a lower engine speed. COand NOx phenomenological models were also used in this study, but the con-clusion about the effect of VVT on the emissions was less reliable than the engineperformance because the predictability of semi-empirical modeling tools for pol-lutant formation is normally poor, especially over a wide range of operatingconditions.

Ibrahim and Bari (2008) adopted a similar approach to optimize a natural gas SIengine using a two-zone combustion model. The EGR strategy in a high pressureinlet condition, the compression ratio, and the start of combustion timing wereoptimized in order to obtain the lowest fuel consumption, accompanied with highpower and low NO emissions. They found that the use of 20–30% EGR effectivelysuppressed engine knock and allowed use of high inlet pressure for compressionratios up to 13 and the optimal EGR rate depended on engine speed.

Parametric studies over a full range of three or more design variables normallycreate a large parametric space, which prohibits practical engine optimizationusing computationally expensive CFD modeling tools. In this case, the enginedesigners’ experience and reliable experimental data are very important to narrowdown the parametric space so that parametric studies can still effectively andefficiently seek optimal solutions of interest. This interactive method that involvesboth computational and experimental efforts and human intelligence is usuallyused in production engine development and optimization. For example, in aseries of optimization works, Lippert et al. (2004a, b) and Szekely et al. (2004) atGeneral Motors and Suzuki Motor, demonstrated that parametric studies usingCFD modeling and well-designed experiments significantly enhanced the under-standing of charge stratification, combustion chamber shape, and spray impinge-ment in a small displacement spark-ignition direct injection (SIDI) gasoline engineand thus expedited the overall engine development and optimization process.Through detailed CFD analysis for the SIDI gasoline engine, Lippert et al. (2004a)found that the reverse tumble that accompanies elevated swirl levels, is pivotal inlifting the mixture towards the spark gap; the piston depth strongly affected theengine performance and emissions; and an adequate bowl volume was key tosufficient mixing at higher loads in the part-load operation regime. Based on thesefindings, Szekely et al. (2004) further optimized the combustion chamber for thisreverse-tumble, wall-controlled gasoline direct-injection engine. This was con-ducted by systematically optimizing each design element of the combustion

1.3 Computational Optimization of Internal Combustion Engines 5

system, including piston-bowl depth, piston-bowl opening width, piston-bowl-volume ratio, exhaust-side squish height, bowl-lip draft angle, distance betweenspark-plug electrode and piston-bowl lip, spark plug-electrode length, and injectorspray-cone angle. They varied each design variable independently to investigate itssensitivity to combustion stability, fuel consumption, and emissions. Finally, a fewoptimal piston designs were recommended by interpreting the simulation resultsusing human intelligence and data analysis tools. On the same engine, Lippertet al. (2004b) also identified several key factors that affect the high-load operatingcondition, which can be grouped as those pertaining to volumetric efficiency, tomixing and stratification, and to system issues. The corresponding design vari-ables, such as the injection timings and strategy, the piston and port designs, andthe intake flow structure and swirl level, were studied separately. Consequently, asignificant improvement in fuel consumption and emissions was obtained relativeto the initial baseline engine configuration, and the expected gains in torque andpower over an equivalent port fuel injection (PFI) engine were also achieved.

Similar parametric studies were also applied in CFD upfront optimization of thein-cylinder flow, spray pattern, and piston shape for a Ford 3.5L V6 EcoBoost GDIengine (Iyer and Yi 2009a, b; Xu et al. 2009). In the first phase, Iyer and Yi(2009a) assessed the effects of intake port design and spray injection timings onthe tumble intensity using the MESIM 3D CFD code. By quantification andvisualization of engine tumble flows they concluded that the effect of intake valvemasking was beneficial for improving the air–fuel mixing, especially at part load.Delaying the start of injection timing allowed for the generation of higher tumbleflow that, in turn, generated higher turbulence intensity at TDC. But a too lateinjection timing had a detrimental effect on air–fuel mixing. The study indicatedthat further optimization of the spray pattern and piston geometry was necessary.Thus, the companion study of Iyer and Yi (2009b) concentrated on optimization ofthe spray pattern. The main target of the second phase was to reduce soot emis-sions and to improve engine cold-start stability, which directly correlates withspray mixing and surface wetting.

Three optimal spray patterns were selected from many parametric studies forfurther experimental assessment on a single-cylinder engine. Finally, a singleoptimal spray pattern with a wide spray angle was tested on a multi-cylinderengine with promising results. Xu et al. (2009) focused on the piston geometry ofthe same Ford GDI engine, particularly under engine cold-start conditions. In theirstudy a multi-component spray model was found to be critical to the accuracy ofthe model prediction of the fuel air preparation process under cold start conditions.The CFD modeling methodology with the multi-component spray model wasapplied to optimize the piston top designs. It was found that robust fuel–airmixture formation was the key for stable combustion under the cold start condi-tion. Effects of piston design parameters on fuel air mixture preparation wereinvestigated and a wide bowl design was developed to generate improved mixtureformation. In addition, they showed that smoothing the dome design of the widebowl achieved further improvement of the turbulence intensity at the boostedcondition while maintaining the same cold start performance.

6 1 Introduction

1.3.2 Engine Optimization with Non-Evolutionary Methods

In computational engine optimization with parametric studies, the designers’knowledge and experience are profoundly important in guiding the simulations tosearch for better design variables. This process is inefficient if a large number ofdesign variables needs to be optimized; objective functions are contradicting; andglobal optimization is desirable. Systematic optimization methodologies canovercome these difficulties by replacing human intelligence with automaticsearching methods. The section reviews a few computational optimization workswith non-evolutionary methods.

The performance of non-evolutionary methods relies heavily on spatial infor-mation, such as the gradient of response surfaces of objective functions to designvariables. In real world optimization problems, such response surfaces can be verycomplicated and non-differentiable, which limits the use of non-evolutionaryoptimization methods. This explains why the application of non-evolutionaryoptimization methods is less popular than evolutionary methods in engine researchcommunity. But with some special algorithm treatments, a few studies haverevealed that non-evolutionary methods can also be efficient and effective for somespecific engine optimization problems. For example, Naik and Ramadan (2004)studied the effects of equivalence ratio (mass of injected fuel), injection timing,ignition timing, engine speed, spray cone angle, and velocity of fuel injection onGDI engine performance and HC emissions. Their optimization work onlyinvolved three parameters, i.e., fuel mass injected, ignition timing, and injectiontiming. Optimal combinations of these parameters were obtained in an automatedoptimization process by linking the engine CFD software KIVA and the optimi-zation software VisualDOC with the Sequential Quadratic Programming (SQP)method. The entire optimization was done in two steps. The first step was to seekfor optimal solutions of fuel mass injected and ignition timing for maximum workoutput. The subsequent step was to further optimize the injection timing of theoptimal solutions obtained in the first step to minimize HC emissions. The twoseparated procedures ensure the effectiveness and efficiency of the SQP method inthe engine design problem. Also, that fact that minimization of HC emissions isusually highly correlated with maximization of engine work, reduces the searchingload of the optimization method for multi-objective functions, so that the use ofSQP method was successful in this study.

Tanner and Srinivasan (2005) explored the conjugate gradient optimizationmethod for a non-road direct injection diesel engine optimization. In their con-jugate gradient method, a line search is performed with a backtracking algorithmand the initial backtracking step employs an adaptive step size mechanism whichdepends on the steepness of the search direction (i.e., based on the gradient of theresponse surfaces). The optimization parameters included the start of injection, theinjection duration and the number of nozzle orifices. The objective was to lowerthe engine soot and NOx emissions with simultaneously reduced fuel consump-tion. Because the conjugate gradient method is only capable of optimizing for a


single objective function, a cost function that includes all objective functions hadto be defined in their study. Consequently, three different optimizations werecarried out using different weights and exponents in the cost function. Theydemonstrated that the final optimal solutions and the convergence of the optimi-zation algorithm were sensitive to the choice of the cost function. In all testedcases, less than twenty-five engine simulations were required for an optimum to bereached. This is much more efficient than other engine optimization problems thathave been reported in the open literature. But such high efficiency came with thefacts that the investigated range of the design parameters was relatively narrow,the response surface of the engine performance to the injection parameters was notcomplicated and good initial values were guessed.

In light of their successful optimization study with the conjugate gradientmethod, Tanner and Srinivasan (2009) pointed out that the development of anadaptive cost function strategy for the gradient-based method is necessary. Theadaptive cost function is based on a penalty method such that the penalty term isstiffened after every line search. In this way, the cost function is adaptively cor-related with the searching direction. The optimization method was used toinvestigate an asynchronous split injection scheme, in which the first and thesecond injection were carried out via two orifices that allow for independentparameter optimization, such as the orifice diameter and injection timing. Theyshowed that this asynchronous split injection scheme outperformed the conven-tional split injection method in terms of engine performance and emissions. It wasshown that only about 30 simulations were needed to achieve the optimal solu-tions. They concluded that the adaptive steepest decent method applied to engineoptimization is a computationally very effective tool to explore new optimalinjection strategies, but is only efficient when good enough initial values areavailable.

Jeong et al. (2006) directly adopted a response surface method, i.e., the Krigingmodel to optimize the combustion chamber for a passenger car diesel engine. TheKriging estimator was used to predict the search direction during the optimizationprocess. However, in order to obtain an unknown model variable for the estimator,they reformulated the problem into a sub-optimization process, in which a geneticalgorithm was used. Technically, they developed a hybrid optimization methodthat involves both non-evolutionary and evolutionary methods. In the optimiza-tion, initial sample points were simulated using engine CFD modeling tools basedon piston geometrical parameters that were generated through Latin HypercubeSampling (LHS). Then the points which had a large probability of being optimumwere estimated using the Kriging model, and used as additional sample points toupdate the Kriging model. The method successfully identified two optimal com-bustion chambers out of a total of 48 initial simulations and 43 additional samples.The CO, soot, and NOx emissions, as well as the engine thermal efficiency of thetwo optimal designs were improved compared to the baseline engine configuration.In terms of the total simulations, the method is more efficient than the previouslyemployed evolutionary method, as claimed by the authors. But it should beemphasized that their method only found two optimal solutions, and the use of the

8 1 Introduction

k-means method to search for additional sample points most likely weakens itscapability of reaching the global optimum.

Aittokoski and Miettinen (2008) used a non-differentiable interactive multi-objective bundle-based optimization system (NIMBUS, Miettinen and Mäkelä1995) to optimize the exhaust pipe dimensions for a two-stroke engine. Within theframework of NIMBUS, the optimality of the solutions is not directly evaluatedbased on objective functions. Instead, there is an interaction phase that requires thedesigners’ wishes to classify optimal solutions into five classes at each optimi-zation iteration. Each class reflects the priority of the optimal solutions, the weightof the objective functions, and the target of the designers’ wishes. Any optimi-zation method can fit in this framework, and particularly in the study of Aittokoskiand Miettinen (2008), an extended Controlled Random Search (CRS, Price 1977;Ali and Storey 1994) method was employed. They found that the classification-based interactive method is a convenient way to express designers’ wishes so thatthe designer can guide the solution process within a limited number of objectivefunction evaluations. Therefore, interactive methods may be a good way to reducethe number of objective function evaluations required, and also enable control ofthe solution process.

1.3.3 Engine Optimization with Evolutionary Methods

Compared to non-evolutionary methods, evolutionary methods, such as geneticalgorithms (GA) and particle swarm optimization (PSO) methods, have been morewidely used in computational engine optimization, because these methods aremore generally applicable for optimizing complex non-linear real world problems.For example, Wickman et al. (2001) integrated a single-objective genetic algo-rithm with the engine CFD code KIVA to optimize nine design variables,including piston geometrical parameters, injection patterns, swirl ratio, and EGRrate, for a high-speed direct injection (HSDI) diesel engine and a heavy-duty dieselengine. Although each task took 2–4 weeks for 400 individual simulations, theoptimization method was still deemed to be efficient considering the large searchspace and the complexity of the problem. They found that the small-bore andheavy-duty diesel engines both favored relatively large diameter shallow pistonbowls, long injection durations at high pressure through small holes, and moderateswirl, at medium speed and high load. The optimal start of injection timing andEGR level were very sensitive to the NOx target value chosen. In addition, precisecontrol over the global air/fuel ratio was very important for achieving simulta-neous emissions and fuel consumption reductions.

A similar approach was adopted by Shrivastava et al. (2002) to investigate theperformance and emissions of a diesel engine using variable intake valve actuationwith boost pressure, EGR and multiple injections. Again, the CFD code KIVA wasextended to interface with a 1-D gas dynamic code in order to accurately predictthe engine intake flow. In their study, a total of eight parameters, including SOI,


injection duration, EGR, percentage of total fuel mass injected in first pulse of asplit injection rate shape, dwell in between the pulses of the split injection, boostpressure, and the gas swirl and tumble ratios at Intake Valve Closing (IVC) weresimultaneously optimized to locate solutions with reduced NOx, soot, and UHCemissions, as well as low fuel consumption for two engine speeds and loads. In allcases, the engine emissions and fuel consumption were considerably reduced forthe optimal designs as compared to their baseline values. They also observed thatthe optimal boost pressure was considerably higher compared to the baselinevalue. The increase in boost pressure, in combination with the other variables suchas the multiple injection parameters, led to a considerable reduction in soot for-mation. The high optimal EGR rate led to a drastic reduction in engine-out NOx.The effect of swirl and tumble ratios on emissions reduction was found to be mostprominent at high speed and low load. Finally, longer intake valve open durationsand a higher value of maximum valve lift led to better flow development at IVC.

Chen et al. (2003) also used genetic algorithms to optimize an HCCI engine,specifically for a power generator. In their study, optimal sets of equivalence ratio,EGR rate, intake temperature, and pressure were sought to achieve maximumengine thermal efficiency and torque and minimum NO emissions. The GA opti-mization revealed that a mixture of high equivalence ratio with a large amount ofEGR can be used to achieve high thermal efficiency and low NOx emission. GA-searched results also suggested that variable power demand can be convenientlymet by only adjusting the intake pressure while keeping other conditionsunchanged.

Many studies have also shown that genetic algorithms are helpful in deter-mining proper injection strategies for diesel engines under various operatingconditions. For example, Kim et al. (2005) applied a micro-genetic algorithm tostudy the injection parameters and intake conditions for a heavy-duty dieselengine. They found that the GA optimization efficiently located optimal engineoperating parameters that demonstrated low emissions and improved fuel con-sumption capabilities of a diesel engine. The predicted optimal injection timingwas very advanced, which suggests that HCCI-like combustion is useful for lowemissions diesel engines at the considered mid-load condition. The optimizationshowed that the resulting long ignition delay allowed enough time for mixing andreduced the extent of fuel rich regions. This indicates that high levels of EGR canbe used to control NOx and prevent soot formation. Not surprisingly, the optimalcombustion system recommended by the GA is exactly the premixed chargecompression ignition (PCCI) engine strategy, which has been well accepted by theengine community recently. The powerful capability of GA is thus proven.

Similarly, Bergin et al. (2005) identified a novel spin spray combustionapproach for a heavy-duty diesel engine. The study demonstrated that 2006 non-road emissions targets were met by optimizing the spray events with an injectorthat featured two rows of nozzle holes with asynchronous injection for each nozzlerow. No other means of emission reduction were needed. The spin-spray com-bustion that is realized by injecting two neighbor sprays with different cone anglesat different times creates large recirculation structures that greatly enhance mixing.

10 1 Introduction

The optimal configuration of spray cone angles, injection timing, and split injec-tion amount leads to an optimal combustion event that favors soot oxidation,because the formation and decay of the spin spray combustion recirculationstructure allows a more efficient transfer of energy from the injected liquid spray tothe bulk fluid. In other words, this novel injection approach stores the kineticenergy within the flow field and leads to greater late cycle turbulence with sig-nificantly reduced soot emissions due to the resultant improved mixing. Theenhanced mixing also results in more homogenous combustion, which directlybenefits NOx reduction and thermal efficiency increase.

It should be pointed out that all these studies were based on single objectivegenetic algorithms. For engine optimization with multiple objective functions, asingle merit (cost) function has to be defined to include the multiple real objectivefunctions. However, similar to the problem that was discussed by Tanner andSrinivasan (2005), the formula of such single merit function influences the finaloptimal solutions and algorithm convergence. Unfortunately, definition of anappropriate merit function is usually unclear to designers in the real world opti-mization process. This motivates interest in studies and application of multi-objective evolutionary methods (Deb 2001). These methods are becoming thepredominant approach for computational engine optimization and design. Forexample, Tibaut and Marohni (2006), Kurniawan et al. (2007), and Genzale et al.(2007) are among the pioneers who coupled multi-objective genetic algorithmswith engine CFD simulations for automatic engine design optimization. Thesestudies used different optimization algorithms which were integrated in the com-mercial optimization software iSIGHT, modeFRONTIER, and from a multi-objective micro-genetic algorithm source code, respectively. None of theseresearchers compared the performance of the different multi-objective geneticalgorithms, so information about which method suits computational engine opti-mization best was lacking.

To address this problem, Shi and Reitz (2008a) assessed three widely usedmulti-objective genetic algorithms, namely, l-GA (Coello Coello and Pulido2001), NSGA II (Deb et al. 2002), ARMOGA (Sasaki and Obayashi 2005). Theyapplied the three methods to optimize the piston geometry, spray targeting, andswirl ratio for a heavy-duty diesel engine at high-load with CFD simulations. Theyalso defined four quantities that quantify the performance of the optimizationmethods in terms of the optimality and diversity of the optimal solutions. NSGA IIwith a large population size was found to perform the best in their study. Chapter 4describes this study in more detail.

Jeong et al. (2008) developed a hybrid evolutionary method that includes agenetic algorithm and a particle swarm optimization method. The basic idea camefrom the fact that GAs maintain diverse solutions, while PSO shows fast con-vergence to the optimal solution in multi-objective optimization problems. Theytested the hybrid algorithm using two sets of mathematical functions and showedthat the hybrid algorithm had better performance than either a pure GA or a purePSO. However, due to the high computational cost, the performance of the hybridmethod was not compared with other methods for engine optimization problems.


Shi and Reitz (2008b) extended their previous optimization work (Shi and Reitz2008a) to low-load operating conditions of the same heavy-duty diesel engineusing NSGA II and the engine CFD code KIVA 3v release 2 (KIVA3v2). Bycomparing the optimal solutions of the high-load condition to those of the low-load, they discovered that the high-load operating condition is more sensitive tothe combustion chamber geometrical design compared with the low-load condi-tion. By choosing an optimal combustion chamber design from the high-loadoptimization study and varying swirl ratio, and injection timing and pressure,excellently performing designs were also found using the high-load optimalchamber geometry for the low-load condition. Thus, they suggested that engineoptimization studies for all operating loads should start with an optimization studyof piston geometry and spray targeting for the high-load condition. Further opti-mization on the spray injection event and swirl ratio should then be conducted forthe low-load condition.

In practice, engine optimization over all operating conditions is of moreinterest, but it is also more challenging due to two facts. First, the optimal sets ofdesign variables achieved from an optimization study of a specific operatingcondition are usually not applicable to other conditions. Second, many enginedesign variables are not adjustable under different operating conditions, such as thepiston geometry. To tackle this difficulty, Ge et al. (2010a) proposed a method-ology for engine development using multi-dimensional CFD and computer opti-mization. A multi-objective genetic algorithm NSGA II and the KIVA3v2 codewere used to optimize a light-duty diesel engine. Design parameters of the dieselengine were divided into two categories: hardware design (piston geometry,number of nozzle orifices, injection angle) and controllable design (SOI, swirlratio, boost pressure, and injection pressure). Hardware design parameters wereoptimized first under the full (high)-load condition, as suggested by Shi and Reitz(2008b). Then, the optimal hardware design was fixed for subsequent optimiza-tions of the controllable parameters under different operating conditions. Theyillustrated that with fixed optimal hardware design and optimal sets of controllableparameters for each case, optimal designs which simultaneously reduce fuelconsumption and pollutant emissions were obtained in all cases except for a verylow load case. In addition, strong correlations among the controllable designparameters were not observed, which implies that these controllable parameterscan be optimized separately.

Different from single objective optimization methods, which always lead to asingle global optimal objective function, multi-objective optimization methodsnormally produce many optimal solutions in engine design problems. It is atedious work to analyze such large volume of data using human intelligence.Therefore, the use of regression methods in computational engine optimization isalso desirable. The data-mining process is sometimes equally as important as theoptimization process. In the studies of Shi and Reitz (2008a, b) and Ge et al.(2010a, b), a non-parametric regression analysis method, the COmponent Selec-tion and Smoothing Operator (COSSO) method (Lin and Zhang 2006) was used toestablish the response surfaces of design variables to objective functions. Jeong

12 1 Introduction

et al. (2008) used the Self-Organising Map (SOM), which is a data mining tech-nique using an advanced variant of unsupervised neural networks and clusteringanalysis. Ge et al. (2009a) employed a K-nearest method to analyze a large amountof optimal solutions in an optimization study with a heavy-duty diesel engine. Shiand Reitz (2010a) assessed four regression methods, including K-nearest neigh-bors (KN), Kriging (KR), Neural Networks (NN), and Radial Basis Functions(RBF), for an engine optimization study. They trained these methods using resultsfrom engine CFD simulations and showed that by dynamically training theregression methods during the course of GA optimization, the predicted resultsfrom trained response surfaces agree well with the real CFD simulations. Theperformance of KN and KR methods was better than that of the NN and RBFmethods in their comparative study. This study is also a subject of Chap. 4.

Many studies have proven that engine CFD modeling tools with simplifiedignition and combustion models, such as the Shell/CTC (Characteristic TimeCombustion) model (Kong and Reitz 1993), can be reliable simulators for dieselengine optimization within conventional operating regimes where fuel/air mixingand diffusion flames dominate the combustion and pollutant formation processes(Bergin et al. 2005; Shi and Reitz 2008a, b). The individual simulation using suchapproaches only requires a few hours on the latest personal computers, so thewhole optimization process can be completed within a week or two with multi-objective evolutionary methods, which is highly attractive for industrial optimi-zation designs. But the advanced combustion techniques in modern diesel engines,such as HCCI, PCCI, and Modulated Kinetics (MK), are primarily controlled byfuel chemistry. In this case, accurate engine CFD simulations require a detaileddescription of the chemical kinetics of the fuels. It is not uncommon to find one totwo orders of magnitude increase in the required computer time when solvingdetailed reaction mechanisms in engine CFD simulations compared to usingsimplified combustion models. Therefore, engine optimization using CFD simu-lation with detailed chemistry is generally not practically feasible, given theexcessively long optimization cycle.

Significant efforts have been made recently to accelerate engine CFD simulationswith detailed chemistry, which can be categorized into four major approaches. First,the development of mesh-independent spray models (Munnannur 2007; Abani et al.2008a; Abani and Reitz 2010) enables engine CFD simulations using coarser mesheswithout losing accuracy compared to those of fine meshes (Abani et al. 2008b).Second, multi-zone or multi-grid methods (Babajimopoulos et al. 2005; Shi et al.2009a; Goldin et al. 2009; Liang et al. 2009a) divide computational domains into sub-domains by grouping thermodynamically-similar cells, which largely reduces thecalling frequency to the chemistry solver in engine CFD simulations. Third, efficientparallelization schemes (Shi et al. 2009b) take advantage of the multi-core archi-tecture of latest central processing units. Finally, reaction mechanism reductiontechniques (Lu and Law 2005; Pepiot-Desjardins and Pitsch 2008a; Sun et al. 2010)and the on-the-fly model reduction schemes (Liang et al. 2009b, c; Shi et al. 2010b)greatly decrease the reaction mechanism size needed to describe the chemical kineticsof fuel oxidation and combustion. These methods are described in Chap. 3 in detail.


Cumulative benefits are attainable by combining these methods for enhancingcombustion modeling efficiency, which makes possible computational engineoptimization. It has been shown that by using one or more such chemistry solveracceleration techniques, the optimization cycle using engine CFD simulationwith detailed chemistry can be reduced to approximately one month (Ge et al.2010a, b; Shi and Reitz 2010c). Ge et al. (2010b) studied a HSDI diesel engineoperated at a low-load condition in the MK combustion mode. They optimizedthe engine piston geometry, spray targeting, and swirl ratio with NSGA II andCFD simulations using the full chemistry solver and with the accelerated solverwith the adaptive multi-grid chemistry (AMC) model (Shi et al. 2009a).Although for individual cases, the accelerated chemistry solver introducesapproximation to the full chemistry solver, they found that the optimizationusing the AMC model produced consistent optimal solutions to those of the fullchemistry model, but only cost half the computer time. In an extended study, Geet al. (2010b) used the engine CFD simulations with the AMC model to optimizethe same HSDI engine for a full range of operating conditions. Shi et al. (2010)integrated a on-the-fly mechanism reduction scheme with the AMC model intothe engine CFD simulation software KIVA3v2, which further improved thecomputational efficiency for their optimization study of a heavy-duty compres-sion-ignition engine fueled with diesel and gasoline-like fuels (Shi et al. 2010c).The entire optimization cycle for six tasks was completed within six weeks,which would be six months if the accelerated chemistry solver were not used.This engine optimization work showed that gasoline-like fuels exhibit greatpotential for cleaner combustion than with conventional diesel fuel. Different in-cylinder flow patterns were identified in the optimal engine designs with thedifferent fuels. Due to the diffusion-type combustion, diesel fuel exhibits stag-nation-point dominated flow fields in many optimal cases, while gasoline-likefuels show more volumetric-heat-release-driven flows due to their premixed-typecombustion. The results of the optimization study also indicate that lower octanenumber gasoline-like fuels may be more helpful to improve the controllability ofcompression-ignition engines in the Partially Premixed Combustion (PPC) modeand to reduce engine noise.

To conclude, high-fidelity CFD modeling tools with detailed fuel chemistryenable engine designers to obtain reliable simulation results. Efficient opti-mization methods and accelerated CFD solvers significantly shorten thecomputer time of optimization cycles, which makes the computational opti-mization approach more competitive than experiments. In the rest of the book,we will revisit several of the aforementioned optimization works in moredetail to show that computational optimization of internal combustion enginesis becoming an indispensable part of practical engine designs, and to providean up-to-date reference to developments and future directions in the field ofengine modeling.

14 1 Introduction

Chapter 2Fundamentals

2.1 Optimization Algorithms

In Chap. 1, a survey was conducted of recent computational optimization studiesof engine design using various methods. Most of these optimization algorithms canbe categorized into two classes, i.e., gradient-based methods and gradient-freemethods, or specifically, evolutionary methods.

This section explores the advantages and limitations of these optimizationalgorithms with three mathematical problems. The commercial software mode-FRONTIER (ESTECO 2008) was used to compare different optimization algo-rithms with model problems. The theoretical fundamentals of three multi-objectivegenetic algorithms (MOGA) are discussed in detail, while the assessment of thesethree MOGAs in computational engine optimization is the subject of Chap. 4.

2.1.1 Comparison of Different Optimization Algorithms

For differentiable mathematical functions, their stationary points (where deriva-tives are equal to zero) correspond to local or global optimal solutions. Usinggradient information, gradient-based methods seek such stationary points to locateoptimal solutions. These methods are usually very efficient provided that thesolution space is everywhere differentiable and the local optimum is also theglobal optimum. For example, the classical Broyden–Fletcher–Goldfarb–Shanno(BFGS) method (Broyden 1970), also known as the quasi-Newton method,requires the optimal function be twice continuously differentiable and the neces-sary condition for optimality is that the zero gradient point exists. Two mathe-matical optimization problems are used here to examine the performance of theBFGS method.

The first problem seeks for the maximum value of the product of two sinefunctions, as


15

maxðf Þ; where f ¼ f1 � f2

f1 ¼ sinðp� x1Þ; x1 2 ½0; 1�f2 ¼ sinðp� x2Þ; x2 2 ½0; 1�

ð2:1Þ

Obviously, the function f is everywhere differentiable within the parameterrange [0, 1], as seen the solution space of function f in Fig. 2.1. The problem hasonly one local optimal solution, which is also the global optimum.

The second problem is more complicated than the first one, which seeks themaximum value of the product of four individual functions with respect to twovariables.

maxðf Þ; where f ¼ f1 � f2 � f3 � f4

f1;x1 ¼ sinð5:1p� x1 þ 0:5Þ½ �6; x1 2 ½0; 1�

f2;x1 ¼ exp �4 lnð2Þðx1 � 0:0667Þ2

0:64

" #

f1;x2 ¼ sinð5:1p� x2 þ 0:5Þ½ �6; x2 2 ½0; 1�

f2;x2 ¼ exp �4 lnð2Þðx2 � 0:0667Þ2

0:64

" #ð2:2Þ

The function f in the second problem is also differentiable, but Fig. 2.2 illus-trates that there are total 25 local optimal solutions distributed in the parametricdomain. There exists a single set of the two variables x1 and x2 (near the origin)that reaches the global optimal solution of unity.

The BFGS optimizer in modeFRONTIER 4 was employed to perform theoptimization tasks for both problems. For the first problem, since it has only onelocal and global optimal solution, the BFGS method started with a single randomset of the two input parameters. Figure 2.3 shows that the method found the

Fig. 2.1 One-peak valueproblem

16 2 Fundamentals

optimal solution of unity with only 31 evaluations, which is quite efficient, asexpected.

Technically, one can also start the BFGS method with a single set of inputvariables for the second problem. However, it is almost impossible to obtain theglobal optimal solution with such configuration as it is easy to see that the methodhas a very high chance of converging towards a local (non) optimal point.Therefore, in practice, one always randomly generates multiple initial sets of inputvariables for the BFGS method, and each initial set will eventually lead to eitherlocal or global optimum. Whether the final global optimal solution will be reachedor not strongly depends on the initial guesses. We initialized the BFGS method forthe second problem with 30 randomly generated datasets which are shown inFig. 2.4(a). Unfortunately, none of these initial datasets led to the maximumfunction value of unity within 1,000 evaluations, as illustrated in Fig. 2.4(b). Themaximum value that was found by the method is close to 0.7, but such finding

Fig. 2.2 Multiple peakvalues problem

Fig. 2.3 Function value ofthe one-peak problem usingBFGS method

2.1 Optimization Algorithms 17

comes from one of the ‘‘lucky’’ initial datasets instead of optimization evaluation.It is anticipated from Fig. 2.2 that in order to reach the function value of unity, theinitial guess point has to be very close to the final optimal solution. Otherwise, it iscertain that gradient-based methods will follow the gradient information near otherlocal optimal points and converge to those values. Increasing the number of initialdatasets eventually leads to the BFGS method finding the global optimal solution,but such treatment is very inefficient.

Real world engineering optimization problems, such as IC engine optimization,are normally much more complicated than these two problems. Furthermore, theproblems are most likely not differentiable and the number of local optimalsolutions can also be large, which renders the application of gradient-basedmethods inefficient or impractical for such engineering problems. Methods that donot rely on the gradient information of the optimization problems are needed.Evolutionary optimization methods, such as genetic algorithms and particle swarmmethods, heuristically use the existing input parameters and present solutions todrive their search towards optimal solutions. These methods are distinguished bytheir heuristic methods that are used to determine the search directions. Forexample, genetic algorithms mimic the nature’s evolutionary principles, particu-larly, the ecosystem behavior that obeys the Darwinian idea of ‘‘survival of thefittest’’, and particle swarm methods specifically imitate swarm social behaviors.Strict mathematical proof of the algorithm convergence of these methods is nor-mally hard or impossible to obtain. But, in engineering practice, these methodshave been found to be widely applicable and efficient in optimization problems.The evolutionary methods, especially multi-objective genetic algorithms, areintensively used in this book to explore IC engine optimal designs.

The concept of genetic algorithms (GAs) was first proposed by Holland (1975)and Goldberg (1989) was among the pioneers who suggested use of GAs inengineering problems. GAs are mathematical algorithms that simulate the evolu-tionary processes of ecosystems. Their broad applicability and ease of use and

Fig. 2.4 Results of the second problem (a) Initial datasets of the input variables (b) Functionvalue of the multiple peaks problem using BFGS method

18 2 Fundamentals

global perspective are the primary reason that they have become increasinglypopular in engineering optimization (Goldberg 1989). GA is a simple searchtechnique that utilizes the ‘‘fittest’’ attributes of previously created designs togenerate new designs with the aim of moving the evolution process towards bettersolutions. In this process, the design-space is coded in mathematical expressions(representing ‘‘genes’’), either with binary strings or real numbers, which areevaluated to provide the ‘‘fittest’’ information for the crossover of genes. Geneticalgorithms are usually initialized with several randomly generated designs, and thenumber of the designs that are evaluated in each generation is called the populationsize. The crossover among evaluated designs gives higher possibility to thosedesigns (genes) with better merit to survive to the next generation. Mimickingnatural evolution, random changes of part of the coded design variables (genemutation) are introduced to avoid local optimization and to maintain the diversityof solutions. Therefore, parameters that influence crossover and mutation arecritical to the performance (optimality and diversity) of genetic algorithms. Thereare many methods for gene coding, crossover function, as well as mutation. Thecombination of these methods and additional ad-hoc treatments for specialapplications result in a variety of genetic algorithms. There also exist severaluseful textbooks on different aspects of genetic algorithms. Interested readers areencouraged to refer the studies of Holland (1975), Goldberg (1989), Gen andCheng (1997), and Deb (2001).

Intuitively, optimization problems with a single objective, such as the previoustwo problems, are just degenerate cases of multi-objective optimization problems.But in fact, there are fundamental differences in single-objective and multi-objective evolutionary optimization algorithms, because the heuristic method thatis used to determine the optimality in the problems of these two classes is totallydifferent, as well as the associated algorithm structure. For single-objective opti-mization problems, the definition of optimality is clear and obvious as there onlyexists a single best solution in any stage of the evolutionary process. But for multi-objective optimization problems, objective functions can contradict each other,which results in a pool of optimal solutions that needs to be tracked simultaneouslyby the optimization methods in the evolution.

The notion of ‘‘optimum’’ in multi-objective optimization problems is normallyreferred as the Pareto optimum. The Pareto optimality of a solution indicates thatthere exist no other solutions that simultaneously out-perform the compared solu-tion with all objective functions. Figure 2.5 gives a more visible illustration of thePareto optimum. As it shows, Cases A-D are Pareto optimal cases because none ofthem are out-performed by other cases in this problem with the aim of minimizingboth objectives. This also highlights another terminology, dominance, which isfrequently used in descriptions of MOGAs. One design is said to be dominatedbecause at least one of its objectives is worse than other cases. Obviously, designsA-D are not dominated by other cases. However, designs E-H are dominated cases.Based on the relationships between dominated and dominating, the cases that arenot dominated by others can be grouped together, and the group in the objective-space where all Pareto optimal solutions are located is called the Pareto front.


Discussion about the algorithm details is deferred to the next section wherethree popular multi-objective genetic algorithms are described. Here, we apply asingle-objective optimization algorithm micro-GA (Senecal 2000) to redo theprevious two problems, and the results are shown in Figs. 2.6 and 2.7,respectively.

Compared to the gradient-based BFGS method for the first problem in Fig. 2.3,the single-objective genetic algorithm micro-GA is slightly less efficient as itapproached the maximum function value at the 38th evaluation. But for the secondproblem in which the BGFG failed to find the optimal solution with 1,000 eval-uations, micro-GA was able to locate the solution with only 331 evaluations. Thisindicates the superior feature of this evolutionary method for optimizing theproposed complex mathematical function.

In principle, single-objective genetic algorithms can also be used to studymulti-objective problems, because any number of objective functions can begrouped into a single merit function. However, the different expressions of the

Fig. 2.5 Definition of Paretooptimum

Fig. 2.6 Function value ofthe one-peak problem usingmicro-GA

20 2 Fundamentals

single merit function usually lead to different performance of SOGAs. Unfortu-nately, in most cases, such definition is unknown prior to completely solving theoptimization problem. We again resort to a mathematical model to examine this,which forms the third problem with two objective functions (Deb 2001).

f1 ¼ x1

g ¼ 2:0� Expð�ðx2 � 0:2Þ=ð0:004Þ2Þ � 0:8Expð�ððx2 � 0:6Þ=0:4Þ2Þf2 ¼ g=x1

x1; x2 2 ½0:1; 1�

ð2:3Þ

In this problem, the task of the optimization method is to seek the smallestpossible f1 and f2 values. With the single-objective genetic algorithm (micro-GA),the present problem can be easily transformed to seek the maximum value of amerit function whose denominator includes both f1 and f2. Two expressions, i.e.,1=ðf1 þ f2Þ and 1=ð2f1 þ f2Þ, were used by assigning different weights to f1 in themerit function. It is seen in Fig. 2.8 that by assigning more weight to the f1 in themerit function, the final optimal solutions are better than those of assigning equalweights to both f1 and f2, although fewer Pareto solutions were found out of thetotal 2,000 evaluations.

Therefore, the use of a single-objective genetic algorithm approach in multi-objective optimization problems is undesirable because the definition of theobjective function can result in large uncertainties in the final optimal solutions. Toillustrate this, we employed the multi-objective optimizer Non-dominated SortingGenetic Algorithm (NSGA II) in modeFRONTIER to solve the third problem, andthe optimal results are reported in Fig. 2.9. The figure shows that there exists onlyone Pareto front and also more Pareto solutions were found by NSGA II.

IC engine optimization typically involves multiple objectives, such as emis-sions reduction and fuel consumption improvement. With this in mind, the rest of

Fig. 2.7 Function value ofthe multiple peaks problemusing micro-GA


CONVERGE2

Highlight

the book focuses on multi-objective genetic algorithms. In the next section, threepopularly used MOGAs are described with respect to their salient features andlimitations.

2.1.2 Multi-Objective Genetic Algorithms

A considerable number of MOGAs have been proposed in the past, among whichthe micro GA or l-GA (Coello Coello and Pulido 2001), Non-dominated SortingGenetic Algorithm II (NSGA II) (Deb et al. 2002) and Adaptive Range Multi-objective Genetic Algorithm (ARMOGA) (Sasaki and Obayashi 2005) have been

Fig. 2.8 Multi-objectiveoptimization problem usingsingle-objective micro-GAwith two merit functions

Fig. 2.9 Multi-objectiveoptimization problem usingmulti-objective NSGA II withtwo objective functions

22 2 Fundamentals

CONVERGE2

Highlight

applied to many engine optimization problems (Genzale et al. 2007; Shi et al.2008a). The three MOGAs share a common feature that an elite-preservingoperator is utilized i.e., the genetic algorithms allow the parents to compete withtheir offspring and elite designs have opportunity to be directly carried over to thenext generation. It has been proven that GAs converge to the global optimalsolution for some functions in the presence of elitism. Moreover, the presence ofelites enhances the probability of creating better offspring (Deb 2001). We areparticularly interested in the performance of these MOGAs in the computationaloptimization of IC engines. The discussion of the technical details of each algo-rithm and the associated complicated tests are beyond the scope of this book. Here,we only introduce the major features of these three genetic algorithms and theirapplication in an engine geometry optimization will be assessed in Chap. 4.

The major feature or advantage of the multi-objective l-GA proposed by Co-ello Coello and Pulido (2001) is that it only needs a very small population size.The smaller population size indicates that it requires fewer computers to completea generation, which is suitable for the situation when computing resources arelimiting. Normally, using small population size may lead to less diversified opti-mal solutions, but the l-GA employs a reinitialization process, combined with anexternal file to store non-dominated cases previously generated, as well as anadditional efficient mechanism to keep diversity. Coello Coello and Pulido (2001)showed that a l-GA carefully designed is sufficiently able to produce the Paretofront of multi-objective optimization problems.

Differing from other MOGAs, the population memory of the l-GA is dividedinto two parts: a replaceable and a non-replaceable portion. They are initially fedby randomly generated populations for the first optimization cycle, and the non-replaceable portion will keep its initial populations during the entire run. Thereforethis algorithm induces an additional variable, which is the percentage of eachportion to be predefined for the optimization problem. l-GA employs conventionalgenetic operators for each cycle, such as tournament selection, two-point cross-over, uniform mutation, and elitism. At the end of each cycle, two non-dominatedpopulations (if there are two or more, otherwise, only one is selected) are com-pared with the external memory and the replaceable population memory, and ifeither of them or both dominate any population in the compared populationmemories, the dominated population will be replaced. In this way, both theexternal and the replaceable memory will tend to have more non-dominated cases.Some of the replaceable populations will be used as initial populations to start anew evolutionary cycle.

There are three types of elitism involved in the l-GA which are described indetail by Coello Coello and Pulido (2001). The technique of selectingnon-dominated populations discussed above is to make the evolution converge tothe true Pareto front. In order to keep diverse solutions distributed on the Paretofront, an approach similar to the adaptive grid proposed by Knowles and Corne(2000) is also employed in l-GA. Briefly the selection of non-dominated solutionsis based on their locations in the objective-space once the defined limit of theexternal memory has been reached, and the less crowded regions are given higher


CONVERGE2

Highlight

preference. This procedure also induces two extra parameters for the optimizationproblem, which are the expected size of the Pareto front and the number ofpositions that determines how to divide the objective-space for each objectivedefined by the user. In general, l-GA focuses on the utilization of elitism toconverge the optimization process, and reducing the population size and keepingdiverse solutions by preserving the initial randomicity and judging the locations ofsolutions.

Motivated by the fact that elitism helps achieve better convergence in multi-objective evolutionary algorithms (MOEAs), Deb et al. (2002) proposed a newelitist non-dominated sorting GA, the Non-dominated Sorting Genetic Algorithm(NSGA II). NSGA II employs both the elite-preserving strategy, as well as anexplicit diversity-preserving mechanism. The evolution process of NSGA II is thatit first randomly generates a predefined size (N) population, which undergoesconventional selection, crossover, and mutation procedures to produce offspringfor the next generation. From the second generation, the parent generation (size N)competes with its offspring generation (size N) to introduce elitism. In this pro-cedure, the crowding tournament selection is used and two rules are applied to theselection operator: (1) Solutions with higher ranks are given preference to beselected; (2) If they have the same rank, the less crowding distances cases areassigned higher priority.

Figure 2.10 illustrates the concepts of rank and crowding distance. As shown,solid circles dominate other cases. However, they do not dominate each other, andthus they form a non-dominated front defined as the first rank. The same procedurecan be applied to the rest of the solutions to find the second rank and so on untilevery solution is assigned a rank. The crowding distance is defined by the averagedistance of a solution to its nearest neighbors. For example, the crowding distanceof solution i in Fig. 2.10 is the average side-length of the rectangle (the dashedbox). The mathematical definition of the crowding distance can be also applied to

Fig. 2.10 Definitions of theRank and the CrowdingDistance

24 2 Fundamentals

higher dimensions, although it is only shown in a 2-D plot for a clear view.Therefore, N populations will be selected from 2N combined populations based onthe aforementioned competition rules. These N populations will later undergoconventional selection, crossover, and mutation to complete an optimization cycle.It is the elitism that makes the GA converge to the optimal solutions and theassistance of the explicit crowding distance maintains the diversity of solution. Inaddition, the crowding distance concept needs no extra user defined nichingparameter (such as dshare) that is used by many other MOGAs, such as theARMOGA discussed next.

An adaptive range technique was proposed by Arakawa et al. (1998). Sasakiand Obayashi (2005) extended and improved the method with a MOGA that issimilar to the one proposed by Fonseca and Fleming (1993) in order to reduce thenumber of evaluations. The idea is that instead of searching the predefined design-space, an adaptive range, based on the statistical study of the distribution of thepreceding optimized solutions is utilized as the search range for the optimizationcycle. The starting generation is determined by the user. ARMOGA focuses itssearch on a concentrated promising design-space where most of the potentialoptimal solutions are located, giving fast convergence to the Pareto front. Math-ematical descriptions of the statistical method of determining the adaptive rangeare given by Sasaki and Obayashi (2005).

It is apparent that the implementation of range adaptation for the design spacecontradicts the goal of achieving diverse optimal results to a certain degree.Therefore, techniques that aim to distribute optimal solutions uniformly need to beapplied to ARMOGA. Similar to NSGA II, a rank is assigned to each individual.However, instead of using the rank and the explicit crowding distance directly,ARMOGA uses a fitness function with the assistance of the standard sharingapproach to determine the preference of population of being selected for the nextGA operation and thus for the next generation. The fitness value of each popu-lation is calculated from

Fi ¼ N �XRi�1

k¼1

lðkÞ � 0:5 ðlðRiÞ � 1Þ; ð2:4Þ

where N is the number of solutions, and lðRiÞ is the number of solutions in rank Ri.The fitness value is then weighed divided by the niche count:

F0i ¼ Fi=nci; ð2:5Þ

where the niche count is calculated from a sharing function

nci ¼XN

j¼1

shðdijÞ; ð2:6Þ


shðdijÞ ¼1� dij

dshare

� �ashare

dij\dshare

0 others

:

0B@ ð2:7Þ

dij is the normalized distance summation between population i and j, which is as

dij ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXM

k¼1

f ik � f j

k

uk � lk

vuut ; ð2:8Þ

where uk and lk are the maximum and minimum k objective values in the presentgeneration respectively, and M is the total number of objectives. Finally, theniching parameter dshare is defined in

ð1þ dshareÞM � 1 ¼ N � ðdshareÞM; ð2:9Þ

and a similar sharing parameter ashare is user-defined. Thus, if the distance betweentwo populations is lower than dshare, then the niche count increases to reduce thefitness of the solution, and thus the diversity is preserved. In addition to the nichingtechnique, ARMOGA also improves the real-coding method detailed in the studyof Sasaki and Obayashi (2005). Other than the above features, ARMOGA usesconventional GA operators.

Engineering optimization problems are usually subject to many constraints,such as cost, mechanical stresses, and so on. These constraints should be handledduring the course of the evolutionary optimization process. An easy and often usedtreatment is to mark designs that violate user-defined constraint(s) as infeasibledesigns, and their representative features are not allowed to participate in cross-over and therefore thrown out from the current optimization generation. Thismethod is effective in removing infeasible designs from the optimal solution pool.It is employed in all three MOGAs discussed above and in this book. However, themethod can be too destructive under the circumstance that some infeasible designsactually can have many merits, especially those boundary designs that onlyslightly violate constraints but with optimal objective functions. In this case, aremedy is needed to recover those designs. Therefore, constraint handling meth-odologies are also an important subject of evolutionary optimization methods, anddetails are discussed in the textbook of Deb (2001).

2.1.3 Genetic Algorithm Source Code and Software

Since Holland introduced the concept of genetic algorithm in 1975, various geneticalgorithm methods have been proposed and many of them have been coded inpopular programming languages. For example, the NSGA II C code that isintensively used throughout this book can be downloaded from the Kanpur Genetic

26 2 Fundamentals

Algorithms Laboratory website (http://www.iitk.ac.in/kangal/codes.shtml). Inaddition, the Illinois Genetic Algorithms Laboratory also provides different geneticalgorithm packages, which are available at http://www.illigal.uiuc.edu/web/. Thegenetic programming community is dedicated to developing evolutionary algo-rithm based tools for different optimization problems. The websites http://www.geneticprogramming.com/ and http://www.genetic-programming.com/ have col-lected useful information in this field.

Usually, these genetic algorithm source packages can be used as black-boxes.The easiest way to interface between the optimization source code and users’ ownprogram is to use file input/output operations and operating system scripts. This isbecause in most optimization problems, the evaluation of the problem itself ismuch more time consuming than the optimization methods and I/O operations.However, for real-time optimization problems, an interface in source code level isnecessary. In the computational optimization of IC engines, the computation costof the engine CFD simulations is much greater than the overhead due to geneticalgorithms. So, in this book Linux shell scripts are employed to communicate theengine CFD results and the genetic algorithm via I/O operations.

Other than source packages, there also exist many commercial software codes,and among them modeFRONTIER produced by ESTECO is widely used in bothindustry and academia. Commercial optimization tools provide integrated envi-ronments that facilitate the whole process of design optimization, such as Designof Experiments, optimal solution search, as well as statistical analysis. This bookbenefits from such software when different MOGAs are compared for engineoptimization problems, which will be discussed in Chap. 4.

2.2 Engine Modeling with Computational Fluid Dynamics

IC engine combustion is a complex process that involves several strongly coupledphysical and chemical processes. The whole procedure is usually decomposed intoa number of parts: liquid-phase spray dynamics, gas-phase fluid dynamics, andgas-phase chemical kinetics. Each part is described by corresponding mathemat-ical formulations. After applying appropriate physical models, the governingequations are solved using numerical methods. In this section, the governingequations for the gas-phase and liquid-phase flows are presented. The corre-sponding physical models and numerical methods are also described. More detailsof the governing equations and spray models are given by Reitz (2006).

2.2.1 Governing Equations

The motion of a gas-phase flow is described using the Navier-Stokes equations. Thegas mixture consists of multiple species. The continuity equation for species k is


oðqYkÞot

þ oðqYkUjÞoxj

¼ o

oxjqD

oYk

oxj

� �þ _xk þ _qs

k; ð2:10Þ

where Yk is the mass fraction of species k, q the total mass density of the mixture,and U is the fluid velocity. D is the single diffusion coefficient with the assumptionof Fick’s Law diffusion. _xk and _qs

i are source terms due to chemical reaction andspray evaporation/condensation, respectively. Summing Eq. 2.10 over all speciesyieds the continuity equation for the whole gas flow:

oqotþ oðqUjÞ

oxj¼ _qs: ð2:11Þ

The momentum equations for the gas-phase mixture is

oðqUiÞot

þ oðqUiUjÞoxj

¼ �op

oxiþ osij

oxjþ Fs

i þ Fbi ; ð2:12Þ

where p is the pressure of the mixture. s is the viscous stress tensor:

sij ¼ loUi

oxjþ oUj

oxi� 2

3oUk

oxkdij

� �; ð2:13Þ

where d is the tensorial Kronecker symbol:

dij ¼1 : i ¼ j

0 : i 6¼ j

(ð2:14Þ

Fsi is a spray induced source term. Fb

i is the body force, which is usually thegravitation force and equals to qg.

The energy conservation equation can be expressed in terms of energy,enthalpy, sensible energy, or sensible enthalpy. In this book, we take sensibleenergy, which is the specific internal energy exclusive of chemical energy, as theprimary physical quantity describing the energy of the gas phase. Its transportequation is

oðqeÞotþ oðqeUjÞ

oxj¼ �p

oUj

oxjþ oJj

oxjþ _Qs þ _Qc; ð2:15Þ

where e is the sensible energy. The heat flux Jj is the sum of contributions due toheat conduction and enthalpy diffusion:

Jj ¼ �KoT

oxj� qD

XNs

k¼1

hkoYk

oxj: ð2:16Þ

_Qs and _Qc are the source terms due to spray and chemical reaction, respectively. Ns

is the total number of species.

28 2 Fundamentals

Assuming an ideal gas, the state equation is used to relate pressure and density:

p ¼ qRTXNs

k¼1

Yk

Wk; ð2:17Þ

where Wk is the molecular weight of the k-th species.To accurately simulate a chemical reaction system, elementary reactions should

be taken into account. Consider the system consisting of Ns species and Nr

elementary reactions. The elementary reactions are written in a general form as:

XNs

k¼1

m0kjvk �XNs

k¼1

m00kjvk; j ¼ 1; . . .;Nr; ð2:18Þ

where vk is the symbol for the k-th species; m0kj and m00kj are forward and reversemolar stoichiometric coefficients, respectively. m0kj and m00kj are integer numbers forelementary reactions and may be non-integers for non-elementary reactions. Eachreaction fulfills element and mass conservation. The mass reaction rate of the k-thspecies is the sum of the reaction rates of all reactions involving this species:

_xk ¼XNr

j¼1

_xkj ¼ Wk

XNr

j¼1

mkjqj; ð2:19Þ

where mkj ¼ m00kj � m0kj is the overall stoichiometric coefficient of the k-th species inj-th reaction. The rate of progress of the j-th reaction qj is written using the molarconcentration ½Xk� ¼ qYk=Wk

qj ¼ Kfj

YNs

k¼1

½Xk�m0kj � Krj

YNs

k¼1

½Xk�m00kj ; ð2:20Þ

where Kfj and Krj are the forward and reverse rates of the j-th reaction, respec-tively. Kfj is usually computed using the empirical Arrhenius law:

Kfj ¼ AfjTbj exp � Ej

RT

� �ð2:21Þ

The pre-exponential constant Afj, temperature exponent bj, and activationenergy are given by the chemical kinetic scheme. The reverse rate is related to theforward rate through the equilibrium constant by

Krj ¼ Kfj=Kcj: ð2:22Þ

And the equilibrium constant Kcj is determined from

Kcj ¼patm

RT

� �PNs

k¼1mkj

expDS0

j

R�

DH0j

RT

!; ð2:23Þ

2.2 Engine Modeling with Computational Fluid Dynamics 29

where DS0j and DH0

j are the change of specific entropy and enthalpy of j-threaction, respectively:

DS0j ¼

XNs

k¼1

mkjS0k ; ð2:24Þ

DH0j ¼

XNs

k¼1

mkjH0k : ð2:25Þ

Theoretically, the liquid phase can also be described using the Navier-Stokesequations in a detailed way. However, its interactions with the gas-phase flow areextremely complicated due to the large differences in time scales and length scales.The first question to be answered in the two-phase flows is how to couple thecarrier and dispersed phases. The simplest way is a one-way coupling whichpredicts the dispersion behavior of transported discrete particles within a giventurbulent gas flow (carrier phase ? dispersed phase). The effects of dispersedparticles on the carrier phase are neglected. However, such effects are not negli-gible in many cases. The turbulence modifies dispersed particles behavior, which,in turn, modifies turbulence, because micro turbulence is produced due to thepresence of the particles. At the interface of the particles, gas phase boundarylayers and wakes develop because of relative motion between the particle centerand the carrier phase. If there is heat and mass transfer between the particles andcarrier phase, which is common in spray flows, two-way coupling must be used(carrier phase$ dispersed phase). Furthermore, when the particle number densityis sufficiently large and the effect of the particle–particle interaction cannot beneglected, four-way coupling must be used (carrier phase $ dispersed phase $dispersed phase). For IC engine simulation, the effects of droplet interactionscannot be neglected and thus four-way coupling is usually considered.

The locally homogeneous flow (LHF) model neglects the slip effect betweenthe liquid phase and gas phase. The two phases are in dynamic and thermodynamicequilibrium. At each point in the flow field, they have the same velocity andtemperature. LHF condition is the limiting case with infinitely small droplets. Totake into account the effects of the finite rate transport between the two phases, theseparated flow (SF) model has been proposed. In general, there are three differentapproaches in the SF model: the discrete-droplet model (DDM); the continuousdroplet model (CDM); and the continuous formulation model (CFM). CDM isapplicable only when a few phenomena must be considered. Otherwise, thecomputational cost will be very high. CFM treats the two phases as continuousphases and solves both of them with an Eulerian formulation. It is referred to as an‘‘Eulerian approach’’ in mathematics, distinguishing it from the ‘‘Lagrangianapproach’’. It takes the dispersed phase as a continuous fluid and introduces severalcontinuous scalar fields to represent the dispersed phase. Quantities relevant to thedispersed phase are defined at nodes, which are generally coincident with thoseused for the continuous-phase grid, and the mean field equations are derived for

30 2 Fundamentals

both phases. Therefore, the dispersed phase is modeled at the macroscopic levelwith this approach. This method leads to significant difficulties in modelingcomplex phenomena such as droplet breakup, droplet interaction, and dropletevaporation, which are essential in IC engine applications. It is also very difficultto establish the representation of the turbulent stresses and transport in the liquidphase.

DDM corresponds to another category: the ‘‘Lagrangian approach’’, which isperformed at a mesoscopic level. In the DDM, the spray is represented by a finitenumber of droplet groups. The motion and transport of these droplet groups aretracked through the flow field using a Lagrangian formulation. The mean quan-tities of the liquid phase are computed through statistical methods. The effects ofthe liquid phase on the gas phase are considered by introducing appropriate spraysource terms into the governing equations of the gas phase. It is convenient for theDDM to construct physical model and numerical algorithms. Thus the Lagrangianapproach dominates current CFD simulations of two phase flows. All the simu-lations in the present book use the Lagrangian approach for the liquid phase (i.e.,the ‘‘Eulerian-Langrangian’’ or ‘‘Lagrangian-Drop Eulerian-Fluid’’ approach forthe two phase flow) and thus only this approach is discussed. This approachassumes that after primary breakup the formed droplets are small enough to beviewed as point sources. Thus, spray dynamics can be described by the sprayequation (Williams 1958), in which the spray is represented by a droplet distri-bution function (DDF), f . All of the droplet properties are considered in the DDF:

f ¼ f ðVd; rd; Td; y; _y; x; tÞ; ð2:26Þ

where x, Vd, rd, and Td are the spatial location, velocity, equilibrium radius (theradius that the droplet would have if it were spherical), and temperature of thedroplet, respectively. y and _y are distortion from sphericity and its time rate ofchange. This droplet distribution function is defined in such a way thatfdVddrddTddyd _y is the probable number of droplets per unit volume at position xand time t with velocity in the interval ðV;V þ dVÞ, radii in the intervalðrd; rd þ drdÞ, temperature in the interval ðTd; Td þ dTdÞ, and displacementparameters in the intervals ðy; y þ dyÞ and ð _y; _yþ d _yÞ. The first moment of f is thenumber density of the droplets:

n ¼Z

fdVddrddTddyd _y: ð2:27Þ

The second moment about radius rd relates to the liquid volume fraction h andliquid macroscopic density q0l:

h ¼Z

43pr3fdVddrddTddyd _y; ð2:28Þ

q0l ¼Z

43pr3qdfdVddrddTddyd _y: ð2:29Þ


The time evolution of f is obtained by solving the spray equation:

of

otþrx � ðf VdÞ þ rV � ðf FÞ þ o

ordðf _rdÞ þ

o

oTdðf _TdÞ

þ o

oyðf _yÞ þ o

o _yðf€yÞ ¼ _fcoll þ _fbu; ð2:30Þ

where F, _rd, _Td, and €y are the time rates of changes of an individual drop’svelocity, radius, temperature, and oscillation velocity _y.

2.2.2 Physical Models

The equations presented in Sect. 2.2.1 cannot be solved directly due to theircomplexity. Physical models are required to simplify the equations or to facilitatetheir numerical solution. In this section, common physical models used in modernCFD simulations of internal combustion engine are summarized.

2.2.2.1 Turbulence Models

Turbulence is the most challenging part of the fluid mechanics, and the onlyunsolved one of the six classical physics problems. A widely accepted conceptabout the turbulence is Kolmogorov’s turbulence law (Kolmogorov 1991).According to his theory, large scale turbulent fluctuations are generated by themean flow through the Reynolds stresses. These large fluctuations give rise tosmaller scales through the same inertial mechanism. When the scale becomessmall enough, the turbulence kinetic energy is converted to heat by the viscousstresses. Thus the whole turbulence process covers a wide rage of length and timescales in physical space, and correspondingly a broad spectrum in wave numberspace. Both the smallest length and time scales, that are called the Kolmogorovscales, are proportional to Re�3=4. As the turbulence scale decreases, the turbulentmotion becomes more independent of the large eddies and locally isotropic. Theturbulence is then characterized by the kinetic energy dissipation rate.

Theoretically, any turbulent flow can be accurately simulated using directnumerical simulation (DNS), which resolves the smallest time and length scales,i.e., Kolmogorov scales. Each simulation produces a single realization of the flow.The total grid number in 3D is therefore proportional to Re9=4. The total time stepis proportional to Re3=4. Thus, the total computational cost is proportional to Re3.Engineering flows usually have very large Reynolds number. Therefore, DNS ofengineering flows is practically unacceptable. It may take several thousand yearsfor a powerful parallel computer to simulate 1 second of flight of an airplane usingDNS (Moin and Kim 1997). The computational cost of DNS will be significantly

32 2 Fundamentals

increased when chemical reaction and/or multiphase flow is involved. Therefore,DNS is currently and will be in the foreseeable future a tool only for fundamentalresearch, rather than a tool for engineering application.

Several strategies have been developed to avoid resolving the smallest timeand/or length scales. The Reynolds averaged numerical simulation (RANS)method only describes time or ensemble averaged quantities of the flow field. Theeffects of the fluctuating variables are described through a turbulent viscositymodel or Reynolds stress model. In the turbulent viscosity models, the turbulentviscosity is obtained from an algebraic relation or from turbulent quantities such asthe turbulence kinetic energy and its dissipation rate, which is solved using amodeled transport equation. Among the turbulent viscosity models, the two-equation k-e model (Launder and Spalding 1972) is the most frequently used. Inthe Reynolds stress models, the modeled transport equations are solved for eachcomponent of the Reynolds stress and for the dissipation rate which provides alength or time scale of the turbulence (Pope 2000). Therefore, the turbulent vis-cosity hypothesis is not needed any longer. For compressible flows, the densitycannot be taken as a constant. Therefore, we must consider the density in the samestatistical fashion as the other fluid-mechanical quantities. If we directly apply thetime-averaging on the Navier-Stokes equations, a wide variety of quantitiesinvolving density fluctuation occur in the averaged equations. Favre (mass)weighted averaging is used to solve this problem. In Favre averaging, all fluid-mechanical quantities except the pressure are mass averaged. The correlations withthe density fluctuation are eliminated. RANS methods are widely used in thesimulation of engineering flows because of their computational simplicity.

Due to its time averaging nature, the RANS methods cannot capture certainunsteady behaviors. An alternative is to use large eddy simulation (LES). LESexplicitly computes the large structures of the flows, usually the ones larger thanthe grid size. The effects of the smaller ones are modeled using a subgrid-scale(SGS) model. The large structures in turbulent flows generally depend on thegeometry of the system, while the small ones are more universal. Therefore, themodels for LES may be more efficient and more global. LES is a powerful tool topredict unsteady phenomena in a turbulent flow, which are associated with com-bustion instability, turbulent mixing, and turbulence-chemistry interactions. LEShas been applied to multiphase flows in last decade (Yeh and Liu 1991), and to thecomplex flows that occur in a variety of engineering applications (Haworth andJansen 2000; Sankaran and Menon 2002; Apte et al. 2003; De Villiers et al. 2004;Bharadwa and Rutland 2009; Papoutsakis et al. 2009; Hu et al. 2010; Zhang et al.2010; Corbinelli et al. 2010). LES of internal combustion engine is currently anactive topic in academia (Naitoh et al. 1992; Haworth 1999; Lee et al. 2002;Kaario et al. 2003; Shethaji et al. 2005; Hu and Rutland 2006; Jhavar and Rutland2006; Hori et al. 2007; Drake and Haworth 2007; Thobois et al. 2007; Richardet al. 2007; Joelsson et al. 2008; Li and Kong 2008; Banerjee et al. 2010), espe-cially for unsteady phenomena prediction such as cyclic variation (Adomeit et al.2007; Vermorel et al. 2007; Vermorel et al. 2009; Hasse et al. 2010). But it is notready for engine optimization yet due to its high computational cost and immature


physical models. A series of workshops on ‘‘LES for Internal Combustion EngineFlows’’ (LES4ICE) has been organized to advance LES applications for enginesimulation.

The Probability Density Function (PDF) method attacks the turbulence problemby capturing its stochastic nature. The turbulent flow is viewed as a randommedium and described using a probabilistic mathematical model. The methodcomputes the probability rather than exact values of certain quantities at certainpositions and/or times. The whole turbulent flow is represented by a PDF which issimilar to the distribution function in Eq. 2.26. The PDF can be either presumed orcomputed by solving its transport equation (Ge 2006). If a presumed PDF is used,the problem turns to determining the first several moments (usually the first andsecond moments) of the PDF from local conditions. In most contexts, the PDFmethod refers to the transported PDF approach where the PDF is computed bysolving its transport equation, which can be deduced from the Navier-Stokesequations (Ge 2006). In the PDF transport equation, the terms of convection, meanpressure gradient, and chemical reaction source appear in a closed form (Pope1985, 2000; Haworth 2010). Thus, it is a very attractive option for modelingturbulent combustion processes. The PDF transport equation is usually solvedusing Monte-Carlo/Langrangian particle methods, whose computational cost isproportional to the total dimension number, i.e., the total number of individualquantities considered in the PDF. According to statistics theory, the error of theparticle method is proportional to N�1=2, where N is the total particle numberconsidered in the simulations. The PDF method has been applied to IC enginesimulation (Haworth and El Tahry 1991; Taut et al. 2000; Zhang et al. 2005; Leeand Mastorakos 2007; Kung and Haworth 2008; Yamamoto et al. 2010). In spite ofits advantages in dealing with detailed chemistry, the PDF method is preventedfrom most engine simulation and optimization application due to its expensivecomputational cost. Even when only 15 * 20 particles per cell are considered(Kung and Haworth 2008), its total computational cost is still not acceptable forindustry application.

RANS is still the dominant technique for current internal combustion enginesimulation and optimization. Among them, the two-equation models are the mostwidely used because of their simplicity and effectiveness (Launder and Spalding1972), while the Reynolds stress model (RSM, Hanjalic and Launder 1972) forengine simulation is rarely used. RSM has been mainly applied to simulate intakeflows (Borgnakke and Xiao 1991; Luo and Bray 1992; Lebrère et al. 1996) and only afew studies on in-cylinder flows (Yang et al. 2000, 2005). In this book, all theexample simulations were conducted using RANS with two-equation models and themodels were developed in the framework of RANS. Some of these models in whichturbulent scales are not involved may be directly applied to other turbulence models.

RANS uses a time-averaging technique and the instantaneous quantities aredecomposed into a time-averaged component and a fluctuating term:

U ¼ �Uþ U0: ð2:31Þ

34 2 Fundamentals

For compressible flows, Favre-averaging is usually used to eliminate the fluc-tuating term associated with density, which is defined as:

~U ¼ qU=�q: ð2:32Þ

The corresponding fluctuating components are defined as:

U00 ¼ U� ~U: ð2:33Þ

Applying time averaging to Eqs. 2.11 and 2.12 yields:

o�qotþ oð�q~UjÞ

oxj¼ �_qs; ð2:34Þ

oð�q~UiÞot

þ oð�q~Ui ~UjÞoxj

þoð�qu00i u00j Þ

oxj¼ �o�p

oxiþ o�sij

oxjþ �Fs

i þ �Fbi ; ð2:35Þ

�qu00i u00j is the Reynolds stress tensor that needs to be modeled. In the k � e models,

two additional quantities, the turbulence kinetic energy k ¼ 12 u00i u00i and its dissi-

pation rate e; are added to close the equations. Their transport equations have beendeduced and modeled. The length and time scales are determined by

lt ¼k3=2

e; ð2:36Þ

ts ¼k

e: ð2:37Þ

The standard k-e model assumes an isotropic turbulence. By introducing akinematic eddy viscosity lt, the Reynolds stress tensor is modeled as

��qu00i u00j ¼ lto~Ui

oxjþ o~Uj

oxi� 2

3o~Uk

oxkdij

� �� 2

3�q~kdij: ð2:38Þ

The turbulent viscosity lt is related to the Favre-averaged turbulence kineticenergy, ~k, and its dissipation rate, ~e, via:

lt ¼ Cl�q~k2

~e; ð2:39Þ

where Cl is a model constant listed in Table 2.1. Substituting Eq. 2.38 into Eq.2.35, the modeled momentum equation is obtained:


oð�q~UiÞot

þ oð�q~Ui ~UjÞoxj

¼ �o�p

oxiþ �Fs

i þ �Fbi

þ o

oxjðlt þ lÞ o~Ui

oxjþ o~Uj

oxi� 2

3o~Uk

oxkdij

� �� : ð2:40Þ

Transport equations for ~k and ~e are modeled as

oð�q~kÞotþ oð�q~k ~UjÞ

oxj¼ o

oxj

lt

rkþ l

� �o~k

oxj

� �þ Pk � �q~eþ _Ws; ð2:41Þ

oð�q~eÞotþ oð�q~e~UjÞ

oxj¼ o

oxj

lt

reþ l

� �o~eoxj

� �

þ~e~k

Ce;1Pk � Ce;2�q~eþ Cs _Ws

; ð2:42Þ

where _Ws is the spray source term. The production term for the turbulence kineticenergy Pk is given by

Pk ¼ ��qu00i u00jo~Ui

oxj¼ lt

o~Ui

oxjþ o~Uj

oxi� 2

3o~Uk

oxkdij

� �� 2

3�q~kdij

� �o~Ui

oxj: ð2:43Þ

rk and re are the effective Prandtl numbers for k and e. The model constants Ce;1,Ce;2, and Cs are listed in Table 2.1. The first term on the right-hand side of Eq. 2.42is the source term accounting for length scale changes due to velocity dilatation.

Applying time averaging to Eqs. 2.10 and 2.15, we have

oð�q~YkÞot

þ oð�q~Yk ~UjÞoxj

¼ �oð�qY 00k u00j Þ

oxjþ o

oxj�qD

o~Yk

oxj

� �þ �_xk þ �_qs

k; ð2:44Þ

oð�q~eÞotþ oð�q~e ~UjÞ

oxj¼ �

oð�qe00U00j Þoxj

� �po~Uj

oxjþ o�Jj

oxjþ �_Q

s þ �_Qc: ð2:45Þ

The species and energy turbulent flux �q Y 00k u00j and �qe00u00j are usually modeledusing a gradient transport hypothesis1:

�qY 00k u00j ¼ �lt

Sct;k

o~Yk

oxj; ð2:46Þ

Table 2.1 Model constantsin the standard k-e model(Launder and Spalding 1974)

rk re Cl Ce;1 Ce;2 Cs

1.0 1.3 0.09 1.44 1.92 -1.0

1 Note that this assumption may not be valid in certain circumstances where counter-gradienttransport may occur.

36 2 Fundamentals

�qe00u00j ¼ �lt

Pr

o~e

oxj; ð2:47Þ

where Sct;k is the turbulent Schmidt number of the k-th species; Pr is the turbulentPrandtl number for internal energy.

The standard k-e model has been used in the original KIVA codes (Amsdenet al. 1989; Amsden 1993) and widely used in engine simulation. It was laterreplaced by the Renormalization Group (RNG) k-e model (Han and Reitz 1995),which has been used in all simulations in this book.

The RNG k-e model was originally derived by Yakhot and Orszag (1986)using Renormalization Group theory. Model constants in the RNG k-e model canbe explicitly evaluated from the theory based on certain assumptions andmathematical development. The RNG k-e model was extended to compressibleflows and two phase flows by Han and Reitz (1995). The resulting transportequation for turbulence kinetic energy has the same form as Eq. 2.42. Thetransport equation for its dissipation rate is different from the standard k-e modeland is written as

oð�q~eÞotþ oð�q~e~UjÞ

oxj¼ �qR� C3�q~e

o~Uj

oxjþ o

oxj

lt

reþ l

� �o~eoxj

� �

þ ~e~k

Ce;1Pk � Ce;2�q~eþ Cs _Ws

: ð2:48Þ

Comparing to Eq. 2.42, one term, �qR, is added to consider rapid distortion andanisotropic large-scale eddies. It can be modeled as

R ¼ffiffiffi23

rClCgg~e

oUj

oxj

��; ð2:49Þ

Cg ¼gð1� g=g0Þ

1þ bg3; ð2:50Þ

where g is the ratio of turbulent to mean strain-time scale:

g ¼ tsS ¼ tsð2SijSijÞ1=2; ð2:51Þ

and Sij is the mean strain:

Sij ¼12

o~Uj

oxiþ o~Ui

oxj

� �: ð2:52Þ

Table 2.2 Model constantsin the RNG k-e model (Hanand Reitz 1995)

rk re Cl Ce;1 Ce;2 Cs g0 b

1.39 1.39 0.0845 1.42 1.68 -1.0 4.38 0.012


The model parameter C3 is written as

C3 ¼ 13½�1þ 2C1 � 3mðn� 1Þ þ ð�1Þd

ffiffiffi6p

ClCgg�; ð2:53Þ

where the temperature exponential factor involved molecular viscosity is m = 0.5;n is the exponent of a polytropic process. d is a Kronecker delta depending on thesign of velocity dilatation:

d ¼1 : r � U\0

0 : r � U [ 0

(: ð2:54Þ

The model constants are listed in Table 2.2.

2.2.2.2 Turbulent Combustion Models

Combustion processes in the gaseous phase involve many complex physical andchemical phenomena: reaction chemistry, turbulence transport, diffusion of heatand species, and thermodynamics. These processes are strongly coupled. Theinteraction between them cannot be neglected, especially the turbulence-chemistryinteractions. The chemical reaction rates are strongly coupled to molecular diff-usion at the smallest scales of turbulence. The heat release from the chemicalreactions affects the turbulent flow, both from variations in the density field andfrom the effects of local dilatation. These processes are modeled using turbulentcombustion models.

The central problem for the turbulent combustion model is how to compute themean reaction rate �_xk (or final composition) from the perfectly stirred reactor (PSR)reaction rate _xk (or initial composition) and turbulent quantities. Because in eitherRANS or LES, the combustion occurs at the unresolved scales of the computations,the mean reaction rates must be approximated using combustion models. Thesimplest model is to assume that each computational cell is a PSR and turbulenceeffects are neglected, i.e., �_xk ¼ _xkð~Y1; . . .~YNs ; ~T ; �pÞ. Despite its evident flaws as aturbulent combustion model, this approach actually gives very good predictions forconventional diesel combustion when coupled with detailed reaction mechanisms(Singh et al. 2007a). Coupled with the CHEMKIN package (Kee et al. 1990), thismodel has been widely used in multi-dimensional engine simulations and is usuallyreferred as the ‘‘KIVA-CHEMKIN model’’. The examples in Chap. 6 use theKIVA-CHEMKIN model when detailed reaction mechanisms are considered.

One simple approach is based on a turbulent mixing-controlled combustionconcept, which assumes that the burning rate of the mixture is mainly determinedby the turbulent mixing rate. Thus, the influence of the chemical kinetics or itsinteraction with the fluid mixing is neglected, and only the fast chemistry limit istaken into account. This class of models includes the eddy breakup model(Spalding 1971) and the eddy-dissipation model (Magnussen and Hjertager 1977),and the characteristic time combustion (CTC) model, etc. Because of their

38 2 Fundamentals

simplicity, these models are very popular in engineering simulations. For instance,the CTC model is widely used in IC engine simulations.

The CTC model considers turbulence effects on combustion process by intro-ducing a turbulent combustion characteristic time scale tc (Abraham et al. 1985).The time rate of change in mass fraction of the k-th species due to chemicalreaction is written as

dYk

dt¼ �Yk � Y�k

tc; ð2:55Þ

where Y�k is the local and instantaneous thermodynamic equilibrium value of themass fraction; and tc indicates the characteristic time to achieve this equilibriumthat is assumed to be the same for all species. tc is determined from the laminartime scale tl and the turbulent time scale tc

s:

tc ¼ tl þ ftcs ; ð2:56Þ

where f is a delay coefficient determining the contribution of the turbulent effects.When a reaction mechanism is employed, the laminar time scale is set to the timestep (Kong and Reitz 1993). When a simple reaction mechanism is employed, thelaminar time scale is estimated from a correlated one-step reaction rate from asingle droplet auto-ignition experiment (Kong et al. 1995):

tl ¼ A�1X0:75fuel X�1:5

O2expðE=RTÞ; ð2:57Þ

where A ¼ 1:54� 1010 and E = 77.3 kJ � mol-1 K-1. The turbulent time scale tcs is

proportional to ts:

tcs ¼ C2ts ¼ C2

~k~e: ð2:58Þ

The model constant C2 is set to 0.142 for the standard k-e model and 0.1 for theRNG k-e model. The delay coefficient is given by

f ¼ 1� e�r

0:632; ð2:59Þ

where r is the mass fraction ratio of the amount of products to that of total reactivespecies (all except N2), which indicates the completeness of the combustionprocess and varies from 0 (no combustion yet) to 1 (complete combustion).

Another category of turbulent combustion models is the flamelet model.Flamelet models view the turbulent flame as an ensemble of stretched laminarflamelets attached to the instantaneous position of the flame surface. The under-lying concept is that the flame reaction zones are very thin.

For the turbulent diffusion flame, the flamelet model assumes that the termsinvolving transients and gradients parallel to the instantaneous surface of theconstant mixture fraction to be small. By assuming equal diffusivity of all species,the species conservation equations can locally and instantaneously be transformedinto a stationary laminar flamelet equation (Peters 1984). The only two controlparameters are the mixture fraction and its dissipation rate v. The mixture fraction


indicates the progress of the chemical reaction, while its dissipation rate indicatesstrain effects. For a given state of the turbulent flow with certain value of mixturefraction and its dissipation rate, the flamelet models assume that the local balancebetween diffusion and reaction is similar to the one in a prototype laminar flamewith the same mixture fraction and its dissipation rate. The balance equations ofspecies are then replaced with the conservation equation of the mean and varianceof the mixture fraction. The flamelet structure is pre-calculated by solving the one-dimensional flamelet equations. Usually the counter-flow structure is used to buildthe flamelet library. The results are stored in a structured table. The compositionstate space can be determined by looking up the table according to the mixturefraction and its dissipation rate. The mean values of the compositions are obtainedusually through a presumed PDF approach, which models turbulence effects. Inthis way, the calculation of the turbulent flow and mixture fields is separated fromthe calculation of the chemistry. Detailed chemical reaction mechanisms andmolecular diffusion processes are then implemented into CFD with acceptablecomputational costs. The Representative Interactive Flamelet (RIF, Pitsch et al.1996) model was developed for diesel combustion simulation, in which only thecylinder-averaged dissipation rate is considered. A multiple flamelet model,the Eulerian particle flamelet model (EPFM), was developed for DI diesel enginesimulation (Hasse et al. 2000). Hu and Rutland (2006) developed a steady-stateflamelet model for LES of diesel combustion.

For the turbulent premixed flame, a unity Lewis number and an infinitely thinflame structure are assumed and the species transport equation is transformed into asingle balance equation for progress variable (Veynante and Vervisch 2002) or aG-equation (Peters 1999). The reaction rate is computed from the laminar burningvelocity, a correction factor representing turbulence stretch, and flame surfacedensity. The Bray-Moss-Libby (BML) model (Bray and Libby 1994) computes theflame surface density from a mean progress variable and a crossing length scaleusing an algebraic formulation. The other approaches compute the flame surfacedensity by solving a transport equation, for instance, the flame surface density model(Boudier et al. 1992; Trouve and Poinsot 1994; Lee et al. 2008), and the coherentflame model (Dillies et al. 1993; Musculus and Rutland 1995; Vermorel et al. 2007).The G-equation model tracks the propagating flame using a level-set method.Turbulent effects are taken into account by the G-equation model, which has beenextensively used for IC engine simulation (Tan and Reitz 2003; Singh et al. 2007b;Liang et al. 2007; Pauls et al. 2007; Yang and Reitz 2009a; Toninel et al. 2009).

The turbulent partially premixed flame is the most common flame type in DIengines. It is usually assumed that the partially premixed flame is a combination ofa diffusion flame and a premixed flame, and it thus is modeled using a hybridmodel (Hu et al. 2007).

The fourth category of turbulent combustion models are the PDF models. Theconvection and chemical reaction source terms are treated exactly in the PDFmodels, which is very attractive for turbulent combustion modeling (Haworth2010). Turbulence-chemistry interaction is also well described. Its challenge is stillthe expensive computational cost.

40 2 Fundamentals

The conditional moment closure (CMC) model focuses on certain statesbetween the fresh mixture and fully burnt products in the premixed flame, orbetween fuel and oxidizer in the diffusion flame (Klimenko and Bilger 1999). Theaverage composition is determined from the conditional moments, qYkjc ¼ c�h i,where c is a progress variable for premixed flames, or the mixture fraction fordiffusion flames. The CMC model may be viewed as a multi-surface description ofturbulent flames. Any conditional quantities correspond to their conditionalaverage values along the iso-surface of c ¼ c�. CMC modeling of IC enginecombustion has been reported (Barroso et al. 2005; Seo et al. 2008; Wright et al.2009).

2.2.2.3 Ignition Models

In an SI engine, the combustion is initiated by a spark. The ignition processconsists of three stages: breakdown, arc, and glow. When the voltage between theanode and cathode reaches the breakdown voltage, an arc will form. If the energyflux rate that dissipates into the charge is large enough and the local mixture fulfillsan ignitibility condition, the mixture will be ignited and a flame kernel will form.Undergoing the influence of flame propagation, spark energy, and flow transport,the flame kernel grows into a self-sustaining propagating flame. A simple approachto model the spark ignition process is to add an energy source to the charge at thespark plug position (Amsden et al. 1989; Yorita et al. 2007). Most of the modelsemploy empirical models for the breakdown and arc phases and a 1D model for theflame kernel, i.e., only the radius and position of the flame kernel is considered(Sher et al. 1992; Yossefi et al. 1993; Shen et al. 1994; Song and Sunwoo 2000;Duclos and Colin 2001; Falfari and Bianchi 2007; Dahms et al. 2009). Duclos andColin (2001) integrated an electrical circuit model, an arc model, and a flamekernel model into a multi-dimensional CFD code. The flame kernel model is also a1D model, with multiple particles representing the kernels in a statistical sense.Fan and Reitz (2000) developed a discrete particle ignition (DPIK) model, inwhich a set of Lagrangian particles are used to represent the flame surface. Themodel was improved by Tan and Reitz (2003). By neglecting the effects of con-vection, the i-th particle’s distance to the spark plug, rk;i, is computed as:

drk;i

dt¼ qu

qbðsplasma þ sTÞ; ð2:60Þ

where qu and qb are the density of unburned and burnt gas mixture, respectively.sT is the turbulent flame speed computed from laminar flame speed s0

L and localturbulent intensity. splasma is plasma induced propagation flame speed and it iscomputed based on energy balance of the ignition kernel:

splasma ¼geff

_Qspk

4pr2k;iquðeb � hu þ p=qbÞ

; ð2:61Þ


where _Qspk is the electrical energy discharge rate. geff is the coefficient that takesinto account the heat loss to the spark plug. The value of geff is about 30%(Heywood 1988). eb and hu are the internal energy of the burnt mixture and thespecific enthalpy of the unburned mixture, respectively. Turbulent strain andcurvature effects on the kernel flame are taken into account by multiplying thelaminar flame speed by a stretch factor I0 (Herweg and Maly 1992):

I0 ¼ 1� lF15lt

� �1=2 u0

s0L

� �1=2

�2lFrk;i

qu

qb; ð2:62Þ

where lF ¼ kCpqus0

Lis the laminar flame thickness, lt is the turbulent integral length

scale, and u0 is the turbulence intensity. Details of the integration of the DPIKignition model with the G-equation flame propagation model for modeling SIengine combustion are given by Tan and Reitz (2006).

For a CI engine, the combustion is initiated by auto-ignition, which depends onthe local chemical kinetic, thermodynamic, and fluid dynamic properties of the in-cylinder mixture. A detailed reaction mechanism, such as the ERC (EngineResearch Center, University of Wisconsin-Madison) reduced n-heptane mecha-nism, is able to accurately predict the auto-ignition events. For computationalefficiency considerations, a single-step Arrhenius kinetics model has been widelyused in CI engine combustion simulations. The Shell ignition model (Halsteadet al. 1977) offers an option that improves accuracy and efficiency, which consistsof five species and eight generic reactions based on the degenerate branchingcharacteristics of hydrocarbon auto-ignition. The model was originally developedto predict knock in gasoline engines. The generic species and reactions involved inthe model are as follows:

RHþ O2 ! 2R� Kq ðR1Þ

R� ! R� þ P + Heat Kp ðR2Þ

R� ! R� þ B f1Kp ðR3Þ

R� ! R� þ Q f4Kp ðR4Þ

R� þ Q! R� þ B f2Kp ðR5Þ

B! 2R� Kb ðR6Þ

R� ! termination f3Kp ðR7Þ

2R� ! termination Kt ðR8Þ

where RH is the hydrocarbon fuel (CnH2m); R* is the radical formed from the fuel;B is the branching agent; P is oxidized products consisting of CO, CO2, and H2Owith specific proportions; Q is a labile intermediate species. Reaction R1 is the

42 2 Fundamentals

initiation reaction, followed by chain-propagation cycle (reactions R2–R6).Reactions R7 and R8 are two termination reactions.

2.2.2.4 NOx Emission Model

The NOx formation process can be modeled by including related elementaryreactions into the detailed reaction mechanism. A successful practice of thisapproach is the ERC reduced n-heptane mechanism with 34 species and 74reactions, which adapted the NOx formation mechanism from the GRI methane/aircombustion reactions (Smith et al. 2009):

Nþ NO� N2 þ O

Nþ O2 � NOþ O

N2Oþ O� 2NO

N2Oþ OH� N2 þ HO2

N2OþM� N2 þ OþM

NOþ HO2 � NO2 þ OH

NOþ OþM� NO2 þM

NO2 þ O� NOþ O2

NO2 þ H� NOþ OH:

This model has proven to be a very reliable model and has been extensivelyused in IC engine simulation and optimization. It is also used in the examples inChap. 6 when the detailed chemistry mechanism is used.

However, when a simple reaction mechanism is used, minor species such as OHand HO2 are absent and the abovementioned model cannot be implemented. Asimpler model, the extended Zel’dovich mechanism (Heywood 1976), is then usedto predict NOx emission. The extended Zel’dovich mechanism consists of thefollowing reactions:

N2 þ O� NOþ N; ðR9Þ

Nþ O2 � NOþ O; ðR10Þ

Nþ OH� NOþ H: ðR11Þ

The mechanism assumes partial equilibrium of the reaction

Oþ OH� O2 þ H;

and steady state of species N:


d½N�dt¼ 0:

The final rate equation for NO is then derived:

d½NO�dt¼ 2K1f ½O�½N2�

1� ½NO�=ðK12½O2�½N2�Þ1þ K1b½NO�=ðK2f ½O2� þ K3f ½OH�Þ: ð2:63Þ

The subscripts 1, 2, and 3 refer to reactions R9, R10, and R11, respectively.Subscripts ‘‘f’’ and ‘‘b’’ indicate the forward and backward reactions. The rateconstants as recommended by Bowman (1975) are:

K1f ¼ 7:6� 1013 expð�38000=TÞK1b ¼ 1:6� 1013;

ð2:64Þ

K2f ¼ 6:4� 109 expð�3150=TÞK2b ¼ 1:5� 109 expð�19500=TÞ;

ð2:65Þ

K3f ¼ 1:0� 1014

K3b ¼ 2:0� 1014 expð�23650=TÞ;ð2:66Þ

K12 ¼K1f

K1b

K2f

K2b: ð2:67Þ

In order to obtain quantitative comparisons with experiments, a calibrationfactor b is introduced:

d½NO��

dt¼ b

d½NO�dt

: ð2:68Þ

The additional factor of b = 1.533 is also used to convert NO to NOxaccording to the EPA standard. This model is employed in the examples in Chap. 6when the simplified reaction mechanism is used.

2.2.2.5 Soot Model

Soot modeling remains one of the biggest challenges in IC engine simulation dueto the complex structure, composition, and formation/oxidation mechanisms ofsoot. Quantitative soot prediction is still not feasible, especially for IC engineoptimization purposes. Hiroyasu’s two-step soot model (Hiroyasu and Kodota1976) is the most widely used soot model in engine simulation. The two-step sootmodel only considers soot formation from a soot precursor and soot oxidation byoxygen. Two empirical expressions for soot formation and soot oxidation are used.The net soot production rate is determined from

44 2 Fundamentals

dMs

dt¼ dMsf

dt� dMso

dt; ð2:69Þ

where the soot formation rate is given by

dMsf

dt¼ Asf qprecpn exp �Esf

RT

� �; ð2:70Þ

where qprec is the partial density of the soot precursor; p is the pressure; T is thetemperature; Esf ¼ 12500 cal/mol is the activation energy; Asf is the Arrheniuspre-exponential factor normally set to 40; and the exponential factor for pressure, nis set to 0.5.

The soot oxidation rate is determined using the Nagle and Strickland-Constablemodel (Nagle and Strickland-Constable 1962), and is calculated as

dMso

dt¼ 6Wc

qsDsMsRox � AsoMs; ð2:71Þ

where Ms is the soot mass; qs is the soot density; Ds is the soot particle diameter;Wc is the molecular weight of carbon. Rox is given by

Rox ¼KApO2

1þ KZpO2

� �xþ KBpO2ð1� xÞ; ð2:72Þ

with

x ¼ PO2

PO2 þ KT=KB:

PO2 is the partial pressure of oxygen. The model parameters are:

KA ¼ 20:0 exp �30000:0RT

� �;

KB ¼ 4:46� 10�3 exp �15200:0RT

� �;

KT ¼ 1:51� 105 exp �97000:0RT

� �;

KZ ¼ 21:3 exp �4100:0RT

� �;

where R ¼ 1:98 kcal�mol�1K�1. Assuming that the transient changes in theoxygen and precursor concentrations are negligible, the change of soot massduring one time step in a computational cell can thus be estimated as

DMs ¼_Msf

Aso�Ms

� �½1� expð�Aso � DtÞ�: ð2:73Þ


When a simple reaction mechanism is employed, the soot precursor is usuallyset as the fuel vapor. Other species such as acetylene or benzene may be taken assoot precursors as long as they have been included in the reaction mechanism. Forinstance, Kong et al. (2007) coupled the two-step soot model with the ERCreduced n-heptane mechanism, which includes acetylene. Acetylene is then takenas the soot precursor in the soot model. In the examples in Chap. 6, if acetylene isincluded in the reaction mechanism, acetylene is taken as soot precursor; other-wise, fuel vapor is taken as soot precursor.

More advanced soot models have been developed for IC engine simulation. Taoet al. (2006) developed a multi-step phenomenological soot model, which con-siders surface growth, soot inception and coagulation, soot oxidation by oxygenand OH, soot precursor oxidation by oxygen. Vishwanathan and Reitz (2009)developed a new reduced n-heptane reaction mechanism which included polycy-clic aromatic hydrocarbons (PAH), and PAH is taken as the soot precursor. In thepresent book, only the two-step soot model is used for simplicity.

2.2.2.6 Nozzle Flow Model

Sprays are produced when the relative velocity between the liquid and the sur-rounding air or gas is high enough. Pressure atomizers and rotary atomizers ejectthe liquid at high velocity, while twin-fluid, air-assist, and air-blast atomizersexpose a low-speed liquid to a high-velocity air flow (Lefebvre 1989). Amongthem, pressure atomizers dominate the IC engine application, and most of theinjectors in IC engines feature a simple circular orifice. The injector nozzlegeometry affects the fuel atomization and consequently influences the enginecombustion and exhaust emissions significantly. However, it is very difficult for anumerical simulation to describe the relevant physics, due to the very small lengthand time scales of nozzle flows. Comprehensive numerical simulations (Gorok-hovski and Herrmann 2008; Ning et al. 2009) and experiments (Liu et al. 2010;Balewski et al. 2010) have been conducted and have provided useful insights aboutthe physics of the nozzle flow. Nevertheless, such expensive simulations are notacceptable for industry. Only phenomenological models can be applied for ICengine simulation and optimization. The ERC nozzle flow model (Sarre et al.1999) has been extensively used in IC engine simulations.

The nozzle flow model provides initial conditions about the initial spraydroplets for the following breakup processes. The input parameters of the nozzleflow model include the liquid flow rate, injection pressure, cylinder pressure,physical properties of the liquid, nozzle hole diameter, ratios L=D and r=d, asshown in Fig. 2.11. The output parameters of the nozzle flow model are theinstantaneous discharge coefficient, spray angle, effective injection velocity, andeffective flow exit area, which relates to the initial droplet size or initial liquid blobsize. The discharge coefficient Cd quantifies the difference between the exact flowrate and the one predicted using the ideal Bernoulli equation and is defined as

46 2 Fundamentals

Cd ¼ Umean=ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2ðpin � poutÞ=ql

p; ð2:74Þ

where Umean is the mean liquid velocity at the exit; and pin and pout are the pressureat the inlet and outlet, respectively. Cd is modeled as

Cd ¼ ðKinlet þ f � L=Dþ 1Þ�1=2; ð2:75Þ

with

f ¼ maxð0:316Re�0:25; 64 Re�1Þ; ð2:76Þ

and the inlet loss coefficient Kinlet is determined from tabulated data (Benedict1980). Based on this discharge coefficient, a first estimation of the inlet pressure is:

pin ¼ pout þql

2Umean

Cd

� �2

: ð2:77Þ

Assuming a flat velocity profile and using Nurick’s expression (Nurick 1976)for the size of the contraction, the velocity at the smallest flow area (vena con-tracta) yields:

Uvena ¼ Umean=Cc; ð2:78Þ

with the contraction coefficient

Cc ¼ C�2c0 � 11:4r=d

�1=2; ð2:79Þ

where Cc0 is the contraction coefficient when r=d ¼ 0. The pressure at the smallestflow area is then given as

pvena ¼ pin �ql

2U2

vena: ð2:80Þ

If pvena is lower than the vapor pressure pvapor , it is assumed that the flow is fullycavitating. The inlet pressure and discharge coefficient are then given as

pin ¼ pvapor þql

2U2

vena; ð2:81Þ

D

d

r

L

Fig. 2.11 schematic oforifice geometry


Cd ¼ Ccpin � pvapor

pin � pout

� �1=2

: ð2:82Þ

The pressure at the vena contracta can also be estimated from the outletpressure:

pvena;r ¼ pout þql

2U2

mean 1� C�2c þ Kexp þ f � L=D

; ð2:83Þ

where Kexp is the expansion loss coefficient for the flow downstream of the cav-itation region and determined from tabulated data (Benedict 1980). If pvena in Eq.2.83 is already lower than pvapor, but pvena in Eq. 2.80 still predicts a turbulent flow,a cavitating reattaching flow is assumed, which is treated like a turbulent flow. Inthe cases of turbulent or cavitating reattaching flows, the exit velocity of thedroplets is set to the mean velocity Umean, and the initial droplet size is set to thenozzle diameter. When the nozzle flow is fully cavitating, the exit velocity andinitial droplet size are set to

Ueff ¼ Uvena �pout � pvapor

qlUmean; ð2:84Þ

Deff ¼ DUmean

Ueff

� �1=2

: ð2:85Þ

2.2.2.7 Primary Breakup Models

The primary breakup process is where the bulk liquid disintegrates into filamentsand drops due to interaction with the surrounding gas. Instabilities on the interfaceare the major driving forces for the breakup process. Although the primarybreakup process is essential for the following spray dynamics and combustionevents, and significant progress has been made in the numerical simulation ofprimary breakup process recently (Gorokhovski and Herrmann 2008), suchaccurate simulations are not acceptable for IC engine simulation due to theirextremely expensive computational cost. Alternatively, the primary breakup pro-cess can be simply modeled using a presumed droplet size distribution (Babinskyand Sojka 2002). Among them, the simplest distribution is a mono-disperse dis-tribution (uniform distribution), i.e., the initial droplet radius is set equal to aninput parameter SMR, or r32. The KIVA-II code offers the v-squared distributionas another option (Amsden et al. 1989):

f ðrÞ ¼ �r�1e�r=�r; ð2:86Þ

where �r ¼ r32=3 is the number—averaged droplet radius and r32 is defined as:

r32 ¼P

r3Pr2¼R

r3f ðrÞdrRr2f ðrÞdr

: ð2:87Þ

48 2 Fundamentals

A Rosin-Rammler distribution (‘‘two-parameter Weibull distribution’’ in themathematics literature) is frequently used to model droplet size distributions(Rosin and Rammler 1933; Han et al. 1997):

f ðrÞ ¼ a�r�ara�1e�ðr=�rÞa

: ð2:88Þ

The Nukiyama-Tanasawa distribution (Nukiyama and Tanasawa 1939) has alsobeen used to model droplet size distributions. It has a more general form as:

f ðrÞ ¼ arpe�brq; ð2:89Þ

where b, p, and q are adjustable parameters. The Maxwell, Rayleigh, v-squared,and Rosin-Rammler distributions are several special forms of the Nukiyama-Ta-nasawa distribution (Ge 2006). Since it has three input parameters, its applicationin IC engine simulations is rare. Other presumed distributions, and other methodsto determine the initial droplet size distribution (e.g., maximum entropy methodand discrete probability function approach) are explained in detail in Babinsky andSojka (2002).

For the pressure-swirl atomizer, the transition from internal injector flow to afully developed hollow-cone spray can be modeled using a linearized instabilitysheet atomization (LISA) model (Schmidt et al. 1999) The LISA model con-siders two stages: film formation and sheet breakup. In the first stage, a liquidfilm surrounding an air core is formed due to centrifugal motion of the liquidwithin the injector. The thickness of the film, df , is related to the liquid massflow rate, _m, by

_m ¼ pqlUadf d0 � df

; ð2:90Þ

where d0 the injector hole diameter; Ua ¼ Uinj cos hð Þ is the axial component of thetotal injection velocity at the injector exit and h is the cone half-angle. The totalinjection velocity Uinj is computed from the pressure drop across the injector exit:

Uinj ¼ Cd;lisa

ffiffiffiffiffiffiffiffiffi2Dp

ql

s; ð2:91Þ

where Cd;lisa is the effective discharge coefficient that is computed from a givendischarge coefficient or the discharge coefficient determined from a nozzle flowmodel (c.f., Sect. 2.2.2.6):

Cd;lisa ¼ max Cd;4 _m

pd20qlcos hð Þ

ffiffiffiffiffiffiffiffiffiql

2Dp

r� �: ð2:92Þ

The second argument in the MAX function is used to guarantee that the size ofthe air core is non-negative.

The sheet breakup process is modeled based on wave stability theory. Themodel assumes that a two-dimensional, viscous, incompressible liquid sheet of


thickness, 2h, moves with velocity, U, through a quiescent, invisid, incompressiblegas medium. A spectrum of infinitesimal disturbances,

g ¼ g0expðikxþ xtÞ; ð2:93Þ

is imposed on the initially steady motion and produces fluctuating velocities andpressures for both the liquid and the gas, where g0 is the initial wave amplitude,k ¼ 2p=k is the wave number, and x ¼ xr þ ixi is the complex growth rate of thesurface disturbances. A simplified form of the dispersion relation for pressure-swirl atomizers (Senecal et al. 1999) is written as

xr ¼ �2mlk2 þ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi4m2

l k4 þ qql

U2injk

2 � rk3

ql

s; ð2:94Þ

where ml is the liquid kinematic viscosity; X is the most unstable disturbance withthe largest value of xr, and is assumed to be responsible for sheet breakup. Oncethe unstable waves on the sheet surface grow to a critical amplitude, ligaments areformed due to the sheet breakup. The breakup time sb;lisa for this process can beformulated based on an analogy with the breakup length of cylindrical liquid jets:

sb;lisa ¼1X

lngb

g0

� �; ð2:95Þ

where gb is the critical amplitude at breakup. The corresponding breakup lengthlb;lisa can be estimated by

lb;lisa ¼ sb;lisaUinj ¼Uinj

Xln

gb

g0

� �; ð2:96Þ

where the quantity lnðgb=g0Þ is given a constant value 12. Based on mass balance,the resulting ligament diameter at the point of breakup can be derived as

dL ¼ffiffiffiffiffiffiffiffi16h

Ks

r; ð2:97Þ

where Ks is the wave number corresponding to the maximum growth rate X. Basedon the assumption that the sheet is in the form of a cone with its vertex at a pointbehind the injector orifice, the sheet half-thickness h at the breakup position lb;lisa

is estimated as

h ¼h0 d0 � sb;lisa

2lb;lisa sinðhÞ þ d0 � sb;lisa

ð2:98Þ

with h0 � ðdf =2ÞcosðhÞ. If it is assumed that breakup occurs when the amplitude ofthe most unstable wave is equal to the radius of the ligament dL, a mass balancegives the drop size dD:

d3D ¼

3pd2L

KL; ð2:99Þ

50 2 Fundamentals

where the most unstable wavelength KL is given by

KL ¼1dL

12þ 3ll

2ðqlrdLÞ1=2

" #�1=2

ð2:100Þ

that is based on an analogy to Weber’s result for growing waves on cylindrical,viscous liquid columns.

2.2.2.8 Secondary Breakup Models

The secondary breakup process is often modeled using the hybridKelvin-Helmholtz wave model and Rayleigh-Taylor model (Beale and Reitz 1999).The Kelvin-Helmholtz (KH) model is based on liquid jet stability analysis (Reitzand Bracco 1986). The analysis examines the stability of the surface of a cylindricalliquid jet to perturbations using a first order theory. The viscous liquid jet withvelocity Ul is injected into a stagnant incompressible inviscid gas. An infinitesimalaxisymmetric surface displacement is imposed to the initially steady surface:

g ¼ <½g0 expðikzþ xtÞ�: ð2:101Þ

A dispersion equation, that includes the physical and dynamical parameters ofthe liquid jet and surrounding gas, relates the growth rate x to its wavelengthk ¼ 2p=k and is derived from the linearized hydrodynamical equations. Velocitypotential and stream functions are written in the form of wave solutions asfunctions of the cylindrical coordinates (r; z) and time t:

U1 ¼ C1I0ðkrÞ expðikzþ xtÞ; ð2:102Þ

W1 ¼ C2I1ðLrÞ expðikzþ xtÞ: ð2:103Þ

C1 and C2 are integration constants. I0 and I1 are modified Bessel functions of thefirst kind. L2 ¼ k2 þ x=ml with ml the liquid kinematic viscosity. The gas pressureat the interface r ¼ r0 is given as

p ¼ �q Urel � ixk

� �2kg

K0ðkr0ÞK1ðkr0Þ

: ð2:104Þ

K0 and K1 are modified Bessel functions of the second kind. With the assumptionof g r0, the kinematic, tangential stress, and normal stress equations at theinterface are written as

Ul;r ¼ogot; ð2:105Þ

oUl;z

or¼ �oUl;r

oz; ð2:106Þ


pl ¼ 2lloUl;r

or� r

r20

gþ r20o2goz2

� �þ p; ð2:107Þ

which forms boundary conditions for Eqs. 2.102–2.104. Ul;r and Ul;z are the radialand axial liquid velocity components. Equations 2.105 and 2.106 are used todetermine the integration constants C1 and C2. Substituting Eqs. 2.102–2.104 intoEq. 2.107, the dispersion equation is obtained as:

x2þ2Ul;rk2x

I01ðkr0ÞI0ðkr0Þ

� 2kL

k2 þ L2

I1ðkr0ÞI0ðkr0Þ

I 01ðLr0ÞI1ðLr0Þ

� �

¼ L2 � r20

L2 þ r20

I1ðkr0ÞI0ðkr0Þ

rk

qlr20

ð1� k2r20Þ þ

qqlðUrelk � ixÞ2K0ðkr0Þ

K1ðkr0Þ

� �: ð2:108Þ

K0 and K1 are modified Bessel functions of the second kind. Equation 2.108 issolved numerically and it is found that there is a single maximum in the wavegrowth rate curve. Curve fits of the numerical solutions have been generated forthe maximum growth rate and the corresponding wavelength, which results in

KKH ¼9:02rdð1þ 0:45Z0:5Þð1þ 0:4T0:7Þ

ð1þ 0:865We1:67air Þ

0:6 ; ð2:109Þ

XKH ¼0:34þ 0:38We1:5

air

ð1þ ZÞð1þ 1:4T0:6Þ

ffiffiffiffiffiffiffiffir

qlr3d

r: ð2:110Þ

The gas Weber number is defined as

Weair ¼ qU2relrd=r; ð2:111Þ

and the Ohnesorge number

Z ¼We1=2d Re�1

l : ð2:112Þ

Urel is the relative velocity between the gas and the droplet, and r is the surfacetension. The droplet Weber number is defined as

Wed ¼ qlU2relrd=r; ð2:113Þ

and liquid Reynolds number is defined as

Rel ¼ qljUrelj2rd=ll: ð2:114Þ

T is the Taylor number:

T ¼We1=2air Z: ð2:115Þ

The KH model is implemented by postulating that a parent parcel with radiusrd, breaks up to form new droplets with radius rd;c, which is determined by:

52 2 Fundamentals

rd;c ¼ B0KKH ; ð2:116Þ

where B0 is a model constant. The rate of change in the radius of the parent dropletparcel is described by

drd

dt¼ rd � rd;c

sKH; ð2:117Þ

where the breakup time scale sKH is defined as

sKH ¼3:726B1rd

XKHKKH: ð2:118Þ

B1 is a model constant.Rayleigh-Taylor (RT) instability is believed to be responsible for additional

droplet breakup. Thus the RT model is usually used in conjunction with the KHmodel to predict instabilities on the surface of the drop that grow until a certaincharacteristic breakup time when the drop finally breaks-up. The RT model is alsobased on wave instability theory. The unstable RT waves are thought to occur due tothe rapid deceleration of the drops. Neglecting both the gas and liquid viscosity, thefrequency of its fastest growing wave and corresponding wavelength are given by

XRT ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2

3ffiffiffiffiffiffi3rp ½�adðql � qÞ�1:5

ql þ q

s; ð2:119Þ

KRT ¼ 2pXRT

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi3r

�adðql � qÞ

s: ð2:120Þ

ad is the droplet acceleration in the direction of travel. When the wavelength issmaller than the droplet diameter, the RT waves are assumed to be growing on thesurface of the droplet. The wave growth time is then tracked. When it reaches itsRT breakup time scale, which is defined as

sRT ¼ Cs=XRT ; ð2:121Þ

the drop is assumed to breakup. The radii of the new droplets is computed using

rd;c ¼ 2CRTKRT ; ð2:122Þ

where Cs and CRT are model constants. A liquid breakup length can be introduced,which is based on the theory that breakup process occurs at a different rate withinand beyond the length of the liquid core (Xin et al. 1998). The RT model is thenonly applied to the decelerating drops beyond this liquid breakup length. However,the drops that are adjacent to the liquid core and within the breakup length aredecelerated by drag with the ambient gas, too. These drops should also be


influenced by the RT model. Thus, activity of the RT model is not determined bythe liquid breakup length, but by the instability condition in Eq. 2.121.

2.2.2.9 Turbulent Dispersion Models

A droplet moves according to its velocity:

dxd

dt¼ Vd: ð2:123Þ

If only the drag force and body force are considered, the acceleration of adroplet is written as:

dVd

dt¼ Fd

md¼ DdðU� VdÞ þ g; ð2:124Þ

with drag function Dd:

Dd ¼38qjU� Vdj

qdrdCdðRedÞ; ð2:125Þ

drag coefficient Cd:

Cd ¼24Re�1

d ð1þ Re2=3d =6Þ; Red\1000

0:424; Red 1000

(; ð2:126Þ

droplet Reynolds number Red:

Red ¼2qrdjU� Vdj

lairðT̂Þ; ð2:127Þ

T̂ ¼ ðT þ 2TdÞ=3; ð2:128Þ

and gas instantaneous velocity U (gas velocity seen by the droplet):

U ¼ ~Uþ u00d : ð2:129Þ

Turbulence effects on a droplet’s movement are modeled by the turbulentdispersion model, which provides a closure form for the gas turbulent velocity u00d .Each component of u00d is randomly chosen from a Gaussian distribution with

standard deviation r ¼ffiffiffiffiffiffiffiffiffiffi2k=3

p. u00d is chosen once every turbulence correlation

time tturb, which is the minimum of an eddy breakup time and a time for the dropletto penetrate an eddy:

tturb ¼ mink

e; cps

k3=2

e1

jU� Vdj

� �; ð2:130Þ

54 2 Fundamentals

where the empirical constant cps ¼ 0:16432. When the cumulative time stepDtc [ tturb, the droplet velocity and position are updated using (Amsden et al.1989):

DVd ¼ Dt½DdðU� VdÞ þ g� þ du0; ð2:131Þ

Dxd ¼ VdDt þ dx0; ð2:132Þ

with

dx0 ¼ tperdu0 þ dx0b: ð2:133Þ

du0 and dx0b are sampled from Gaussian distributions with variances r2u0 and

r2x0 � t2

perr2u0 , with

r2u0 ¼

1� e�Ddtturb

1þ e�Ddtturb1� e�2DdDt

r2; ð2:134Þ

r2x0 ¼ tsDt � 2tturb

Dd1� e�2DdDt

þ r2u0

D2dr

2

� �r2; ð2:135Þ

and turbulent persistence time tper:

tper ¼r2

r2u0

tturbð1� e�DdDtÞ � 1Dd: ð2:136Þ

2.2.2.10 Droplet Deformation Model

The drops are assumed to be spherical, which in reality is only true for very smalldrops. Especially when the relative velocity between the drop and the surroundinggas is high, the drop deforms, which will change its drag coefficient. Its defor-mation depends on the drop’s Reynolds number and oscillation amplitude. In thiscase, the liquid drop drag coefficient has been related empirically to the magnitudeof the drop deformation using

Cd ¼ Cd;sphereð1þ 2:632yÞ; ð2:137Þ

where Cd;sphere is the drag coefficient of the spherical drop; y is a dimensionlessparameter describing drop distortion in Eq. 2.26 and is proportional to the dis-placement of the drop’s surface from its equilibrium position divided by the dropradius. y ¼ 0 represents the lower limit of a sphere, and y ¼ 1 the upper limit of aflat disk. y can be computed using the Taylor analogy breakup model (O’ Rourkeand Amsden 1987) or the droplet deformation and breakup (DDB) model (Ibrahimet al. 1993). The TAB breakup model considers a liquid drop to be analogous to aspring-mass system (Taylor’s analogy), and the drop breakup is due to an increase


in the amplitude of the drop oscillation. The acceleration of the drop distortionparameter is given as

€y ¼ �5ll

ql

_y

r2d

� 8ry

qlr3d

þ 23

qql

U2rel

r2d

: ð2:138Þ

The DDB model is formulated based on energy and volume conservation of thedistorting drop and is written as

€y ¼ �4ll

ql

_y

r2dy2� 27

16p2r

qlr3d

1� 24

3py

� �6" #

þ 38

qql

U2rel

r2d

: ð2:139Þ

The DDB model takes into account the increased frontal area of the distorteddrop and thus is more accurate (Tennison et al. 1998).

2.2.2.11 Droplet Collision Model

The original collision model in the KIVA-II code, the O’Rourke model (O’ Rourke1981) only considers collisions between particles that are located in the samecomputational cell. The collision frequency of a certain pair of particles is

m ¼ Nmp

Vcellpðrlp þ rmpÞ2jVlp � Vmpj: ð2:140Þ

The subscripts mp and lp denote the more populous and less populous dropletparcels, respectively. Vcell is the volume of the local cell containing the drops. Theprobability that the larger particle undergoes n collisions with the smaller particlefollows a Poisson distribution, and thus the probability of no collision is

P0 ¼ e�mDt; ð2:141Þ

where Dt is the computational time step. A random process is utilized to determinewhether the collision event will occur or not. Another independent random numberYY from the interval (0,1) is used to calculate the collision impact parameter b:

b ¼ YY1=2ðrlp þ rmpÞ; ð2:142Þ

which determines the collision outcome by comparing with the critical impactparameter bcr:

bcr ¼ ðrlp þ rmpÞfmin½1; 2:4ðc3 � 2:4c2 þ 2:7cÞ=Welp�g1=2 ð2:143Þ

with c ¼ rS=rL, and Weber number of the larger drop

Welp ¼ qdjVlp � Vmpjrlp=að�TdÞ: ð2:144Þ

56 2 Fundamentals

The mean temperature �Td is:

�Td ¼r3

mpTd;lp þ r3mpTd;mp

r3lp þ r3

mp

; ð2:145Þ

and a is the liquid surface tension coefficient:

að�TdÞ ¼�Td � Tcr

T0 � Tcra0: ð2:146Þ

When b\bcr , coalescence occurs. Otherwise, each collision is assumed to be agrazing collision.

In the case of a coalescence collision, the droplet number of the new parcel ismDt and the properties of the new parcel are determined from the conservation lawsof mass and momentum. If it is a grazing collision, momentum conservation and acertain fraction of loss in kinetic energy and angular momentum is taken intoaccount. The new velocities of the droplet parcels are given as:

Unewmp ¼

mlpUlp þ mmpUmp þ mmpðUlp � UmpÞmlp þ mmp

ffiffiffiffiffiffiffiffiffiffiffiffi1� fE

p; ð2:147Þ

Unewmp ¼ 1� Nlp

Nmp

� �Ump þ

Nlp

Nmp

mlpUlp þ mmpUmp þ mlpðUmp � UlpÞmlp þ mmp

ffiffiffiffiffiffiffiffiffiffiffiffi1� fE

p;

ð2:148Þ

where m is the mass of droplet parcel. The fraction of energy dissipation during thecollision fE is given as

fE ¼ðb� bcrÞ2

ðrlp þ rmp � bcrÞ2� 1: ð2:149Þ

Since the O’Rourke model only considers collision events between groups ofidentical droplets (parcel) that are located in the same computational cell, theoutcome of the model depends on mesh size. To remove mesh dependency,Munnannur and Reitz (2009) proposed a Radius-of-Influence (ROI) collisionmodel. The ROI model considers potential collision between every pair of dropletparcels whose distance Dlp;mp is smaller than the maximum of their influence radii,Rlp and Rmp:

Dlp;mp� maxðRlp;RmpÞ: ð2:150Þ

The collision frequency is then computed as:

m ¼ Nmp

Vcolpðrlp þ rmpÞ2jVlp � Vmpj: ð2:151Þ


The collision volume Vcol is based on the radii of influence:

Vcol ¼43pðRlp þ RmpÞ3: ð2:152Þ

Thus, the influence of mesh topology is removed and the collision events onlydepend on the droplet parcel distribution in space. The other elements of the ROImodel are the same as the O’Rourke model.

2.2.2.12 Evaporation Model

Assuming a single composition and homogeneous distribution of temperatureinside the droplet, the rate of droplet radius due to evaporation is given by theFrossling correlation (Faeth 1977):

_rd ¼drd

dt¼ � qD

2qdrdBmShd; ð2:153Þ

where Shd is the Sherwood number for mass transfer:

Shd ¼ ð2:0þ 0:6Re1=2d Sc1=3

d Þlnð1þ BmÞ

Bm; ð2:154Þ

with Schmidt number Scd ¼ lairðT̂ÞqD . qD is the fuel vapor diffusivity in air and it is

calculated from the estimated temperature T̂ in Eq. 2.128 and:

qDðTÞ ¼ D1TD2 ; ð2:155Þ

where D1 and D2 are model constants. Bm ¼ YF;s�YF;11�YF;s

is the Spalding mass transfer

number, with YF;s and YF;1 the fuel vapor mass fraction at the droplet’s surfaceand at the outer boundary of the film surrounding the droplet. The surface massfraction YF;s is computed from the Clausius-Clapeyron equation:

YF;sðTdÞ ¼1

1þ WairWF

ppvðTdÞ � 1h i; ð2:156Þ

where WF is the molecular weight of fuel vapor; Wair is the local averagemolecular weight of all species except fuel vapor. pv is the equilibrium fuel vaporpressure.

The rate of droplet temperature change is determined from the energy balanceequation:

43qdpr3

dCl _Td � 4qdpr2d _rdLðTdÞ ¼ 4pr2

d_Qd; ð2:157Þ

58 2 Fundamentals

where Cl is the liquid specific heat; LðTdÞ is the latent heat of vaporization; _Qd isthe rate of heat conduction to the droplet surface per unit area and is computedusing the Ranz-Marshall correlation (Faeth 1977):

_Qd ¼kairðTÞðT � TdÞ

2rdNud; ð2:158Þ

where the Nusselt number Nud:

Nud ¼�

2:0þ 0:6Re1=2d Pr1=3

d

� lnð1þ BmÞBm

; ð2:159Þ

with Prandtl number Prd ¼lairðTÞCpðTÞ

kairðTÞ, local specific heat at constant pressure

Cp, and thermal conductivity coefficient of air kair:

kairðTÞ ¼K1T3=2

T þ K2; ð2:160Þ

where K1 and K2 are model constants.Ra and Reitz (2009) developed a more accurate model that considers transient

heat transfer inside the droplet. Instead of setting a uniform droplet temperature,the droplet surface temperature Td;s is computed from a heat and mass transferbalance at the interface between the droplet and surrounded gas when the dropletsize is larger than a preset critical value. The energy balance at the interface iswritten as

4qdpr2d _rdLðTd;sÞ ¼ 4pr2

dðQi þ QdÞ; ð2:161Þ

where Qi is the energy flux from inside the droplet to the surface. It is modeled as aconvective heat transfer process with internal circulation taken into account andwritten as

Qi ¼kl

deðTd � Td;sÞ; ð2:162Þ

where kl is the liquid thermal conductivity. de is the unsteady equivalent thicknessof the thermal boundary layer and calculated from the effective thermal diffusivity:

de ¼ffiffiffiffiffiffiffiffiffiffiffipaeff t

p¼

ffiffiffiffiffiffiffiffiffiffiffipvaltp

; ð2:163Þ

with

v ¼ 1:86þ 0:86 tanh 2:225 log10 Pel=30ð Þ½ �;

and Pel is the Peclet number of the droplet. Qd is also computed from the dropletsurface temperature Td;s. Equation (2.158) is then turned into


Qd ¼kairðTÞðT � Td;sÞ

2rdNud: ð2:164Þ

Since the effective heat transfer coefficient for the outer heat flux is coupledwith the vaporization rate, the surface temperature of the droplet is determined bysolving two balance equations iteratively, and assuming a quasi-steady heattransfer process.

Other evaporation models consider multi-component fuel effects. Continuousmulti-component models (Lippert and Reitz 1997; Zuo et al. 2000; Zhu and Reitz2002; Ra and Reitz 2003, 2004; Yang and Reitz 2009b, 2010), discrete multi-component models (Ra and Reitz 2009), and discrete/continuous multi-componentmodels (Yang et al. 2010) have been developed and applied to IC engine simu-lation. However, in the examples of this book, multi-component effects are notconsidered.

2.2.2.13 Spray Wall Impingement Model

Spray wall impingement is very important for both PFI and DI engines. Fuel wallfilms in the intake ports can cause an undesirable fuel delivery delay and anassociated fuel metering error in PFI engines. In some DISI engines, the fuel isdirectly injected into a specially designed piston bowl and the spray wallimpingement is used to generate an optimal stratified mixture. While in DI dieselengines, the spray wall impingement may lead to unacceptable UHC and/or sootemission, as well as low fuel efficiency. Therefore, an accurate spray/wall inter-action model also plays important role in engine simulations.

The outcome of the wall impingement event depends on the properties of thedrop, wall surface, and gas boundary layer in the near-wall region. If the walltemperature Tw is less than the liquid boiling temperature TB, a collision of a dropon the solid surface may result in sticking, bouncing, spreading, or splashing.

The stick regime occurs when the impact energy is low and the wall temper-ature is below the pure adhesion temperature Tpa. The impinging drop adheres tothe solid surface or coalesces with a liquid film existing on the surface.

As the Weber number is increased, drop rebound occurs from the wall or liquidfilm due to the effect of an air layer that is trapped between the drop and the wall orliquid film. The velocity and direction of the rebounding drop is often determinedfrom experimental and analytical correlations.

The spreading regime occurs at higher incident drop Weber numbers. Here thedrop spreads on the wall surface for a dry wall, or merges with the liquid wall filmupon impact for a wet wall. When a train of drops impacts the wall surface, thetime between multi-drop impacts, or the impact frequency, must be considered.

The splash regime occurs at high incident Weber numbers. The splash-back ofliquid corresponds to the development of the crown instability, which leads tosecondary atomization of the impinging drop and/or wall film. FollowingO’Rourke and Amsden’s approach (2000), the criterion for splash is

60 2 Fundamentals

E2splash ¼

We

minðHf=dd; 1Þ þ Re�1=2d

[ E2splash;crit; ð2:165Þ

where Hf is the thickness of the liquid film. The drop Reynolds number here isabout the drop velocity normal to the surface. E2

splash;crit ¼ 3330:0 is used in thisbook (O’Rourke and Amsden 2000). Splashed drop radii are assumed to have aNukiyama-Tanasawa distribution:

PðrdÞ ¼4ffiffiffipp r2

d

r3d;max

exp � rd

rd;max

� �2" #

; ð2:166Þ

where rd;max relates to the incident drop radius rd;0 as

rd;max ¼ rd;0 maxE2

splash;crit

E2splash

;6:4We

; 0:06

!: ð2:167Þ

The normal component of the splashed droplet velocity Un is also assumed tohave a Nukiyama-Tanasawa distribution:

PðUnÞ ¼4ffiffiffipp U2

n

U3n;max

exp � Un

Un;max

� �2" #

ð2:168Þ

with Un;max ¼ 0:2Un;0 and Un;0 is the normal component of the incident dropvelocity. The fluctuating component of the secondary droplet tangential velocity un

is assumed to follow a Gaussian distribution with variance of 0:01U2n;0. The final

velocity of the secondary droplet is written as

Ud ¼ Unnþ ð0:12Un;0 þ unÞðet cos Wþ ep sin WÞ þ 0:8Ut;0et; ð2:169Þ

where Ut;0 is the tangential component of the incident drop velocity. n is the unitvector normal to the surface. et is the unit vector tangent to the surface and in theplane of n and the incident drop velocity. ep ¼ n� et. W is the angle of tangentialvelocity with the vector et in the plane of the wall that lies in the interval ofð�p; pÞ. Its value is chosen from the following distribution (Naber and Reitz1988):

PðWÞ ¼

12p; b ¼ 0

b2pðeb � 1Þ exp b 1� jWj

p

� �� ; b[ 0

8>><>>: ; ð2:170Þ

where b is a parameter related to the impact angle a:

sin a ¼ eb þ 1eb � 1

b2

b2 þ p2: ð2:171Þ


The liquid film is modeled using a thin film assumption and integrating crossthe film thickness. Continuity, momentum, and energy equations are reduced to a2D film. The continuity equation is transformed into

qlAwalloHf

otþ ðUf � UwÞ � rSHf

� �¼ _Mimp � _Mvap; ð2:172Þ

where Awall is the wall area; Uw is the wall velocity; rS is the gradient operator onthe surface. _Mvap is the rate of fuel vaporization. _Mimpis the mass source terms dueto impingement:

_Mimp ¼ �Z

43

pr3dqdVd � nf ðVd; rd; Td; y; _y; xs; tÞdVddrddTddyd€y: ð2:173Þ

The wall film momentum equation is

qloðHf Uf Þ

otþ ðUf � UwÞ � rSðHf Uf Þ

� �þ HfrSpf ¼ swet

� llðTf ÞUf � Uw

Hf =2þ _Pimp � ð _Pimp � nÞn

þ _Mimp½ðUw � nÞn� Uf � þ dpf nþ qlHf g; ð2:174Þ

where sw is the stress tensor on the gas-side of the film; et is the unit vector tangentto the surface in the direction of Uf � Uw; Tf is the mean film temperature; _Pimp isthe momentum source terms due to impingement:

_Pimp ¼ �Z

43pr3

dqdVdVd � nf ðVd; rd; Td; y; _y; xs; tÞdVddrddTddyd€y; ð2:175Þ

with xs is the coordinates of the wall. pf is the film pressure that is assumed to ariseentirely from the impingement:

pf ¼ ð _MimpUw � _PimpÞ � n: ð2:176Þ

dpf is the pressure difference across the film; g is the acceleration due togravity.

The mean film temperature Tf is assumed to be a piecewise linear profile(Stanton and Rutland 1998). The profile varies from the wall temperature Tw to aninterface temperature Ts. The energy equation of the film is written as (Stanton andRutland 1998):

qlCv;lAwalloðTf Hf Þ

otþ Hf ðUf � UwÞ � rS Tf þ

Ts � Tw

6

� ��

¼ klAwallTs � Tf

Hf =4� Tf � Tw

Hf =4

� �þ _Qimp � _Qsplash; ð2:177Þ

62 2 Fundamentals

where Cv;l and kl are specific heat and thermal conductivity of the liquid,

respectively; _Qimp and _Qsplash are the energy source terms due to impingement andsplash, respectively. Energy conservation at the interface with the gas flow iswritten as

klTs � ½2Tf � ðTw þ TsÞ=2�

Hf=2þ _MvapL ¼ hlðT1 � TsÞ; ð2:178Þ

with L the latent heat, hl the heat transfer coefficient of the film, and T1 the gastemperature.

2.2.2.14 Liquid Phase Source Terms

Effects of the liquid phase on the gas phase flow are modeled by introducingappropriate source terms in the conservation equations of the gas flow (c.f., Eqs.2.10–2.12, 2.15, and 2.41. The averaged source terms are given as

_qs ¼ �Z

4pr2d _rdqdfdVddrddTddyd€y; ð2:179Þ

Fs ¼ �Z

43pr3

dF0 þ 4pr2d _rdVd

� �qdfdVddrddTddyd€y; ð2:180Þ

_Qs ¼ �Z

43

pr3d Cp;l _Td þ F0 � ðVd � ~U� u0Þ� �

þ4pr2d _rd elðTdÞ þ

12ðVd � ~UÞ2

� ��qdfdVddrddTddyd€y; ð2:181Þ

_Ws ¼ �Z

43pr3

dF0 � u0qdfdVddrddTddyd€y: ð2:182Þ

where F0 ¼ F� g.

2.2.2.15 Crevice Flow Model

Crevice flow processes are the major sources of unburned hydrocarbons in SIengines (Reitz and Kuo 1989). Accurate modeling of the crevice flow is still achallenge for multi-dimensional engine simulation (Lee and Reitz 2010). Some-times, when the crevice volume is not resolved in the computational mesh, aphenomenological crevice flow model is required.

The crevice flow model used in the present book solves coupled ordinarydifferential equations that describe the piston ring dynamics and the flows through


the ring-side clearances and ring gaps (Reitz and Kuo 1989). The solution providesa boundary condition to the multi-dimensional engine simulation. Figure 2.12shows a schematic of a piston with two compression rings and an oil ring, whichseparate the whole crevice volume into five regions. Any two regions are con-nected through the ring end-gap as shown in Fig. 2.12. Neighboring regions maybe connected by the ring-side clearance depending on the position of the ring in thegroove. The crevice flow model assumes that: (1) each crevice region has uniformpressure, and the pressure in the top crevice region is the same as the pressure inthe combustion chamber; (2) the crevice volume has a large surface-to-volumeratio so that the flow in the crevice is isothermal and at the wall temperature; (3)the gas composition in all regions is the same; (4) the flow through the ring creviceis laminar; (5) the cylinder bore is round with the piston always centered in thebore. The model crevice volume is then viewed as a reservoir. This reservoirexchanges mass with the cells along the periphery, acting as a source or sink forcylinder mass. Mass exchange between connected regions is based mass conser-vation, e.g., for region i,

Vidqi

dt¼ _mi�1;i � _mi;iþ1; ð2:183Þ

where Vi and qi are the volume and density of region i, respectively. _mi�1;i is the flowthrough the ring-side clearances and is computed from isothermal compressible flowequations for the flow in a narrow channel of height h and ring width w:

_m

A

� �2

¼ p2u � p2

d

2RT fwh þ ln pu

pd

� �h i; ð2:184Þ

Head

Combustion Linear

Chamber

Ring-side clearance h

1

32

4

5

Oil RingPiston

Fig. 2.12 schematic ofpiston-cylinder-ring creviceswith 5 different regions andgas flow path

64 2 Fundamentals

where pu and pd are the pressure upstream and downstream, respectively; A is thearea normal to the flow direction; T is wall temperature; and f ¼ 24=Rec is thefriction factor. Here the Reynolds number is defined as:

Rec ¼_m

A

2h

l: ð2:185Þ

The flow through the ring end-gaps represents additional source terms forregions 1, 3, and 5. The flow rate _m is calculated using the isentropic orifice-flowequation:

_m ¼ Cd;cAgqag; ð2:186Þ

where Cd;c ¼ 0:86 is the discharge coefficient; Ag is the area of ring end-gap; a isthe speed of sound; and g is the compressibility factor for isentropic flow:

g ¼

2c� 1

piþ1

pi

� �2c

� piþ1

pi

� �cþ1c

" #( )12

;piþ1

pi[ 0:52

2cþ 1

� � cþ12ðc�1Þ

;piþ1

pi� 0:52

8>>>>><>>>>>: : ð2:187Þ

The motion equation of the piston ring is written as:

mrdh

dt¼ Fp þ Ff þ Fi þ Fs; ð2:188Þ

where mr is the ring mass and h is the ring top-side clearance. The pressure forceon the top ring is calculated as:

Fp ¼ ðp1 � p3ÞAr=2; ð2:189Þ

where Ar is the ring-side surface area. The friction force Ff is calculated as

Ff ¼ �f pdrhrpbr; ð2:190Þ

where dr is the outside diameter of the ring; hr is the thickness of the ring; pbr isthe pressure behind the ring. The friction coefficient f is given as

f ¼ 4:8

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiloil

Up

pbrhr

s; ð2:191Þ

where loil is the oil viscosity; and Up is the instantaneous piston velocity. Theinertia force is given as

Fi ¼ �mrap; ð2:192Þ


where ap is the acceleration of the piston. The oil resistance force is calculated as

Fs ¼ �0:1loilLrdh

dt

w

hs

� �3

; ð2:193Þ

where Lr is the ring length in the circumferential direction and hs is the distancebetween the piston groove and the ring in the direction of the ring motion.

2.2.2.16 Boundary Conditions

Accurately imposed boundary conditions are essential for IC engine simulation.For instance, heat loss on the solid wall, which is important for engine efficiency,exhaust emissions, and component thermal stresses, is very sensitive to the cor-responding boundary conditions used in the simulation. Four types of boundaryconditions are considered in the present book: inflow boundary; outflow boundary;rigid wall boundary; periodic boundary.

For the inflow boundary, the Dirichlet (or first-type) boundary condition isusually used, i.e., the quantities are set to known values. For the outflow boundary,a Neumann (or second-type) boundary condition is usually used, i.e., the normalcomponents of the gradients of the quantities are set to zero.

Several options are available for the rigid wall boundary. The velocity boundaryconditions on rigid walls can be free slip, no slip, or turbulent law-of-the-wall.Temperature boundary conditions on the rigid walls can be adiabatic, isotherm, orturbulent law-of-the-wall. The turbulent law-of-the-wall boundary conditions forboth velocity and temperature have been proven to be more accurate options (Hanand Reitz 1997). In the near wall region, it is assumed that: (1) the normalcomponents of the gradients are much larger than tangential components; (2) gasvelocity is parallel to the wall; (3) pressure gradients are neglected; (4) viscousdissipation, and Dufour and enthalpy diffusion effects on the energy flux areneglected. The normal components of the gas velocity are set to the normal wallvelocity:

U � n ¼ Uwall � n: ð2:194Þ

The tangential components of the velocity are determined by matching to alogarithmic profile (Amdsen et al. 1989):

v

u�¼

j�1 ln Clw17=8� �

þ Blw; 1[ Relw

11=2; 1�Relw

8<: ; ð2:195Þ

where 1 ¼ qyv=lairðTÞ is the Reynolds number based on the gas velocity relativeto the wall v¼jU� Uwallj, which is evaluated a distance y from the wall; y is smallenough to be in the logarithmic region or the laminar sub-layer region of theturbulent boundary layer. The Reynolds number Relw defines the boundary

66 2 Fundamentals

between these two regions; u� is the shear speed which is related to the tangentialcomponents of the wall stress by:

rw � ðrw � nÞ � n ¼ qu�2v

vð2:196Þ

with v ¼ U� Uwall. Other constants are related to the model constants in the k-emodel:

j ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiC1=2

l ðCe;2 � Ce;1Þre

q; ð2:197Þ

Blw ¼ Re1=2lw � j�1 ln ClwRe7=8

lw

� �: ð2:198Þ

For commonly accepted values of the k-e model, constants Blw ¼ 5:5 andClw ¼ 0:15. Friction heating is taken into account by introducing a source to theinternal energy:

fw ¼ rw � v ¼ qu�2v: ð2:199Þ

The temperature wall function is given as (Han and Reitz 1997):

Tþ ¼ 2:1 ln yþ þ 2:1Gþyþ þ 33:4Gþ þ 2:5; ð2:200Þ

with yþ ¼ u�ylairðTÞ and Gþ ¼ QclairðTÞ

qwu� . Qc is the chemical heat release. The corre-

sponding wall heat flux qw is written as:

qw ¼qCpu� lnðT=TwÞ � ð2:1yþ þ 33:4ÞGlairðTÞ=u�

2:1 ln yþ þ 2:5: ð2:201Þ

Neglecting the source term G, Eq. 2.201 is simplified as

qw ¼qCpu� lnðT=TwÞ2:1 ln yþ þ 2:5

: ð2:202Þ

Boundary conditions for the turbulence kinetic energy and its dissipation rateon the rigid walls are given as (Amdsen et al. 1989):

rk � n ¼ 0; ð2:203Þ

ew ¼ jk3=2

y: ð2:204Þ

Periodic boundaries are used only when the flow field is assumed to have an N-fold periodicity about the axis, i.e., a sector mesh is used. If the whole physicaldomain is viewed in a cylindrical coordinate system, the periodic boundaries arethose for which h ¼ 0 and h ¼ 2p=N. For a scalar quantity q and a vector v, theboundary condition states


qðr; h; zÞ ¼ qðr; hþ 2p=N; zÞ; ð2:205Þ

vðr; h; zÞ ¼ R � vðr; hþ 2p=N; zÞ; ð2:206Þ

where R is the rotation matrix corresponding to the angle 2p=N.Swirl flow that is common in the IC engine affects turbulent mixing and the

consequent combustion process. Initialization of the swirl flow is required for anengine simulation without a full intake flow simulation. Assumption of a wheelflow profile is usually not accurate enough because the turbulent boundary layernear the wall forces the swirl velocity to decrease in the wall region. A Besselfunction profile represents the flow more accurately (Amsden et al. 1989). Adimensionless constant that lies between zero (the wheel flow limit) and 3.83 (zerovelocity at the wall) is used to define the azimuthal velocity profile. For IC engineapplication, a value of 3.11 is usually used (Wahiduzzaman and Ferguson 1988).

Combustion chamber wall temperatures are usually estimated based on limitedexperimental data. However, conjugate heat transfer analysis have been performedthat allow wall temperatures to be predicted accurately (Wiedenhoefer and Reitz2003a, b; Yoshikawa and Reitz 2009). In the examples considered in this bookestimated wall temperatures are applied.

2.2.3 Numerical Methods

The CFD code used in the present book, KIVA3v2, employs a finite volumemethod with a structured staggered mesh consisting of arbitrary hexahedrons.Convective fluxes are computed using a quasi-second-order upwind (QSOU)scheme (Amsden et al. 1989). A SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) algorithm (Patankar and Spalding 1972) is used to computepressure. An explicit scheme is used for temporal differencing. The spatial dif-ferencing is based on the Arbitrary Lagrangian–Eulerian (ALE) computing method(Hirt et al. 1997). Except for the velocity, all gas flow quantities are stored in thecells. The gas velocities are stored in momentum cells which are centered aboutthe vertices. Thus, the velocities are located at the vertices while other quantitiesare located at the cell centers. A ghost fluid technique is used to deactivate cells asthe piston moves.

The spray equation, Eq. 2.30, is solved using a Monte-Carlo/particle method.The spray is represented by a set of drop parcels. Each parcel p is composed of anumber of droplets Np with equal locations xp, velocities Vd;p, sizes rd;p, tem-peratures Td;p, and oscillation parameters yp and _yp. The continuous distribution fis approximated by the discrete distribution f �:

f � ¼XNP

p¼1

Npdðx� xpÞdðVd � Vd;pÞdðrd � rd;pÞ

� dðTd � Td;pÞdðy� ypÞdð _y� _ypÞ: ð2:207Þ

68 2 Fundamentals

The particles evolve following the corresponding equations described in Sects.2.2.2.8–2.2.2.13.

Time steps Dt are determined in a dynamic way to fulfill accuracy and stabilityrequirements with good computational efficiency, and the global time step is set tothe smallest time step. The Courant–Friedrichs–Lewy (CFL) condition is used todetermine the convection time step Dtc:

Dtnþ1c ¼ fcDtn

c minVi

dVflux;i

� �; ð2:208Þ

where subscript i is the cell index and superscript n is the time step index. dVflux isthe flux volume. A factor fc ¼ 0:2 is typically used for confidence in stability andaccuracy. The acceleration time step is determined as

Dtnþ1acc ¼ fa min

Dxi

jUni � Un�1

i j

� �; ð2:209Þ

where fa is a positive real number of order unity with default value of 0.5. Dx is thecharacteristic cell size. The rate-of-strain tensor time step is given as

Dtrst ¼ fr min jkij�1; ð2:210Þ

where k is the eigenvalue of the rate-of-strain tensor (Asmden et al. 1989). Thechemistry time step is based on the change rate of the energy:

Dtnþ1ch ¼ fch min

_Qc;ni

qni en

i

� �: ð2:211Þ

The spray time step is determined in a similar way:

Dtnþ1sp ¼ fsp min

qni

_qs;ni

;qn

i eni

_Qs;ni

!; ð2:212Þ

which limits the change rate of mass and energy due to spray evaporation. A timestep Dtnþ1

gr is considered to limit the rate that the time step can grow:

Dtnþ1gr ¼ fgrDtn: ð2:213Þ

fgr is greater than unity and is usually set to 1.02. The final time step is given by

Dtnþ1 ¼ minðDtnþ1c ;Dtnþ1

acc ;Dtnþ1rst ;Dtnþ1

ch ;Dtnþ1sp ;Dtnþ1

gr ;Dtmx;DtmxcaÞ: ð2:214Þ

Dtmx and Dtmxca are the input maximum time step and maximum time step based oninput maximum crank angle, respectively.


2.2.4 CFD Codes and Software for Engine Simulations

The KIVA family of codes from the Los Alamos National Laboratory dominatedthe multi-dimensional IC engine simulation open source codes for more than threedecades. The first of the family was RICE (Rivard et al. 1975), which was a 2DEulerian code that used rectangular computational zones as its mesh. The effect ofpiston motion was added in the REC code (Gupta and Syed 1979). Although it wasdeveloped specifically for IC engine simulation, the KIVA codes are also appli-cable to various other multi-dimensional problems in fluid dynamics. TheAPACHE code (Ramshaw and Dukowicz 1979) followed RICE and added thegenerality of arbitrarily shaped computational cells. A general Eulerian–Lagrangian formulation and a subgrid scale turbulence model were added to theCONCHAS code (Butler et al. 1979) that followed the APACHE code. TheCONCHAS-SPRAY code (Cloutman et al. 1982) included a statistical spraymodel, wall functions for solid wall boundaries, and a generalized chemistrysolver. The KIVA code (Amsden et al. 1985) followed the CONCHAS-SPRAYcode and featured extended spray models and the ability for both 2D and 3Dsimulations. Improvements of the KIVA-II code (Amsden et al. 1989) over KIVAincluded improved computational efficiency and accuracy, the k-e turbulencemodel, improved spray models, and improved boundary conditions, etc. TheKIVA-3 (Amsden 1993) utilized a block-structured mesh to improve computa-tional efficiency in dealing with complex engine geometries, such as intake portsand valves. KIVA-3 V (Amsden 1997) retained all the features of the KIVA-3code and added an effective model for intake and exhaust valves (Hessel 1993).Other improvements that were mainly driven by the Engine Research Center at theUniversity of Wisconsin-Madison included advanced physical models (RNG k-emodel, LES model, nozzle flow model, KH-RT breakup model, ROI collisionmodel, KIVA-CHEMIKIN model, G-equation model, evaporation model, LISAmodel, wall function model, soot model, combustion model, as discussed above),code parallelization, and applications for automated engine optimization. All ofthe codes of the KIVA family use structured meshes, except for the latest memberof the KIVA family, the KIVA-4 code (Torres and Trujillo 2006), which usesunstructured meshes that can be composed of a variety of elements includinghexahedra, prisms, pyramids, and tetrahedra. Modules are used to exchange thedata between subroutines and versions of the KIVA-4 code are parallelized.

OpenFOAM is a free, open source CFD software package produced by acommercial company, OpenCFD Ltd (OpenFOAM). It consists of a flexible set ofC ++ modules for different engineering applications including IC engine simula-tion. A 3D unstructured mesh of polyhedrals is used in Open FOAM.

Commercial software that is capable of IC engine simulation include Star-CD(Star-CD 2001), FLUENT (2006), FIRE (2006), VECTIS (2006), CONVERGETM

(Senecal et al. 2002, 2007), and FORTÉTM (Liang et al. 2010; Naik et al. 2010;Puduppakkam et al. 2010). Star-CD and VECTIS are multi-purpose CFD softwarecodes with advanced automatic meshing techniques. FLUENT are FIRE are also a

70 2 Fundamentals

multi-purpose CFD software with dynamic unstructured mesh technique. CON-VERGETM uses an orthogonal structured mesh with adaptive mesh refinement andmesh embedding, which simplifies mesh generation. FORTÉTM is mainly based onthe KIVA3v Release 2 code and has implemented the most advanced chemistrysolvers and pioneers detailed chemistry applications in IC engine simulation. Theintegration of detailed chemistry in engine modeling is discussed in Chap. 3.

2.3 Regression Analysis Methods

A great amount of data can be generated in an engine optimization study usingCFD tools. It is necessary to apply data-mining to the results in order to selectdesigns of interest and also to explicitly illustrate the influences of designparameters on engine performance and emissions. Once the relationship (responsesurface) is established between the design parameters and the objectives ofinterest, information about this relationship can be used to further improve enginedesigns. Therefore, regression analysis is a very important procedure in compu-tational engine optimization.

Liu et al. (2006) used a non-parametric regression (NPR) method, namely thecomponent selection and smoothing operator (COSSO), to study a high-speeddirect injection (HSDI) diesel engine optimization problem and analyzed thecomplex correlations between NOx and soot emissions, and fuel consumptionresponses and control factors. They validated that the interactions between designparameters and their influence on responses could be quantitatively assessed.

COSSO is based on a smoothing spline analysis of variance (SS-ANOVA)model and it was originally proposed by Lin and Zhang (2006). Within thisframework, the response function can be expressed as following:

f ðxÞ ¼ bþXd

j¼1

fjðxðjÞÞ þXj\k

fjkðxðjÞ; xðkÞÞ þ � � � ð2:215Þ

where b is a constant for fitting, fj are the main effects of each inputs, fjk are two-way interactions for each pair of input parameters, and the sequence can becontinued for higher order interactions, but it is usually truncated to enhanceinterpretability. Usually only main effects or two-way interactions are considered.The response function f is determined by minimizing:

1n

Xn

i¼1

½yi � f ðxiÞ�2 þ kJðf Þ; ð2:216Þ

where yi is the i-th measured data point and f ðxiÞ is the corresponding predictedvalue with the form of Eq. 2.215. Therefore, the first term of Eq. 2.216 ensures aleast-square fit of the data. The role of the second term is to penalize the roughnessof the response function to avoid an excessively noisy fit, and Jðf Þ quantifies the


roughness of the response function f . The smoothness parameter k works as aweight to control the trade-off between fitting data and removing noise. COSSOdetermines the penalty function J from the sum of component norms and thesmoothness parameter k, from a cross validation technique. An iterative techniqueto optimize the number of components to be included in Eq. 2.215 is alsoemployed in COSSO to determine the response function based on the frameworkof the SS-ANOVA. It is also worth noting that with the COSSO method a designneeds to be selected as the reference point (center id) for the non-parametric study,and in this sense, the study can be regarded as sensitivity analysis of all parametersabout the reference design of interest. So, care has to be taken when interpretingthe response surfaces constructed using such regression methods, such as COSSO,because the shape of the response surfaces can be sensitive to the selection of thereference design. It is suggested to perform such regression analysis based onseveral optimal solutions that represent the most important design features. Thisanalysis methodology is employed throughout this book.

In non-parametric regression methods, no assumption is made about the dis-tribution of the data. This is particularly useful for engine optimization problemsdue to the complexity of the response surfaces between design parameters andobjectives. There are other regression or data-mining methods that can also beused for data analysis. For example, in the optimization study of a heavy-dutydiesel engine, Ge et al. (2009a) analyzed a large amount of data from enginesimulations over a wide range of operating conditions using a K-nearest neighbormethod.

Accordingly, four methods, including K-nearest neighbors (KN), Kriging (KR),Neural Networks (NN), and Radial Basis Functions (RBF) methods, are brieflyintroduced here. They will be used to explore their capacity of data-mining forengine optimization in Chap. 4.

The K-nearest neighbors method is a very simple regression method, whichestimates the value of the objective functions of the evaluated design based on itsnearest K neighbor designs. The distance between the evaluated design and itsneighbors can be used to weight the neighbors’ contribution, so that the nearerneighbors contribute more to the average than the more distant ones. The methodis not computationally intensive, so it is suitable for very large databases, i.e.,greater than 1,000. But it is poorly informative and highly localized on smalldatasets, and thus its prediction ability is limited, especially for data extrapolation.In addition, the regression results can be sensitive to the number of nearestneighbors (parameter K).

Kriging belongs to the family of linear least-squares estimation algorithms andwas originally the main tool for applications in geostatistics (named after D.A. Krige (1951)). Its behavior is controlled by a covariance function, called avariogram (e.g., Gaussian), which rules the correlation between the values of thefunction at different points. Essentially Kriging is a spatial interpolation techniquethat fits a random function to sampled known points to calculate unknowns.Similar to many other regression methods, the interpolates are weighted averagesof the known points, and the weights are calculated based on minimization of the

72 2 Fundamentals

Kriging variance of the estimate. A function can be rougher or smoother, canexhibit large or small ranges of variation, can be affected by a certain amount ofnoise, and all these features are embodied in the Kriging variogram model. In thisregard, the Kriging method is particularly applicable for highly non-linearresponses, but it is relatively computationally expensive compared to othermethods, e.g., the K-nearest neighbors method.

The neural network methods have also been widely and successfully applied tomany engineering problems. They are also normally called artificial neural net-works, which process data information by mimicking the structure and functionalaspects of biological neural networks. The most important aspect of any neuralnetwork method is learning, i.e., to find a solution to unknowns based on theknown observations in some optimal sense. So, intuitively the learning process onthe existing observations can be conducted using optimization methods to mini-mize the cost criterion and to approximate real solutions. The neural networkpackage available in the commercial software modeFRONTIER that is used in thisbook is based on classical feed-forward neural networks, with one hidden layer,and with an efficient Levenberg–Marquardt back propagation training algorithm.The initialization of the network’s parameters is based on the proper initializationapproach by Nguyen and Widrow (1990). It is noted that the computational cost ofusing neural networks can be high, especially with large data samples. Also, itusually requires a large diversity of trained data in order to achieve good per-formance of neural network methods.

Radial Basis Functions (RBF) are powerful tools for multivariate scattered datainterpolation. The values of those radial basis functions only depend on the dis-tance from a specified reference origin. The typical presumed representative RBFsare Gaussian, Multiquadric, Polyharmonic spline, and Thin plate spline functions.They can be used to build an approximation function that is represented as a sumof N radial basis functions, each associated with a different center and weight. Theweights can usually be estimated based on linear least-squares. So, the perfor-mance of RBF methods largely relies on the choice of the function type. Thecomputational cost of RBF methods is slightly less than or similar to neuralnetwork methods, but it is more expensive than the K-nearest neighbor method andKriging families.

The assessment of different regression methods is a subject of Chap. 4, spe-cifically to explore the feasibility of using regression analysis to partially replaceCFD evaluations. Chap. 6 intensively uses the COSSO method and proves itsreliability in engine optimization problems.

2.3 Regression Analysis Methods 73

Chapter 3Acceleration of Multi-Dimensional EngineSimulation with Detailed Chemistry

Detailed chemistry is necessary for kinetics-controlled combustion processes, suchas HCCI and low-temperature combustion. However, the use of detailed chemistrycan lead to significantly increased computational costs. This chapter summarizesseveral different strategies available to reduce computational costs when detailedchemistry is solved in the simulations.

3.1 Methods for Reducing Mesh- and Timestep-Dependencyin Engine CFD Modeling

Numerical models that have less mesh- and timestep-dependency are essential forconsistency in simulations, which is very important for engine combustion chamberoptimizations in which the mesh topology and structure vary. For computationaloptimization purposes, if a CFD model gives close numerical results when coarsemeshes or fine meshes are used, the coarse meshes should be considered for higherefficiency in optimization. In the single phase flow CFD simulation, grid conver-gence analysis is usually conducted at first to determine an appropriate mesh res-olution that can balance accuracy and efficiency. For two phase flows that aresimulated using the Lagrangian-Drop Eulerian-Fluid (LDEF) approach, issues ofmesh- and timestep-dependency become more severe. As pointed out by Mckinleyand Primus (1990), when mesh resolution is inadequate, the LDEF approach doesnot accurately capture strong gradients of velocity, temperature and fuel vaporconcentration in the gas phase. This deficiency can be explained by considering thetwo-way coupling procedure of the LDEF approach.

Figure 3.1 illustrates four-way coupling in the LDEF approaches with differentmesh resolutions in the 2D case. Liquid drops (or parcels of drops) are representedas circles. Take an example that one property of the gas phase (e.g., density,temperature) is stored at cell centers denoted by small green circles in the plots. Ifthis quantity is used in the spray equation, it needs to be interpolated from the cell


75

centers to the droplet’s position in a zero-order (assumption of homogeneousproperties in one cell) or first-order (linear interpolation) way. In the case of zero-order interpolation, the gas properties seen by the droplets in Fig. 3.1 are the samein the coarse mesh, while they are not for the fine mesh. The droplet propertiesneed to be assigned back to the Navier-Stokes equations as spray source terms. Asdepicted in Fig. 3.1, because of the different cell volumes, the resulting spraysource terms may be very different. As an extreme example, the spray source termsin the left two cells in the finer mesh are zero, while in the coarser mesh they arenon-zero at that position. In another words, the spray source terms that are betterresolved in a fine mesh are averaged on a coarse mesh. Thus, many spray-inducedgradients are smoothed out in the coarse mesh. Another source of mesh-depen-dency arises from the droplet interaction (collision). The original collision modelused in the KIVA code only considers collision events between droplet parcelslocated in the same computational cell. For instance, the collision event in thecoarse mesh that is indicated by the dashed line is not considered in the fine mesh(c.f., Fig. 3.1).

Apparently, a sufficiently refined mesh will give more accurate results. How-ever, the resulting prohibitive computational cost is not acceptable for currentengineering simulations, especially for optimization studies. Additionally, too finea mesh may violate the assumption that the liquid volume fraction is negligible inthe LDEF approach.

There are a number of efforts in the literature on the development of mesh-independent spray models. One strategy is to use a fixed mesh resolution in thenear nozzle region, so that at least the numerical results of spray simulations areconsistent. Schmidt and Rutland (2000) introduced a collision mesh method.A mesh that is independent of the mesh used for the CFD calculation of the gasflow is used for the collision calculations. Adaptive mesh techniques (Lippert et al.2005; Senecal et al. 2007; Xue and Kong 2009) have been developed in which themesh resolution is automatically refined based on gradients of certain quantitiessuch as velocity. The local mesh resolution of the near nozzle region then dependson the spray-induced high velocity gradient, which will also reduce meshdependency. However, this adds computational cost.

Béard et al. (2000) and Abani and Reitz (2010) developed subgrid gas particlemodels to improve liquid-to-gas phase coupling. The vaporization-induced subgridgradient in vapor concentration is modeled in a more accurate way. Abraham andMagi (1999) proposed a ‘‘Virtual Liquid Source’’ approach to avoid the two-waycoupling between liquid and gas where the near-nozzle liquid drops are replaced

Fig. 3.1 LDEF Approach on(left) coarse mesh and (right)fine mesh (Wang et al. 2010)

76 3 Acceleration of Multi-Dimensional Engine

with a liquid core. Liquid was assumed to move with the injection speed within thecore, and spray source terms were added in the cells adjacent to the core surface.A similar approach was adopted by Versaevel et al. (2000). Wan and Peters (1997)used a one-dimensional model for the liquid spray and coupled it with a three-dimensional Eulerian gas simulation. Since the spray was modeled, instead of two-way coupled with the gas phase cell, the mesh-dependency of the spray sourceterms could be removed.

Mesh-dependency in the droplet collision model is resolved by using the ROImodel (c.f., Sect. 2.2.2.11), in which the volume of the local cell is removed fromthe model formulation.

Mesh dependency in coupling from the gas to liquid phases is mainly from thegas velocity in the droplet momentum equation, Eq. 2.124 (Béard et al. 2000;Yang et al. 2000; Abani et al. 2008a, b). To improve this issue, a gas-jet model hasbeen developed based on unsteady turbulent round jet theory (Yang et al. 2000;Abani and Reitz 2007). The gas velocity in Eq. 2.124 is estimated from the gas-jetmodel instead of interpolating from the CFD solution. The unsteady gas jet theorystates that the jet tip develops with:

dx

dt¼ 3

K

Uinj;eff ðx; tÞdeq

x; x� x0: ð3:1Þ

where x is the jet tip penetration; K is an entrainment constant; Uinj,eff is theeffective injection velocity; deq is the equivalent diameter, which is related to thenozzle diameter dnoz and liquid-gas density ratio by:

deq ¼ dnoz

ffiffiffiffiql

q

r: ð3:2Þ

The downstream spray-axial location x0 is computed as:

x0 ¼3deq

K: ð3:3Þ

The unsteady gas jet theory assumes the effective injection velocity to be anintegral of the responses to any change of the injection speed from the start ofinjection t0 to the current time t:

Uinj;eff ðx; tÞ ¼ Uinjðt0Þ þZ t

t0

Rðx; t � sÞ dUinjðsÞds

� �s

ds; ð3:4Þ

in which the response function R yields:

Rðx; t � sÞ ¼ 1� exp � t � ssvðx; sÞ

� �; ð3:5Þ

where sv is a response time scale that is related to a local flow time scale sf by aStokes number St:

3.1 Methods for Reducing Mesh- and Timestep-Dependency in Engine CFD Modeling 77

svðx; sÞ ¼ St � sf ðx; sÞ ¼ St � x

UinjðsÞ: ð3:6Þ

Considering the fact that downstream particles respond to any change from thenozzle injection more slowly than near-nozzle particles, Eqs. 3.4 to 3.6 aremodified by replacing the spray tip penetration x with the local spray-axial locationof the particle y (Wang et al. 2010):

Uinj;eff ðy; tÞ ¼ Uinjðt0Þ þZ t

t0

Rðy; t � sÞ dUinjðsÞds

� �s

ds; ð3:7Þ

Rðy; t � sÞ ¼ 1� exp � t � ssvðy; sÞ

� �; ð3:8Þ

svðy; sÞ ¼ St � sf ðy; sÞ ¼ St � y

UinjðsÞ: ð3:9Þ

The local gas jet speed at the spray axis is correspondingly calculated as:

Ujet;axðy; tÞ ¼3K

Uinj;eff ðy; tÞdeq

y; y� x0: ð3:10Þ

Assuming axi-symmetry, the gas jet speed at any radial location r can becalculated as:

Ujetðy; r; tÞ ¼3Uinj;eff ðy; tÞdeq

Ky 1þ 12r2

K2y2

� � ; y� x0: ð3:11Þ

The mean gas velocities in the droplet momentum equation as well as thebreakup models are then replaced with this gas velocity.

Unlike mesh-dependency, investigation of the timestep-dependency of spraymodels is rarely reported in the literature. Multiple physical processes in engineshave different time scales that vary according to the change of engine conditions.A globally-imposed CFD timestep with stability criterion could keep the coderunning robustly, but would not always accurately capture the time scale of eachphysical process. On one hand, if the timestep is larger than the time scale but doesnot violate numerical stability criteria, the physical process is predicted in anunder-resolved way; on the other hand, if the timestep is smaller than the timescale, the computation will not run efficiently. In terms of spray models, Mun-nannur (2007) reported a ‘‘Mean Collision Time’’ approach, in which a collisiontime scale is estimated and included into the global CFD timestep determination,Eq. 2.213. Since this collision time scale is much smaller during the early stage ofspray development, the computational cost is increased significantly. Wang et al.(2010) proposed a sub-cycle method that uses a different timestep for the spraybreakup and collision calculation from the CFD timestep, and thusthe computational cost is reduced to an acceptable level. Timestep-dependency in


the RT breakup model is reduced by describing the evolution of drop radii using anequation similar to Eq. 2.116 in the KH model and the equation is solvedanalytically. The models have been applied to simulate direct injection enginecombustion (Shi et al. 2010d).

In the present book, the gas-jet model and the ROI collision model are used insome examples to reduce mesh-dependency.

3.2 Efficient Methods for Reaction Mechanism Reduction

3.2.1 Overview of Reaction Mechanism Reduction

The development of reaction mechanisms for surrogate fuels has significantlyimpacted engine design using CFD. For example, the comprehensive n-heptane(Curran et al. 1998a), iso-octane (Curran et al. 2002), and methyl decanoate (MD)(Herbinet et al. 2008) mechanisms, which are used as surrogates for diesel, gas-oline, and bio-diesel, respectively, have been used to investigate HCCI engines ina few studies (Hwang et al. 2008; Hoffman and Abraham 2009). Although theincreasing capacity of computers enables the use of large chemical mechanisms inengine simulations, it is also noted that the size of reaction mechanisms isincreasing rapidly. The increased mechanism size is a consequence of the highercarbon number of the surrogate fuel species and the larger number of fuel com-ponents considered. For instance, the use of n-heptane (C7, 561 species) as aconventional diesel surrogate is being supplemented with the use of n-octane (C8)to n-cetane (C16, 2116 species) (Westbrook et al. 2009). Iso-octane (C8, 857species) as a gasoline surrogate is being replaced by the combined n-heptane andiso-octane Primary Reference Fuel (PRF) mechanism (1,034 species (Curran et al.1998b)) to better reflect the fuel reactivity of gasoline. The bio-diesel surrogateMethyl Butanoate (C5, 264 species) (Fisher et al. 2000) is being replaced by MD(C11, 2,878 species) to better represent the long molecular chain of real bio-dieselfuels. In practice, a large number of simulations are required to optimize enginedesign. This further renders the use of comprehensive chemical mechanismsprohibitive for practical engine CFD simulations.

To overcome this difficulty, large detailed reaction mechanisms are usuallyreduced to mechanisms with smaller sizes, i.e., with less species and reactionnumbers. It is required that the reduced mechanisms are able to maintain the majorfeatures and predictive capacity of the detailed ones. A variety of methodologiesthat employ different mathematical approaches and emphasize different physicaland chemical aspects have been proposed for mechanism reduction. These methodsinclude but are not limited to, sensitivity analysis and reaction rate analysis (such asPrincipal Component Analysis (PCA)) (Turanyi et al. 1989; Turanyi 1990a),chemical lumping (Huang et al. 2005; Pepiot-Desjardins and Pitsch 2008b),intrinsic low-dimensional manifolds (ILDM) (Maas and Pope 1992), computational

3.1 Methods for Reducing Mesh- and Timestep-Dependency in Engine CFD Modeling 79

singular perturbation (CSP) (Lam and Goussis 1994), directed relation graph(DRG) (Lu and Law 2005) and its derivative version directed relation graph witherror propagation (DRGEP) (Pepiot-Desjardins and Pitsch 2008a) and a similargraph-based method path flux analysis (PFA) (Sun et al. 2010), and optimization-based methods (Bhattacharjee et al. 2003; Mitsos et al. 2008).

Sensitivity analysis on chemical mechanisms investigates the effects ofparameter perturbations on the local or overall performance of chemical kineticmodels. In the context of mechanism reduction, the presence of a species or areaction is parameterized and the redundancy of a species or a reaction to chemicalmechanisms can be identified by a brute force method that investigates the sensi-tivity of each species or reaction in the chemical mechanisms. It is evident that thisis a very time consuming process, especially for reducing large mechanisms.Turanyi et al. (1989) pointed out that kinetic information about chemical mecha-nisms can be derived from a matrix whose elements are rate sensitivity coefficientscalculated in reaction rate analysis. The matrix directly provides information aboutoverall rate sensitivities of reactions, and thus unimportant reactions can be iden-tified. However, the study of Vajda et al. (1985) showed that the overall ratesensitivity analysis resulted in over-elimination of important reactions under somecircumstances. In their study, eigenvalues and eigenvectors of the transpose productof the rate sensitivity matrix were used to identify the principal component vectorsof the rate sensitivity matrix in order to extract important reactions, and a betterreduced formaldehyde oxidation mechanism was obtained in that study. Thismethod is called Principal Component Analysis (PCA), which has been used toassist mechanism reduction in several studies (Turanyi 1990b; Nagy and Turanyi2009). Chemical lumping methods group species with similar composition, func-tionalities, or evolutionary history into representative lumped species or pseudo-species, so that the overall number of species is reduced. The key issues in chemicallumping methods are identification of lumped species and estimation of kineticparameters of the lumped groups. Lumped groups may (Pepiot-Desjardins andPitsch 2008b) or may not (Huang et al. 2005) have chemical meanings dependingon the lumping method used. Timescale analysis methods, ILDM and CSP, aresimilarly based on the Jacobian analysis of Ordinary Differential Equations (ODEs)of species concentrations. The analysis decomposes the Jacobian matrix into fastand slow sub-spaces. Consequently, quasi-steady-state (QSS) species and fastelementary reactions are identified and simple algebraic expressions of the QSSspecies concentrations and global reaction rates are obtained. The software packagedeveloped by Lu et al. (2001) reduces mechanisms using the CSP method andprovides automatically generated Chemkin-II compatible subroutines for applica-tion purposes. However, the Jacobian analysis is computationally expensive forlarge chemical mechanisms. In addition, the global reaction rates can no longer beexpressed in Arrhenius form and this renders the direct use of reduced mechanismsin standard chemistry packages difficult.

For the purpose of this book efficient methods for mechanism reduction are ofparticular interest. The term efficient here has no strict definition, but in general itindicates that the computational overhead of the method is negligible compared to


the gain due to the reduced mechanism size. In addition, the computational cost ofthe method should scale less than quadratically with the size (i.e., species number)of the mechanism. Otherwise, the mechanism reduction method is not suitable foran on-the-fly mechanism reduction scheme, as will be discussed in Sect. 3.4.

The directed relation graph (DRG) (Lu and Law 2005), the directed relationgraph with error propagation (DRGEP) (Pepiot-Desjardins and Pitsch 2008a) andthe path flux analysis (PFA) (Sun et al. 2010) methods fall into this categorybecause they are efficient and effective for mechanism reduction. Essentially, allthree methods are based on graph theory, which measures the connectivity amongspecies. Species that are not closely (with user-specified tolerance) connected topre-selected important species are deemed to be redundant and thus are removedfrom the detailed mechanisms.

In the original DRG approach (Lu and Law 2005), a graph is constructed usingthe method that each species represents a vertex in the graph and each directededge represents the immediate dependence of one species on another. Thedependence is quantified by the normalized contribution of species B to A as:

rAB ¼P

i¼1;I tAixidBij jPi¼1;I tAixij j ; ð3:12Þ

with

dBi ¼1 if reaction i involves B0 otherwise

�;

where i is the reaction index for the total I reactions, vAi is the stoichiometriccoefficient of species A in the ith reaction, and xi is the progress variable (rate) ofthe reaction i. Therefore, rAB is a measure of the error introduced to the productionrate of A due to elimination of all the reactions that contain B. Once the search-initiating species are determined, a depth first search (DFS) is applied to the graphconstructed by Eq. 3.12 for all species to identify the dependent set recursively.If the connectivity quantified by Eq. 3.12 is less than the user-specified tolerance,the searched species can be safely removed from the active species list withoutintroducing a large error to the reduced mechanism. Lu and Law (2006a) alsoproved that the computational cost of the DRG method scales linearly with themechanism size.

However, as pointed out by Pepiot-Desjardins and Pitsch (2008a) and Lianget al. (2009b), the DRG method assumes equal importance of all species selectedto be kept in the mechanism, which is not necessarily the case. Furthermore,considerable information about contribution strengths, as captured by the rAB

values, is lost due to the binary truncation. In order to overcome these short-comings and to produce smaller mechanisms, an error propagation technique wasintroduced to measure the dependency of a search-initiating species to otherspecies. Thus, the mechanism reduction procedure is equivalent to identifyingspecies (vertex in the graph) for which there exist ‘‘strong’’ paths connecting them

3.2 Efficient Methods for Reaction Mechanism Reduction 81

to a species in the initial set. In this DRGEP method, the connection strengthbetween the initiating species and the species being visited diminishes as the pathextends (geometrically damped error). To quantify the decreasing dependence, an‘‘R-value’’ is defined at each vertex V with reference to the initial vertex V0, i.e.,

RV0ðVÞ ¼ maxXfPrijg; ð3:13Þ

where X is the set of all possible paths leading from V0 to V, and Prij is the chainproduct of the weights of the edges along the given path and rij is given byEq. 3.12. Based on this definition, vertex V will be marked as ‘‘reachable’’ ifRV0(V) is larger than a user-specified threshold value e. Thus, all vertices reachablefrom initial vertices V01 to V0i (including V01 to V0i themselves) comprise thespecies of the reduced mechanism. Consequently, unreachable species and theircorresponding reactions are removed from the detailed mechanism.

It is noted that the measure of dependence between two species, as defined inEq. 3.12 was initially used in the DRGEP method proposed by Pepiot-Desjardinsand Pitsch (2005). However, Lu and Law (2006b) argued that this might be riskyin the case that two species are only connected by long-chain series reactions thatinvolve intermediate QSS species. Later, Pepiot-Desjardins and Pitsch (2008a)adopted an improved expression to measure the dependence of one species toanother as,

rAB ¼P

i¼1;I tAixidBi

�� maxðPA;CAÞ

; ð3:14Þ

with

PA ¼X

i¼1;Imaxð0; tAixiÞ;

CA ¼X

i¼1;Imaxð0;�tAixiÞ;

where PA and CA indicate the production and consumption rate of species A,respectively. It has been demonstrated by Pepiot-Desjardins and Pitsch (2008a)that the use of Eq. 3.14 for the geometrically damped error calculated in Eq. 3.13 isable to resolve the issue mentioned above. In addition, the graph search can beconducted using an efficient R-value-based breadth-first search (RBFS) algorithm,such as the one proposed by Liang et al. (2009b).

The path flux analysis (PFA) method proposed by Sun et al. (2010) shares asimilar idea with the DRG and DRGEP methods, namely, measuring the contri-bution of candidate species to the pre-selected important species based on theirconnectivity. However, instead of measuring such connectivity directly or indi-rectly using Eqs. 3.12 to 3.14, the PFA method adopts different formulae to cal-culate the reaction path fluxes among species. The direct interactions (normalizedfluxes) for production and consumption of species A and B are defined as:


rpro�1stAB ¼ PAB

maxðPA;CAÞ; ð3:15Þ

rcon�1stAB ¼ CAB

maxðPA;CAÞ: ð3:16Þ

The direct fluxes between species A and species B are defined by PAB and CAB

as:

PAB ¼Xi¼1;l

maxðmA;ixidBi; 0Þ; ð3:17Þ

CAB ¼Xi¼1;l

maxð�mA;ixidBi; 0Þ: ð3:18Þ

In addition to the direct interaction, the indirect interactions between A and Bvia a third species (Mi) are also defined for production and consumption as:

rpro�2ndAB ¼

XMi 6¼A;B

rpro�1stAMi

rpro�1stMiB

� �; ð3:19Þ

rcon�2ndAB ¼

XMi 6¼A;B

rcon�1stAMi

rcon�1stMiB

� �: ð3:20Þ

The overall lumped normalized flux between species A and B is the summary ofall direct and indirect fluxed defined in Eqs. 3.14, 3.19 and 3.20:

rAB ¼ rpro�1stAB þ rcon�1st

AB þ rpro�2ndAB þ rcon�2nd

AB : ð3:21Þ

Once this flux is below the user-specified tolerance, the connectivity betweenspecies A and B is deemed to be low. Similar to the DRG methods, a recursivemethod is employed in the PFA method to detect the importance of each species tothe pre-selected major species in order to screen out redundant ones. The study ofSun et al. (2010) showed that the PFA method was able to recover more reactionfluxes among species in the generated reduced mechanism as compared to theDRG and DRGEP methods. They also demonstrated that the reduced mechanismgenerated using the PFA method is slightly smaller and better than that of the DRGmethod. Nevertheless, it should be noted that the computational cost of the PFAmethod is higher than the DRG and DRGEP methods because of the calculation ofthe indirect reaction fluxes among species.

It is of interest to compare the performance and efficiency of the three mech-anism reduction methods, particularly for engine applications. Therefore, weexplored the three methods to reduce detailed n-heptane (561 species and 2,539reactions, Curran et al. 1998), iso-octane (857 species and 3,606 reactions, Curranet al. 2002), and methyl decanoate (MD) (2,878 species and 8,555 reactions,


Herbinet et al. 2008) mechanisms for HCCI engine simulations. The results arelisted in Table 3.1. The user-specified tolerance of each mechanism reductionmethod was gradually increased in order to generate smaller reduced mechanismsuntil the differences in the simulation results between the detailed mechanism andthe reduced mechanism exceeded allowed values. In this comparison, the differ-ences in CA50 (engine combustion phasing), peak pressure, and maximum heatrelease were limited to 1.5 �CA, 3%, and 3% between the detailed and reducedmechanisms. The discussion on the detailed methodology of mechanism reductionis deferred to the next section.

It is seen in the table that the DRGEP method produces the smallest mech-anisms within the allowed small error tolerances, which is followed by the PFAand DRG methods. In general, the three mechanism reduction methods are veryefficient as the time spent on mechanism reduction is negligible compared to thesimulation time using the detailed mechanisms, but the PFA method costs moretime than the other two. The small computational cost makes the three methodssuitable for the on-the-fly mechanism reduction scheme discussed in Sect. 3.4.One of the common shortcomings of the three methods is that the accuracy ofthe generated reduced mechanism heavily relies on the user-specified tolerancewhich is determined empirically and lacks a physical meaning. Although grad-ually increasing the user-specified tolerance will normally produce smallermechanisms with worthy performance, the relation between the performances ofthe generated reduced mechanisms and the user-specified accuracy tolerance istypically not a function of the user-specified algorithm tolerance. In the presentcomparison, the authors have found that for the DRG and PFA methods thereexist critical tolerances above which the generated reduced mechanisms showdrastically poor performance, while for the DRGEP method, this performancedrop is smaller. This comparison has strengthened the authors’ confidence inusing the DRGEP method for both automatic and on-the-fly mechanism reduc-tions in the following sections.

Table 3.1 Comparison of three efficient mechanism reduction methods for HCCI enginesimulation

Method Red.Mech.

No.SP

No.RXN

CA50(�)

Peak pres.(%)

Max HR(%)

Simulationtime (s)

Reductiontime (s)

DRG n-hep. 130 445 1.30 0.34 0.04 28.0 0.03i-oct. 165 651 0.78 0.59 0.41 66.0 0.07MD 625 2,370 0.89 1.1 2.2 1470.0 0.51

DRGEP n-hep. 126 459 0.84 1.9 3.0 28.0 0.04i-oct. 161 693 0.96 1.5 1.9 66.0 0.08MD 513 1719 0.67 2.26 2.7 1470.0 0.53

PFA n-hep. 129 501 0.81 0.06 0.17 28.0 0.25i-oct. 155 613 0.99 0.76 0.63 66.0 0.55MD 562 1,931 1.46 0.42 1.6 1470.0 3.98


3.2.2 Automatic Mechanism Reduction of Hydrocarbon Fuelsfor HCCI Engines Based on DRGEP and PCA Methodswith Error Control

With the systematic mechanism reduction methods discussed above, the process ofreducing the size of detailed reaction mechanisms becomes more convenient andefficient than using intuition- and experience-based methods. However, such aprocess can be still tedious given the fact that mechanism reduction is usuallyconducted over a wide range of thermodynamic conditions in order to achievebetter performance of the generated reduced mechanisms. To facilitate this pro-cess, an automatic methodology is proposed in this section. Practical examples aredemonstrated for reducing three large hydrocarbon surrogate fuel mechanisms forHCCI engine simulations. The DRGEP and PCA methods are employed forspecies and reaction elimination, respectively. The detailed theory of the DRGEPmethod can be found in the previous section and also in the study of Pepiot-Desjardins and Pitsch (2008b). The PCA method has wide application in differentresearch areas, and interested readers are encouraged to read the papers publishedby Vajda et al. (1985) and Turanyi (1990b) for its particular use in reactionmechanism reduction.

The SENKIN program (Lutz et al. 1988) integrated with engine physicalmodels was used to conduct closed-cycle, single-zone HCCI engine simulations.The program requires engine specifications, operating conditions, and a fuelreaction mechanism as inputs. Parameters of interest, such as CA50 (crank anglewhere 50% accumulated heat is released), peak in-cylinder pressure, and maxi-mum total heat release, are output to an ASCII file. Concurrently, pressure, tem-perature, as well as the mass fraction of each species in the mechanism are storedin a binary file for each time-step of the simulation. The binary file serves as aninput for the DRGEP method or the PCA method. Mechanism reduction is thenperformed on user-specified sampling points during the engine cycle.

Six sampling points, namely, in-cylinder temperatures of 600, 800, 1,000,1,200, 1,500, and 2,000 K, were found sufficient to generate the reduced mecha-nism. At each sampling point, a set of important species and reactions is identifiedbased on the thermal conditions and species mass fractions at that point using themechanism reduction methods. The overall set of important species and reactionsare the union of the individual subsets, which are flagged and stored in two binary(0 or 1) arrays. The authors have developed a Chemkin-II-library-based FOR-TRAN subroutine that transforms the information in the binary arrays to areduced mechanism in ASCII format, thereby automating the reduced mechanismgeneration process.

Based on the theory of the DRGEP and PCA methods, smaller tolerances resultin reduced mechanisms of larger size. However, the complex non-linear nature ofcomprehensive reaction mechanisms does not necessarily ensure that reducedmechanisms of larger size perform better than those of smaller size when com-paring parameters such as the combustion phasing, peak pressure, and maximum


heat release in HCCI engine simulations. Also, reduced mechanisms may begenerated from detailed mechanisms of different sizes and require different tol-erances to achieve a good compromise between accuracy and efficiency. There-fore, an approach is needed to find an appropriate set of tolerances when applyingthe DRGEP and PCA methods in an automatic mechanism reduction scheme thatensures the reduced mechanisms satisfy user-specified accuracy requirements. Inthis context, a trial-and-error method is proposed. Namely, the mechanismreduction process begins with a set of small error tolerances and the performanceof each generated reduced mechanism is compared with the detailed mechanismfor parameters of interest. The algorithm error tolerances are monotonicallyincreased until the user-specified tolerances of accuracy are violated. In this way,the desired accuracy of the reduced mechanism is always satisfied and the reducedmechanism achieves a minimum size. It is noted that consecutive reductions arenot performed using engine simulations with the comprehensive mechanism.Instead they are conducted on the simulation results from the preceding genera-tion, as explained next.

A two-stage mechanism reduction was employed by performing the DRGEPmethod and the PCA method sequentially. The primary goal of mechanismreduction is to eliminate as many unimportant species as possible, and the DRGEPmethod is a very effective approach for this purpose. Once the unimportant speciesare removed, additional reduction is possible by considering the reactions usingthe PCA method. As seen in the theory of the PCA method, eigenvalue-eigen-vector analysis on an n� n matrix is required, where n is the number of reactions.The computational time dependency of this manipulation is scaled by the power of3 to 4 of n, while the DRGEP method scales linearly with n. Consequently, thecomputational time for mechanism reduction can be significantly reduced byapplying the PCA method to the mechanism generated by the first-stage DRGEPreduction.

Finally, the mechanism reduction process is automated using a script program.The program flow chart is illustrated in Fig. 3.2. In general, an HCCI enginesimulation and subsequent DRGEP reduction are first performed using the com-prehensive chemical mechanism and user inputs that include engine specificationsand operating conditions, initial algorithm tolerances, as well as errors allowed forthe absolute differences of CA50, peak pressure, and maximum heat releasebetween the detailed mechanism and generated reduced mechanisms. If the resultsof the present HCCI simulation using the mechanism of the preceding generationdo not violate the user-specified tolerances, a reduced mechanism is generated forthe next generation HCCI simulation. For each consecutive generation the DRGEPtolerance is linearly increased in a log-scale, e.g., 0.0002–0.0003 or 0.002–0.003.The loop is repeated until the user-specified tolerances are exceeded.

Instead of immediately applying the second stage PCA reduction, the DRGEPreduction is conducted to the last valid HCCI simulation with a reduced tolerance(restore the tolerance from the last valid HCCI simulation), so that a smallerreduced mechanism may be obtained. This loop, which usually involves 0 to 3generations, is repeated with the DRGEP tolerance fixed until either the user-


specified tolerances are violated or the reduced mechanism does not change. Thesecond-stage reduction with the PCA method is conducted to the reduced mech-anism of the last valid HCCI simulation from the DRGEP stage. The processfollows the same procedure used in the DRGEP reduction, except that two algo-rithm error tolerances (identical in the present study) are altered in each generationfor the PCA method. The final reduced mechanism is generated from the lastHCCI simulation that satisfies all user-specified tolerances. Errors introduced bythis automatic reduction process are well bounded within the user-specified ranges.

To test the proposed approach, the three comprehensive hydrocarbon fuelmechanisms described above including the n-heptane (Curran et al. 1998), iso-octane (Curran et al. 2002), and methyl decanoate (MD) (Herbinet et al. 2008)mechanisms were selected. They are widely used as surrogate fuels for diesel,

Fig. 3.2 Flow chart ofautomatic mechanismreduction


gasoline, and biodiesel in engine simulations. HCCI simulations were conductedon a Caterpillar 3401E engine whose specifications are summarized in Table 3.2.Six cases that cover practical operating conditions of the HCCI engine wereselected. The low load (Cases 1 to 3) and medium load (Cases 4 to 6) conditionscorrespond to Mode 2 and Mode 5 of the federal test procedure (FTP) tests for theCAT engine. It is noted that in order to obtain reasonable intake valve closure(IVC) conditions and ignition timings, the IVC temperatures were adjusted basedon the fuel reactivity and operating conditions. IVC pressures were calculatedbased on temperature, amount of fuel, as well as global equivalence ratio.

Similar to the DRGEP studies of Liang et al. (2009b, 2009c) and Shi et al.(2010b), fuel, CO, and HO2 were chosen as the initial species, because each of theinitial species plays a primary role in the three major combustion processes ofhydrocarbon fuels, namely, fuel decomposition, CO oxidation, as well as H2-O2

reactions. For the first-stage DRGEP reduction, 1 9 10-4 was used as the initialtolerance for the three comprehensive mechanisms. For the second stage PCAreduction, 1 9 10-2 was used as the two initial tolerances for the MD mechanismand 1 9 10-3 was used for the smaller n-heptane and iso-octane mechanisms. Theperformance of the reduced mechanisms in HCCI engine simulations was evalu-ated by comparing the predicted CA50, peak pressure, and maximum heat releasewith those of the detailed mechanism. Here, allowed differences in CA50, peakpressure, and maximum heat release are limited to 1.5�CA, 3%, and 3% betweenthe detailed mechanisms and reduced mechanisms.

Table 3.2 Enginespecifications

Engine Caterpillar DI diesel

Combustion chamber QuiescentBore 9 Stroke (mm) 137.16 9 165.1Bowl width (mm) 97.8Displacement (L) 2.44Connection rod length (mm) 261.6Geometric compression ratio 16.1:1IVC timing (�CA ATDC) -143EVO timing (�CA ATDC) 130

Table 3.3 Operating conditions of test cases

Test k IVC temperature (K) IVC pressure (bar) IMEP (bar) speed (rev/min)

n-hep. iso-oct. MD n-hep. iso-oct. MD

1 0.2 350 390 350 1.888 2.096 1.906 5 8212 0.6 370 410 370 0.670 0.739 0.675 5 8213 1.0 390 440 390 0.427 0.480 0.429 5 8214 0.6 350 430 350 1.374 1.630 1.384 11 1,7375 1.0 370 450 370 0.878 1.061 0.882 11 1,7376 1.4 390 470 390 0.666 0.798 0.668 11 1,737


The mechanism reduction approach was first applied to the detailed MDmechanism. For the six tests listed in Table 3.3, six reduced mechanisms wereobtained, each with different final algorithm tolerances and different final sizes.Figure 3.3 shows the evolutionary process of the mechanism reduction for eachtest. In the figure, each generation number represents a set of algorithm errortolerances and the values of the tolerances increase with the generation number.The two numbers at the right bottom corner of Fig. 3.3 indicate the final size of

Fig. 3.3 Methyl Decanoate (MD) mechanism reduction. a Test 1, b Test 2, c Test 3, d Test 4,e Test 5, f Test 6


each reduced mechanism, which correspond to the number of species (solidsquare) and the number of reactions (solid circle). The vertical dashed line in eachsub-figure of Fig. 3.3 distinguishes the first-stage DRGEP reduction and the sec-ond-stage PCA reduction. As expected, it is seen that the DRGEP method effec-tively removed redundant species as the process evolved and the PCA methodprimarily reduced unimportant reactions after the DRGEP method was applied.The performance of the reduced mechanism at each generation was monitored bycomparing the three parameters, i.e., CA50, peak pressure, and maximum heatrelease, with those of the detailed mechanism, as illustrated by the open symbols inFig. 3.3 (relative errors are expressed in percentage). An important observation isthat the errors between the detailed mechanism and the reduced one do not nec-essarily monotonically increase as the algorithm error tolerances increase. Forexample, in Fig. 3.3(a), for test 1, the reduced mechanism obtained at generation13 is better than those of generations 11 and 12. This again indicates that thepresent trial-and-error method is necessary and effective for mechanism reductionusing the DRGEP and PCA method. This approach can be also applied to anyother mechanism reduction methods without rigorous error control.

The reduced mechanism generated from each test is assured to satisfy the user-specified error tolerances for that test. In practice, it is desired to have a finalreduced mechanism that is able to be applied to all cases within the investigatedoperating conditions. A common and conservative way is to combine all thereduced mechanisms obtained from each test, and the overall reduced mechanismshould be able to cover the investigated range. However, by further testing theperformance of each reduced mechanism, it can be seen that this is not necessaryfor the present problem. In Fig. 3.4, each sub-figure indicates the performance ofusing the reduced mechanism of an individual test for all other test cases. It is seenthat the largest reduced mechanism from Test 1, Fig. 3.4(a), maintains very goodresults compared to the detailed MD mechanism for all cases studied. In addition,it is observed that the reduced mechanism from the mid-load and stoichiometriccase of Test 5, Fig. 3.4(e), is also representative for all cases. The Test 5 reducedmechanism well reproduced the results of detailed mechanism within the user-specified error tolerances yet has far fewer species compared to the Test 1mechanism. As seen in Fig. 3.4(c) and (f), the two smallest reduced mechanismsfrom the rich mixture cases failed to predict satisfactory results for all conditionstested. Figure 3.5 further illustrates the performance of the reduced mechanisms ofTest 1 and Test 5, respectively, by comparing the pressure traces for each testcondition to those predicted by the detailed mechanism.

As an example, the algorithm error tolerances as a function of generationnumber are illustrated in Fig. 3.6 for the mechanism reduction process of Test 5.As described earlier, the present approach applies error tolerances to the reducedmechanism of the preceding generation by gradually increasing their values. It isseen that for Test 5 the DRGEP reduction terminated with the tolerance of 0.02,and the PCA reduction terminated with tolerances of 0.09. An attempt was made todirectly apply a tolerance of 0.02 to the detailed mechanism simulation using asingle run of the DRGEP method. However, it was found that the simulation


results largely exceeded the user-specified error tolerances. Thus, the DRGEPtolerance was lowered to 0.01 and PCA tolerances of 0.09 were sequentiallyapplied to the detailed mechanism simulation for the Test 5 conditions. Thegenerated reduced mechanism contained 502 species and 1,265 reactions, which islarger than that of the present approach. This may be due to the fact that a largeDRGEP tolerance can be applied to a mechanism of small size, as also found byShi et al. (2010b). It can be concluded that the present proposed step-wiseapproach not only saves computational time for mechanism reduction (since thereduction methodologies are only applied to evaluate the results using reducedmechanisms), but also is able to produce smaller reduced mechanisms.

Fig. 3.4 Performance of the reduced MD mechanisms. a Reduced mechanism of Test 1 (657species, 1,637 reactions). b Reduced mechanism of Test 2 (414 species, 1,160 reactions).c Reduced mechanism of Test 3 (381 species, 823 reactions). d Reduced mechanism of Test 4(534 species, 1,033 reactions). e Reduced mechanism of Test 5 (435 species, 1,098 reactions).f Reduced mechanism of Test 6 (327 species, 683 reactions)


Following the same procedure as the MD mechanism reduction, the detailediso-octane and n-heptane mechanisms were automatically reduced for the inves-tigated cases. Figures 3.7 and 3.8 indicate the evolutionary processes and theperformance of the reduced mechanisms of iso-octane and n-heptane, respectively.Only Test 2 and Test 5 are shown since the former one generated reducedmechanisms of the largest size for both iso-octane and n-heptane, and the latter onewas found to be representative in the previous MD mechanism reduction. As seenin Fig. 3.7(b), the largest reduced mechanism of iso-octane predicts satisfactoryresults for all cases investigated. Figure 3.7(d) shows that except for the peakpressure of Test 2, the reduced mechanism of Test 5 is also able to well reproducethe detailed mechanism of other cases. For n-heptane, Fig. 3.8(b) illustrates thatthe reduced mechanism of Test 2 reproduced the detailed mechanism reasonablywell. Using the reduced mechanism of Test 5, the very lean combustion case wasnot well matched in terms of the combustion phasing. However, for all other cases,the errors are well bounded within the user-specified tolerances.

Fig. 3.5 Comparison of pressure trace between the detailed MD mechanism and the reducedmechanisms of Test 1 and Test 5. a Reduced mechanism of Test 1. b Reduced mechanism of Test 5

Fig. 3.6 Algorithm errortolerances for Test 5 of MDmechanism reduction


It is seen that the automatic mechanism reduction approach is able to achievereduced mechanisms with minimum user intuition and input. The approachincludes a two-stage mechanism reduction procedure. In the first stage, thedirected relation graph with error propagation (DRGEP) method is used to effi-ciently and effectively remove redundant species and reactions. In the secondstage, a more time-consuming method, the Principal Component Analysis (PCA)method is applied to the reduced mechanism of the first stage to further removeunimportant reactions and species. During the mechanism reduction process, theoverall performance of reduced mechanisms is monitored by comparing parame-ters of interest with the corresponding detailed mechanisms to ensure that user-specified error tolerances are satisfied. Nevertheless, it should be pointed out thateach reduced mechanism has only a narrow applicable range as they are generatedbased on a set of particular state variables. This suggests that reduced mechanismsthat are generated with local and instantaneous thermal conditions may be bettersuitable for those conditions. So, an on-the-fly mechanism reduction scheme mayperform better in terms of accuracy and efficiency, which is the subject ofSect. 3.4.

Fig. 3.7 iso-octane mechanism reduction. a Reduction process of Test 2. b Performance of thereduced mechanism of Test 2 (195 species and 647 reactions). c Reduction process of Test 5.d Performance of the reduced mechanism of Test 5 (167 species and 640 reactions)


3.3 An Adaptive Multi-Grid Chemistry (AMC) Model

3.3.1 Background

An approach called multi-zone modeling was developed by Aceves et al. (2000,2001) in order to accelerate the calculation of HCCI engine combustion withdetailed reaction mechanisms. The multi-zone model assumes a decoupling of theturbulent mixing process and chemistry prior to and during the main heat release.It has been demonstrated to be able to predict overall engine performance, but hasdifficulty of predicting quantitative emission levels. This is because the modelneglects the details of the fluid flow and mixing process after starting to apply themulti-zone approach. Flowers et al. (2003) improved this model by introducing acoupled CFD/multi-zone model and obtained better predictions of emissions. Butthis multi-zone model has been shown by Aceves et al.’s further work (2005) to besensitive to the transition temperature above which the model is applied. Baba-jimopoulos et al. (2005) further extended the multi-zone model by consideringequivalence ratio zones in addition to temperature zones, and applied the model tostudy stratified charge HCCI cases. The approach of determining zones in their

Fig. 3.8 n-heptane mechanism reduction. a Reduction process of Test 2. b Performance of thereduced mechanism of Test 2 (140 species and 491 reactions). c Reduction process of Test 5.d Performance of the reduced mechanism of Test 5 (120 species and 431 reactions)


work is relatively complicated, but the gradient-preserving remapping method thatwas used to distribute zone information back onto individual cells is very effective.A factor of eight timing reduction was reported in their study, in which the GRI-Mech 3.0 (53 species, 325 reactions) (Smith et al. 2009) was employed.

Here, an adaptive neighbor search method called the Adaptive Multi-grid Che-mistry model is presented, which groups thermodynamically-similar cells in thesimulation of complex combustion systems, such as DI engines. The method issystematically compared with generic search methods in order to study its appli-cability under different circumstances. These methods have been coupled with theimproved ERC KIVA3v2 code, such that the AMC model can be used in an engineCFD code for simulation of HCCI and DI engine combustion with comprehensivechemistry.

3.3.2 Model Description

Most reactive flow CFD codes, such as KIVA3v2, use a splitting-operator schemethat separately evaluates the chemistry source term and transport terms on stag-gered time steps. This requires solving the change of species composition and heatrelease due to chemical reactions for each cell at every staggered time step. TheChemkin II library with the VODE ODE solver (Brown et al. 1989) has beencoupled into the KIVA code to satisfy this requirement, which solves for the massdensity of species in the continuity equation and the energy equation. Compared tosolving for the turbulence and spray development, this process is very computa-tionally expensive, even with relatively simple chemical kinetics mechanisms.This indicates that efforts of reducing computing time need to be placed onreducing the calling frequency to the Chemkin solver. This can be achieved bygrouping cells on multiple grids with similar gas properties. Two key steps areinvolved: 1) map (group) eligible cells together and solve the grouped cellstogether with the chemistry solver; 2) redistribute the group information back ontothe individual cells so that the gradients can be preserved, as discussed next.

The key of mapping appropriate cells into a group is to find proper measures ofsimilarity, as well as establishing the grouping criteria. In a Well Stirred Reactor(WSR), the temperature, pressure, and species factions describe the compositionspace that determines the reaction progress. Due to the temperature sensitivity ofchemical reactions, it is obvious that temperature should be used as one of thegrouping criteria. In the low Mach number flows in DI and HCCI engines, pressuregradients are small, and thus the pressure is not needed as a grouping criterion.Strictly, grouping cells with similar composition requires search and comparisonfor every individual species, but this is inapplicable because of two concerns. First,the search expense would be too large and thus would reduce the computationalefficiency of the multi-grid model. Second, it is difficult to define an appropriatecriterion of similarity for each species and thus to efficiently group as many cellsas possible. Hence, it is necessary to define an indicator that can represent both

3.3 An Adaptive Multi-Grid Chemistry (AMC) Model 95

composition information and combustion progress. The so called progressequivalence ratio (Babajimopoulos et al. 2005) was used here, which is defined by

/ ¼2C#�CO2

þ H#�H2O=2� z0C#

�CO2

O#�CO2�H2O � z0C#

�CO2

: ð3:22Þ

In this equation, the superscript # denotes the number of atoms of each species.The equivalence ratio is defined based on complete combustion, but the productsCO2 and H2O are excluded as indicated by the subscripts in /. Z0 defines theproportion of fuel oxygen to fuel carbon, and for hydrocarbon fuels withoutoxygen, Z0 is zero. In the multi-zone model of Babajimopoulos et al. (2005), allcells in the cylinder were sorted in ascending order with temperature to form aspecified number of zones based on prescribed fraction of mass within eachtemperature bin. In each temperature zone the cells were again sorted in ascendingorder using the progress equivalence ratio. The cells of each temperature zonewere divided into as many zones as needed to reach the criterion that the maximum/ range in each zone is D/max ¼ 0:02. This mapping procedure is similar to amethod in which all cells are sorted in temperature ascending order, and then usingeach sorted cell as a reference, all other cells are grouped with cells that havesimilar equivalence ratio as the reference cell. This grouping procedure is simplerand more straightforward than the previous multi-zone approach, and it is referredas the global mapping method here. The global mapping method is appropriate forHCCI engines, because cells with similar equivalence ratio are most likely to alsohave close species compositions. However, for DI engines, because significantgradients of mass fraction of species can exist, there is no guarantee that cells withsimilar equivalence ratio contain similar mass fractions of each species, especiallyfor those cells that are distributed in very different physical locations. The globalmapping method will be compared with the present alternatively adaptive neighbormapping method to be described next.

Based on the above discussion, it is necessary to limit the searching area inorder to better group cells that have similar species composition. However, due toconvection and diffusion, neighbor cells can have similar thermodynamic condi-tions, as well as species composition. In the early stages of combustion when largegradients, such as temperature gradients exist, the similarity may merely existamong closely adjacent cells and therefore the grouping process needs to belimited in a narrow region. However, as time progresses energy and species aretransported and mixed such that there is a trend toward local uniformity. Corre-spondingly, the grouping process can be extended to larger and larger regions. Thismeans the grouping region should be determined adaptively.

Accordingly, a temperature inhomogeneity measure was used as an indicatorfor assessing the grouping region adaptively, where

rT ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

1n� 1

Xn

i¼1

ðTi � TÞ2s

: ð3:23Þ


In Eq. (3.23), T denotes the average in-cylinder temperature and Ti is theindividual temperature of each of the n cells. The concept of adaptive neighborsearch is further illustrated in Fig. 3.9 using a 2-D schematic mesh. It can be seenthat the first level search just covers four adjacent cells (six if 3-D mesh) of thereference cell. If the in-cylinder temperature inhomogeneity is below pre-specifiedvalues, the search can then be expanded to the second level or higher. In this study,the maximum search level was limited to four, where a maximum of 129 cells canbe reached using the fourth level search in 3-D block structural mesh. It should benoted that a similar treatment can also be applied to unstructured meshes. In thiscase, a convenient approach would be to pre-define a representative search radiusand to define the search level as a multiplier used to adjust the search areaaccordingly.

In general, the present adaptive multi-grid mapping method can be summarizedas follows. Calculation of temperature inhomogeneity is performed first in order todetermine the search level. All cells are then sorted in temperature ascending orderto form a temporary array. From the first sorted cell, a neighbor search is con-ducted based on the computed level, and the neighbor cells are recorded in anothertemporary array. Within the recorded cells, a cell is selected as the reference cell,and the remaining cells are compared with the reference cell individually. If theabsolute difference of their temperature is within a prescribed tolerance D (K) andthe relative difference of their progress equivalence ratio is within D/ (%), thecells are grouped. This procedure is repeated using each cell as the reference cell,and the group that contains the most cells is selected and the corresponding cellsare flagged to prevent them from being grouped again in later operations on thearray of sorted cells. The temperature of the cells in the group is mass-averaged toform a representative average of the group, and the group’s pressure is volume-averaged. The concentration of species is integrated over the grouped cells toconserve the mass of the group. The grouping procedure is then repeated for otherungrouped and sorted cells until all cells are assigned to a group. In this procedure,it is likely that some groups just contain one cell, and the likelihood is higher forcells at high temperatures since they may be spatially isolated during the groupingprocedure. After the mapping process, because the number of groups is less than

Fig. 3.9 Adaptive multi-gridgrouping


the number of cells, the computational time spent on the chemistry solver can bereduced dramatically.

After the cells are mapped into a group and the group is allowed to react usingthe averaged conditions, it is not possible to exactly remap the mass fractions ofeach species back onto the original cells, because that requires solving thechemistry for each cell. Thus, an algorithm is needed to redistribute the speciesback to the cells, such that the gas properties of each cell remapped from the groupwould be comparable with those if the chemistry of each cell were to be solvedindividually.

A straightforward way of remapping the information of groups back onto theircells is to assign the mean value of the group’s characteristics to each includedcell. This means that all the cells in a group would have the same gas properties.It is obvious that this procedure contributes an artificial diffusion to the speciescontinuity equations if composition gradients are present among the grouped cells.This relatively inaccurate method is referred to as the averaged remapping method.

An improved method adopted from Babajimopoulos et al. (2005) was also usedhere, which attempts to preserve gradients of temperature and species composition.The method is described as follows. First, before the mapping procedure, a newquantity ch is defined using the number of C and H atoms of all participatingspecies except the combustion products, CO2 and H2O, where

ch ¼ 2C#�CO2

þH#�H2O

2: ð3:24Þ

The ch number of a group is the sum of the ch number of all cells in that group.After the chemistry calculation, all species, except CO2, H2O, O2, and N2 areassigned back to the group’s cells based on ch. In this case, the mass of species k inan individual cell is obtained from the ratio

mk;cell ¼ mk;group

chcell

chgroup

ð3:25Þ

In this way the mass of each species in the group is also conserved. Evidently,some cells can have more or fewer C or H atoms than before the mapping process,and thus the rest of the cells in the group need to be adjusted to maintain the totalnumber of C and H atoms in that group. The number of C atoms in a cell is thenbalanced from the remaining CO2 species from

Xk

mk;cell

Wkck þ

mCO2 ;cell

WCO2

¼ C#cell; ð3:26Þ

where Wk is the molecular weight of species k and ck is the number of carbonatoms in species k, and Eq. (3.26) is solved for mCO2;cell. Similarly cells that areshort of H atoms are balanced using the remaining H atoms from H2O species.Finally, O2 is distributed to maintain the total number of O atoms in each cell andadjustment of N2 is used to conserve the mass of each cell. Since after the


remapping process the mass fraction of each species in each cell is known, thechange of the specific internal energy of each cell can be obtained from thedifference between the internal energy of formation of the species present inthe cell before the grouping process and that after the remapping process. The celltemperature can be computed from the updated specific internal energy and themass faction of species. The method is called the gradient-preserving remappingmethod in this study.

It is shown in by Shi et al. (2009a) that both global and neighbor groupingmethods are satisfactory to predict HCCI engine combustion, but the simplerglobal grouping method leads to inaccuracies in the predicted emissions for DIcases. The global mapping saves more computer time for HCCI engine simula-tions, as compared to using the neighbor mapping. An averaged remapping methodis explored but not suggested in the AMC model due to increased numericaldiffusion. Instead, a gradient-preserving method is found to be applicable for bothHCCI and DI cases. In addition, the AMC model predictions are shown to be fairlyinsensitive to convergence tolerance parameters in parametric studies. A transitiontemperature of 1,000 K is used to study DI engine cases in the next section.

It should be pointed out that there exist several similar multi-zone or multi-gridtechniques that modify existing CFD codes in order to accelerate the chemistrycalculation. No general conclusion can be drawn with regard to which modelperforms the best because the demonstrated combustion problems are different indifferent studies. Table 3.4 surveys the major features of four multi-zoneapproaches (including the AMC model) that were developed in recent years.

Table 3.4 Comparison of different multi-zone models

Models Mapping method Remapping method Case studyexamples

Speed-upfactor

Multi-zone(Babajimopouloset al. 2005)

/-T mapping Mass and elementconservation

HCCI enginecombustion

*9

AMC model (Shiet al. 2009a)

/-T mapping withgrid spatialinformation

Mass and elementconservation

HCCI, diesel DI,and gasoline DIengines (Geet al. 2010c)

3–10

Cell agglomeration(Goldin et al.2009)

Selected species andtemperature inhash table

Species gradient ofgrouped cells.Ad-hoctreatment formassconservation

1D and 2Dpremixed anddiffusion flames.Partiallypremixed ICengine

2–20

DMZ (Liang et al.2009a)

Dynamicpartitioningscheme usingdata-miningmethods based on/-T map

Species densitygradient massconservation isguaranteed

HCCI and DIengines

8–20


Readers are encouraged to refer to the corresponding citations for more detailsabout those models. In the rest of the book, the present AMC model is applied toaccelerate the chemistry solver.

3.3.3 Results and Discussion

In order to test the efficiency of the AMC model, all simulations in this sectionwere conducted on computers with the same hardware configurations (3.00 GHzIntel P4 CPU and 2G bytes memory), and the wall clock time was recorded for thecomparisons.

Kranendonk et al. (2007) used swept-wavelength H2O absorption thermometryto directly measure in-cylinder temperature and H2O mole fraction for a Hondagasoline engine fueled with n-heptane and operated under HCCI conditions. Thespecifications of the engine are listed in Table 3.5. The position of the line-of-sightlaser beam and the numerical mesh are illustrated in Fig. 3.10. The measured datarepresent the averaged value of the spatial locations that are traversed by the laserbeam. The engine operating conditions are given in Table 3.6 for two different

Table 3.5 Specifications ofthe Honda engine

Engine Honda

Bore (mm) 86Stroke (mm) 86CR 8.9IVC (ATDC) -158EVO(ATDC) 153

Fig. 3.10 Position of laserbeam path for in-cylindertemperature and H2O molefraction measurements of theHonda engine


speeds. The measured temperature and H2O concentration provide validation datafor chemical kinetics mechanisms, such as the ERC PRF mechanism (Ra and Reitz2008) used in this study. Table 3.7 summaries the sub-models of the KIVA3v2code used in both HCCI and DI engine studies.

The present AMC model reduced the computer time by an order of magnitudewith results consistent with those predicted using the full chemistry model. Usingthe AMC model, for the low speed case (600 rev/min) the computer time wasreduced from 48.27 to 3.99 h, and for the high speed case (1,500 rev/min) thecomputer time was reduced from 48.23 to 4.06 h. Figures 3.11 and 3.12 comparethe calculated results using the AMC model with the full chemistry and themeasured data for the two different speeds. The simulations correctly predictthe onset of cool flame and main heat release for both cases, which also validatesthe PRF chemistry mechanism regarding to its ability to describe ignition andcombustion characteristics.

Two simulated temperatures are compared with the experimental data inFigs. 3.11(b) and 3.12(b). They are the average in-cylinder temperature in the entirecomputational domain and the average temperature of only those cells that aretraversed by the laser beam in the pent-roof region, as shown in Fig. 3.10. It can beseen that the average cell temperature for the lower speed case agrees very wellwith the measured data. However, the calculated temperature of the higher speedcase is slightly lower than the experimentally measured value. Note that both theaverage in-cylinder temperatures are significantly lower than the measured tem-peratures. This indicates that even for this HCCI case a significant temperature

Table 3.6 HCCI operatingconditions of the Hondaengine

Operating conditions Low-speed High-Speed

Speed (rev/min) 600 1,500IMEP (bar) 2.503 2.597EGR (%) 0 0A/F 36.7 42.7IVC temperature (K) 459 512

Table 3.7 KIVA3v2 sub-models

Functions Models

Turbulence Modified RNG k-e (Han and Reitz 1995)Spray development KH-RT Model (Beale and Reitz 1999), Gas-jet and ROI collision models

(Abani et al. 2008a)Spray

impingementStandard KIVA model (O’ Rourke and Amsden 2000)

Ignition andcombustion

ERC PRF mechanism (Ra and Reitz 2008) (n-heptane part, 39 species and141 reactions including NOx chemistry)

Soot Two-step model with C2H2 as precursor (Kong et al. 2007)NOx Twelve-step kinetics model (extracted from GRI 3.0 mechanism (Smith

et al. 2009) embedded in the fuel mechanism


gradient exists in the combustion chamber. This is also observed in Fig. 3.13 whichdemonstrates the stratified temperature distribution of the lower speed case. Thestratification is due to the effects of wall heat transfer. Figures 3.11(c) and 3.12(c)show that simulations slightly under-predicted H2O mole fractions during the coolflame and main heat release stages.

A GM-Fiat engine was experimentally and numerically investigated by Opatet al. (2007) under PCCI conditions with ultra-high EGR rates. The study suc-cessfully explained experimental CO and unburned hydrocarbons (UHC) emissiontrends as a function of SOI. It was found that advancing the injection timingincreased the proportion of the fuel that was targeted above the piston bowl,leading to high CO emissions. Retarding the injection timing reduced the spraymixing time and targeted the fuel into the piston bowl where the lack of availableoxygen also resulted in high CO emissions. Therefore, there exists an optimalinjection timing that produces minimum CO emissions, which was called the‘‘sweet spot’’.

The AMC model was applied to those cases to assess its performance in pre-dicting emission trends. The engine specifications and operating conditions aregiven in Tables 3.8 and 3.9, respectively. The mesh had 7,419 cells at BDC with a51.4� closed-valve sector (seven hole nozzle).

Fig. 3.11 Honda engine at 600 rev/min. a Comparison of pressure trace. b Comparison oftemperature. c Comparison of H2O mole fraction


Fig. 3.12 Honda engine at 1,500 rev/min. a Comparison of pressure trace. b Comparison oftemperature. c Comparison of H2O mole fraction

Fig. 3.13 Temperature distribution of the Honda engine at 600 rev/min. a CA = -10 ATDC,b CA = -5 ATDC

Table 3.8 Specifications ofthe GM-Fiat engine

Engine GM-fiat

Bore (mm) 82Stroke (mm) 90.4CR 16.6IVC (ATDC) -132EVO (ATDC) 112Inj. Pre. (bar) 860Nozzle Hole 7Spray angle � 155


In the experimental tests, a large amount of EGR, including unburned fuel, wasrecycled and mixed with the intake gases. Therefore, a reactive mixture waspresent initially even before the injection event. This increases the computationalburden for the full chemistry model. Thus, the global mapping method wasadopted before the injection due to the assumed homogeneous initial composition.As seen in Fig. 3.14, the average computer time of all cases using the AMC modelwas about 5 h compared to about 16 h using the original code with full chemistry.The timing reduction is close to a factor of three. The results are also quantitativelyconsistent with those of the full chemistry simulations, as can been seen inFig. 3.15. The AMC model successfully predicts the emission trends over theentire SOI sweep for the soot, NOx, and CO emissions. The UHC emissions areover-predicted as the SOI is retarded, but the emissions trend is correctly captured.

To summarize, with the present reduced chemistry mechanism, the AMC modelis able to reduce computing time by more than factors of ten for HCCI cases andthree for DI cases without losing prediction accuracy compared to the originalcode. If a larger and more comprehensive chemical kinetics mechanism is used,the computer time reduction would be expected to be further increased.

Table 3.9 PCCI operatingconditions of the GM-Fiatengine

Operating conditions GM-fiat

Speed (rev/min) 2,000IMEP (bar) 5.5EGR (%) 65Boost pressure (bar) 1.9Equivalence ratio 0.95SOI (ATDC) -39 to -21

Fig. 3.14 Comparison ofcomputer time of the fullchemistry model and theAMC model.


3.4 An Extended Dynamic Adaptive Chemistry (EDAC) Scheme

3.4.1 Background

In the preceding section the use of the multi-grid technique where thermody-namically-similar computational cells are grouped and solved together was seen tosave a great amount of computer time. The efficiency of the multi-grid technique isbased on reducing the calling frequency to the chemistry solver. Therefore, inorder to further accelerate the chemistry solver, the computer time of each call tothe chemistry solver (either for a cell or a group if the multi-grid technique isapplied) needs to be reduced.

Reduced mechanism combustion and emissions predictions aim to reproducecorresponding detailed mechanisms over a wide range of thermodynamic condi-tions. Further mechanism reduction should be determined adaptively and auto-matically based on the local and instantaneous thermodynamic conditions. Lianget al. (2009b) developed a dynamic adaptive chemistry (DAC) scheme based onthe DRGEP method. In their study, single zone adiabatic HCCI engine simulationswere conducted using a detailed n-heptane mechanism (578 species) and multi-component fuel cases (Liang et al. 2009c), and it was found that the on-the-fly

Fig. 3.15 Comparison of experimental and simulated results for the GM engine operated underPCCI conditions. a Soot emissions. b NOx emissions. c UHC emissions. d CO emissions


mechanism reduction scheme not only resulted in negligible computationaloverhead but also achieved as much as 30-fold time reduction. The present workassesses the use of the DAC scheme for HCCI and DI engine multi-dimensionalsimulations using relatively small mechanisms, and issues associated with itsimplementation are discussed.

3.4.2 Model Description

The goal of mechanism reduction is to eliminate as many unimportant species andreactions as possible, while maintaining the prediction accuracy of the reducedmechanism to be comparable to the detailed mechanism under the conditions ofinterest. In the aforementioned DRG, DRGEP, and PFA methods, unimportantspecies are identified based on their connectivity to pre-selected initial species,such as fuel, CO, and HO2. Once a species is removed from the detailed mech-anism, its associated reactions are also removed. In this way, the methods attemptto directly reduce the number of species with which the computer time of thechemistry solver scales quadratically. We have also shown in Sect. 3.2 that theDRGEP methods performed better than the other two in mechanism reduction forHCCI engine simulations, and therefore the present adaptive chemistry schemeemphasizes this method.

The DRGEP method extracts a set of active species including the initial speciesand their strongly connected species based on the local and instantaneous ther-modynamic conditions. Consequently, a reaction is active (thus is included) in thereduced mechanism only if all participating species are in the set of active species.Species not in the active set are treated as inactive, with their mass fractions arekept fixed. The principle of the DRGEP method gives surety that, were they to beincluded, the small changes in the mass fraction of these inactive species wouldhave negligible effect on heat release rate and the evolution of key species.However, though the inactive species are not chemically active in the adaptivelyreduced mechanism, they do play an important role in three-body reactions andpressure-dependent reactions, and thus their mass fractions have to be considered.

Liang et al. (2009b) proposed a formulation of the kinetics equations thatminimizes the size of the ODE system while still accounting for third body effects.The ODE equations can be expressed as

_ya1 ¼ f1ðXðT ; p; ya

1; . . .; yam; y

i1; . . .; yi

nÞÞ...

_yam ¼ fmðXðT ; p; ya

1; . . .; yam; y

i1; . . .; yi

nÞÞ_T ¼ fmþ1ðXðT ; p; ya

1; . . .; yam; y

i1; . . .; yi

nÞÞ: ð3:27Þ

8>>>><>>>>:

In Eq. 3.27, the reaction system involves m active and n inactive species:X ðT; p; ya

1; . . .; yam; y

i1; . . .; yi

nÞ, where the superscripts ‘‘a’’ and ‘‘i’’ denote active


and inactive species, respectively. The ODEs are formulated with respect to onlyactive species, eliminating redundant equations due to inactive species and thusleading to a compact Jacobian matrix. All species are considered when the ratefunctions are evaluated, which eliminates the need to explicitly include the thirdbody species in the reduced mechanisms. Note that the species mass fractions inEq. 3.27 refer to the total mixture, and therefore their summation is unity. Alsonote that since only the reaction rate of the active reactions is evaluated in theright-hand-side terms of Eq. 3.27, the set of active reactions must be distinguishedfrom the inactive set. This is done by using a binary flag array to mark the activereactions.

The DAC scheme has been successfully employed to study HCCI enginecombustion (Liang et al. 2009b, c). However, the application of the method in DIengine simulations is not straightforward and its good performance and efficiencyare not obvious. This is because the single-zone HCCI model neglects convectionand diffusion effects that can superimpose perturbations on the DAC schemewhose mechanism reduction considers reaction fluxes only. In HCCI engines, theconvection and diffusion processes exist mainly in boundary layers, but in DIengines they are more significant due to the non-premixed combustion.

In the study of Liang et al. (2009b), the search-initiating species were fixed asfuel, CO, and HO2, but these three species are not all necessarily importantthroughout the simulated engine cycle (Liang et al. 2009c). This is also true for DIengine simulations. Thus, the search-initiating species should be determinedspatially and temporally based on information obtained from the combustionprocess. The study of Liang et al. (2009c) concluded that NO and its effect onhydrocarbon ignition can be well predicted and captured without adding NO to thesearch-initiating species. However, it was found that this conclusion depends onthe specific NOx sub-mechanism that is coupled with the hydrocarbon oxidationmechanism, as well as the simulation conditions, and does not always hold for allcases. Therefore, a remedy is needed to ensure that NO is accurately predictedwhen the DAC scheme is applied to DI engine simulations. Furthermore, the errortolerance of the DAC scheme that is suitable for the single-zone model and aparticular chemical mechanism does not necessarily globally meet the requirementof multi-dimensional simulations and mechanisms with different sizes. The causesof the above issues and proposed solutions are discussed in the present study. Tosimplify the analysis, HCCI simulations using a single-zone model combined witha posteriori studies using the DAC scheme are employed.

The performance of the DRGEP method depends on a proper set of search-initiating species from which the connected species can form the most represen-tative reduced mechanism based on the local and instantaneous thermal conditions.In the original DAC scheme (Liang et al. 2009b), fuel, CO, and HO2 were selectedto initiate the DRGEP method search for important species. Each of the initialspecies should play a primary role in the three major combustion processes ofhydrocarbon fuels, namely, fuel decomposition, CO oxidation, as well as H2-O2

reactions. However, the inclusion of the original DAC species for all combustionprocesses could overestimate the importance of a certain initial species for a

3.4 An Extended Dynamic Adaptive Chemistry (EDAC) Scheme 107

particular combustion stage. For example, during the post-ignition stage at hightemperature almost all fuel molecules and large hydrocarbons have been decom-posed to small molecules, and thus only CO oxidation and H2-O2 reactionsdominate the combustion processes. Since each initial species can lead to a sub-sidiary set of connected species in the reduced mechanism, the exclusion ofunnecessary initial species would increase the efficiency of the DAC scheme.In addition, once a system undergoes complete combustion (or reaches equilib-rium), none of the three DAC species should be considered as proper initial speciesas the chemical system has shifted to produce CO2 and H2O. Therefore, due to thenature of heterogeneous combustion in DI engine simulations, it is necessary todynamically select the search-initializing species for each cell based on its com-bustion status.

In order to select a proper set of the search-initializing species, the combustionstate of each cell has to be known prior to applying the DRGEP method formechanism reduction for that cell. Thus, to quantify the combustion state, the celltemperature and progress equivalence ratio were monitored. These two quantitieshave been extensively used in multi-grid approaches (Babajimopoulos et al. 2005,Shi et al. 2009a) to group cells with similar combustion characteristics. Theso-called progress equivalence ratio was defined in Eq. (3.12).

However, the progress equivalence ratio merely indicates the completeness ofthe combustion, and thus no information is provided about the degree of fueldecomposition. Following Eq. (3.12), we define the equivalence ratio as.

/l ¼2C#

l þ H#l =2

O#lþO2

: ð3:28Þ

Here, the subscript l represents all large hydrocarbons (more than 3 carbonatoms), and O2 is the only oxidizer considered. / and /l are shown in Fig. 3.16 fortwo HCCI simulations using a single-zone model. It is seen in Fig. 3.16 (a) that forlean mixture combustion, both the progress equivalence ratio (/) and the equiv-alence ratio of large hydrocarbons (/l) drop rapidly to zero as the temperatureincreases, which indicate the completeness of fuel decomposition and combustion,

Fig. 3.16 Profiles of temperature and equivalence ratio with different initial equivalence ratio.a Initial equivalence ratio = 0.5. b Initial equivalence ratio = 1.5


respectively. However, for rich mixtures, Fig. 3.16(b) shows that the progressequivalence ratio increases after the combustion occurs due to the incompleteoxidation of CO and therefore the inclusion of CO in the search-initializing speciesis necessary for the DRGEP method. Regardless of the mixture initial conditions,the large hydrocarbons equivalence ratio continuously decreases to zero as thecombustion proceeds, which means the fuel species can be excluded from the setof the initial species once /l is below a critical value.

In order to choose a proper critical value for a wide range of thermal conditions,the contribution matrices of the heat formation rate due to a single reaction to theentire combustion system are listed in Table 3.10(a) and (b) for the two studiedHCCI cases, as suggested by Ando et al. (2009). The contribution of a singlereaction is quantified based on the percentage of its heat formation rate (- heatrelease, ? heat absorption) to the overall heat release or absorption rate of thesystem at a particular temperature. Reactions which contribute more than 10percent to the heat formation rate for any of the temperatures from 700 to 2,300 Kat an interval of 100 K are listed in the tables for lean and rich mixture HCCIsimulations.

It is observed that for both lean and rich combustion, when /l is below 0.001,reactions involving large hydrocarbons contribute no or negligible heat formationto the combustion system, and the combustion chemistry shifts from fueldecomposition to small hydrocarbons and H2–CO combustion. Consequently, fuelshould be excluded from the set of initial species to avoid unnecessary largehydrocarbons being included into the active species set. It is also found that theinclusion of CO as the initial species enables the connection to small hydrocarbonswhen they are deemed important by the DRGEP method. Therefore, using CO andHO2 as the initial species when /l is below 0.001 produces suitable reducedmechanisms to describe the post-ignition stage of hydrocarbon combustion. Inaddition, when both / and /l are below 0.001 the combustion process is deemed tobe complete. As a result, the combustion products CO2 and H2O are used as theinitial species when this condition is satisfied.

Species that comprise the NO sub-mechanism are not necessarily closelyconnected to any of the search-initializing species under the conditions that theDRGEP method is performed. HCCI engine simulations using a single-zone modelwere investigated with two different n-heptane mechanisms, including a NO sub-mechanism (Patel et al. 2004, Golovitchev 2006), and the results showed thatspecies that are included in the NO sub-mechanism were only reachable (thus wereincluded in the reduced mechanism) from the search initializing species (n-hep-tane, CO, HO2) when the temperature was above 2,300 K and the equivalenceratio was below stoichiometric. Obviously, this could introduce a large error whenthe DAC scheme is applied to study DI engines. Therefore, in order to ensure thegenerality of the DAC scheme in engine simulations, a special treatment is needed.Since NO is the primary NOx species in engines, a straightforward method is toinclude NO into the set of search-initializing species.

The DRGEP method’s predictive accuracy as compared to the full chemistryshould scale with the error tolerance. However, the involvement of NO into the


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=[c2

h5?

c2h4

?c3

h6

0.1

1.5

1.2

8.7

18.1

17.7

12.3

6.6

1.6

00

00

00

00

c3h7

\=[

c2h4

?ch

30.

415

.822

5.6

1.6

0.6

2.1

3.8

4.5

5.6

3.7

2.5

1.7

1.2

0.4

00

ch3

?ho

2\

=[ch

3o?

oh0

-0.

6-

7.5

-6.

8-

9.2

-9.

7-

9.4

-9

-9.

5-

10.6

-9.

7-

8.4

-5.

6-

2.4

-0.

40

0

ch3o

?co

\=[

ch3

?co

20

0-

0.6

-8.

4-

9.8

-9.

4-

8.2

-6.

8-

6.8

-10

.4-

8.8

-6.

9-

5-

2.8

-0.

60

0

co?

oh\

=[co

2?

h0

00

0-

0.1

-0.

1-

0.3

-0.

5-

1.8

-5.

4-

7.9

-11

.5-

17.7

-24

.6-

29.1

-27

.94

o?

oh\

=[o2

?h

00

00

0.1

0.6

2.5

5.2

8.7

1924

.829

.534

3740

.842

.38.

7

2oh\

=[o

?h2

o0

00

00

0.1

0.4

1.2

2.6

7.9

1421

.228

.835

.141

.249

.2-

0.2

h?

o2?

M\

=[ho

2?

M0

-0.

1-

0.9

-0.

5-

0.9

-5

-15

.6-

23-

24.3

-23

.1-

24.3

-25

.4-

27.4

-29

.8-

31.2

-31

.719

.5

h2o2

?M

\=[

2oh

?M

00

050

.467

.470

.156

42.7

35.4

9.7

6.4

5.6

6.3

8.2

85.

8-

0.4

ch2o

?oh

\=[

hco

?h2

o0

-1.

4-

14.4

-15

.3-

16.8

-17

.6-

18.6

-19

.5-

18-

12.5

-11

.6-

10-

7.1

-3.

7-

1.4

-0.

40

hco

?o2

\=[

ho2

?co

0-

1.7

-18

-38

.6-

28-

21.8

-11

.2-

3.4

-0.

7-

0.2

-0.

10

00

00

0

hco

?M

\=[

h?

co?

M0

00

0.1

17.

725

.139

.245

.550

.445

.337

.326

.215

.56.

92.

30

ch3

?ch

3o\

=[ch

4?

ch2o

0-

2.1

-24

.8-

4.6

-9.

5-

12-

13.9

-15

.8-

17.6

-13

.3-

13.7

-13

.3-

8-

2-

0.1

00

oh?

ho2\

=[h2

o?

o20

0-

0.2

0-

0.1

-0.

2-

0.3

-0.

6-

1.3

-1

-1.

6-

3.4

-8.

4-

15.7

-22

.7-

30.4

27.1

(b)

Init

ial

equi

vale

nce

rati

o=

1.5

/of

larg

ehy

droc

arbo

ns1.

500

1.49

51.

389

0.98

20.

818

0.67

90.

516

0.32

30.

186

0.09

00.

036

0.01

10.

002

0.00

00.

000

0.00

00.

000

/(p

rogr

ess

equi

vale

nce

rati

o)1.

500

1.50

01.

516

1.53

31.

551

1.57

31.

597

1.62

41.

650

1.67

81.

708

1.73

81.

774

1.81

51.

861

1.93

12.

024

nc7h

16?

oh\

=[c7

h15-

2?

h2o

-20

.3-

20.3

-10

.2-

3.5

-3.

9-

3.9

-3.

1-

2-

1.1

-0.

5-

0.2

-0.

10

00

00

nc7h

16?

o2\

=[c7

h15 -

2?

ho2

88.6

-0.

1-

2.3

-1

0.5

0.3

0.2

0.2

0.2

0.4

0.2

0.1

00

00

0

c7h1

5-2

?o2

\=[

c7h1

5o2

-37

.2-

31.9

-11

.8-

0.7

-0.

20

00

00

00

00

00

0

c7h1

5o2

?o2

\=[

c7ke

t12

?oh

-42

.4-

38.2

-17

.1-

1.7

-0.

30

00

00

00

00

00

0

c7ke

t12\

=[c5

h11c

o?

ch2o

?oh

8.2

51.2

40.5

37.2

1.1

0.2

00

00

00

00

00

0

c5h1

1co\

=[c2

h4?

c3h7

?co

127

.729

.429

0.8

0.1

00

00

00

00

00

0

(con

tinu

ed)


Tab

le3.

10(c

onti

nued

)T

empe

ratu

re(K

)70

080

090

010

0011

0012

0013

0014

0015

0016

0017

0018

0019

0020

0021

0022

0023

00

c7h1

5- 2\

=[c2

h5?

c2h4

?c3

h6

0.2

3.2

9.3

11.1

3532

.827

.820

.914

.710

.65.

11.

60.

40.

10

00

c3h7

\=[

c2h4

?ch

30.

417

.119

.520

.60.

31.

97

11.2

12.8

12.2

8.2

4.9

3.7

3.7

4.8

4.4

2.6

ch3

?ho

2\

=[ch

3o?

oh0

-1

-6.

2-

10.2

-9.

3-

10.1

-9.

9-

9.1

-8.

8-

9.5

-8.

3-

7.1

-6.

3-

5.5

-4.

8-

4-

2.9

ch2

?o2

\=[

ch2o

?o

00

00

00

0-

0.1

-0.

2-

0.4

-1

-1.

9-

2.7

-4.

2-

7.4

-11

.4-

12.5

ch3o

?co

\=[

ch3

?co

20

0-

0.3

-2.

1-

10.2

-9.

4-

7-

4.6

-4

-5.

6-

4.9

-3.

4-

2.6

-2

-1.

6-

1.3

-1

co?

oh\

=[co

2?

h0

00

00

-0.

1-

0.1

-0.

1-

0.2

-0.

2-

0.3

-0.

4-

0.7

-1.

4-

3.8

-7.

9-

11.3

o?

oh\

=[o2

?h

00

00

0.1

0.5

1.8

3.5

610

.314

.517

.719

.320

.724

.629

.932

.8

2oh\

=[o

?h2

o0

00

00

0.1

0.3

0.7

1.4

2.8

4.5

6.6

8.4

10.9

16.6

2530

.8

h?

o2?

M\

=[ho

2?

M0

-0.

1-

0.6

-0.

9-

0.7

-3

-8

-11

.8-

13.5

-14

-15

.4-

15.5

-14

.8-

13.7

-12

.9-

12.7

-12

.6

h2o2

?M

\=[

2oh

?M

00

00

54.6

54.6

42.5

34.4

27.4

10.6

41.

70.

80.

40.

10.

10

ch2o

?oh

\=[

hco

?h2

o0

-1.

5-

10.3

-14

.4-

13.8

-14

.7-

16.6

-18

.6-

19.8

-20

-22

.6-

25-

26.2

-26

.2-

22.8

-16

.7-

14.1

hco

?o2

\=[

ho2

?co

0-

1.9

-12

.8-

19.5

-28

.5-

19.7

-9.

5-

2.7

-0.

6-

0.2

-0.

10

00

00

0

hco

?M

\=[

h?

co?

M0

00

00.

96.

518

.527

.133

.842

.947

.851

51.5

49.9

4636

.331

ch3

?ch

3o\

=[ch

4?

ch2o

0-

3.4

-20

.7-

31-

9.1

-13

.9-

18.5

-21

.4-

21.7

-20

.2-

17.8

-17

-16

-14

.7-

13.1

-10

.9-

8


search-initializing species adds more species to the set of active species andtherefore decreases the efficiency of the DAC scheme. To achieve a compromisebetween the prediction accuracy and computational efficiency, NO was only addedto the search-initializing species when the cell temperature was above a pre-specified critical temperature in the present DAC scheme. In this research, thecritical temperature was chosen as 1,800 K. The critical temperature was deter-mined based on many previous studies that have shown this is a temperature belowwhich negligible NO formation is found in engine combustion processes (Park andReitz 2007, Akihama et al. 2001). It should be noted that if NO is present in EGRgases, the DAC scheme is able to account for the effect of NO on the ignitionprocess without including it in the initiating-species pool (Liang et al. 2009c).

As seen in Fig. 3.17, the error propagates along the reaction pathway from thesearch-initializing species to a target species in the DRGEP method. Therefore,the error depends on both the dependence between the intermediate species and thelength of the pathway. This indicates that the connectivity between the same twospecies in different mechanisms could be different, and a proper error tolerance hasto be determined based on the chemical mechanism used in simulations. It is alsointuitive that since the dependence between two directly connected species is lessthan or equal to one, so the propagated error between species could be smaller in amechanism of larger size, which has longer pathways. Rigorously, an error controlmechanism is needed to determine the error tolerance based on a real-time com-parison between the predicted results of the reduced mechanism and those of thefull mechanism.

Nagy and Turanyi (2009) proposed a method to produce reduced mechanismsfrom very large reaction mechanisms based on simulation error minimization.However, it is not practical for the present on-the-fly mechanism reductionbecause of the large computational overhead of the method, which suggests that a

Fig. 3.17 Illustration ofreaction pathways of differentmechanisms using DRGEPmethod


priori comparison would be more appropriate to determine the error tolerance forthe application of the DAC scheme in multi-dimensional engine simulations. In thepresent study, a 2-D HCCI simulation was employed to determine the error tol-erance values for different mechanisms. As a further simplification, once a cell hascompleted combustion, i.e., its progress equivalence ratio and temperature arebelow the pre-specified critical values, the error tolerance of that cell can beincreased, so that more species can be removed to further reduce the size ofmechanism while maintaining the accuracy.

DI engine simulations involve spray development and droplet evaporationprocesses. Consequently, the vapor distribution in the cylinder is critical tocombustion. The DAC scheme introduces numerical error in computing chemicalheat release that can affect the evaporation process. Thus, the present methoddecouples the DAC scheme from the evaporation process by not applying thescheme to cells that contain liquid fuel droplets. This does not sacrifice compu-tational efficiency significantly because the number of cells that contain liquid fueldroplets and are undergoing chemical reaction is usually small compared to thenumber of CFD cells.

The present improved DAC scheme is termed the extended dynamic adaptivechemistry (EDAC) scheme. To highlight the details of the EDAC scheme, a flowchart is depicted in Fig. 3.18. Symbols with solid lines represent the main flow ofthe EDAC scheme, and the dashed lines indicate the selection of the search-initializing species. The dotted lines indicate the parameters that that determine theerror tolerance. The error tolerance is e and ec is the pre-selected tolerance basedon 2-D HCCI simulations.

Fig. 3.18 Flow chart of EDAC scheme



The 2-D HCCI tests were used to select an appropriate error tolerance for DIsimulations (c.f., Table 3.5). The 2-D mesh had 136 cells at bottom dead center(BDC). Three error tolerances 1e-4, 1e-3, and 1e-2 were tested for the originalDAC scheme with four initial species including n-heptane, CO, HO2 and NO. Thetest n-heptane mechanisms including the NOx chemistry were the ERC reduced

Fig. 3.19 HCCI simulations. a Pressure trace using ERC mech. b NOx and Soot using ERCmech. c Pressure trace using CHA mech. d NOx and Soot using CHA mech.e Pressure trace usingLLNL mech. f NOx and Soot using LLNL mech


mechanism (34 species and 77 reactions, Patel et al. 2004), the Chalmers reducedmechanism (61 species and 262 reactions, Golovitchev 2006), and the LLNLdetailed mechanism (543 species and 2,538 reactions, Curran et al. 1998). Exceptas otherwise mentioned, all the tests in this section were calculated on PCs with the3.00 GHz Intel P4 CPU and 2G bytes of memory.

Figure 3.19 shows pressure traces and NOx and soot emissions using the dif-ferent mechanisms and error tolerances. The computational times are included inthe legends of the figures. It is seen that for the smallest ERC mechanism, thepressure calculated by the full chemistry solver is well matched using the DACscheme with all selected error tolerances. However, inaccurate emission results areseen in Fig. 3.19(b) with error tolerance of 1e-2. For the Chalmers mechanism, it isseen in Fig. 3.19(c) that peak pressure was over-predicted using error tolerance of1e-2. Error tolerance of 1e-3 calculated had good agreement with the full chem-istry pressure while under-predicting the soot emissions. Neither 1e-3 nor 1e-2gave good results with the LLNL mechanism (Fig. 3.19(e) and (f)). The resultsindicate that the error tolerance of the DAC scheme should decrease as the size ofmechanism increases.

The DAC scheme reduced the computer time by a factor of 9 for the HCCIsimulation with the LLNL mechanism (e = 1e-4). Even though the reduction is

Fig. 3.20 Honda engine at 600 rev/min. a Comparison of pressure trace. b Comparison oftemperature. c Comparison of H2O mole fraction


significant, its efficiency is less than the factor of 30 of Liang et al. (2009b) in asimilar single-zone adiabatic HCCI simulation.

To examine the performance of the combination of the AMC model and theEDAC scheme in 3–D HCCI engine simulations, the simulations of the HondaHCCI engine that were conducted with the AMC model in the preceding sectionwere repeated while also activating the EDAC scheme (with error tolerance of 1e-3 as the small ERC PRF mechanism was used). The computer times were 2.88 and2.95 h for the low speed and high speed cases, as compared to 3.99 and 4.06 hwith the AMC model only, and 48.27 and 48.23 h, respectively, with the fullchemistry solver. Figures 3.20 and 3.21 prove that using both the AMC model andthe EDAC scheme predict very consistent results with the full chemistry solver, ingood agreement with the experiments.

The detailed LLNL mechanism alone was not used for the DI simulationsbecause of its unacceptably long computer times. Instead, the present schemeswere tested against the full chemistry solver for the ERC n-heptane mechanismand Chalmers n-heptane mechanism. The 3-D sector mesh has 7,419 cells at BDC,which is the same with that of Sect. 3.3.3 with engine specifications of Table 3.5.In order to assess the performance of the EDAC scheme over a wide range ofoperating conditions, for each mechanism three operating conditions including

Fig. 3.21 Honda engine at 1,500 rev/min. a Comparison of pressure trace. b Comparison oftemperature. c Comparison of H2O mole fraction


FTP1, FTP4, FTP5 were studied as listed in Table 3.11. It is noted that for thehigh-load FTP5 case, a dual-injection strategy was also investigated, as indicatedby case FTP5D.

The simulation results are summarized in Tables 3.12 and 3.13 for the ERCn-heptane mechanism and the Chalmers mechanism. The parentheses indicatethe percentage time saving or computational error in emissions compared to thebaseline cases. It is seen that for the ERC mechanism, as much as 30% timingreduction was achieved, while for the larger CHA mechanism, this increased toalmost 50%. For the ERC mechanism, the error tolerance of 1e-3 from the 2-DHCCI simulation is satisfactory under all operating conditions, as seen inTable 3.12. However, the same tolerance introduced discrepancies in the emis-sion results for non-premixed combustion cases (FTP 5 cases in Table 3.13(c)and (d)) with the CHA mechanism, which indicates that 1e-4 is a better option.For the ERC mechanism, no apparent differences are observed by avoiding spraycontaining cells. This is attributed to the fact that the connection between thespecies in a small mechanism is very strong and thus the influence of the DACscheme on the evaporation is not pronounced. For the CHA mechanism,decoupling of the evaporation process from the DAC schemes considerablyimproved the emission results for non-premixed combustion cases. When aproper error tolerance was selected, the differences of the emissions predictedusing the DAC schemes to those of the full chemistry solver are below 5%,except at some extremely low emission levels. It is also noted that an additional8–10% time saving can be obtained without losing accuracy using the presentDAC scheme.

The top-left plot in Fig. 3.22 shows the temperature distribution in a cut planeon the spray axis and the locations of liquid droplets using the full chemistry solverat 15� ATDC. The other plots illustrate how many species were solved in each cell

Table 3.11 Engine operating conditions for tests of the EDAC scheme

Operating conditions FTP1 FTP4 FTP5 FTP5D

Speed (rev/min) 1,500 2,000 2,500 2,500Inj. Pres. (bar) 860 860 860 860IMEP (bar) 2.1 5.5 8.8 8.8EGR (%) 0 65 20 20Equivalence ratio 0.2 0.95 0.75 0.75IVC temperature (K) 350.0 350.0 350.0 350.0IVC pressure (bar) 1.09 1.9 1.5 1.5Pilot SOI (�ATDC) N/A N/A N/A -25.0Pilot fuel amount (g/cycle) N/A N/A N/A 0.00768Pilot injection duration (CA) N/A N/A N/A 5.4Main SOI (�ATDC) -10.0 -20.0 -5.0 -5.0Main fuel amount (g/cycle) 0.0064 0.016 0.0256 0.01792Main injection duration (CA) 2.7 9.0 18.0 12.6


Tab

le3.

12D

Ien

gine

sim

ulat

ions

usin

gth

eE

RC

n-he

ptan

em

echa

nism

(34

spec

ies,

77re

acti

ons)

Ful

lch

em.

App

lyD

AC

toal

lce

lls

App

lyD

AC

toce

lls

that

cont

ain

noli

quid

fuel

DA

C1e

-4D

AC

1e-3

DA

C1e

-4D

AC

1e-3

ED

AC

1e-4

ED

AC

1e-3

(a)

FT

P1

Cas

eT

ot.

tim

e(h

)11

.60

10.2

8(1

1)9.

14(2

1)10

.19

(12)

9.21

(21)

9.12

(21)

7.96

(31)

Che

m.

tim

e(h

)10

.79

8.85

(18)

7.80

(28)

8.83

(18)

7.90

(27)

7.87

(27)

6.73

(38)

DA

Cov

erhe

ad(h

)N

/A0.

560.

510.

550.

510.

450.

43S

oot

(g/k

gfu

el)

0.00

015

0.00

014(

6.7)

0.00

014(

6.7)

0.00

015

(0)

0.00

017(

13)

0.00

014(

6.7)

0.00

017(

13)

NO

x(g

/kg

fuel

)38

.23

38.8

5(1

.6)

40.3

2(5

.5)

39.0

9(2

.2)

41.1

8(7

.7)

38.9

7(1

.9)

40.8

1(6

.7)

UH

C(g

/kg

fuel

)20

.90

21.2

0(1

.4)

20.5

0(1

.9)

20.9

0(0

)20

.30

(2.9

)21

.10

(0.9

6)20

.70

(0.9

6)C

O(g

/kg

fuel

)76

.10

77.4

0(1

.7)

75.5

0(0

.79)

77.5

0(1

.8)

76.4

0(0

.39)

78.3

0(2

.9)

77.8

0(2

.2)

(b)

FT

P4

Cas

eT

ot.

tim

e(h

)9.

788.

97(8

.3)

8.39

(14)

8.94

(8.6

)8.

51(1

3)8.

06(1

8)7.

52(2

3)C

hem

.ti

me

(h)

9.15

7.81

(15)

7.28

(20)

7.80

(15)

7.39

(19)

6.98

(24)

6.47

(29)

DA

Cov

erhe

ad(h

r)N

/A0.

510.

470.

500.

470.

430.

41S

oot

(g/k

gfu

el)

0.38

0.37

(2.6

)0.

37(2

.6)

0.37

(2.6

)0.

37(2

.6)

0.37

(2.6

)0.

37(2

.6)

NO

x(g

/kg

fuel

)0.

0032

0.00

34(6

.3)

0.00

36(1

3)0.

0035

(9.4

)0.

0035

(9.4

)0.

0035

(9.4

)0.

0035

(9.4

)U

HC

(g/k

gfu

el)

69.2

067

.30

(2.7

)66

.90

(3.3

)67

.00

(3.2

)67

.30

(2.7

)66

.50

(3.9

)67

.30

(2.7

)C

O(g

/kg

fuel

)36

5.00

357.

00(2

.2)

359.

00(1

.6)

358.

00(1

.9)

360.

00(1

.4)

354.

00(3

.0)

361.

00(1

.1)

(c)

FT

P5

Sing

lein

ject

ion

case

Tot

.ti

me

(h)

16.3

715

.24

(6.9

)14

.22

(13)

15.5

5(5

)14

.32

(13)

14.2

6(1

3)13

.32

(19)

Che

m.

tim

e(h

)15

.45

13.8

0(1

1)12

.81

(17)

14.1

0(6

.8)

12.9

2(1

.6)

12.8

8(1

7)11

.96

(23)

DA

Cov

erhe

ad(h

)N

/A0.

540.

490.

530.

480.

460.

43S

oot

(g/k

gfu

el)

1.15

1.15

(0)

1.16

(0.8

7)1.

15(0

)1.

13(1

.7)

1.13

(1.7

)1.

14(0

.85)

NO

x(g

/kg

fuel

)7.

226.

94(3

.9)

7.26

(0.5

5)7.

03(2

.6)

7.32

(1.4

)7.

01(2

.9)

7.54

(4.4

)U

HC

(g/k

gfu

el)

14.2

014

.90

(4.9

)14

.50

(2.1

)15

.00

(5.6

)14

.00

(1.4

)14

.20

(0)

14.6

0(2

.8)

CO

(g/k

gfu

el)

216.

0021

8.00

(0.9

3)22

0.00

(1.9

)21

8.00

(0.9

3)22

0.00

(1.9

)21

0.00

(2.8

)22

9.00

(6.0

)

(con

tinu

ed)


Tab

le3.

12(c

onti

nued

)

Ful

lch

em.

App

lyD

AC

toal

lce

lls

App

lyD

AC

toce

lls

that

cont

ain

noli

quid

fuel

DA

C1e

-4D

AC

1e-3

DA

C1e

-4D

AC

1e-3

ED

AC

1e-4

ED

AC

1e-3

(d)

FT

P5

Dua

lin

ject

ion

case

Tot

.ti

me

(h)

18.3

016

.64

(9.1

)15

.49

(15)

16.8

7(7

.8)

15.7

3(1

4)15

.58

(15)

14.2

8(2

2)C

hem

.ti

me

(h)

16.8

014

.63

(13)

13.5

8(1

9)14

.89

(11)

13.7

9(1

8)13

.71

(18)

12.4

2(2

6)D

AC

over

head

(h)

N/A

0.51

0.44

0.49

0.43

0.41

0.38

Soo

t(g

/kg

fuel

)1.

041.

01(2

.9)

1.04

(0)

1.01

(2.9

)1.

01(2

.9)

1.02

(1.9

)1.

05(0

.96)

NO

x(g

/kg

fuel

)16

.08

15.9

3(0

.93)

16.2

1(0

.81)

16.0

0(0

.50)

16.3

1(1

.4)

16.1

2(0

.25)

16.5

6(3

.0)

UH

C(g

/kg

fuel

)9.

849.

26(5

.9)

10.4

0(5

.7)

9.25

(6.0

)9.

27(5

.8)

9.58

(2.6

)10

.50

(6.7

)C

O(g

/kg

fuel

)11

7.00

113.

00(3

.4)

119.

00(1

.7)

113.

00(3

.4)

114.

00(2

.6)

113.

00(3

.4)

122.

00(4

.3)


Tab

le3.

13D

Ien

gine

sim

ulat

ions

usin

gth

eC

halm

ers

n-he

ptan

em

echa

nism

(61

spec

ies,

262

reac

tion

s)

App

lyD

AC

toal

lce

lls

App

lyD

AC

toce

lls

that

cont

ain

noli

quid

fuel

Ful

lch

em.

DA

C1e

-4D

AC

1e-3

DA

C1e

-4D

AC

1e-3

ED

AC

1e-4

ED

AC

1e-3

(a)

FT

P1

Cas

eT

ot.

tim

e(h

)44

.87

27.5

0(3

9)24

.05

(46)

27.8

7(3

8)24

.36

(46)

24.7

2(4

5)22

.38

(50)

Che

m.

tim

e(h

)43

.97

24.1

8(4

5)21

.83

(50)

25.5

1(4

2)22

.11

(50)

22.5

9(4

9)20

.25

(54)

DA

Cov

erhe

ad(h

)N

/A1.

441.

351.

431.

331.

251.

20S

oot

(g/k

gfu

el)

0.00

018

0.00

018

(0)

0.00

012(

33)

0.00

018

(0)

0.00

014(

22)

0.00

018

(0)

0.00

017(

5.6)

NO

x(g

/kg

fuel

)24

.05

24.4

9(1

.8)

25.6

3(6

.6)

24.0

6(0

.04)

25.8

8(7

.6)

24.7

3(2

.8)

26.9

9(1

2)U

HC

(g/k

gfu

el)

47.1

047

.30

(0.4

2)46

.00

(2.3

)46

.50

(1.3

)45

.70

(3.0

)46

.30

(1.7

)45

.00

(4.5

)C

O(g

/kg

fuel

)11

3.00

112.

00(1

.3)

110.

00(2

.7)

111.

00(1

.8)

111.

00(2

.7)

111.

00(1

.8)

110.

00(2

.7)

(b)

FT

P4

Cas

eT

ot.

tim

e(h

)39

.85

26.1

2(3

4)23

.04

(42)

26.5

2(3

3)23

.41

(41)

22.9

2(4

2)20

.98

(47)

Che

m.

tim

e(h

)39

.06

24.0

0(3

9)20

.99

(46)

24.3

8(3

8)21

.37

(45)

20.9

3(4

6)19

.04

(51)

DA

Cov

erhe

ad(h

)N

/A1.

351.

261.

341.

241.

201.

15S

oot

(g/k

gfu

el)

0.14

0.14

(0)

0.14

(0)

0.14

(0)

0.13

(7.1

)0.

13(7

.1)

0.14

(0)

NO

x(g

/kg

fuel

)0.

020

0.02

1(5

)0.

021

(5)

0.02

(0)

0.02

1(5)

0.02

(0)

0.00

7(6

5)U

HC

(g/k

gfu

el)

62.0

058

.60

(5.5

)57

.80

(6.8

)58

.60

(5.5

)58

.40

(5.8

)58

.90

(5)

58.8

0(5

.2)

CO

(g/k

gfu

el)

288.

0027

9.00

(3.1

)27

8.00

(3.5

)27

9.00

(3.1

)28

1.00

(2.4

)28

1.00

(2.4

)28

3.00

(1.7

)(c

)F

TP

5Si

ngle

inje

ctio

nca

seT

ot.

tim

e(h

)59

.47

47.7

0(2

0)44

.53

(25)

46.6

6(2

2)42

.71

(28)

42.0

4(2

9)37

.93

(36)

Che

m.

tim

e(h

)58

.28

44.9

7(2

3)41

.86

(28)

43.9

9(2

5)40

.14

(31)

39.5

2(3

2)35

.50

(39)

DA

Cov

erhe

ad(h

)N

/A1.

511.

391.

441.

341.

301.

22S

oot

(g/k

gfu

el)

0.83

1.00

(20)

1.01

(22)

0.86

(3.6

)0.

93(1

2)0.

87(4

.8)

0.94

(13)

NO

x(g

/kg

fuel

)3.

713.

12(1

6)3.

54(4

.6)

3.47

(6.5

)3.

80(2

.4)

3.52

(5.1

)4.

34(1

7)U

HC

(g/k

gfu

el)

12.7

014

.30

(13)

13.6

0(7

.1)

12.7

0(0

)14

.10

(11)

13.3

0(4

.7)

14.7

0(1

6)C

O(g

/kg

fuel

)25

7.00

308.

00(2

0)35

9.00

(40)

277.

00(7

.8)

311.

00(2

1)27

8.00

(8.2

)31

1.00

(21)

(con

tinu

ed)


Tab

le3.

13(c

onti

nued

)

App

lyD

AC

toal

lce

lls

App

lyD

AC

toce

lls

that

cont

ain

noli

quid

fuel

Ful

lch

em.

DA

C1e

-4D

AC

1e-3

DA

C1e

-4D

AC

1e-3

ED

AC

1e-4

ED

AC

1e-3

(d)

FT

P5

Dua

lin

ject

ion

case

Tot

.ti

me

(h)

58.4

948

.12

(18)

44.0

4(2

5)46

.83

(20)

43.1

5(2

6)42

.08

(28)

38.4

9(3

4)C

hem

.ti

me

(h)

56.7

645

.01

(21)

40.9

8(2

8)43

.73

(23)

40.2

2(2

9)39

.16

(31)

35.6

1(3

7)D

AC

over

head

(h)

N/A

1.40

1.27

1.34

1.20

1.18

1.12

Soo

t(g

/kg

fuel

)0.

760.

84(1

1)1.

20(5

8)0.

78(2

.6)

0.89

(17)

0.76

(0)

0.86

(13)

NO

x(g

/kg

fuel

)7.

655.

48(2

8)5.

37(3

0)6.

85(1

0)6.

38(1

7)7.

09(7

.3)

7.25

(5.2

)U

HC

(g/k

gfu

el)

5.91

4.15

(30)

9.00

(52)

5.14

(13)

6.45

(9.1

)5.

70(3

.6)

6.57

(11)

CO

(g/k

gfu

el)

115.

0018

0.00

(57)

330.

0(1

87)

130.

00(1

3)17

9.00

(56)

117.

00(1

.7)

177.

00(5

4)


on that cut plane when the various DAC schemes were applied. The top-right plotshows the original DAC scheme when decoupling the spray is not considered, andthe bottom-left one excludes the spray containing cells in the scheme. The bottom-right is the EDAC scheme without spray cells. It is seen if the spray containingcells are excluded, the number of species is increased, especially near nozzleregion where the liquid droplets cluster.

The present EDAC scheme is able to reduce computational times, and itsefficiency increases with the size of the mechanism. It was also combined with theadaptive multi-grid chemistry (AMC) model and applied to simulate the GM-Fiatengine that was investigated previously using the AMC model alone. In addition,the detailed LLNL n-heptane mechanism was used show that it is now practical touse mechanisms of such large size for DI engine simulations.

Figure 3.23 shows that the computational time is reduced by a factor of 3 usingthe AMC alone. By combining with the EDAC scheme, the new chemistry solverreduces the computer time by a factor of more than 4. As seen Fig. 3.24(a–d), thepredicted emissions of the efficient methods are highly consistent with those of thefull chemistry solver.

Fig. 3.22 Comparison ofnumber of species usingdifferent DAC schemes(FTP5D, dual-injection,Chalmers mechanism)

Fig. 3.23 Comparison ofcomputer times of differentsolvers (Open symbols: timereduction; Closed symbols:computer time)


An additional simulation with SOI timing of -21 �ATDC from the SOI sweepwas performed with the detailed LLNL mechanism. In this case dynamic load-balancing parallel scheme (Shi et al. 2009b) was also used to parallelize thecomputation of the efficient chemistry solver. The simulation took 116.0 h walltime and 426.0 h CPU time using four individual Pentium IV 3.0 G PCs, ascompared to an estimated 4 months or 13 months if the full chemistry solver wereused on four processors or a single processor, respectively. The simulated pressuretrace matches the experimental data well, as shown in Fig. 3.25. Considering thecapability of current multi-core processors, the parallel computation was alsorepeated on a PC with an Intel Core2 2.4 G Quad-CPU, and it took 64.6 h tocomplete and the total CPU time was 241.8 h.

3.5 Summary

In order to accelerate the chemistry solver of the improved ERC KIVA3v2 engineCFD code, an adaptive multi-grid chemistry (AMC) model and an extendeddynamic adaptive chemistry (EDAC) scheme have been developed. The methods

Fig. 3.24 Comparison of chemistry solvers and experimental data. a Soot emission. b NOxemission. c UHC emission. d CO emission


have been systematically studied with respect to their sensitivity to the modelconstants, and their accuracy and efficiency for HCCI and DI engine simulations. Itwas found that by combining both methods and with the use of the present ERCreduced n-heptane mechanism the new chemistry solver accelerated the calcula-tion more than ten fold for HCCI engine simulations and by as much as four-foldfor DI simulations, without losing prediction accuracy as compared to the fullchemistry solver. A successful example of applying the very detailed LLNL n-heptane mechanism (543 species) to a DI engine simulation was also demonstratedin this chapter. To the authors’ knowledge, this is the first attempt to use chemicalmechanisms of this large size in DI engine simulations. The efficiency of the newchemistry solver is essential for engine optimization using CFD tools with detailedchemistry, as will be further examined in Chap. 6.

Fig. 3.25 Comparison ofexperimental pressure tracewith simulated results usingfull LLNL mechanism (543species)


Chapter 4Assessment of Optimizationand Regression Methods for EngineOptimization

Engine optimization problems by nature are multi-objective problems, whichinvolve simultaneously optimizing multiple design parameters. Based on thereview of optimization methods in Chap. 2, it was determined that multi-objectivegenetic algorithms (MOGA) are an appropriate optimization method. This chapterassesses the performance of different MOGAs for engine optimization problems.The assessment was conducted using three popular MOGAs [l-GA (Coello Coelloand Pulido 2001), NSGA II (Deb et al. 2002), ARMOGA (Sasaki and Obayashi2005)] applied to a heavy-duty diesel engine operated at a high-load condition. Inaddition to this assessment, the niching technique of NSGA II was also evaluated.Convergence and diversity metrics of MOGAs were defined to complete theassessment of different niching techniques. Regression analysis was then con-ducted on the design datasets that were obtained from the optimizations with twoniching strategies. Four regression methods, including K-nearest neighbors (KN),Kriging (KR), Neural Networks (NN), and Radial Basis Functions (RBF), werecompared. The purpose of the comparison was to evaluate whether it is appropriateto use a regression tool to partially replace the actual CFD evaluation tool inengine optimization design using genetic algorithms. As a result, a dynamiclearning strategy was proposed.

4.1 Assessment of Multi-Objective Genetic Algorithms

The assessment was conducted by comparing the performance of the three MO-GAs for optimization of a heavy-duty diesel engine under high-load. The effects ofthe piston geometry, spray-relevant parameters, as well as initial swirl ratio onemissions and fuel economy were of particular interest. Reductions of NOx andsoot emissions were two main objectives. In addition, Gross Indicated SpecificFuel Consumption (GISFC) was also investigated. Tables 4.1 and 4.2 list theengine specifications and operating conditions, respectively.


125

The piston geometry was parameterized and automatically meshed using anautomated grid generator, Kwickgrid (Wickman 2003), which simplifies the gridgeneration process by decoupling the geometry from the mesh structure. Thepiston shape is described using a reduced set of dimensionless input parameters,allowing more flexibility than the standard KIVA grid generation code (Amsden1993). The input parameters include outline parameters that define the overallpiston bowl shape, and Bezier curvature parameters that describe the curvesbetween the outline points. For example, two outline parameters, Ax and Bx, andthree Bezier curvature parameters, Xa0, X0a, Xab, were used for defining thecombustion chamber geometry in the optimization study of Chap. 6, and they arealso illustrated in Fig. 4.1. As shown in the figure, points A and B determine themajor geometrical dimensions of the chamber, and curves 1–3, corresponding toXa0, X0a, and Xab control the shapes. Bx is defined as the ratio of the bowldiameter and the cylinder diameter. Ax is defined as the ratio of the bottom bowland outer bowl diameters. If the position of one outline point varies in thez-direction, the height is normalized by bowl depth, e.g., Az and Cz in Fig. 6.35.After the outline parameters are determined, the Bezier parameters can vary tocover a wide range of different piston shapes. Quadratic Bezier curves are con-sidered, such that: given two fixed points A and B, and Bezier point 3 (c.f.,Fig. 4.1), the Bezier curve can be written as:

BðtÞ ¼ ð1� tÞ2PA þ 2ð1� tÞtP3 þ t2PB; t 2 ½0; 1�; ð4:1Þ

Table 4.2 Baselineoperating condition

Speed (rev/min) 1672

IVC temperature (K) 385IVC pressure (kPa) 310SOI (�BTDC) 13Injection quantity (mg/cyc) 229Injection duration (�CA) 19EGR level (%) 25Global equivalence ratio 0.6O2 Concentration (vol.%) 17.65

Table 4.1 Engine andinjector specifications

Engine Caterpillar DI diesel

Combustion chamber Quiescent, direct injectionSwirl ratio 0.7Bore 9 Stroke (mm) 137.16 9 165.1Bowl width (mm) 97.8Displacement (L) 2.44Connection rod length (mm) 261.6Geometric compression ratio 16.1:1Fuel injector nozzles 8 holes, equally spacedSpray pattern included angle 154�Rail pressure (bar) 2,000Nozzle orifice diameter (mm) 0.217

126 4 Assessment of Optimization and Regression Methods for Engine Optimization

where PA, PB, and P3, are the coordinates of the points A, B, and 3, respectively.The related Bezier curvature parameters are given by

Xab ¼x3 � xA

xB � xA; ð4:2Þ

Yab ¼y3 � yA

yB � yA: ð4:3Þ

Examples of the Bezier curves are given in Fig. 4.2, in which Yab = 0. WhenXab = 0, the point 3 is identical to point A, and the resulting curve is a straight linebetween points A and B. If Xab is greater than unity, a reentry bowl shape isreproduced.

To keep bowl volume constant, the depth of the bowl is usually varied. Anapproximating and iterative methodology is used to generate meshes with thedefined geometry and to maintain the compression ratio and user-selected mesh size(usually about 2 mm or smaller) until a convergence criterion is satisfied. Table 4.3lists the investigated ranges of these five geometrical variables, as well as the sprayinjection angle and swirl ratio. This technique enables a wide search of differentpiston designs, including re-entrant shapes and open-type bowls. The ERC improvedKIVA3v2 code was employed for the CFD evaluation of the engine design. It is alsonoted that the Shell/CTC combustion model was used to save computational time.The sub-models of the KIVA code are summarized in Table 4.4.

A

1

2 3

Bcylinder axis

cylinder wall

A -B -

1-3 -

bottom bowl diam.

bowl diam.

points

Fig. 4.1 Parameters of bowlgeometry

Fig. 4.2 Examples of Beziercurvature parameters

4.1 Assessment of Multi-Objective Genetic Algorithms 127

Based on the discussion in Chap. 2, the performance of MOGAs is defined byoptimality and diversity, namely the goals for multi-objective optimization prob-lems are:

1. To find a set of solutions as close as possible to the Pareto-optimal front.2. To find a set of solutions that are as diverse as possible.

Correspondingly, the five groups of numerical experiments listed in Table 4.5were evaluated for the design optimization of the engine specified in Table 4.1.Both an in-house code (for l-GA) and commercial optimization software,modeFRONTIER (for NSGA II and ARMOGA) were used. Because the goals ofMOGAs are to find a set of solutions as close as possible to the true Pareto frontand also to make the solutions as diverse as possible, the corresponding featuresneed to be quantified with the information given by the Pareto solutions. Fourquantities were defined for assessing MOGAs as follows: the Number of Pareto

Table 4.3 List of optimization parameters and their ranges

Parameter Range

A- diam. of bowl bottom 74–80% bowl diameterB- bowl diameter 71–84% cylinder diameter1 – Bezier curve control point (from 1 to 2) 0.1–0.72 – Bezier curve control point (from 2 to 1) 0.3–0.93 – Bezier curve control point (from A to B) 0.8–1.5Injector spray half-angle 60–85�Swirl ratio 0.5–2.0

Table 4.4 KIVA3v2 sub-models

Functions Models

Turbulence Modified RNG k-e (Han and Reitz 1995)Spray development KH-RT Model (Beale and Reitz 1999),Spray Impingement Standard KIVA model (O’ Rourke and Amsden 2000)Ignition and Combustion Shell/CTC (Kong et al. 1995)Soot Two-step model (Nishida and Hiroyasu 1989, Patterson et al. 1994)NOx Extended Zel’dovich (Heywood 1988)

Table 4.5 Parameter configurations for the assessment of MOGAs

Group 1 2 3 4 5

MOGAs l-GA NSGA II ARMOGA NSGA II ARMOGACoding Binary Binary Real Binary RealCrossover possibility 0.7 0.9 0.9 0.9 0.9Mutation possibility 0.1 0.143 0.143 0.143 0.143Start gen. of adaptation N/A N/A 20 N/A 15Pops. 4 4 4 32 32Gens. 320 320 320 40 40Total Evals. 1,280 1,280 1,280 1,280 1,280


Solutions (NPS), the Mean Distance to the Pareto Front (MDPF), the Mean Dis-tance between Extreme Pareto Solutions (MDEPS), and the Mean Deviation of theDistance between Neighbor Pareto Solutions (MDDNPS). It is obvious that NPScan be observed from the Pareto front directly, and it represents how many optimaldesigns are available to the decision maker. The other three quantities are definedthe next. The optimization goal is to minimize fuel consumption and emissionsrepresented by the three objectives that are GISFC, NOx, and soot. However, thethree objectives have different orders of magnitude. Therefore, it is necessary tonormalize the objectives with the corresponding maximum and minimum values ofthe investigated group of solutions. By doing so all objectives are given the sameweight in assessing MOGAs.

The MDPF indicates how close the Pareto solutions of a MOGA are to the truePareto front. Since the location of the true Pareto front for the engine designproblem is unknown, the global maximum and minimum values of each objectiveof Pareto solutions were used and the objectives of every Pareto solution werenormalized with the global values. The normalized values were then averaged toyield MDPF, which is expressed mathematically as

MDPF ¼ 1M

XMi¼1

1N

XN

i¼1

Objj � Objglobal min

Objglobal max � Objglobal min

!; ð4:4Þ

where M is the NPS for a MOGA, and N is the number of objectives. It is obviousthat smaller MDPF is preferred for approaching the true Pareto front.

It is of interest to investigate the boundaries of the objective-space defined bythe Pareto solutions of each MOGA, because it represents how large the space iscovered by optimal solutions. Similar to the MDPF, MDEPS is also normalizedwith the global maximum and minimum values of each objective. The extremePareto solutions are searched for each MOGA on its Pareto front, which haveeither maximum or minimum objective values. These are referred to as the groupmaximum and minimum values. Therefore the MDEPS is defined as:

MDEPS ¼ 1N

XN

i¼1

Objgroup max � Objgroup min

Objglobal max � Objglobal min

; ð4:5Þ

where N again is the number of objectives. Larger MDEPS implies that the Paretosolutions for the MOGA are distributed in a larger optimal objective-space.

A large optimal objective-space is a desirable feature of MOGAs. However, itis also preferred that the optimal solutions are distributed in the optimal spaceuniformly. The MDDNPS is used to evaluate how evenly the optimal solutions arespread. Different from the previously defined two quantities, the normalization ofMDDNPS is based on the group maximum and minimum objective values. Theneighbor solution is defined as a solution on the Pareto front, which has thesmallest Euclidean distance to another Pareto solution, and the Euclidean distancebetween solutions i and j is given by:


Dij ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1N

XN

i¼1

Obji;k � Objj;k

Objgroup max;k � Objgroup min;k

!2vuut : ð4:6Þ

After all neighbor solutions are determined, their mean value can be obtained,and then the standard deviation is given by

MDDNPS ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

M � 1

XM

i¼1

Di;neighbor � Dmean

� �2

vuut ; ð4:7Þ

where M is the NPS. Thus, a smaller MDDNPS indicates a more even spread of thePareto solutions in the objective-space.

The performance of the various MOGAs was assessed by Shi and Reitz (2008a),and the results of an engine study are presented in Fig. 4.3.

As observed in Fig. 4.3(a), NSGA II with a population number of 32 producesthe most Pareto solutions. It is also observed that MOGAs with large populationsgenerate more Pareto solutions than those with small populations. Like the proverb‘‘A good beginning is half done’’, a large initial population enlarges the search

Fig. 4.3 Assessment of performance of MOGAs. a NPS. b MDPF. c MDEPS. d MDDNPS


parametric space and thus increases the possibility that initial designs containneeded characteristics to generate optimal designs with respect to all objectives ofinterest. Therefore, the increased randomicity introduced by the large initialpopulations is very important for highly non-linear multi-objective optimizationproblems (MOPs), such as engine optimal design. However, simply increasing theinitial population does not help increase the number of Pareto solutions forMOGAs, such as for l-GA. Because the merits of the initial designs need to bepreserved in the subsequent evolutionary processes, and the populations arerequired to be of the same order of magnitude as the initial populations. A largepopulation in each generation allows for tournament selection and crossover to beconducted in a large space that diversifies objectives, and thus produces moretrade-offs that lead to more Pareto solutions.

The greater the number of generations, the closer the MOGAs approach the truePareto front, and this is illustrated in Fig. 4.3(b), which also shows that l-GA andARMOGA with population 4 give smaller values of MDPF compared to NSGA IIand ARMOGA with population 32. The exception is NSGA II with population 4gives the worst results of MDPF, which indicates that NSGA II does not performwell when its population size is too small.

The MDEPS shown in Fig. 4.3(c) represents the ability of a MOGA to extend theboundaries of its objective-space. As indicated in this figure, NSGA II performsbetter than the other MOGAs in general. MOGAs with large populations generallyoutperform the ones with small populations, and this again is due to the effect of theinitial randomicity discussed before. It is also interesting to observe that ARMOGAwith a population of 4 has the best MDEPS after the number of evaluations reach1,000, which is due to the adaptive range searching technique applied in thealgorithm. The start of adaptation for this case begins at the 20th out of the total of320 generations, and there is increasing possibility that the search range will focuson a parametric space that produces solutions that are distributed on the boundariesof the objective-space with increasing generations. Although ARMOGA with apopulation size of 32 started its initial adaptation at the 15th generation, comparedto its total 40 generations, the chance of searching boundaries was less. Unfortu-nately in the current study it seems that this case focused its search range far fromthe boundaries during the last generations, which resulted in the decreased MDEPS.This finding suggests that the adaptive range technique is a very promising methodto extend the optimal objective-space, but it requires a sufficient number of gen-erations, so an early application of the adaptation is recommended.

Figure 4.3(d) shows MDDNPS that represents how evenly the optimal solutionsare spread along the Pareto front. NSGA II again shows better performance,especially when it is run with large populations. It is understandable since NSGAII employs an explicit and parameter-independent methodology to avoid apotential optimal solution being selected in an optimization cycle that is sur-rounded by crowded existing solutions. The niching technique of ARMOGAdiffers from NSGA II in that it relies on the setup of two niching parameters, whichare also problem-dependent. Because of the adaptation of the search space, thecapacity of evenly distributing optimal solutions using ARMOGA is limited.


Although l-GA also applies the concept of a crowding distance into its evolu-tionary processes, the diversity-preservation of the l-GA depends on its externalmemory and non-repeatable initial populations, which results in the largest value(worst performance) of MDDNPS.

Figure 4.4(a) and (b) further illustrates the Pareto solutions that are distributed inthe objective-space and are collected from 640 to 1,280 evaluations, respectively.Although more Pareto solutions are produced as the optimization process proceeds,it is seen in Fig. 4.4(a) and (b) that the location of the Pareto front does not movesignificantly from 640 evaluations to 1,280 evaluations. This indicates that theoptimization process can be ceased at 640 evaluations or even earlier. Together withFig. 4.3(a), it is observed in Fig. 4.4 that the number of Pareto solutions using NSGAII or ARMOGA is much larger than that of l-GA which was employed in the engineoptimization study of Genzale et al. (2007). When using a large population size, thePareto solutions produced by NSGA II and ARMOGA sufficiently and uniformlycover the Pareto front as depicted in Fig. 4.4.

4.2 Assessment of NSGA II: Niching Technique, Convergenceand Diversity Metrics

4.2.1 Design- and Objective-Space Niching of NSGA II

In engineering optimization problems, it is usually required to achieve diversifiedsolutions. This requirement can be further explained by an example of engineoptimization. For instance, in-cylinder clean combustion techniques are usuallycombined with aftertreatment methods for the reduction of emissions. In this case,optimal solutions of in-cylinder combustion can guide the selection of aftertreat-ment devices. This requires that the optimization process provides solutions with

Fig. 4.4 Pareto solutions distributed in the objective-space. a Pareto solutions from 640evaluations. b Pareto solutions from 1,280 evaluations


diversified objective functions, such as emission results. However, under othercircumstances, more diversified parameters of the solutions indicate that it is morelikely to obtain a design that can minimize the changes to the current baselinedesign in order to save redesigning costs, such as the piston geometry of engines.The diversity of optimal designs may focus on different aspects (either on theobjective-space or design-space) based on the requirements of customers anddesigners. This can be achieved by performing different niching strategies withMOGA, as shown next.

Although it is applied with different methodologies in different MOGAs, theniching strategy is a method that can detect whether optimal designs are forming acrowded cluster, and if so, to guide the MOGA to produce more diversified designsbased on the existing information.

Figure 4.5 illustrates the concepts of rank and crowding distance. As shown,the solid circles are the Pareto cases that dominate (out-perform) other cases.However, they do not dominate each other, and thus they form a non-dominatedfront defined as the first rank. The same procedure can be applied to the rest ofthe solutions to find a second rank, and so on until every solution is assigned arank. The crowding distance is defined by the average distance of a solution toits nearest neighbors. For example, the crowding distance of solution i in Fig. 4.5is the average side-length of the rectangle (the dashed box). The mathematicaldefinition of the crowding distance can obviously be applied to higher dimen-sions, although it is only shown in a 2-D plot here for a clear view. Therefore, Npopulations will be selected from 2 N combined populations based on thecompetition rules of NSGA II. In this way, a crowded cluster of solutions can beprevented from evolving into the next generation, and the optimal solutions canbe distributed on the Pareto front more uniformly. In the original NSGA IIsource code, such niching strategy is applied to the objective-space whichensures that diversified objective functions are produced during the optimizationprocess. The NSGA II source code was modified to integrate the niching strategyto the design-space so that more diverse design parameters can be expected. Itwas thought that performing both niching strategies concurrently to the

Fig. 4.5 Illustrations ofPareto solutions, ranking andcrowding distance

4.2 Assessment of NSGA II 133

objective- and design-spaces would reduce the optimization efficiency, and thuseither the objective niching or the design niching was performed for each of thecase studies.

4.2.2 Convergence and Diversity Metrics

Observation on the movement of the Pareto front as the optimization proceedsindicates if the optimization process moves towards convergence. However, if thenumber of objectives exceeds three, visualization of the Pareto front becomesimpossible. Therefore, a convergence metric of the optimization process usingMOGA has to be defined in order to better monitor the optimization process.Defining a convergence metric can be regarded as reducing the dimensionality ofthe Pareto front to one-dimension. The method proposed by Deb and Jain (2002)was adopted and modified here for engine optimization studies and it is describedin the following steps.

1. Identify the Pareto (non-dominated) solutions of each generation that has beendone, and those n solutions form a solution pool P;

2. From the second generation, the Pareto solutions of the current generation canbe compared with solutions in the pool P that is formed by the previous gen-eration(s) in Step 1. For each Pareto solution of the current generation, calculatethe smallest normalized Euclidean distance to the n solutions of the poolP using

di ¼ min

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXMk¼1

fk;i � fk;j

f maxk � f min

k

� �2vuut ; j ¼ 1; . . .; n; ð4:8Þ

where M is the total number of objectives, and f maxk and f min

k are the maximumand minimum values of the k-th objective from all n solutions in the pool P;

3. A convergence metric is determined by averaging the normalized distance forall nn Pareto solutions of the current generation:

CN ¼ 1nn

Xnn

i¼1di; ð4:9Þ

4. In order to keep the value of the convergence metric within [0,1], it is nor-malized by its maximum value after all N generations are assigned a convergentvalue from Step 3:

�C j ¼ C j=maxðCi; i ¼ 1; . . .;NÞ; j ¼ 1; . . .;N: ð4:10Þ

Usually, the maximum value is from the beginning generations, e.g., the secondgeneration.


In order to assess the diversity of the Pareto solutions in either the objective-space or design-space, a corresponding metric is needed. Although more com-plicated methods were employed in the studies of Deb and Jain (2002) and Far-hang-Mehr and Azarm (2002), this work introduces a simplified method formeasuring the diversity, which is proper for the present engine optimization andsimilar engineering problems as well. Taking the objective-space for example, themethod divides the space into many sub-grids based on the user-specified spansand if more sub-grids contain sole or few Pareto solutions, the results are deemedto be more diverse. As further illustrated by Fig. 4.6, the set of the Pareto solutionsin the left figure is better than the right one in terms of the diversity of the twoobjectives. The method can also be extended to study more objectives. However,since the number of Pareto solutions is usually of the order of 100 in typical engineoptimization problems, it is suggested that the number of studied objectives shouldnot exceed 3 and the number of spans of each objective should not exceed 10 inorder to keep the total sub-grids of the order of 1,000. Obviously, the same methodcan be applied to investigate the design-space as well.

To further quantify the diversity metric, different weights are assigned to the sub-grids that contain different numbers of Pareto solutions, and these sub-grids con-taining fewer solutions are given higher weights (1/n, n is the number of Paretosolutions that are located in that grid). Therefore, the averaged weighting summationfor all sub-grids that include the Pareto solutions represents a quantified diversitymetric, and a larger value indicates more diversified solutions (maximum value is 1).

4.2.3 Assessment of Niching Strategies

Optimization results from using KIVA3v2 and NSGA II with two niching strat-egies are compared in terms of their convergence and diversity metrics and per-formance. The same optimization case of high-load condition evaluated in Sect.4.1 (Shi and Reitz 2008a) was repeated with the two niching techniques.

Fig. 4.6 Illustration of diversity metric


Figure 4.7(a) shows normalized convergence metrics using objective nichingand design niching. The fluctuations that appear in both curves imply that the latergenerations in the optimization process do not necessarily produce solutions betterthan the previous ones. However, in general, the value of the convergence metricbecomes smaller as the optimization proceeds. It is seen that both optimizationprocesses converge very fast (in the first ten generations), and after about 20generations, the curves become relatively flat, which indicates that the Pareto frontdoes not move significantly from generation 20 to the end of the optimization. Tofurther illustrate this, Pareto fronts in the objective-space of generations 20 and 51for the two niching strategies are depicted in Fig. 4.7(b) and (c), respectively. It isobserved that the Pareto fronts of generation 20 and 51 overlap in many places andtheir relative locations with respect to the origin are very close as well. Theconsistency between Fig. 4.7(a–c) also proves the fidelity of the present method ofcalculating the convergence metric for MOGA. This figure also concludes that theobjective niching and the design niching perform similarly in terms of theirconvergent rates. The results discussed here reveal the significance of dynamicallygenerating the convergence metric in optimization, because the designer can havesufficient confidence to terminate the optimization process if it is seen that furtherevaluations are redundant.

Fig. 4.7 Comparison of convergence metric. a Convergence metric. b Pareto front from theoptimization using the objective niching. c Pareto front from the optimization using the designniching


Since the study of convergence metrics of the two niching methods merelyrepresents their historic performance (comparison between the later generationsand previous generations), it is important to also compare the two methods directlyin terms of the optimality of their Pareto solutions. The same method (Shi andReitz 2008a) described in Sect. 4.1 was used to assess their performance bycomparing two quantities. The comparison is given in Fig. 4.8 which shows thatthe two niching methods perform closely with respect to these two quantities,although it is seen that the design niching method generated slightly better resultssince its MDPF values are a little smaller than those with objective niching.

The diversity metric was analyzed based on the values of the objectives anddesign parameters of the Pareto solutions of the optimizations using the twoniching methods. For the objectives, the investigated ranges were determinedautomatically by the maximum and minimum values of that objective over allPareto solutions up to the current generation, and the ranges were discretized with10 spans (this corresponds to 1,000 grids in the three-dimensional objective-space). For the design parameters, the investigated boundaries were pre-specifiedprior to the optimization, and in this work, only three parameters, the SOI, swirlratio, and spray angle, were analyzed. Because the investigated range of the start ofinjection was limited to -12 to -15 ATDC (Shi and Reitz 2008a), it was dis-cretized by 3 spans and 10 spans were used for the other two parameters, which arein ranges of 0.5–2.0 and 60.0–85.0 for swirl ratio and spray angle, respectively.

Figure 4.9(a) shows that the diversity metrics in the objective-space for the twoniching methods are close, which further indicates that using both niching strat-egies can produce similar sets of Pareto solutions with respect to the diversifiedobjectives, i.e., emissions and fuel consumption. But, by simply altering theobjective niching to design niching, the optimization process produced morediversified designs as seen in Fig. 4.9(b). At the end of the optimization forobjective niching, there was no grid in the design-space containing just one Paretosolutions, and there was one grid containing two Pareto solutions, and the unde-sirable result was that 27 Pareto solutions were clustered in one grid. For the

Fig. 4.8 Comparison ofperformance (MDPF)


design niching, there were 6 grids containing only one Pareto solution, and amaximum 14 Pareto solutions were found in one grid. The results prove thesuperiority of design niching when implemented into the NSGA II code for engineoptimization.

4.3 Assessment of Regression Methods for Replacing CFDEvaluations

Regression analysis over existing CFD evaluation results reveals the relationship(response surface) between design parameters and objective functions. Withsufficient existing datasets and regression methods of high fidelity, designparameters can be mapped to objective functions through algebraic expressions,and thus this can be used to partially or entirely substitute real CFD evaluationsin practical optimization problems to save computational expense. This sectioninvestigates the four regression methods (including K-nearest neighbors (KN),Kriging (KR), Neural Networks (NN), and Radial Basis Functions (RBF)) thatare described in Chap. 2 in order to assess their performance in engine opti-mization problems. Datasets calculated from KIVA were used to train thoseregression methods to generate corresponding response surfaces that reflect therelationships between the design parameters and the objectives. Predictions of anentire GA generation (24 cases with the present population size) based on theresponse surfaces (virtual design) were compared with the results calculated bythe KIVA code (real design), and the relative errors between the objectives ofthe virtual and real designs were used to quantify the performance of eachregression method. To gain more statistical information, the mean, maximum,median, and minimum values of the error are reported as well as the standarddeviation of the error.

Fig. 4.9 Comparison of diversity metric. a Diversity metric in the objective space. b Diversitymetric in the design space


As a preliminary test, a Design of Experiment (DoE) method, the OptimumLatin Hypercube method, was used to produce a set of design parameters. A totalof 120 cases were created based on the investigated range (Shi and Reitz 2008a) ofthe design parameters and the KIVA code was first run to obtain the objectives ofthese cases. This process created a data pool (more uniformly distributed than theGA generated data pool) to train the regression methods. Since KIVA results areavailable from the previous optimization studies, several generations were selectedto test the performance of the regression methods, and without losing generality,only generations from the group using objective niching are considered here.According to Brahma et al. (2008) and the authors’ experience, a logarithmictransformation (similar to the concept of Box-Cox transformation (Draper andSmith 1981)) was applied to the objectives, i.e., the objectives (GISFC, NOx, andsoot) of the trained dataset were transformed by a logarithm function and corre-spondingly the predicted results based on this dataset need to undergo a power of10 transformation before comparing with the KIVA results. It is noted that thevalues of soot emissions ranged from 10-3 to 101 g/kg fuel in the present study,and if a logarithmic transformation was directly applied, the resulting values couldbe negative and positive. In the authors’ experience, this deteriorates the predictionaccuracy of the virtual designs, and thus the logarithm transformation for sootemissions was given by:

sootlog¼ 1� logðsootÞ ð4:11Þ

to ensure positive soot values after logarithmic transformation. Another advantageof using this formula is that it prevents unrealistic negative soot values from beingproduced for the virtual designs.

The generated response surfaces using the four regression methods were used topredict the objectives for the cases from five generations (11, 21, 31, 41, and 51) ofthe group using the objective niching, and only the mean errors are reported here.It is seen in Fig. 4.10 that the mean error of the GISFC is the smallest, whichimplies that the relationship between the GISFC (i.e., engine power since theamount of injected fuel was fixed) and the design parameters is less complicatedthan that of emissions and thus can be well captured by the regression methods.The complicated influences of the design parameters on the soot emissions causeunsatisfactory prediction accuracy, as shown in Fig. 4.10(c). In general, the meanerrors of all regression methods for each objective are of the same order ofmagnitude, and the RBF method performs slightly better than the others on theemissions, which could be due to its suitability for scattered data (generated byDoE here) interpolations. Further observation shows that the implementation of thelogarithm transformation improves the prediction accuracy for most of cases,especially for soot emissions, although this is not true for the RBF method, whichcould be due to the use of Gaussian function (the exponential transformation isalready applied intrinsically) in the RBF.

As stated before, the ultimate goal is to explore the feasibility of using aregression method to partly replace actual computationally-expensive CFD

4.3 Assessment of Regression Methods for Replacing CFD Evaluations 139

simulations. The next comparisons aim at this purpose, and the methodology isdescribed as follows.

As can be seen in Fig. 4.10, the prediction accuracy of the emissions is notsatisfactory for replacing a part of the real CFD simulations. This can be under-stood, because it is somewhat unreasonable to expect 120 DoE-generated designswith nine parameters over such wide ranges to reveal all the complicated rela-tionships between the design- and objective-spaces for the current engine designproblem. However, the inherent characteristics of the genetic algorithms provide amethod for possible improvement of utilizing regression methods. Since each ofthe cases in a GA generation inherits design features from the previous genera-tions, it is expected that this could benefit the learning process of regressionmethods if all previous generations were trained to form the response surfaces,which are then used to predict the next generation.

It is also of interest to compare results trained on these two niching groups toinvestigate how the niching method influences the training process by producingdifferent data pools for the regression methods. The logarithmic transformationhelped to improve the prediction accuracy for the KN, KR and NN methods and

Fig. 4.10 Comparison of regression methods trained with a dataset generated with a DoEmethod. a Mean percentage error for GISFC. b Mean percentage error for NOx. c Meanpercentage error for soot. d Legend


thus it was adopted for them, but for the RBF method no transformation wasapplied.

Statistical studies of the relative errors between virtual designs predicted by theregression methods and the real designs from KIVA simulations are reported in

Fig. 4.11 Comparison of regression methods trained with datasets from the optimization processusing different niching strategies: percentage errors of GISFC. a Mean percentage error.b Maximum percentage error. c Median percentage error. d Minimum percentage error.e Standard deviation of the percentage error. f Legend


Figs. 4.11, 4.12, and 4.13 for GISFC, NOx, and soot, respectively. Five genera-tions (11, 21, 31, 41, and 51) were analyzed for each group. For each analyzedgeneration, all of its previous generations were used as the training dataset. Thesolid lines with solid symbols represent the error of the regression methods trained

Fig. 4.12 Comparison of regression methods trained with datasets from the optimization processusing different niching strategies: percentage errors of NOx. a Mean percentage error.b Maximum percentage error. c Median percentage error. d Minimum percentage error.e Standard deviation of the percentage error. f Legend


with the dataset from the optimization process using objective niching, and thedashed lines with open symbols represent design niching.

Compared to results of Fig. 4.10 the regression methods trained with datasetsfrom the optimization processes show a similar trend that the mean error of GISFCis the smallest and is followed by NOx and soot. But the absolute values of the

Fig. 4.13 Comparison of regression methods trained with datasets from the optimization processusing different niching strategies: percentage errors of soot. a Mean percentage error. b Maximumpercentage error. c Median percentage error. d Minimum percentage error. e Standard deviationof the percentage error. f Legend


mean errors are much smaller, which indicates that it is important to dynamicallylearn from previous datasets in order to better predict the next. Results predictedusing regression methods trained with the dataset from the optimization processusing objective niching are much better than those with design niching. This ismost likely due to the proximity of designs in the dataset using objective nichingsince it is also seen in the figures that the K-nearest neighbors method (indicatedby the black squares) performs the best in most of the cases, followed by theKriging method.

It is conjectured that the performance of interpolation of the regressionmethod is more important than that of extrapolation if it is trained with datasetsfrom the MOGA optimization processes. Figures 4.11, 4.12, and 4.13 also showthat the errors increase with the size of the trained dataset, especially for the NNand RBF methods. A possible cause is bad-fitting or over-fitting data whichcould be more likely produced as the size of the trained dataset increases. Thisindicates that the training process does not necessarily need to be conducted overall previous existing results. Furthermore, different from training with a scattereddataset in Fig. 4.10, the RBF method did not predict satisfactory results. Theneural network method behaved unexpectedly poorly in the prediction of sootemissions. Another important finding is that for all objectives, the median errorsare less than the mean errors. The median errors of the K-nearest neighbors andKriging methods are below 1, 5, 15% for GISFC, NOx, and soot if they aretrained with the datasets from the optimization using objective niching, as shownin Figs. 4.11(c), 4.12, and 4.13(c), respectively. This indicates that half of thereal KIVA simulations could be possibly replaced by virtual designs predictedusing a reliable regression method, which promises savings in computationalresources.

Remaining questions are (1) does the computational expense of using aregression method exceed that of the KIVA CFD evaluations because thenumber of trained cases increases as the optimization proceeds? (2) prior toeach generation, how to determine which cases are calculated from theregression methods and which should use KIVA in order to minimize theerrors? As far as concerns about computational time, it was observed that byusing the Response Surface Methods (RSM) package of modeFRONTIERTM

4.0 the learning time of the K-nearest neighbors method and the Krigingmethod increases approximately linearly with the number of trained data, and itis about quadratic for the RBF method and cubic for the neural networkmethod. However, even with over a thousand cases, none of the learning timesexceeded the running time of a KIVA case. This means that just one processoris needed to complete learning and evaluation of N virtual designs, and thusN-1 processors can be saved for every generation. Regarding the secondconcern, error control should be based on the proximity of the cases in thecurrent generation to the trained previous cases. It is unnecessary to fix thenumber of virtual designs in each generation. Instead it can be determinedadaptively based on the proximity.


4.4 Summary

The assessment of multi-objective genetic algorithms indicates that the NSGA IIalgorithm performs well with a large population size. As will be seen in Chap. 6,the KIVA code coupled with NSGA II enabled a variety of engine optimizationstudies, including studies of piston geometry, injection parameters, and others.Convergence and diversity metrics for engineering optimization problems withMOGAs are defined and quantified to dynamically monitor the optimizationprocess. It has been shown that with dynamic learning, regression methods,especially the K-nearest neighbors and Kriging methods, predicted results in goodagreement with the KIVA CFD evaluations for the next generation. A logarithmtransformation in the objective-space improved the prediction accuracy for theKN, KR, and NN methods, but not for the RBF method. These findings promise aproposed methodology, where a part of the real evaluations can be replaced byvirtual designs through learning from previously existing data.

4.4 Summary 145

Chapter 5Scaling Laws for Diesel CombustionSystems

Scaling laws are developed to guide the transfer of combustion system designsbetween diesel engines of different sizes using simple formulations. In this chapter,the concepts and formulation of scaling laws are presented. A practical example isprovided to study a light-duty and a heavy-duty production diesel engines usingthe established scaling laws.

5.1 Introduction

Engine design is a time consuming and expensive process in which many costlyexperimental tests are usually conducted. Even with efficient and reliable CFDtools, engine optimization could take a very long time to complete. Engine designwork is often repeated for different engines that share similar features. Thismotivates a study of scaling laws, which describe scaling relationships betweenengines with different sizes, such as large off-road heavy-duty diesel engines andsmall high-speed auto engines. CFD simulation again offers an efficient andinformative option for this task. The intent of the scaling laws is to maintaingeometric similarity of key parameters influencing diesel combustion, such as in-cylinder spray tip penetration and flame lift-off length. Based on relatively simpleformulations, one well-established engine can be down-scaled or up-scaled toanother engine, which has similar features as the original engine. In this way, theamount of engine design work is significantly reduced in both time and cost.

Initial work was proposed by Bergin and Reitz (2005) who proved that similarcombustion behavior in two different size engines can be obtained by scaling a fewbasic engine geometry parameters, engine speed, and the injected fuel mass. Stagerand Reitz (2007) developed an extended model by adding a law to scale the flamelift-off length. The scaling laws were applied to two ideally-scaled engines wherethe small engine was obtained by halving the dimensions of the larger engine.Numerical results of multidimensional simulations showed that the scaling lawsworked well over a range of injection timings for engines with low temperature


147

combustion, and the results also suggested that three regions could be defined inthis range where turbulence and chemical kinetics timescales played different rolesin influencing combustion and emissions.

Shi and Reitz (2008c) conducted a CFD-based scaling study of two productiondiesel engines (one 0.5 L light-duty GM-Fiat engine and one 2.5 L heavy-dutyCaterpillar engine). It was found that the in-cylinder pressure trace and heat releaserate results could be well predicted based on the scaling laws. Emission results werewell captured in combustion regions controlled by turbulent time scales. Someprocesses (such as soot and NOx formation) are determined by chemical reactiontime scales and thus previous scaling laws had difficulty to reproduce them. Thesame two engines were also investigated experimentally (Staples et al. 2009), andthe scaling laws in Bergin and Reitz (2005) and Stager and Reitz (2007) werevalidated where the Caterpillar engine was modified before testing in order to beconsistent with the scaling laws. Experimental results showed that overall engineperformance including IMEP and ISFC were in good agreement for two scaledengines. Extended scaling laws accurately predicted the SOC, CA10, and CA90.NOx and PM emissions matched trend-wise and in approximate magnitude. NOxemissions showed dependence on chemical timescale differences that are caused byengine speed and temperature. Higher PM emissions in the small engine werethought to be due to reduced time and increased heat transfer. Lee et al. (2010)investigated the impact of design constraints/limitations on the applications ofscaling laws and identified key physical parameters that need to be respected withinengine design constraints. Ge et al. (2011) applied the scaling laws for downsizing alight-duty HSDI diesel engine from 450 to 400 cc. They found that the scaling lawswork well at least for engine downsizing with small size variations.

5.2 Scaling Laws

Scaling laws are desired to produce identical performance and emission levels inengines of different sizes. However, it is very difficult to achieve this aim in reality.Establishment of any scaling arguments for diesel engines should at least target thefollowing goals: (1) geometric similarity should be maximized, so that the twoscaled engines have similar boundary conditions. This includes scaling of the bore,stroke, squish height, and piston bowl shape, and the resulting compression ratioshould be the same in the two engines. By setting the same boost pressure andtemperature, the same wall temperatures, and the same initial flow conditions, suchas the swirl ratio, similar initial thermodynamic and fluid dynamic conditions priorto spray injection can be achieved in the combustion chamber; (2) similarity inspray dynamics should also be considered. Spray development has a primary effecton engine performance and pollutant emissions as it determines the mixing of thefuel and air. The aim is to have similar fuel distributions before the combustionevent. It is usually quantified in terms of spray tip penetration, which is the essentialparameter determining the fuel distribution; (3) similarity in the combustion

148 5 Scaling Laws for Diesel Combustion Systems

characteristics in the scaled engines should be maintained in order to providesimilar engine performance and emissions.

5.2.1 Combustion Chamber Geometry

Volume-related quantities are scaled by V, such as the displacement volume andthe volumes at TDC and BDC, while length is scaled by L, such as the bore, stroke,squish height and bowl diameter. The resulting compression ratios should be thesame. Valve opening and closing timings, swirl, wall temperatures, boost pressuresand temperatures are also kept the same. All of these scaling laws ensure that thethermodynamic and fluid dynamic conditions before spray injection are similarbetween two engines.

As an internal flow, the diesel combustion process is strongly influenced by thepiston bowl geometry. The in-cylinder flow after spray injection is dominated bythe spray-induced flow because the injected droplets have much higher speeds.The surrounding gas flow is dragged by droplets and interacts with the piston bowlmovement. This can form a tumble flow, which has a significant impact on theconsequent processes of mixing, combustion, and pollutant formation. Optimiza-tion of piston bowl shape is thus an important part of the whole process of enginedesign. In engine scaling, the piston bowl shape is also kept the same so that theresulting spray targeting, and the interaction of the spray induced tumble flow andgeometry are the same for the two engines.

5.2.2 Power Output

The power outputs of the two engines should scale with their displacement volumes.Assuming that the down-scaled engine has the same combustion and thermal effi-ciencies, its power output should be scaled by the injected fuel mass m. Thus, theinjected fuel mass m scales with V. The injected fuel mass is related to the fuel injectornozzle hole diameter d0, injection velocity Uinj, and injection duration Dt by:

m ¼ p4qld

20UinjDt: ð5:1Þ

5.2.3 Spray Tip Penetration

In direct injection engines spray tip penetration, which is defined as the distancebetween the spray plume tip and nozzle tip, is a primary parameter that characterizesthe following fuel distribution and mixing. Additionally, if the spray tip penetrationis too long, spray wall impingement may occur, which will lead to poor emission

5.2 Scaling Laws 149

results. To maintain similarity in the fuel distributions, the spray tip penetrationsshould be scaled by the length scale of the cylinder, which is L. Parameters that affectspray tip penetration include the injector orifice diameter, ambient gas conditions,and fuel characteristics (Siebers 1999). Hiroyasu et al. (1978) experimentallyinvestigated the effects of nozzle orifice size, injection pressure, fuel density, andambient density on transient spray tip penetration. They found that spray tip pene-tration is directly proportional to time in the early stages of injection, but becomesproportional to the square root of time as the injection progresses according Eq. 5.2.The time duration of the first stage is defined as breakup time tbreak. Modest changesin ambient temperature had little to no effect on spray tip penetration. Even inexperiments where the temperature varied from room temperature to 320�C, thechange in spray tip penetration was minimal. The jet disintegration theory of Levich(1962) gives consistent results and the spray tip penetration s were described usingthe following empirical explicit equations:

s ¼0:39t 2Dp

ql

� �12; t\tbreak

2:95 Dpq

� �14ðd0tÞ

12; t� tbreak

8>><>>: ;

ð5:2Þ

with the breakup time scale tbreak ¼ 28:65qld0ðqDpÞ1=2. ql and q are density of theliquid fuel and air, respectively. Dp is the pressure drop across the injector, whichis related to the injection velocity Uinj, through Bernoulli’s principle:

Dp ¼ 12

qlU2inj: ð5:3Þ

Generally, only the second stage (t� tbreak) is considered except for very shortinjections. Substituting Eq. 5.1 into Eq. 5.2 gives

s2 / Uinjd0t: ð5:4Þ

5.2.4 Flame Lift-Off Length

The combustion process of diesel combustion can be well characterized by theflame lift-off length, which is defined as the length away from the injector tip thatthe combusting flame stabilizes once the initial auto-ignition phase is over.

Dec (1997) developed a conceptual model of DI diesel combustion based onlaser sheet imaging. His study indicated that a rich reaction zone exists justdownstream of the lift-off length in the central region of the fuel jet. Significantlocal heat release and fuel-rich product gases are generated in this region. Fur-thermore, it has also been hypothesized that soot formation begins in the productgas in this region under typical diesel conditions, and then the soot concentrationand particle size grow as the product gas is transported further downstream.


Siebers et al. (2002) investigated the effects of oxygen concentration on flamelift-off on DI diesel fuel jets, and concluded that lift-off length is inversely pro-portional to the ambient gas oxygen concentration. They also confirmed previouslyobserved trends in lift-off length with respect to other parameters, such as theinjector hole size, ambient gas temperature, and injection pressure. Pickett et al.(2005) extended Siebers’ study on lift-off length and studied the relationshipsbetween ignition processes and the lift-off length. A power-law relationship of thelift-off length to various parameters was summarized in their paper (Pickett et al.2005) based on an extensive database obtained using #2 diesel fuel. The expres-sion is:

H / T�3:74q�0:85d0:340 UinjZ

�1st : ð5:5Þ

T is the ambient temperature. Zst is the stoichiometric mixture fraction. Thiscorrelation was also compared with a scaling law for lift-off length proposed byPeters (2000), which is based on a flame stabilization concept and given as

H / UinjZstaTS�2L ðZstÞ; ð5:6Þ

where aT is thermal diffusivity, and SL as a function of Zst is laminar flame speed.Equation 5.6 was found to be in reasonable agreement with Eq. 5.5 regarding tothe scaling of ambient temperature and density, and injection velocity. However, itwas shown that the experimental lift-off length trends for orifice diameter andambient oxygen concentration were not in agreement with Eq. 5.6. Both injectorgeometry and injection conditions are of much interest to the present scaling study.Therefore, Eq. 5.5 was selected as one of the scaling arguments (Stager and Reitz2007; Shi and Reitz 2008c; Staples et al. 2009).

5.2.5 Swirl Ratio

Swirl is usually defined as organized rotation of the charge about the cylinder axis(Heywood 1988) and is generated by the confined, annular jet flow through thevalve, which gives rise to strong recirculation regions and high turbulence levels(Arcoumanis et al. 1984). Due to friction swirl decays during the engine cycle butit persists through the compression, combustion and expansion processes. Whenswirl is discussed in an operating engine, a mathematical term swirl ratio is nor-mally used to define the swirl, which is (Arcoumanis et al. 1984):

Rs ¼xs

2pN; ð5:7Þ

where xs is the angular velocity of a rigid-body rotating flow, and N represents theengine speed. In diesel engines swirl is used to improve mixing of the injected fueland surrounding air charge. Ogawa et al. (1996) numerically investigated the


effects of swirl ratio on NOx and soot emissions of DI diesel engines. Kook et al.(2006) focused their research on the effects of swirl motion on CO emissions andfuel consumption of low-temperature combustion engines by means of numericalstudies and experiments. Optimization studies (Genzale et al. 2007; Shi and Reitz2008a; Ge et al. 2009a, b) also found significant influence of swirl on engine-outemissions and fuel economy on heavy-duty and light-duty diesel engines. Theseprevious studies indicated that swirl motion is influential during the post-combustion process besides its direct influence on the fuel mixing process prior tocombustion.

Hiroyasu et al. (1978) proposed two factors to supplement the empiricalequations of spray tip penetration and angle in quiescent air in order to considerthe fact that the spray is bent by air swirl. These two dimensionless correlationfactors are defined as:

Cs ¼ 1þ pRsNs

30Uinj

� ��1

; ð5:8Þ

Ch ¼ C�2s ¼ 1þ pRsNs

30Uinj

� �2

; ð5:9Þ

where Cs and Ch are proportional to the reduction in axial penetration and theazimuthal deflection of the spray axis, respectively; s is the spray tip penetration.

5.2.6 Summary of Scaling Laws

All of the time scales (Dt and t) are scaled by the same factor. When Eq. 5.1 isdivided by Eq. 5.4, we get:

d0 /m

s2/ L3

L2¼ L: ð5:10Þ

Thus, the nozzle diameter d0 should be scaled by the factor L.The flame lift-off length H should be scaled by the geometry length L, and since

the scaled engines should have the same ambient conditions and fuel properties, itcan be directly deduced from Eq. 5.5 and Eq. 5.10 that

Uinj / Hd�0:340 / L � L�0:34 � L2=3: ð5:11Þ

Therefore, the injection velocity Uinj should be scaled by L2=3. Consequently, theinjection pressure should be scaled by L4=3 with the help of Eq. 5.3. And scalingrelation for time scales can be deduced from Eq. 5.4:

t / s2U�1inj d�1

0 / L2 � L�2=3 � L�1 ¼ L1=3: ð5:12Þ


In order to achieve the same injection duration on a crank angle basis such that thein-cylinder pressure as a function of a crank angle and the specific indicated workare independent of scales,

N / t�1 / L�1=3: ð5:13Þ

Thus, the engine speed is scaled with L�1=3.To keep similarity in the swirl flow, the non-dimensional parameters Cs and Ch

should be kept the same, which implies

Rs / UinjN�1s�1 / L2=3 � L1=3 � L�1 ¼ 1: ð5:14Þ

Thus, swirl ratio should be kept the same for scaled engines.The final scaling relations are listed in Table 5.1.

5.3 Validation of Scaling Laws on a Light-Dutyand a Heavy-Duty Diesel Engine

5.3.1 Engine Specifications

The scaling laws described in the previous section were validated in a light-dutyGM-Fiat engine and a heavy-duty Caterpillar engine, which are single-cylinderexperimental engines corresponding to respective production models. The speci-fications of these two engines are described in Table 5.2.

As indicated in Table 5.2 and examined by the scaling relations in Table 5.1,the two engines differ in many geometrical parameters and injection relatedvariables. Figure 5.1 shows a comparison of the piston profiles of the two engines,which shows that the engines also feature different bowl curves. The GM-Fiatengine has a deep bowl design with vertical side wall, but the bowl shape of theCaterpillar engine is shallow and the curved chamber wall is relatively closer tothe cylinder wall.

Table 5.1 Scaling relations Parameter Scaling factor: length Scaling factor: volume

m L3 Vs L V1/3

H L V1/3

d0 L V1/3

Uinj L2/3 V2/9

Dp L4/3 V4/9

Dt, t L1/3 V1/9

N L-1/3 V-1/9

Rs = =


To eliminate the differences in bowl geometrical similarity the baseline pistonbowl profile of the GM-Fiat engine was up-scaled to produce the bowl profile for amodified Caterpillar engine. Correspondingly, other parameters, such as theinjection related parameters and operating conditions were scaled based onthe scaling arguments listed in Table 5.1. More detailed discussion is given in thefollowing sections.

5.3.2 Numerical Models

An improved version of the KIVA3v2 code was used to simulate the closed-valveportion of the engine cycle. The ignition and combustion processes were solved bya direct chemistry solver (Chemkin II) coupled in the KIVA code and a reducedn-heptane reaction mechanism (Patel et al. 2004) was used to simulate diesel fuelchemistry. A reduced NO mechanism (Kong et al. 2007) that contains only fourspecies (N, NO, NO2, N2O) and nine reactions extracted from the GRI NOmechanism was used to calculate the sum of NO and NO2 to give the engine-outNOx emissions. Soot emissions were predicted with a two-step model acetylene(C2H2) as the soot precursor (Kong et al. 2007).

The simulated results of the present KIVA-Chemkin code were compared withthe experimental study conducted on the GM-Fiat engine by Lee and Reitz (2006).Figure 5.2 represents one of the comparisons. The engine was operated at low-loadwith IMEP around 5 bar, and SOI equal to 10 BTDC. The EGR rate was 51% inorder to suppress the ignition and realize low-temperature combustion. As can beseen in Fig. 5.2, the numerical pressure trace matches the experimental result well,although it gives slightly higher peak pressure and earlier ignition. The predictedengine-out NOx is in very good agreement with the experimental value. However,

Table 5.2 Engine specifications

Engine type GM-fiat Caterpillar

Bore (cm) 8.2 13.716Stroke (cm) 9.04 16.51Bowl diameter (cm) 4.99 9.8Connecting rod length (cm) 14.5 26.16Squish height (cm) 0.067 0.157Displacement (L) 0.477 2.439Compression ratio 16.53 16.1Swirl ratio 2.2 * 5.6 0.5IVC 142 BTDC 143 BTDCEVO 142 ATDC 130 ATDCInjector type High-pressure solid-cone High-pressure solid-coneManufacturer Bosch HEUIInjection pressure (bar) 1,600 1,500Number of holes 8 6Nozzle holes diameter (lm) 133 158


higher soot emissions are produced. Possible reasons include discrepancies of theinitial mixture composition at the intake valve closing time between the simulationand experiment (which were found to have a significant influence on soot). Basedon the present and many previous validation studies (Patel et al. 2004; Sun andReitz 2006; Opat et al. 2007), the model was deemed adequate.


Before exploring the scaling relationships between the investigated engines, theissue of the mesh size dependency needed to be addressed for the CFD scaling

Fig. 5.1 Original pistonbowl profiles

Fig. 5.2 Comparisons ofexperimental and numericalresults (SOI = 10 BTDC)

5.3 Validation of Scaling Laws on a Light-Duty and a Heavy-Duty Diesel Engine 155

study. In addition to the numerical issues, other practical concerns are alsohighlighted and discussed in this section, such as the effect of injection rate shape,engine heat transfer, and initial flow motion at IVC. Next, a numerical study wasconducted on the two engines based on the displacement scaling factor ofTable 5.1. The investigation was done for the two engines operated at low-andmid-load. Inspired by the results obtained from the displacement scaling, a newscaling factor based on the TDC volume was suggested, and improved matchingresults were obtained for the engines at low-load. This work was also extended toengines at low and high speed with TDC scaling.

5.3.3.1 Mesh Size Dependency

It is known that current CFD engine simulation tools show grid dependency to acertain degree due to their spray, turbulence, and combustion models. However,the models are usually calibrated for a certain mesh size. For diesel applications,the grid dependency of the spray model is important and it is necessary to mini-mize the interference of grid-dependent models from the present CFD enginescaling study in order to obtain comparable results on both the small and largeengines. For the same resolution, the same computational mesh size in the smalland large engine is required. However, this would increase the computationalburden of simulating the large engine, since the computational time increasesproportionally with L3, where L is the ratio of bore sizes of the large and smallengines, 1.672 for the present study.

Note that the spray targeting in the present study targets the piston bowl, andthus the grid size in the axial direction in the squish region is less important thanthat of the radial and azimuthal directions in the bowl region. So focus was placedon a study of mesh sizes in the bowl region. A sector of the large Caterpillarengine was created with the same mesh size as in the small GM-Fiat engine in thebowl, and the simulation results were compared with a coarse mesh sector of theCaterpillar engine, which are shown in Fig. 5.3. As can be seen in Fig. 5.3b, thethermal characteristics predicted with the two meshes are almost identical.Although there is some discrepancy in the soot emissions using the different meshsizes as shown in Fig. 5.3c, considering the similar in-cylinder details shown inFig. 5.3d, the coarse mesh of the Caterpillar engine was used in this scaling workto make the computational time affordable.

5.3.3.2 Injection Rate Shape

According to the scaling relations listed in Table 5.1, the smaller engine has a lowerinjection pressure, thus smaller injection velocity, which is proportional to the 4/3power of the scaling factor. This suggests that care must be taken in the large engineif the maximum injection pressure is limited. The current investigated Caterpillarengine has a maximum injection pressure 1500 bar, as listed in Table 5.2, and


based on the scaling relations and the ratio of the sizes of the two engines, themaximum injection pressure of the GM-Fiat engine would be around 750 bar.

The injection rate shape defines how much fuel is injected into the cylinder ineach crank angle during the injection event, and this influences the combustionphasing. In order to match the combustion phasing of the small engine and thescaled large engine, the injection rate shape has to be scaled to supply a propor-tionally injected fuel amount. In this study, the experimental injection rate shape

Fig. 5.3 Comparison of results using coarse and fine meshes. a Mesh density at TDC. b Pressuretrace and heat release. c Emissions. d In-cylinder details-soot distribution (side view)


obtained with injection pressure of 700 bar from the GM-Fiat engine was selectedand scaled for use in the large engine, which is described in Fig. 5.4.

5.3.3.3 Engine Heat Transfer

Based on the specifications given in Table 5.2, the ratios of the surface area to thedisplacement volume are 0.71 and 0.41 for the GM-Fiat and the Caterpillarengines, respectively. The convection heat loss component through the cylinderwalls of the small engine is larger than that of the large engine. If it is assumed thatthe heat release of the two engines is proportional to the injected fuel amount(which is required in the current study), the thermal efficiency of the small enginewill be lower than that of large engine. Therefore a treatment is needed to considerthe effect of heat transfer for an engine scaling study.

To compensate for the relatively greater heat loss of the small engine, the intaketemperature was increased. The increment of the intake temperature of the smallengine was determined such that the motoring pressure trace of the small enginematched that of the scaled large engine under the same compression ratio. Anincrease of 10 K intake temperature was found to be required from this procedure.Although it might be argued that for a fired engine more heat loss is produced thanthat of the motoring case, the important consideration is that the combustionprocess starts at the same thermal conditions in the two engines. It was also foundthat a large difference of intake temperature between the engines affects the initialthermal condition significantly, and therefore can influence the controlling roles ofchemistry and turbulence scales between the scaled engines. For example, theignition timing would be advanced in the small engine due to an increase ofthe intake temperature. However, the increase of 10 K will be further justified inthe subsequent discussion, and was found to be an appropriate value in this study.

Fig. 5.4 Comparison ofscaled injection rate shapes ofthe small and large engines


5.3.3.4 Intake Flow and Initial Flow Field at IVC

As described above, the swirl ratios of the investigated engines have to be equal toproduce similar initial flow fields at IVC with comparable influences on the spraytip penetration. However, the intake systems of the two real engines have differentcapabilities of generating initial swirl. Referring to Table 5.2, it is seen that thesmall GM-Fiat engine generates variable swirl ratios from 2.2 to 5.6 (steadybenchmarking results) using butterfly valves, but the Caterpillar engine has a fixedswirl ratio of about 0.5. It is of interest to numerically investigate how to producethe same swirl level for the two engines, and thus to provide guidelines forpractical engine design. As a preliminary work, the mesh of the Caterpillar enginewith the intake system was scaled down to the GM-Fiat engine based on the ratioof the bore sizes. Other parameters, such as the valve-lifts and engine speeds werealso scaled based on the scaling relations in Table 5.1. A motoring simulation wasconducted to compare the intake flow and initial flow fields at IVC of the twoengines.

Figures 5.5 and 5.6 show swirl ratio and tumble flow profiles during thecompression stroke. It can be seen that the swirl and tumble ratios in the radial andazimulthal directions (averaged momentum values) are almost identical in bothengines. Further examination of Fig. 5.7 reveals that the velocity distribution inthe small engine also resembles that of the large engine at BDC. The large enginehas higher values of velocity, which was also found to roughly scale with the meanpiston speed with the scaling factor L2/3. These findings confirm that the geometryof the intake system and the lift profiles of the valves determine the intake flow andflow field in the cylinder. As long as they are geometrically scaled and the enginespeed is also scaled, similar flow fields result. Furthermore, the results of Figs. 5.5and 5.6 verify the current scaling factor with respect to the engine speed, since theswirl ratio and tumble flow are the normalized results with respect to the enginespeed, and they show matching trends. Note that the self-consistency of the results

Fig. 5.5 Comparison ofswirl ratio duringcompression stroke


Fig. 5.6 Comparison of tumble flow during compression stroke. Left: tumble in radial direction;right: Tumble in azimuthal direction

Fig. 5.7 Velocity distribution at the BDC. Top: side view; bottom: top view


also confirms that numerical grid size effects are unimportant for modeling theintake process. For the next study to simplify the problem, sector meshes wereused, but the flow field at IVC was initialized using a swirl ratio, which was set tobe equal for the two engines.

5.3.3.5 Displacement Volume Scaling

It is well known that the thermal efficiency of a diesel engine is correlated with itscompression ratio. In order to match the thermal efficiency of the scaled engines, itis necessary to keep the same compression ratio. This presents two options, whichare either to use the relation of the displacement volume to scale the TDC volume,or to use the TDC volume to scale the IVC volume. The use of displacementvolume scaling is discussed in this section, and inspired by the results, an inves-tigation based on TDC volume scaling was further explored.

Following the scaling relations listed in Table 5.1, the scaled parameters of theCaterpillar engine based on the displacement scaling factor V = 2.439/0.477 arecompared with the corresponding parameters of the GM-Fiat engine in Table 5.3.

As indicated in the fourth column of Table 5.3, it is not possible to simultaneouslyscale some primary geometrical parameters of the Caterpillar engine, such as boresize, stroke, and connecting rod length. The bowl profile of the Caterpillar engine wasscaled from the bowl profile of the GM-Fiat engine, which gives the scaled bowlvolume. However, the squish height at TDC was not scaled due to the presence ofvalve cut-out volumes at TDC of the practical engine. The geometrical compressionratio for the two engines was adjusted to be 15.5, and since they have similar IVCtimings, their effective compression ratios are also close. The simulation was

Table 5.3 Scaled parameters of the displacement volume scaling engines

Engine type GM-fiat Caterpillar(Scaled)

Scaled?

Bore (cm) 8.2 13.716 N/AStroke (cm) 9.04 16.51 N/ABowl diameter (cm) 4.99 8.59 YesConnecting rod length (cm) 14.5 26.16 N/ASquish height (cm) 0.163 0.223 NoDisplacement (L) 0.477 2.439 YesTDC volume (L) 0.0329 0.1682 YesCompression ratio 15.5 15.5 YesSwirl ratio 1.8 1.8 YesIVC 142 BTDC 143 BTDC NoEVO 142 ATDC 130 ATDC NoInjection pressure (bar) 726 1,500 YesNumber of holes 8 8 YesNozzle holes diameter (lm) 133 229 YesSpray angle 130 130 Yes


conducted under low-load (for HCCI, Case A) and mid-load (for SOI sweep, Case B)operating conditions, which are shown in Table 5.4.

Stager and Reitz (2007) found that for early injection timings the scaling ofengine combustion and emissions were dependent on mixing and charge prepa-ration processes that are controlled by turbulent timescales. For late injectiontimings, however the scaling was found to be controlled by kinetic (chemistry)timescales and hot gas residence times. Scaling of mid-range injection timingswere controlled by a combination of both the turbulence and kinetic timescales. Itis of interest to further investigate the scaling relations between the engines ofdifferent sizes over a broad range of injection timings. Therefore, Start of Injection(SOI) sweeps from 35 BTDC to 5 BTDC were conducted on the two engines. Inaddition, the two engines were also explored under a Homogeneous ChargeCompression Ignition (HCCI) condition in order to remove the influence of spraymixing and charge preparation from the scaling study and to gain a more directsense of the influences of chemistry timescales in engine scaling.

5.3.3.6 HCCI Engines

The HCCI simulation was run at low-load (Case A in Table 5.4), which makes itrelevant to practical engines. The research was also extended to low and highspeed cases in order to study the influence of residence times on engine scaling.

Table 5.4 Operating conditions for the displacement volume scaled engines. A: low-load;B: mid-load

Engine type GM-fiat Caterpillar(Scaled)

Scaled?

Speed (rpm) A 1,000 834 Yes2,000 1,668 Yes3,000 2,502 Yes

B 2,000 1,668 YesGross IMEP (bar) A 5.0 5.0 Yes

B 7.5 7.5 YesEquivalence ratio A 0.25 0.25 Yes

B 0.75 0.75 YesEGR rate (%) A 0 0 Yes

B 55 55 YesOxygen (volume%) A 20.91 20.91 Yes

B 11.97 11.97 YesIVC Temperature(K) A 380 370 Yes

B 380 370 YesIVC Pressure (bar) A 1.791 1.736 Yes

B 1.791 1.736 YesInjected fuel (mg/cyc.) A 12.8 65.5 Yes

B 22.2 114 YesInjection duration

(�CA)A N/A N/A N/AB 13.2 13.2 Yes


In Fig. 5.8, the pressure trace and heat release rates of the scaled engines arecompared. Two stage heat release is seen in the HCCI engines. The cool flamestage occurs slightly later in the large engine than in the small engine, which is dueto the higher intake temperature of the small engine in order to compensate for itsgreater heat loss, as discussed previously. But the main heat release (scaled) of thelarge engine matches that of the small engine, and they have matched pressuretraces. This indicates that the simple strategy of treating the unscaled heat loss isvalid in the present study.

The early ignition of the small engine is also reflected in the start of combustiontimings (defined as the crank angle when 10% of accumulated heat is reached)with different engine speeds shown in Fig. 5.9. It can be seen that the start ofcombustion timing is linearly retarded with the linearly increasing engine speeds.This confirms that the ignition delay on a real time basis is the same for bothengines operating under different speeds, which is understandable since the HCCIcombustion is chemistry-controlled. In addition, the chemistry ignition delaybetween the two engines can be estimated from the linear relation in Fig. 5.9 to beabout 0.375 ms in all cases.

The later combustion phasing of the large engine is the reason that it producesslightly less NOx than the small engine, which is shown in Fig. 5.10 (left). Thematched soot emissions in Fig. 5.10 (right) further confirm the chemistry pro-cesses in the two engines are equally scaled. To summarize, the scaling laws ofTable 5.1 work very well for scaling engines at HCCI conditions, which meansthat the influence of the chemistry timescales on the combustion and emissionsare considered and scaled. The discrepancy of ignition timing that leads todifferent NOx emissions is essentially caused by the unscaled heat loss due tothe different surface-to-volume characteristics of the two engines. However, theproposed method of treating this problem by increasing the intake temperature iseffective.

Fig. 5.8 Pressure trace andheat release rate for HCCIconditions (Case A,Table 5.4)


5.3.3.7 SOI Sweep

Simulations were conducted over a SOI sweep to investigate the scaling relationsdue to turbulence and chemistry timescales, and their interactions. Figures 5.11,5.12, 5.13 illustrate the comparison for the engines at mid-load (Case B inTable 5.4).

As indicated in Fig. 5.11, the pressure traces of the scaled Caterpillar engine areclose to those of the GM-Fiat engine over the broad range of injection timings, aswell as its heat release rates (scaled by the displacement volume). This indicatesthat the current scaling argument regarding the engine power output works fairlywell. The small inset plots in Fig. 5.11 are included to show that the scaled liquidspray tip penetrations in the Caterpillar engine also agree with those in the GM-Fiat engine, which further supports the scaling argument for spray tip penetration.However, the combustion phasing of the large engine is earlier than that of thesmall engine, which is also represented by the shorter ignition delay (the time frominjection timing to the crank angle when 10% of accumulated total heat release isreached) as shown in Fig. 5.12.

Based on the scaling relations the large engine has lower speed, and thusthe mixture preparation during the spray development is longer in real time for the

Fig. 5.9 Comparison of startof combustion timing (10%burn) of the HCCI engineunder different speeds

Fig. 5.10 Comparison of NOx (left) and soot (right) emissions of the HCCI engine underdifferent speeds


large engine. Therefore, a more flammable mixture is formed compared to thesmall engine, which results in the earlier ignition timing on a crank angle basis.This result differs from the HCCI engine comparison, since the ignition is pri-marily determined by how much flammable fuel-air mixture has been prepared.The timescale of spray mixing and interaction with turbulence is much larger thanthe chemistry timescale. More support for this conclusion is also revealed inFig. 5.12 that illustrates the difference in the ignition delay increases with retardedSOI timing where less time is available for mixing.

The NOx and soot emissions show opposite trends over the SOI sweep inFig. 5.13. With retarded injection timing, the difference in NOx emissions betweenthe two engines decreases, and in the traditional diesel combustion region(SOI [ -15), the results are close. Inversely, the soot emissions are close at earlyinjection timings, and then the difference increases with retarded injection timing.

The comparison of the temperature distributions shown in Fig. 5.14 explainswhy the large engine produces more NOx emissions at early injection timings. Ithas a larger high temperature area where the NOx formation is active. Thedifference is caused by the different injection pressures since for the large engine,the higher injection pressure benefits the mixing process and produces a moreflammable mixture close to the piston symmetry axis, which is later ignited.Although the spray tip penetration is found to be scaled with the current scaling

Fig. 5.11 Comparison of the displacement volume scaled engines at mid-load: pressure traceand heat release rate with different SOI.a SOI = -35, b SOI = -20, c SOI = -5


law, the spray mixing process appears to be weakly scaled due to the differentinjection pressures. The soot formation region is located at the bottom of the bowl,as shown in Fig. 5.15, due to the similar temperature distribution in that regionseen in Fig. 5.14. Examination of the turbulence quantities and local equivalenceratios also revealed local similarity (not shown). Considering that the ignitiondelay for this early injection case is about twice the injection duration, it can beconcluded that the effects of local turbulence levels and bulk flow on the mixingprocess after the end of injection are scaled or are not important.

For the late injection case, a difference in the temperatures is also seen inFig. 5.16 for the same reasons as discussed before. However, it is noticed that thehigh temperature area around the piston axis in the large engine is around 1,900 K,at which temperature NOx formation is not prominent. This explains why with theretarded SOI timing, the difference in NOx emissions reduces. Compared to the

Fig. 5.12 Comparison of thedisplacement volume scaledengines at mid-load: ignitiondelay

Fig. 5.13 Comparison of the displacement volume scaled engines at mid-load: NOx (left) andsoot (right) emissions


early injection case, the combustion temperature of the late injection case is lower,and thus the chemistry timescales of reactions relevant to NOx formation are alsolarger. Therefore, the difference of NOx formation in the two scaled engines isrelatively insensitive to the difference of real time (due to the difference of speed).

As can be seen in Fig. 5.17, more soot is formed in the squish region of thelarge engine. In addition, the concentration of soot is also larger in the largeengine. For the late injection case the ignition delay is comparable to (or less than)the injection duration, which results in more interaction between the spraydevelopment and the turbulent flow. Furthermore, the preparation of the flammablemixture is faster for the late injection case due to higher ambient temperature(consequently faster vaporization) and stronger squish flow, and the chemistrytimescale also becomes smaller under more thermally active ambient conditions.This leads to stronger interaction between the mixing process and the chemistry.

Fig. 5.14 Comparison ofSOI = 35 BTDC cases:Temperature distribution(side view, in the plane ofthe spray)

Fig. 5.15 Comparison ofSOI = 35 BTDC cases:Distribution of soot massfraction (side view, in theplane of the spray)

Fig. 5.16 Comparison ofSOI = 5 BTDC cases:Temperature distribution(side view, in the plane ofthe spray)


5.3.3.8 TDC Volume Scaling

The results from the displacement volume scaling above imply that the flow andthermal conditions at TDC are very important to combustion and emissions. Thismotivated consideration of an alternative scaling strategy referred as TDC volumescaling. The idea is that instead of matching the displacement volume, the ratio ofthe bore sizes of the two engines is used to scale the piston bowl geometry, squishheight, and crevice volume at TDC. This gives the same in-cylinder geometry atTDC based on the scaling arguments. In this section, the piston geometry of theCaterpillar engine used in the previous section of the displacement volume scalingwas maintained and the GM-Fiat piston geometry was scaled from the Caterpillarpiston with the scaling factor L = 8.2/13.716. Table 5.5 lists the scaled parametersfor the TDC volume scaling study.

Note that the strokes of the two engines are not scaled linearly with the boresize, with the result that the displacement volume cannot be scaled with the currentscaling factor. Therefore the geometrical compression ratio defined with the

Fig. 5.17 Comparison ofSOI = 5 BTDC cases:Distribution of soot massfraction (side view, in theplane of the spray)

Table 5.5 Scaled parameters for the TDC volume scaled engines

Engine type GM-Fiat (Scaled) Caterpillar (Scaled) Scaled?

Bore (cm) 8.2 13.716 N/AStroke (cm) 9.04 16.51 N/ABowl diameter (cm) 5.13 8.59 YesConnecting rod length (cm) 14.5 26.16 N/ASquish height (cm) 0.133 0.223 YesDisplacement (L) 0.477 2.439 NoTDC volume (L) 0.0359 0.1682 YesGeometrical compression ratio 14.3 15.5 NoEffective compression ratio 13.3 13.3 YesSwirl ratio 1.8 1.8 YesIVC 142 BTDC 126 BTDC YesEVO 142 ATDC 130 ATDC NoInjection pressure (bar) 755 1,500 YesNumber of holes 8 8 YesNozzle holes diameter (lm) 137 229 YesSpray angle 130 130 Yes


displacement volume is no longer the same for the two engines. In order to obtainthe same effective compression ratio, the IVC timing of the Caterpillar engine hasto be retarded to 126 BTDC. The simulation was extended to consider moreoperating conditions from low-load to high-load, which are given in Table 5.6.Cases A, B, and C represent low-, mid-, and high-load respectively.

Similar to the study of displacement volume scaling, simulations were con-ducted with SOI sweeps on the engines operated at low- and mid-load.

With the TDC volume scaling, the pressure, heat release rate, and the scaledspray tip penetration for both engines at low-load match very well over the SOIsweep, which are shown in Fig. 5.18. However, because the IVC timing of thelarge engine needs to be altered to match the effective compression ratio, itscompression processes differ slightly from those of the small engine, but nonoticeable influence of this discrepancy was seen on the combustion andemissions.

Compared to Fig. 5.13, more similarities of the emission trends are seen inFig. 5.19 using the TDC volume scaling. This indicates that TDC conditions are

Table 5.6 Operating conditions of the TDC volume scaled engines: A, B, and C are low-, mid-,and high-load, respectively

Engine type GM-Fiat(Scaled)

Caterpillar(Scaled)

Scaled?

Speed (rpm) 2,000 1,685 YesGross IMEP (bar) A 4.5 4.5 Yes

B 7.0 7.0 YesC 1.0 1.0 Yes

Equivalence ratio A 0.25 0.25 YesB 0.75 0.75 YesC 0.75 0.75 Yes

EGR rate (%) A 55 55 YesB 55 55 YesC 25 25 Yes

Oxygen (volume%) A 17.93 17.93 YesB 11.97 11.97 YesC 17.65 17.65 Yes

IVC Temperature(K) A 380 370 YesB 380 370 YesC 380 370 Yes

IVC Pressure (bar) A 1.790 1.736 YesB 1.791 1.732 YesC 1.791 1.732 Yes

Injected fuel (mg/cyc.) A 11 51.5 YesB 22.2 104 YesC 32.5 151 Yes

Injection duration(�CA)

A 6.2 6.2 YesB 12.4 12.4 YesC 18 18 Yes


significant to diesel combustion and emissions due to the interactions between thesquish flows and the fuel mixing and post-combustion processes.

The injection duration of the low-load case (6.2�CA) is about half that of themid-load case (see Tables 5.4 and 5.6). The short injection duration reduces the

Fig. 5.18 Comparison of the TDC volume scaled engines at low-load: pressure trace and heatrelease rate with different SOI. a SOI = -35, b SOI = -20, c SOI = -5

Fig. 5.19 Comparison of the TDC volume scaled engines at low-load: NOx (left) and soot(right) emissions


time of spray jet flow interaction with the ambient turbulent flow. This leaves moretime for the transport of evaporated fuel by turbulence and bulk flow. Figure 5.20reveals that the ignition delay is larger than the injection duration for all SOItimings, which allows time for mixing before combustion. As in the HCCI enginestudy with similar fuel distribution, the combustion should be expected to scale ifthe chemistry timescale is more influential. Therefore, the explanation of bettermatching of the combustion characteristics and emission trends in the two enginesat low-load can be understood.

Simulation of the two engines at low-load was repeated at 1,000 and 843 rev/minfor the small and large engine, respectively. The balance of bulk flow andchemistry timescales is changed due to the longer injection duration in real time.

Fig. 5.20 Comparison of theTDC volume scaled enginesat low-load: ignition delay

Fig. 5.21 Comparison ofengines at low speed and low-load (1,000 and 843 rev/minfor the small and largeengine, respectively): ignitiondelay


This results in less scaled results in Fig. 5.21 and 5.22, especially for the NOxemissions. However, close soot trends were found, as seen in Fig. 5.22 (right),which is due to the increased time for soot oxidation during the expansion process,since both engines have the same low global equivalence ratio. In spite of the factthat the ignition delays are similar, the NOx is higher in the larger engine which

Fig. 5.22 Comparison of engines at low speed and low-load (1,000 and 843 rev/min for thesmall and large engine, respectively): NOx (left) and soot (right) emissions

Fig. 5.23 Comparison of the TDC volume scaling engines at mid-load: pressure trace and heatrelease rate with different SOI. a SOI = -35, b SOI = -20, c SOI = -5


has more time for NOx formation. This again demonstrates the significant role ofchemistry on emissions in engine scaling.

Compared to the results obtained with displacement volume scaling inFigs. 5.11, 5.12, 5.13, the results of the TDC volume scaling at mid-load do notshow noticeable improvement with respect to the differences of the emissionstrends, which are shown in Figs. 5.23, 5.24, 5.25. In general, the large engineproduces more NOx and soot emissions. The discrepancy of soot emissionsincreases as the SOI timing is retarded, but the difference in NOx emissionsdecreases. As discussed before, the longer injection duration at mid-load, and thusthe longer time of interaction of the jet flow with the bulk flow and weaker effectof the chemistry on the combustion is one of the reasons that the emissions are lessscaled. Together with the previous discussion on scaling engines at low speed and

Fig. 5.24 Comparison of theTDC volume scaling enginesat mid-load: ignition delay

Fig. 5.25 Comparison of the TDC volume scaling engines at mid-load: NOx (left) and soot(right) emissions


low-load, the scaling results of the engines at higher speed and mid-load suggeststhat scaled operation at low speed and mid- or high-load is more challenging.

In the current study, acetylene (C2H2) is taken as the precursor of sootformation, and higher concentration areas of C2H2 correspond to more soot pro-duction propensity. Before acetylene was formed, the distributions and quantitiesof the local temperature, evaporated fuel, as well as oxygen concentration werefound to be very similar in the two engines. However, a comparison betweenFig. 5.26 (top) and (middle) regarding the C2H2 mass fraction reveals that in thesame two �CA span, more C2H2 is generated in the large engine (note that the largeengine is shown at one �CA ahead of the small engine because of its earlierignition). This directly results in more soot emissions in the large engine shown inFig. 5.26 (bottom). The large engine has lower speed based on the current scalinglaws, and therefore longer real time in one �CA. The C2H2 formation reactions arefast under conditions of high temperature and low oxygen concentration, whichmeans that the chemistry timescale is much smaller than the time period of one

Fig. 5.26 Distributions ofC2H2 and soot mass fraction(SOI = 5 BTDC). Top andmiddle: C2H2. Bottom: soot


�CA. Therefore, a longer reaction time results in more C2H2 being formed. Forearly injection cases, the chemistry timescale of reactions of C2H2 is relative largedue to the higher local oxygen concentration (better mixing), which makes the sootformation less sensitive to the timing difference in one �CA span between twoengines. It should be pointed out that the better scaled soot emissions trend for thelow-load case was primarily due to the effect of the soot oxidation process, whosechemistry timescale is much larger than soot formation (or C2H2 formation). Basedon this discussion, it is expected that scaled engines operated at a higher speedwould produce smaller differences in soot emissions. This is proved in Fig. 5.27that shows less discrepancy of soot emissions between the two engines whenoperated at high speed. The small and large engines were run under the consid-eration of Case C listed in Table 5.6 with engine speeds of 3,000 and 2,502 rev/min, respectively.

5.4 Summary

Engine size-scaling arguments based on power output, spray tip penetration, andflame lift-off were explained. Several important issues for a study of engine size-scaling were addressed prior to investigation of the scaling relations between twoproduction engines. These include numerical mesh dependency and turbulence andheat transfer effects. Different scaling behaviors related to turbulence and chem-istry timescales and their effects on combustion and emissions in engines of diff-erent size were considered. The following conclusions can be drawn:

• The present scaling arguments are useful for analysis of engine size-scaling.Global performance results, such as the pressure trace and heat release rates arewell scaled based on the scaling laws.

Fig. 5.27 Comparison ofsoot emissions of engines athigh speed (engine speed3,000 and 2,502 rev/min forthe small and large engines,respectively)


• Soot emissions for the large engine operated at mid- or high-load conditions didnot scale as well as at light load. This is due to the fact that the soot formationprocess, which is controlled by chemistry timescales, at mid- or high-load ismore significant compared to that at light-load, in which the soot oxidation,which is controlled by turbulence mixing timescales, dominates. Therefore, atdifferent engine speeds (or different real time) the different timescales thatcontrol the net soot emissions contribute to the more poorly-scaled soot emis-sions for engines operated at mid- or high-load. For the low-load operatingcondition, better scaling of soot emissions was seen because sufficient time isavailable for oxidation.

• The large engine has longer time available for reactions compared to high speedsmall engines. Therefore, more NOx is produced, especially in cases with earlyinjection timings. Hence, higher EGR ratios may be needed to suppress the NOxformation.

• Unscaled heat losses and NOx can be compensated for by slightly increasing theintake temperature of the small size engine. Thermal management of the coolingsystem can be used to scale the heat losses for engines of different sizes.

• Engines operated under HCCI conditions that are chemistry-controlled exhibitwell-scaled thermal and emissions results since the power output is scaled withthe fuel amount and global equivalence ratio.

• In order to generate the same level of swirl, the geometry of the intake systemmust be scaled. The swirl ratio was found to affect the engine heat transfer.Therefore, for HCCI engines, the swirl level influences the ignition timing, andcan be used to control the ignition timing for different size engines operated atdifferent speeds.

• Conditions with reduced interaction time between the injection-generated jetflow and the bulk flow, or with increased time available for chemistry had betterscaled combustion characteristics and emissions. This is because the currentscaling laws consider lifted flames and lifted flames are more likely under theseconditions.


Chapter 6Applications

This chapter presents several examples of engine optimization using multi-dimensional CFD and genetic algorithms. The examples in the first part use simplecombustion models to benefit efficiency. The ones in the second part use detailedchemistry for better accuracy, especially for the cases in which the simple com-bustion models fail. The third part discusses strategies for simultaneous optimi-zation of multiple operating conditions. The fourth part presents a methodologythat combines scaling laws and computational optimization for enginedevelopment.

6.1 Engine Optimization with Simple Combustion Models

Under certain conditions, such as in the conventional diesel combustion regimes,engine simulations using simple combustion models, such as the CharacteristicTime Combustion (CTC) model, are able to predict satisfactory results if themodel constants are fine tuned against experimental data. Such models enableefficient evaluation of engine performance and emissions. For example, an indi-vidual closed-cycle engine simulation using the CTC model with the KIVA3v2CFD code and with around 50,000 computational grids only costs several hours ona regular personal computer. Given sufficient computational resources, computa-tional engine optimization can be completed within a week, which considerablyexpedites engine development. This section provides four examples to demonstratethe use of relatively simple combustion models, particularly the CTC model inengine computational optimization problems. The first case study seeks the optimaldesigns of a gasoline spark-ignition engine. The next two examples investigate theoptimal combinations of combustion chamber geometry and injection parameters ofheavy-duty diesel engines. Optimization of a high-speed passenger-car diesel engineis the subject of the last example.


177

6.1.1 Optimization of a 2-Stroke Direct-Injection Spark-IgnitedEngine

6.1.1.1 Research Background and Objectives

Direct-injection (DI) technology has made many appearances throughout thehistory of internal combustion engines. In the 1950s, direct-injection was adoptedin aircraft engines using existing diesel injection techniques. In 1954, direct-injection was applied to the Mercedes Benz 300SL in an attempt to overcomecarburetor limitations (Iwamoto et al. 1997). The return to direct-injection todayhas been motivated chiefly by the desire to improve fuel economy. Direct-injectiontechniques that employ charge stratification at light load have tremendous potentialfor reducing fuel consumption. At part load, combustion occurs at extremely leanconditions (overall lean) and thermal efficiency is increased. Some manufacturersof DI technology have claimed thermal efficiencies that are comparable to that ofdiesel engines. Reductions in fuel consumption have been reported to be as high as30% (Iwamoto et al. 1997). Another benefit of DI technology is that the engine isrun in unthrottled mode. This eliminates the irreversibility associated with thethrottling process, resulting in a reduction in the overall pumping loss of the cycle.At full load, fuel is injected early in the cycle and results in a homogeneous mixturesimilar to that found in port fuel injected or carbureted engines. A further benefit atfull load is an improvement in volumetric efficiency. This is accomplished throughcharge cooling that occurs as the fuel droplets being sprayed into the cylinderevaporate. This lowers the kinetic energy (and hence the back pressure) of the gas inthe cylinder, allowing more air to be inducted.

One of the critical necessities of a successful DI system is the ability to establisha stratified, fuel-rich mixture in the region of the spark plug. Several differentapproaches to this have been made. Among these approaches include controllingthe shape and penetration of the fuel spray, the creation of a cavity in the piston, andmanipulation of engine bulk gas motion (i.e., swirl and tumble). Direct-injectionengines suffer from high unburned hydrocarbon and nitrogen oxide emissions.Spray impingement on piston and wall surfaces is the cause of high unburnedhydrocarbon emissions. High local temperatures are responsible for the elevatedproduction of oxides of nitrogen. The promise of substantial reductions in fuelconsumption and in some cases improvements in power and performance, make DItechnology extremely attractive. The many intricate details of the mixture forma-tion and the challenges associated with emissions make direct injection a complex,multifaceted problem. Following this, it is therefore desirable to develop a tech-nique to first model, and then optimize the many variables involved in a DI system.

In this example, an optimization study combining multidimensional CFDmodeling and a genetic algorithm has been carried out on a 2-stroke, spark-ignited, direct-injection, single-cylinder research engine. The goal of the studywas to optimize the part load operating parameters of the engine in order toachieve the lowest possible emissions, improved fuel economy, and reduced

178 6 Applications

wall heat transfer. Parameters subject to permutation in this study were the start-of-injection timing, injection duration, spark timing, fuel injection angle, dwellbetween injections, and the percentage of fuel mass in the first injection pulse.A part load, intermediate-speed condition representing a transition operatingregime between stratified charge and homogeneous charge operation was stud-ied. Two candidate optimal designs emerged from this optimization study, eachoffering distinct advantages and benefits over the baseline operating case. Thesebenefits included reduced emissions of nitrogen oxide and unburned hydrocar-bons, and improved fuel efficiency. Injection angle was found to have aninsignificant effect on engine performance at this operating condition. Somecandidate optimal designs were obtainable with both single and split-fuel-injection strategies, while others were unique to the latter. Split-fuel-injectionwas found to be a versatile, and useful technique for enhancement of engineperformance. Soot production was not taken into account in the present study,and could have brought about a different optimization direction, should it havebeen considered.

6.1.1.2 Numerical Models

Pressure boundary conditions used in the present study were obtained from a1-dimensional gas dynamics code developed at the University of Wisconsin-Madison Engine Research Center (ERC) (Zhu and Reitz 1999). The code utilizesthe Method of Characteristics (MOC) to model the unsteady gas exchange processof the internal combustion engine. The MOC technique is different from otherfinite-difference or finite-volume based methods, in that it provides insight aboutwave propagation, and effective time-varying boundary conditions. The ERC 1-Dcode not only solves for the intake and exhaust flow, but also includes calculationof in-cylinder mixing, and tracking of species. The code is used to provide realisticpressure boundary conditions at the intake and exhaust ports. These boundaryconditions are fed into the KIVA code for the multidimensional simulation.

The KIVA simulation of the two-stroke DISC engine in the present study isconducted from exhaust port open (EPO) all the way through the time before thenext EPO event (i.e., one complete cycle is simulated). The full gas exchangeprocess is modeled three-dimensionally with KIVA. Pressure boundary conditionsare from the 1-D simulation, and exhaust gas composition in the cylinder isspecified in the main KIVA input file. Initial temperatures and pressures are alsoset for the various intake ports (1 boost port, and two transfer ports), the exhaust

Table 6.1 Initial Conditions for Simulations

Intake ports Exhaust ports Cylinder

Initial pressure (kPa) 101.3 98.1 270Initial temperature (K) 320 490 1,220

6.1 Engine Optimization with Simple Combustion Models 179

port, and the cylinder. Table 6.1 gives these initial conditions that were based onexperimental data of Hudak (1998). Head and liner temperatures are set as 400 K,while the piston is given a temperature of 450 K (Stiesch et al. 2001). Swirl isinitialized to zero. A strong clockwise tumble is set up in the cylinder as the intakecharge scavenges the cylinder. The spray, ignition, and combustion calculationsproceed directly from the scavenging, being affected by the flow field set up by thisgas exchange process.

The Linearized Instability Sheet Atomization (LISA) model (Schmidt et al.1999) is used to represent the breakup process whereby fuel in the injector isdischarged as a thin, film-like conical sheet. The TAB (Taylor Analogy Breakup)breakup model (O’Rourke and Amsden 1987) is used to estimate the secondarybreakup of droplets. After breakup, a Rosin-Rammler function is applied to pro-vide the droplet size distribution (Han et al. 1997). The ignition process and earlystages of combustion were modeled using the Discrete Particle Ignition Kernel(DPIK) model (Fan and Reitz 2000). A one step reaction is used to represent thechemistry in the early spark kernel growth stage of combustion, with:

C8H18þ12:5O2 ! 8CO2 + 8H2O; ð6:1Þ

where gasoline fuel is modeled using the properties of iso-octane, and with theassumption of stoichiometric combustion. The change in the density of species,i, is given by:

dqi

dt¼ �CW �min

qf

Wf;

qO2

12:5WO2

� �� SL � Zst �Wi � R; ð6:2Þ

where CW = 80.0 is a model constant that compensates for flame wrinkling andassures complete combustion within the flame kernel; Zst is the stoichiometriccoefficient of the species in Eq. 6.1. MWi is the molecular weight of i-th species,and R is the flame surface density in any given computational cell of volume Vcell:

R ¼ Np;cell

Np;tot

pd2k

Vcell; ð6:3Þ

where Np,cell and Np,tot are the number of ignition kernel particles in the cell andthe total number of particles, respectively. Energy is supplied to the ignitioninitiation cell at a constant rate of 0.001 J/s for approximately 0.75 ms. Thisrepresents the actual spark energy and is in addition to the energy release thatresults from the chemical reaction of Eq. 6.1.

Once the ignition kernel achieves a certain critical diameter, the CharacteristicTime Combustion model is invoked and this model replaces the ignition model.The critical diameter, dk, is given by a constant multiplied by the integral turbulentlength scale, lt:

dk�Cm1lt ¼ Cm1 � 0:16k1:5=e; ð6:4Þ

180 6 Applications

where Cm1 is set to 2.1. Further details of the combustion model are given bySubramanian et al. (2003).

6.1.1.3 Optimization Methodology

A micro-genetic algorithm (a single objective GA) was used in this study. Oncethe current population has converged, the best individual is maintained, while theother four individuals are randomly generated (Carrol 1996). This creates a pop-ulation that has opportunities for completely new characteristics (the four randomones), while at the same time maintaining the best individual from the pastevolutionary process. The genetic algorithm does not determine when an optimumis found. It is up to the user to determine that a particular solution is indeed theoptimum. This is generally indicated by a prolonged period where no improvementin the merit function value is seen (Senecal 2000).

The genetic algorithm checks for convergence to determine whether it shouldrestart the population with the best individual thus far and four other randomlygenerated designs. In the present code, a particular gene is considered to haveconverged if 95% of the individuals in the population have the same value for thatparticular gene (Senecal 2000). The population in turn, is regarded as convergedwhen every gene in the population has converged. It is important to note thatconvergence of a micro-population does not mean that an optimum has been found.

The present genetic algorithm code can be configured to run in either series orparallel mode. Series execution conducts each individual evaluation one afterthe other, on a single processor. This type of execution requires the least amountof hardware and can be effective for simpler problems that involve seconds orminutes of computer time per function evaluation. For complex calculations likethe present multidimensional engine simulation problem, parallel execution is themost effective method. This method involves the use of four different machines,each performing one individual evaluation. A UNIX shell script automates the filetransfer and job submission processes.

6.1.1.4 Optimization Parameters and Ranges

The optimization study was comprised of six parameters that were subject topermutation. These were SOI timing, injection duration, spark timing, injectioncone angle, time between injections, and the percentage of mass in the first injectionpulse. The ranges and resolution of these parameters is given in Table 6.2.

The form of the merit function utilized in the present study was inspired by thework of Senecal and Reitz (2000) in their operating parameter optimization of aheavy-duty, direct injection diesel engine. The form was originally proposed byMontgomery (2000). The function was modified to account for the specific per-formance and emissions characteristics of interest in the present study, and has theform:


Merit ¼ 1000

NOxþHCNOx;mþHCm

� �2þ ISFC

ISFC0þ WHEAT

WHEAT0

; ð6:5Þ

where NOx and HC are the compounded nitrogen oxide and hydrocarbon emis-sions in units of g/kW h. The subscript m denotes ‘‘mandated’’ values for emis-sions, which were based on the EPA mandated value (years 2008 and later) foroutboard and personal watercraft engines under 4.3 kW in power (81 g/kW h).ISFC is the brake specific fuel consumption in units of g/kW h. WHEAT is thetotal cylinder wall heat transfer in units of ergs. ISFC0 and WHEAT0 are the fuelconsumption, and wall heat transfer values obtained in the KIVA simulation of thebaseline operating case (261.95 g/kW h and 5.21 9 108 ergs respectively). Wallheat transfer is calculated according to the work of Han and Reitz (1996).

6.1.1.5 Engine and Computational Mesh

The engine modeled in this study was a 2-stroke, direct injection, single-cylinderresearch engine (SCRE). It is a single-cylinder version of the 2.4 L V-6 outboardengine, designed and manufactured by Mercury Marine. The engine is loop-scavenged, and has a displacement of 389 cm3. It has a rated power of 20 kW atan engine speed of 5,000 rev/min. The engine features a pump driven liquidcooling system. Intake of fresh air into the crankcase is accomplished byreed valves. Lubrication is sprayed into the incoming air upstream of the reedvalves. The fuel-to-oil ratio in experiments was 100:1 and was accomplished bycontrolling oil pump speed (Hudak 1998). Air induction into the cylinder isaccomplished by a boost port, and two transfer ports. The boost port sets up atumbling flow in the cylinder that aids the scavenging of exhaust products, andsubsequent mixture preparation. Blow-down and displacement of exhaust gasoccurs through a single exhaust port. The engine is equipped with a flat-surfacepiston. There is no piston cavity, and the combustion chamber is formed by ahemispherical dome in the engine head. Fuel injection is accomplished with apressure-swirl injector manufactured by Chrysler (Hudak 1998). Engine specifi-cations are given in Table 6.3.

The computational mesh employed in this study is a Cartesian-type meshcontaining 11,000 computational cells. The mesh is shown in Fig. 6.1.

Table 6.2 Optimizationstudy parameters and ranges

Parameter Range Resolution

Start-of-injection (CA �) 260–340 64Injection duration (CA �) 6–24 32Spark timing (CA �) 300–370 32Injection cone angle (�) 0–180 64Time between injections (CA �) 10–30 32Mass in first pulse (%) 10–100 32

182 6 Applications

6.1.1.6 Results and Discussion

The full six parameters of interest, SOI timing, injection duration, injection coneangle, spark timing, percentage of mass in the first pulse, and time betweenconsecutive injection pulses (split-injection) (see Table 6.2), were varied. Themerit function was as defined in Eq. 6.5, and its variation as a function of gen-eration number is shown in Fig. 6.2. The vertical axis gives the maximum meritfunction value achieved in the micro-population of the current generation. Thegeneration number is indicated on the horizontal axis. The initial best design (bestindividual in Generation 1) and the Optimum (best individual in the final gener-ation) are indicated on the plot with their accompanying merit function value. Thebaseline design had a merit function value of 467 and is indicated across allgenerations with a horizontal line. In order to demonstrate convergence, theoptimization was run through 85 generations. This means that 85 different micro-populations were created one after the other, based on the best genetic material ofthe previous generation.

The optimization was terminated at Generation 85, but the optimum wasessentially found in Generation 14. After Generation 14, the basic design stayedthe same, with only mild fine-tuning of individual parameters, which occurred in

Table 6.3 Enginespecifications

Bore 85.8 mmStroke 67.3 mmConnecting rod length 139.7 mmCombustion chamber volume 32.3 cm3

Geometric compression ratio 11.2Actual compression ratio 7.4Exhaust port timing 95� ATDCIntake transfer port timing 117� ATDCIntake boost port timing 117� ATDC

Fig. 6.1 2-stroke enginecomputational mesh(Subramanian et al. 2003)


Generation 60 and 66 respectively. These changes yielded very small increases inMMF. Interestingly, the MMF value at Generation 12 was already close to that ofthe optimum (MMF at Generation 12 was 479 while the optimum had MMF of482). What is of interest between these two relatively comparable designs in termsof MMF, is that they in fact embodied completely different characteristics fromeach other. Table 6.4 lists the characteristics of these two individuals, along withthose of the baseline operating case, for reference. It can be seen that the twodesigns indeed represent radically different operating strategies. The best ofGeneration 12 (referred to as individual A-2) involved a substantially advancedSOI timing compared to the baseline case. It featured a longer injection duration of19.9� compared to 12.4� in the baseline case. The spark timing was also advancedin relation to the baseline case. A smaller spray cone angle than that of the baselinecase was selected. A-2 also features a small pilot injection of about 19% of thefuel, followed by a 15 crank angle degree (1.25 ms) pause. The remaining 81% ofthe fuel is then injected. The Optimum design (A-1) on the other hand selected aretarded SOI timing that even overlaps with the ignition event. A much shorterinjection duration is selected, giving an extremely high injection velocity (thebaseline case has an injection velocity of approximately 84 m/s, while A-1

Fig. 6.2 Maximum meritfunction (MMF) history

Table 6.4 Characteristics of successful designs

Baseline case Best of generation #12 (A-2) Optimum (A-1)

SOI (CA �) 280 263.8 323.5Duration (CA �) 12.4 19.9 7.7Spark timing (CA �) 334.0 324.8 324.8Spray angle (�) 54 31.4 137.1Dwell (CA �) 0 15.1 18.4Mass in 1st pulse (%) 100.0 18.7 71.0Merit function value 467 479 482

184 6 Applications

features an injection velocity of about 260 m/s). The first injection contains over70% of the fuel, and 18 crank angle degrees (1.5 ms) elapse before the second,smaller injection occurs. The fuel is sprayed out an extremely wide angle of 137�.Figure 6.3 shows the fuel injection and spray development of individual A-2during the second injection (282 �ATDC). The left image shows the secondinjection pulse occurring with the first pulse, already dispersing and evaporating.The in-cylinder temperature distribution is indicated in color with the scaleincluded below the image. The right image shows the air-fuel ratio in the cylinderprior to ignition. The scale is included below the image.

From both images, it can be seen that the strong clockwise tumble created bythe boost port persists beyond the scavenging period. This tumbling flow mixes thefuel and carries a substantial number of fuel particles over to the right-hand-side(exhaust port-side) spark plug. At the time just prior to ignition (Fig. 6.3 (right)) anear-stoichiometric charge exists in the vicinity of this spark plug.

Figure 6.4 shows the fuel injection event for the optimum, or individual A-1. Itcan be seen that the actual spreading angle of the fuel spray is much smaller thanthe injector-supplied angle of 137�. The spray collapses into a slug-like jet thatpenetrates into the cylinder. It is thought that this collapse is due to the very highinjection pressure that, in turn, results in highly atomized fuel particles. Theseparticles transition rapidly to the vapor phase, except for a small portion of themthat remain in liquid form, deep within the spray near the axis of the cylinder. It isthese particles (at the cylinder axis) that form the slug-like jet. The droplet Sautermean diameter (SMD) during the injection event for design A-1 was found to beapproximately 4 microns. In the baseline case, the droplets had an averagediameter of about 27 microns. Table 6.5 shows the improvements in emissions,heat transfer, and fuel consumption achieved with both designs A-1 and A-2.

Fig. 6.3 In-cylinder images for Design A-2. Left: CA = 282 �ATDC; right: CA = 334 �ATDC

Table 6.5 Improvementsachieved by designs A-1 andA-2

A-2 (%) A-1 (%)

WHEAT 9: 3.5:NOx 16.6; 2.9;HC 37.7; 53.8;ISFC 6.9; 0.9;


These performance parameters are indicated as improvements over the baselinecase, as a percentage.

The direction of the arrows indicates either an increase (upward pointing arrow)or a decrease (downward pointing arrow) over the baseline case. It can be seen thatboth designs experience higher wall heat transfer, with A-2 having the highestincrease. A-2 achieves a sizeable reduction in both NOx and HC emissions, whilereducing fuel consumption by about 7%.

Design A-1 is able to reduce engine-out hydrocarbon emissions by a staggering54%. It achieves about 20% of the NOx reduction of A-2, and manages a marginalreduction in indicated specific fuel consumption.

To explain these performance characteristics, cylinder pressure and temperaturetraces for designs A-1 and A-2 are contrasted against those of the baseline case inFig. 6.5. From the upper graph it can be seen that design A-2 provides a sub-stantially higher peak pressure and temperature than the baseline case. This givesbetter power, which translates into lower fuel consumption, as indicated inTable 6.5. The fuel utilization is better, and this is probably what gives thereduction in hydrocarbon emissions. Uniform combustion and flame travel, result

Fig. 6.4 In-cylinder images for Design A-1

Fig. 6.5 Pressure and temperature comparison between baseline case and designs A-2 and A-1

186 6 Applications

in fewer hot spots, that, in turn, help abate the formation of NOx. These goodcombustion and fuel utilization characteristics, naturally result in higher heattransfer, which is what is observed.

From the lower graph it can be seen that design A-1 has only slightly higherpeak temperatures and pressures than the baseline case. Power is improved mar-ginally and, hence, so is the fuel consumption. The simultaneous injection andignition, probably results in richer combustion, converting the fuel into incom-pletely burned components like CO and possibly even soot-but this was notmodeled. The extremely good reduction in unburned hydrocarbons is probably dueto the fact that the fuel is burned as soon as it gets to the spark plugs, and has lessopportunity to wet the piston or to collect elsewhere in the chamber and remainunburned. Also, the high atomization and vaporization seen, reduces the possibilityof impingement greatly. The combustion rate on the other hand is slower and givesa lower pressure and temperature rise, as compared to design A-2. This is whypower improvement, is minimal. NOx reduction was relatively small, indicatingthat there are probably more high temperature regions in design A-1 compared todesign A-2. These hot regions are likely to be in the vicinity of the spark plugs,where the rich combustion is occurring. Figure 6.6 shows a scatter plot of HCversus NOx emissions for many of the individuals from the Case A evolution (85generations in all). Some individuals have been omitted because their values of HCwere extremely high and would mask the details of the other individuals with morereasonable HC values. These outliers are caused by extremely poor or unsuccessfulcombustion designs. Hence most of the fuel remains as unburned HC and power isextremely low which gives a very large value for HC in g/kW h. The optimum(A-1) and individual A-2 are indicated on the plot, along with the baseline oper-ating case for reference. It can be seen that a wide range of possible emissionscharacteristics are possible with the different designs.

It is also clear that the optimization strategy was able to successfully findcandidate optimal designs, in terms of the performance characteristics studied.Figure 6.7 shows a similar scatter plot, displaying the indicated specific fuelconsumption (ISFC) versus total wall heat transfer (WHEAT). The plot verifies thefact that both designs A-1 and A-2 act to increase wall heat transfer. A-2 is able toachieve a sizeable reduction in fuel consumption (around 7%), while A-1 gives amarginal reduction over the baseline case.

6.1.1.7 Summary

Optimization of the part load operating parameters for reduction of emissions,fuel consumption, and heat transfer in a 2-stoke, direct-injected engine has beensuccessfully conducted. Two candidate optimal designs have been revealed, eachoffering distinct characteristics, and advantages over the baseline operatingstrategy. The results demonstrate the successful application of single merit func-tion, evolutionary search techniques with multidimensional engine modelingfor engine performance enhancement. Additionally, the results are insightful and


cost-effective, while allowing considerable flexibility in the variety, and diversityof parameters investigated.

This study has shown that it is possible to obtain similar performance charac-teristics using substantially different operating strategies in the engine studied.Additionally, the computational evidence suggests that the fuel injection angleplays a relatively unimportant role in the performance characteristics of thisengine, at the operating condition studied. This is likely due to the effective sprayatomization which produces drops that are so small that their dispersion is con-trolled by the injector jet momentum. At the operating condition of the study,comparable performance was seen to be achievable with both single and split-fuel-injection strategies. It should however be noted that a unique good performingoperating strategy did emerge from the investigation of split-injections that was

Fig. 6.6 Scatter plotdisplaying HC versus NOx

Fig. 6.7 Scatter plotdisplaying ISFC versusWHEAT

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not replicated in the single injection designs (i.e., design A-2). This demonstratesthe ability of split injections to produce varied engine responses, some that are notpossible with a single-fuel injection strategy.

Finally, it should further be mentioned that in the present optimization study,emissions such as carbon monoxide and soot were not considered in the deter-mination of the engine performance merit function. Should they have been con-sidered, the outcome of the study could potentially be quite different. Also, designsA-1 featured some form of rich, diffusion-flame-like combustion near the sparkplug locations that may very well have given rise to soot formation. The version ofthe CFD code used did not feature a gasoline soot model. This and the fact thatsoot is not a regulated emission for spark-ignited engines at that time, are reasonswhy it was not considered in merit function calculations. The use of the multi-objective methodology is discussed in the next sections.

6.1.2 Optimization of a Caterpillar Heavy-Duty Diesel Engine


Due to its superior durability, drivability and fuel efficiency, the diesel enginehas found broad application in both heavy-duty vehicles and off-highway engi-neering vehicles and equipment. Concerns about the effects of global warminghave stimulated increased interest in diesel engines since fuel consumption basedon the power output of the diesel engine is lower than that of the gasolineengine. However, the traditional diesel engine suffers from relatively highnitrogen oxide (NOx) and soot emissions, and strategies to reduce either theNOx or soot usually result in increased emission of the other. With more-and-more stringent emission standards, the diesel is facing the challenge of meetingthese more environmentally-friendly emissions regulations while maintainingfuel economy.

For any combustion process, boundary and initial conditions are two influentialaspects, and particularly the preparation of the fuel-air mixture also criticallyinfluences compression ignition diesel combustion. For a diesel engine operated atdifferent loads, the in-cylinder thermal conditions vary considerably, which resultsin different spray behaviors, combustion characteristics, and pollutant formation.It can be anticipated that different injection strategies and matching of the pistongeometry and spray plume are needed for engines under different operating con-ditions in order to reduce emissions and fuel consumption. This example presentsan optimization study of a heavy-duty diesel engine operated at both high-load andlow-load for better understanding of the effects of bowl geometry, spray targeting,and swirl ratio on engine operation. KIVA3v2 code with the Characteristic TimeCombustion (CTC) model was integrated with NSGA II code (http://www.iitk.ac.in/kangal/codes.shtml) to perform the optimization. The non-parametric regressionanalysis tool (Lin and Zhang 2006; Liu et al. 2006), COSSO, is also used to


post-process the optimized results to provide more visible relations between designparameters and objectives.

Three primary objectives of the present study are summarized as follows:

1. To search for optimal combinations of piston bowl geometry, spray targeting,and swirl ratio to enhance the mixing and post-combustion oxidation processesin order to simultaneously reduce both NOx and soot emissions and to improvefuel economy for a heavy-duty diesel engine at high-load and low-load.

2. To identify dominant design parameters that influence combustion and pollu-tant formation for this type of engine at the specific operating conditions ofinterest.

3. To reveal the relationships between design parameters and objectives bothqualitatively and quantitatively by an advanced regression technique and within-cylinder visualization.

6.1.2.2 Engine Description and Operating Condition

The modeled engine is a single-cylinder, direct-injection, 4-stroke diesel researchengine, based on a Caterpillar production engine. The geometric specifications andfuel injector parameters are summarized in Table 6.6.

The investigated operating conditions were determined based on Mode 4 andMode 6 investigated by Montgomery and Reitz (1996) which correspond to 95%and 20% load at high speed, respectively. However, slight changes were made forthe modeling work, as indicated below. The global equivalence ratio and EGRrate play different roles on emissions reduction. For high-load operation, they areusually limited by current turbo chargers. For the low-load case, the EGR ratecannot be increased to a high level due to the low available exhaust pressure thatdetermines the mass flow rate of the recirculated exhaust gases. In this situation,the global equivalence ratio and EGR levels need to be balanced by consideringthe engine operating conditions, the intake charge conditions, and emissions

Table 6.6 Engine andinjector specification

Baseline engine Caterpillar DI Diesel

Combustion chamber Quiescent, direct injectionSwirl ratio 0.5Bore 9 Stroke (mm) 137.16 9 165.1Bowl width (mm) 97.8Displacement (L) 2.44Connection rod length (mm) 261.6Geometric compression ratio 16.1:1Fuel injector nozzles 8 holes, equally spacedSpray pattern included angle 154�Injection pressure (bar) 1,600Nozzle orifice diameter (mm) 0.217

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trade-off relations. Based on the assumption of complete combustion, Shi andReitz (2008a) used a simple analysis code to estimate the initial conditions, whichis also adopted here. The engine speed of Mode 6 was adjusted to be the same asMode 4 in order to isolate the effect of speed on the results. Table 6.7 lists theoperating conditions considered.

6.1.2.3 Optimization Parameters and Objectives

The primary goal of this study is to find optimal combustion boundary conditions,i.e., combustion chamber (bowl) shapes, for a heavy-duty engine at high-load andlow-load. In addition, optimal combinations of spray targeting and swirl ratiolevels as a function of combustion chamber shape were searched simultaneously inorder to further understand the effects of the initial flow conditions and the spraydevelopment on combustion, with the objectives of reducing both NOx and sootemissions and improving fuel economy.

Shi and Reitz (2008a) found that the SOI and the bowl pip height also influencethe spray targeting and development significantly. These two parameters weretherefore included to supplement their previously considered seven design vari-ables. For the low-load case, Montgomery and Reitz (1996) pointed out that highinjection pressure does not necessarily benefit emissions reduction and decreasefuel consumption due to over-mixing of the mixture and the possibility of largeamounts of spray impingement. This motivates the interest of investigating theeffects of injection pressure at the low-load operating condition.

To summarize, a total of nine parameters, including the injector spray angle,swirl ratio, SOI, and six different parameters that define the bowl geometry werestudied for the high-load case. An additional parameter of injection pressure wasapplied to the low-load case. The compression ratio was kept fixed as 16.1 and thesix bowl geometric parameters enable a search of a wide range of bowl shapes, andalso allow for the consideration of reentrant-type bowls. The number of geometryparameters used gives a reasonable search space using the Kwickgrid methodology(Wickman 2003) that is described in Sect. 4.1, although more parameters areavailable in the grid generator to define the bowl shapes. Figure 6.8 illustrates thesix bowl geometry parameters optimized.

Table 6.7 Baselineoperating conditions

Conditions High-load Low-load

Speed (rev/min) 1,672 1,672IVC temperature (K) 385 370IVC pressure (kPa) 310 153Load (%) 95 20Injection quantity (mg/cyc) 229 70.9EGR level (%) 25 20Global equivalence ratio 0.60 0.33O2 Concentration (vol%) 17.65 19.52


Table 6.8 provides the ranges of the parameters, which were determined soas to avoid infeasible bowl designs but still to maintain diversity. Examples ofdifferent bowl shapes (axisymmetric) within the parametric space given byTable 6.8 are shown in Fig. 6.9. The spray angles target a wide region of the pistoncurvature, from the bowl floor up to the bowl lip. Considering the ability of theintake system of the experimental engine (Montgomery and Reitz 1996), the rangeof swirl ratio was restricted to a relative narrow range. The SOI range for the high-load operation was determined based on maximum power-output of the baselinedesign of the engine, and for the low-load case a broader range was considered toexplore more emissions trade-offs. The injection pressure for the high-load casewas fixed at 2,000 bar in order to reduce the injection duration.

NOx and soot emissions are two of the most important concerns for dieselengine designs, and the existence of a trade-off relation is well known to engineresearchers. Therefore reductions of these two emissions were two main objec-tives. Gross indicated specific fuel consumption (GISFC1) was also included as thethird objective.

Fig. 6.8 Parameters of bowlgeometry

Table 6.8 List ofoptimization parameters andtheir ranges

Parameters Range

High-load Low-load

A—(% bowl depth) 65 to 75 65 to 75B—(% bowl diameter) 74 to 80 74 to 80C—(% cylinder diameter) 71 to 84 71 to 841—Bezier curve control point 0.1 to 0.7 0.1 to 0.72—Bezier curve control point 0.3 to 0.9 0.3 to 0.93—Bezier curve control point 0.8 to 1.5 0.8 to 1.5Injector spray half-angle 60� to 85� 60� to 85�Swirl ratio 0.5 to 2.0 0.5 to 2.0SOI (�ATDC) -15 to -13 -10 to +10Injection pressure (bar) 2,000 850 to 2,000

1 GISFC refers to the work delivered to the piston over compression and expansion strokes, i.e.,from BDC to TDC to BDC. In the present work, ‘‘GISFC’’ is defined as the output work fromIVC to EVO for convenience. Apparently, there is a difference between these two ‘‘GISFC’’. Thisdifference is a constant for the same engine and same operating conditions. Therefore it will notaffect the results and conclusions.

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The most important and interesting optimal solutions are located on the Paretofront. In the present optimization study of the high-load engine with the ninedesign parameters, a total of 65 optimal designs were found on the Pareto front,which is shown in Fig. 6.10. These optimal designs were found to be able toreduce NOx and soot emissions and to improve fuel economy simultaneously,compared to the baseline engine under the same operating conditions. Since the

Fig. 6.9 Illustration ofrepresentative bowlgeometries generated byKwickgrid (one halfgeometry shown due tosymmetry)

Fig. 6.10 Pareto front and optimal solutions relative to the baseline shown at upper right for thehigh-load condition


goal of the current work is to minimize three objectives, it might be expected thatPareto solutions would form a surface in a three-dimensional objective-space.However, examination of Fig. 6.10 reveals that the shape is more line-like. Thisimplies that two of the objectives are somewhat correlated. Further observation ofthe figure indicates that GISFC and soot have very similar trends in that designsthat feature low GISFC also have low soot, and vice versa. The general infor-mation collected from the Pareto solutions shows that a design with a small anddeep bowl has higher GISFC, but favors low NOx emissions. For a shallow andwide bowl design, soot is reduced dramatically, and so is GISFC. However, apenalty has to be paid in NOx emission, which demonstrates the well-known sootand NOx trade-off in diesel engines. It is also found that all Pareto solutionsfeatured a flat spray included angle and medium level swirl ratios. The fact thatadvancing SOI timing increases the portion of premixed combustion and thusproduces more NOx emissions can also be concluded based on the analysis of thePareto solutions.

The low-load optimization results are shown in Fig. 6.11. Differing fromFig. 6.10, the solutions cover more of the objective-space, and the Pareto cases arealso more diversified. This is mainly due to the fact that broader ranges of injectionparameters were optimized, including SOI and injection pressure. The injectionprocess also found some extreme Pareto cases, which have very high values forsome of the objectives (up and down arrows indicate change compared to baselinealso shown in the figure), but show promise for the other two objectives, suchas Cases 1 and 5. Compromise results, such as Cases 2 to 4, are of more interest.

Fig. 6.11 Pareto front and optimal solutions relative to the baseline shown at upper right for thelow-load condition

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Case 3 simultaneously reduces emissions and fuel consumption compared to thebaseline case. Compared to the high-load optimization, the GISFC is less corre-lated with soot, which makes the line-like Pareto front appear as a surface (notshown with current view angle).

Further examination of the low-load optimal designs indicates that the Paretosolutions feature different aspects from the high-load optimal solutions. Firstly, thespray included angles are no longer restricted to high values, although most of theoptimal solutions still have flat spray targeting. Secondly, the effect of bowl sizebecome less important compared to that of the high-load optimal designs. No smallbowl design was found on the Pareto front, and all optimal designs feature midrange or large bowl diameters and also have a relatively large bowl floor. Thirdly,the Pareto solutions seek high swirl ratios, and most of them are larger than 1.5.Fourthly, high injection pressure does not certainly benefit emissions and fueleconomy, and most of optimal solutions have a moderate injection pressure in therange of 1,400–1,700 bar. All these observations imply that spray target and itsmatching with the bowl geometry and initial flows behave differently under high- andlow-load conditions. Therefore more details were explored with non-parametric andparametric studies as follows.

In order to explore the relationships between the design-space and objective-space, as well as to identify influential design parameters on emissions and fuelconsumption, a non-parametric regression method, COSSO, was employed in thisstudy. This method allows all of the GA results to be unified into response surfacesfor visualization of trends.

As shown in Fig. 6.10, Design 1 has a small and deep bowl, and Designs 2 and3 feature with wide and shallow bowls. The first and second designs were selectedas reference designs for the non-parametric studies, which are referred to asthe small bowl and large bowl designs. They were systematically chosen suchthat their SOIs, swirl ratios, and spray targeting, as well as their general bowlcurvatures were similar. It is of more interest to know the interacting effects ofspray targeting and swirl motion on emissions and fuel consumption, and thusthe response surfaces constructed on the related design parameters are given inFigs. 6.12 and 6.13, respectively.

The trends of soot and GISFC on the objective-space were similar, and theirresponse surfaces also resemble each other. Therefore, the response surfaces ofGISFC are not listed in Figs. 6.12 and 6.13. Comparison between Figs. 6.12 and6.13 shows that the response surfaces of NOx and soot for the small and large bowldesigns are similar in general. For NOx emissions, the spray included angle is themost influential parameter, and the peak NOx emissions were found at mediumvalues of the spray angle as illustrated in Figs. 6.12a, b and 6.13a, b, respectively.In Figs. 6.12b and 6.13b, reduced NOx emissions are favored by a low swirlcondition, however, changes with swirl ratio are less than those associated withspray angle changes, so that the swirl ratio was the secondary effect on NOxemissions. SOI has less effect on NOx emissions for the small bowl design inFig. 6.12a, but a slightly larger variation with SOI can be observed in Fig. 6.13afor the large bowl design.


The order of parameters and how significantly they influence soot are the sameas that obtained from the response surfaces of NOx, and the spray angle is still thedominant parameter. Similar to its effect on NOx, medium values of the sprayangle contribute more soot. For both small and large bowls, the soot emissionsreduce slightly as the swirl ratio increases, as shown in Figs. 6.12d and 6.13d. Notethat NOx scale in Fig. 6.13 is larger than in Fig. 6.12. This means that NOxemissions are more sensitive to changes of spray angle, swirl ratio, as well as SOIin large bowl pistons. However, the soot emissions are affected more by thechanges of those parameters in small bowl designs.

Since it was shown previously that low-load operation was relatively insensitiveto the bowl size compared to the high-load condition, the focus of the present non-parametric study and the subsequent parametric analysis were placed on sprayinjection parameters. The compromise Design 3 in Fig. 6.11 was selected as thereference design for COSSO. As indicated in Fig. 6.11, the results of GISFC are

Fig. 6.12 Response surfaces for the small bowl design (Design 1 in Fig. 6.10) under the high-loadcondition. a Interaction of SOI and spray angle on NOx. b Interaction of spray angle and swirl onNOx. c Interaction of SOI and spray angle on soot. d Interaction of spray angle and swirl on soot

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less correlated with soot emissions at low-load, and thus it is necessary to visualizethe response surface for GISFC as well.

The response surfaces of NOx with respect to SOI, spray angle, swirl ratio, andinjection pressure and their interacting effects are given in Fig. 6.14. It is observedthat retarding SOI has the primary influence of reducing NOx emissions, which isconsistent with experimental observations, since the combustion temperaturereduces as the SOI is retarded. But note that after 5 �ATDC, the effect of SOIbecomes weaker since the surface along with spray angle becomes flat. NOxemissions peak at about 77� spray angle, and this finding is similar to that obtainedfrom the study on the high-load cases. Decreasing injection pressure helps reduceNOx emission as shown in Fig. 6.14c. Compared to the other parameters, the swirlratio has the least effect on NOx emissions, though it can be seen that a high swirlratio slightly promotes NOx production in Fig. 6.14b and c.

Fig. 6.13 Response surfaces for the large bowl design (Design 2 in Fig. 6.10) under the high-loadcondition. a Interaction of SOI and spray angle on NOx. b Interaction of spray angle and swirl onNOx. c Interaction of SOI and spray angle on soot. d Interaction of spray angle and swirl on soot


For the soot emissions, the SOI is still an important parameter, but the effects ofother parameters become more important than they were on NOx. As seen inFig. 6.15a, soot emissions are minimized at about 77� spray angle, opposite to theobservation on NOx. However, retarding SOI also helps to reduce soot emissions,and this is believed to be the reason that most of the Pareto designs for low-loadcondition feature very late injection timings. Increasing swirl ratio or injectionpressure benefits soot emissions as seen in Fig. 6.15b and c, which also indicatesthe difficulty of engine design due to the trade-off between NOx and soot.

Comparison of Figs. 6.15 and 6.16 demonstrates that GISFC responds differ-ently to the investigated parameters, which is a further challenge to engine designfor low-load operation. For example, it was found above that retarding SOI helpsreduce both NOx and soot emissions, However, Fig. 6.16a frustrates this finding inthat the late injection timing deteriorates fuel economy significantly. However, it isalso seen that if a large spray angle is employed, the effect of SOI on GISFCweakens. Therefore, in order to obtain both emissions reduction and fuel economy,a combination of large spray angle and late injection is needed. Figure 6.16cillustrates that GISFC decreases as the injection pressure increases. Furthermore,the effect of swirl ratio is again seen to be the least.

Fig. 6.14 NOx response surfaces for the selected design (Design 3 in Fig. 6.11) under low-loadcondition. a Interaction of SOI and spray angle on NOx. b Interaction of spray angle and swirl onNOx. c Interaction of swirl and injection pressure on NOx

Fig. 6.15 Soot response surfaces for the selected design (Design 3 in Fig. 6.11) under low-loadcondition. a Interaction of SOI and spray angle on soot. b Interaction of spray angle and swirl onsoot. c Interaction of swirl and injection pressure on soot

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The above non-parametric analysis offers a pictorial view of the relationshipsbetween the design parameters and the objectives in the form of response surfaces.It is also of interest to explore the in-cylinder flow details in order to betterunderstand how the emissions and fuel consumption are influenced by the spraytargeting, as well as its matching with particular optimal combinations of the swirland bowl geometry. Therefore, some representative designs were further studiedparametrically and visualized. The parametric study also provides a validation ofconclusions drawn from the non-parametric analysis.

Two piston designs representing the small and large bowls were selected toperform the parametric analysis. The SOI, initial swirl ratio, and spray includedangle were varied independently in different numerical experiments for eachdesign as listed in Tables 6.9 and 6.10. Figure 6.17a and b illustrate the spraytargeting with the different spray included angles for the two bowls. The simu-lations were conducted with the same KIVA-code with the CTC model used forthe optimization study, and simulation results are listed in Tables 6.11 and 6.12 forthe two designs, respectively.

Compared to the baseline cases, advancing SOI (Case 1) increases NOxemissions slightly, but its effect on soot and GISFC are smaller. However, for thelarge bowl (Case 2 in Table 6.12) both emissions and fuel economy are deterio-rated. High swirl ratio case leads to insignificant improvements for the small bowldesign on soot and GISFC (Case 2 in Table 6.11). For the large bowl design, alower value of spray angle of 60� reduces the NOx emission (Case 3 inTable 6.12), but soot and GISFC are increased. For the other cases, in Tables 6.11or 6.12, small spray angles of 60� and 77� predict increased emissions and higher

Fig. 6.16 GISFC response surfaces for the selected design (Design 3 in Fig. 6.11) underlow-load condition. a Interaction of SOI and spray angle on GISFC. b Interaction of spray angleand swirl on GISFC. c Interaction of swirl and injection pressure on GISFC

Table 6.9 Parametric studyon the small bowl design forthe high-load condition

Parameters SOI (�ATDC) Swirl Spray (�)

Baseline -11.09 0.62 84.59Case 1 -15.00 0.62 84.59Case 2 -11.09 2.0 84.59Case 3 -11.09 0.62 60.00Case 4 -11.09 0.62 77.00


fuel consumption, compared to the baseline cases. It is apparent that the resultsobtained from the parametric study are consistent with the response surfaces givenby the non-parametric analysis in Figs. 6.12 and 6.13, and the reliability of themethod is thus further verified.

Table 6.10 Parametric studyon the large bowl design forthe high-load condition

Parameters SOI (�ATDC) Swirl Spray (�)

Baseline -11.09 0.80 84.53Case 1 -15.00 0.80 84.53Case 2 -11.09 2.0 84.53Case 3 -11.09 0.80 60.00Case 4 -11.09 0.80 77.00

Fig. 6.17 Spray targeting and piston profiles (high-load). a Spray targeting of the small bowldesign. b Spray targeting of the large bowl design

Table 6.11 Results ofparametric study for the smallbowl design for the high-loadcondition

Objectives NOx(g/kg fuel)

Soot(g/kg fuel)

GISFC(g/kW h)

Baseline 20.12 0.34 213.44Case 1 26.27 0.35 214.93Case 2 27.56 0.30 212.20Case 3 23.71 0.58 220.49Case 4 34.05 0.81 228.78

Table 6.12 Results ofparametric study for the largebowl design for the high-loadcondition


Soot(g/kg fuel)

GISFC(g/kW h)

Baseline 31.66 0.18 200.14Case 1 34.14 0.18 201.14Case 2 46.74 0.42 203.45Case 3 29.98 0.51 216.24Case 4 38.02 0.66 225.83

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Since the results are relatively insensitive to the change of SOI, these cases arenot analyzed further. Figure 6.18 shows a comparison of pressure traces, heatrelease rates and emissions between the baseline case and Cases 2 to 4 for thesmall bowl design, and the comparison for the large bowl design is given inFig. 6.19.

As can be seen in Fig. 6.18a, although the baseline case has the lowest peakpressure, its HRR trace implies that significant late cycle-combustion occursstarting around 20�CA, which contributes more expansion work, and this explainswhy the baseline case has the best fuel economy. Because of its lower peakpressure (corresponding to a lower mean temperature), the baseline case also hasthe lowest NOx emission, as indicated in Fig. 6.18b. In Fig. 6.18b, except forCase 4, the soot production rates are roughly the same for all cases. But theoxidation rates are lower for Cases 3 and 4, in which the spray angles are smallercompared to the baseline case and Case 2. The high soot oxidation rates for the

Fig. 6.18 Thermal conditions and emissions history for the small bowl design at the high-loadcondition. a Pressure traces and heat release rate (HRR). b NOx and soot emissions

Fig. 6.19 Thermal conditions and emissions history for the large bowl design at the high-loadcondition. a Pressure traces and heat release rate (HRR). b NOx and soot emissions


baseline case and Case 2 are due to their relatively high temperatures during theexpansion process. This phenomenon points out the importance of the late cycle-combustion process on soot reduction. Case 2 has higher swirl ratio than that of thebaseline case, which probably strengthens the soot oxidation process and thusproduces less engine-out soot emissions.

For the large bowl design, as indicated in Fig. 6.19a, the late cycle-combustionof the baseline case is still the reason that it has the lowest fuel consumption, butthe peak pressure of Case 3, in which spray targeted directly to the bowl crown(Fig. 6.17b), has the lowest value. It is therefore not surprising to find that Case 3has the lowest NOx emissions in Fig. 6.19b. For the large bowl design, the highswirl ratio does not result in a high soot oxidation rate for Case 2, and thus thebaseline case has the lowest soot emissions. The above discussions are furtherexamined with the help of visualization of in-cylinder temperature distributionsand flow motions, as illustrated in Figs. 6.20 and 6.21.

The crank angle when the temperature distribution is plotted in Figs. 6.20 and6.21 is 25 �ATDC during late cycle-combustion. For the small and large bowls,cases with flat spray angles that target the piston top-land have slower burning rateat TDC compared to other cases. This is due to the fact that the small space aroundthe piston top-land limits the spray mixing process. For Cases 4 in Figs. 6.20 and6.21, the 77� spray included angle causes the spray jet to be injected towards thebowl edge, where sufficient ambient air can be entrained during the mixing andcombustion process, and thus the burning rate is accelerated. Due to the highcombustion temperature, NOx formation is favored and the soot production ratealso increases.

Fig. 6.20 Temperature distribution for the small bowl design at the high-load condition(side view)

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As the piston descends, during the reverse squish process, the soot is trans-ported to the area close to the piston top (not shown here) by the in-cylinder bulkflow, for which the direction is indicated by the velocity vectors in the figures.However, during this stage, the relatively low temperature (due to less late cycle-combustion) does not benefit soot oxidation and thus eventually the highestengine-out soot emissions result. For the cases with the smallest spray angle 60�,the spray jet is targeted at the bowl floor, where a fuel film is formed because ofthe large spray impingement. The evaporation rate of the fuel film is much slowerthan for atomized spray droplets, which leads to a slower combustion rate and thusa lower temperature. This is the reason that Cases 3 for the small and large bowldesign produce less NOx, but the fuel film contributes to increase the soot emis-sions. The piston profile of the large bowl has a smaller distance between thepiston top and the bowl floor than that of the small bowl. Stronger squish flow istherefore formed during the spray development and this enhances the spraymixing. On the other hand, considering that the spray penetration is almost thesame for each piston design (because they have the same injection conditions),the jet in a large and shallow bowl entrains less air along its trajectory than a jet inthe small and deep bowl does, which results in higher local equivalence ratios, andthus higher combustion temperatures. The higher NOx emissions and combustionefficiency in large bowl designs can thus be explained.

It was shown in the non-parametric study section that both emissions and fuelconsumption are subject to the interaction effects of the SOI, spray angle, swirlratio, as well as the injection pressure for low-load. A parametric study was alsoconducted on the reference design, Design 3 in Fig. 6.11, in order to further revealand understand the behavior of the optimal designs. For each parameter, two

Fig. 6.21 Temperature distribution for the large bowl design at the high-load condition(side view)


values were studied independently, and thus a total of eight cases were examined,as listed in Table 6.13 and in Fig. 6.22. Note that the swirl ratio of Case 5 wasselected to be 3.00, which is beyond the upper boundary of the previous searchrange.

The results of the parametric study are listed in Table 6.14, which also agreewith the results from the response surfaces predicted by the non-parametric study.Figures 6.23, 6.24, 6.25, and 6.26 show the in-cylinder pressure, heat release rate,and emissions as functions of crank angle for Cases 1 to 8 compared with thebaseline case. As shown in Fig. 6.23, the late injection event of the baseline caseprevents high temperature combustion and increases the piston work during thelate expansion stroke. This is the reason that the baseline design produced lowNOx and improved fuel consumption due to lower heat losses. Similarly, the lowcombustion temperature also suppresses soot formation, but does not negativelyaffect the soot oxidation. This can be observed from the fact that the slopes of thesoot histories for the three cases are close in Fig. 6.23b, which implies that they

Table 6.13 Parametric studyfor low-load condition

Parameters SOI (�ATDC) Spray (�) Swirl Inj. Pre.

Baseline 9.81 83.87 1.87 1,683Case 1 5 83.87 1.87 1,683Case 2 0 83.87 1.87 1,683Case 3 9.81 77.00 1.87 1,683Case 4 9.81 60.00 1.87 1,683Case 5 9.81 83.87 3.00 1,683Case 6 9.81 83.87 0.50 1,683Case 7 9.81 83.87 1.87 2,000Case 8 9.81 83.87 1.87 1,200

Fig. 6.22 Spray targetingfor the reference design(low-load)

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have similar soot oxidation rates. This is understandable considering that at thepresent low-load condition the global equivalence ratio is very low, and the excessin-cylinder air oxidizes soot very fast after the combustion starts. The oxidationtime determined by SOI then becomes a secondary effect on soot oxidation.However, the approach of retarding SOI to reduce emissions and fuel consumptioncannot be applied to the high-load case, because the large amount of fuel injectedalso reduces in-cylinder temperatures, which causes difficulty with ignition.Moreover, the high local equivalence ratio decreases the soot oxidation rate, andthe available time for the soot oxidation process becomes more important.

It is apparent that the highest fuel consumption of Case 4 is due to its largespray impingement, as indicated in Fig. 6.22. The formed fuel film contributesmost to soot production for this case, and because less fuel is burned, the com-bustion temperature of Case 4 is lower than that of the other cases, which benefitsNOx reduction. According to the spray targeting with a spray angle of 77� picturedin Fig. 6.22, the utilization of the surrounding air during combustion for this caseis the best, and thus more NOx emissions are produced and fuel consumption is

Table 6.14 Results ofparametric study for low-loadcondition


Soot(g/kg fuel)

GISFC(g/kW h)

Baseline 21.81 0.044 193.14Case 1 20.44 0.127 195.53Case 2 34.53 0.120 191.51Case 3 34.00 0.060 191.37Case 4 11.99 0.100 238.64Case 5 27.93 0.030 189.49Case 6 18.90 0.069 203.26Case 7 25.19 0.034 190.99Case 8 15.80 0.069 200.32

Fig. 6.23 Thermal conditions and emissions history for low-load (Cases 1 and 2—effect of SOI).a Pressure traces and heat release rate (HRR). b NOx and soot emissions


reduced. But the baseline case provides more oxygen after the main combustionstage, which reduces engine-out soot emissions through an enhanced oxidationprocess. The above discussions are illustrated by the corresponding curves inFig. 6.24.

The change of swirl ratio in Cases 5 and 6 influences emissions and fuelconsumption as depicted in Fig. 6.25. It is worthy of note that the effect of swirlratio directly reveals the trade-offs among NOx, soot and GISFC. The increase ofswirl ratio helps promote fuel-air mixing and thus improves the premixed com-bustion, which favors reduction of soot emissions and fuel economy, but results inmore NOx emissions. A decrease of swirl ratio leads to reverse trends of emissionsand fuel consumption. Therefore simply altering the swirl level is unable to reduceboth NOx and soot emissions, while simultaneously obtaining fuel economy.Optimal spray targeting with corresponding bowl designs are both crucial in termsof reducing emissions and fuel consumption.

Fig. 6.24 Thermal conditions and emissions history for low-load (Cases 3 and 4—effect of sprayangle). a Pressure traces and heat release rate (HRR). b NOx and soot emissions

Fig. 6.25 Thermal conditions and emissions history for low-load (Cases 5 and 6—effect of swirlratio). a Pressure traces and heat release rate (HRR). b NOx and soot emissions

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Similar to the effect of swirl ratio, the present study on the effect of injectionpressure also shows the existence of trade-offs among NOx, soot and GISFC. Thiscan be explained since increasing the injection pressure increases the liquid phasemomentum that helps the fuel/air mixing, similar to the effect of increasing themomentum of the gas phase, for example, by increasing the swirl level. The effectof injection pressure becomes more complicated when spray impingement has tobe considered. In the present study, Case 7 has the highest injection pressure,and its heat release rate is also the largest, as shown in Fig. 6.26, which is thesource of high NOx emissions, but this drives fast soot oxidation and improves fuelconsumption.

Cases 3, 5, and 7 were also visualized to show how the combination of spraytargeting, swirl motion, as well as injection pressure influences the emissions andcombustion efficiency.

As depicted in Fig. 6.22, the spray targeting of Case 3 favors utilization of thesurrounding air along the jet trajectory. Therefore, better mixing and combustioncan be expected, which contributes to the largest high temperature region in thecylinder, as shown in Fig. 6.27a. The high temperature region is where NOxmainly forms. Because the spray jet of Case 3 targets the bowl edge close to thebowl floor, it is difficult to further oxidize burnt residual gases that are trapped bythe swirl centrifugal effect (Liu et al. 2006). This results in a relatively high sootconcentration area in Fig. 6.27b for Case 3. The swirl ratio was increased to 3.0 forCase 5, and this apparently improved fuel-air mixing, which can be confirmed bythe reduced combustion area in the mid range of the bowl close to piston top, asshown in Fig. 6.27b. The stronger centrifugal effect of the higher swirl ratio trapssoot near the bowl edge, where the oxidation rate is relatively low.

Case 7 has a very similar temperature distribution to that of the baseline case,but its high temperature area is larger than that of the baseline case, which isattributed to its increased spray penetration. No significant fuel film is found due tothe higher injection pressure, because the spray jet is targeted at the bowl lip andalso the fuel evaporates fast under the thermal conditions prevailing at this

Fig. 6.26 Thermal conditions and emissions history for low-load (Cases 7 and 8—effect ofinjection pressure). a Pressure traces and heat release rate (HRR). b NOx and soot emissions


injection timing. Because of the low boost pressure and intake temperature, thespray penetration for the low-load case is longer than that for the high-load case.This is why the optimal solutions for low-load are relatively insensitive to the bowlsize, since mid-size or large-bowls are needed to avoid spray impingement.According the present study, the curvature of the bowl top edge becomes moreimportant if the combined effect of swirl ratio and spray targeting are taken intoconsideration. For the low-load condition more focus on piston bowl design detailsmay be needed, and for the high-load condition, the global geometry is moreimportant. Hence, it is suggested to start the search for an optimal piston bowl

Fig. 6.27 In-cylinder details of representative designs. a Temperature distribution (side view).b Soot distribution (side view)

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geometry design with the high-load case, and then to improve the details under alow-load condition.

For a practical engine, the combustion chamber geometry and the sprayincluded angle cannot be varied easily. Thus it is of interest to seek a compromiseoptimal design for both conditions. It is desired to achieve emissions reduction andimproved fuel consumption at both high-load and low-load by optimizing otherflexible design parameters, such as the swirl ratio and the injection timing andpressure. It was shown in Fig. 6.10 that high-load Design 2 reduced emissions andfuel consumption simultaneously, compared to the baseline design. In addition, itis also observed that its combustion chamber shape shares similar features withDesign 3 in Fig. 6.11 for the low-load optimization. Therefore, Design 2 and itscorresponding spray angle (84.53�) were selected to conduct a study under thelow-load condition. The three cases listed in Table 6.15 were studied, and theresults are given in Table 6.16.

Compared to the results from the original optimized bowl design, Cases 1 and 2are seen in Table 6.16 to reduce both NOx and soot emissions, without sacrificingfuel economy significantly. This indicates that optimal piston designs exist forboth high-load and low-load conditions, but it would be necessary to providedifferent swirl ratios through intake system design and to employ different injec-tion pressures and timings, for example by using a common-rail injection systemto accommodate the different loads in order to achieve clean and highly efficientcombustion.

6.1.2.5 Summary

This example demonstrates the use of multi-dimensional CFD simulations codewith a relatively simple combustion model and with a multi-objective geneticalgorithm, NSGA II, to optimize the piston bowl geometry, spray targeting, sprayinjection event, and swirl ratio for a heavy duty diesel engine at high- and low-load. Optimal solutions were obtained that simultaneously reduced emissions and

Table 6.15 Parametric studyfor the low-load conditionusing the second high-loadpiston design in Fig. 6.10

Parameters SOI (�ATDC) Spray (�) Swirl Inj. Pre.

Case 1 9.81 84.53 1.87 1,683Case 2 9.81 84.53 0.8 1,683Case 3 9.81 84.53 0.8 1,200

Table 6.16 Results ofparametric study for thelow-load condition using thesecond high-load pistondesign in Fig. 6.10


Soot(g/kg fuel)

GISFC(g/kW h)

Case 1 20.34 0.049 196.21Case 2 17.32 0.047 201.00Case 3 13.12 0.078 211.93


improved fuel consumption for both low- and high-load operating conditions.A non-parametric regression analysis tool (COSSO) enabled a quantitative studyof the influences of each parameter and their interactions on the optimal objectives.The results from the non-parametric study were then verified by a detailed para-metric study that further explored several of the most influential design parame-ters. In-cylinder visualization was used to enhance the understanding of the flowinteractions. The following conclusions can be drawn from the present study:

• The use of MOGA enables an efficient search of global optimal solutions withconflicting objectives. The use of non-parametric regression analysis togetherwith the GA optimizations helps to quantify the influences of design parameterson the optimal objectives, which were also consistent with the results obtainedfrom a stand-alone parametric study. This study confirmed that the trendsrevealed by the NPR method are reliable.

• The optimization showed that the high-load operating condition is more sensi-tive to the combustion chamber geometrical design compared to the low-loadcondition. This was revealed by examining the optimal solutions for the high-load optimization, in which the Pareto cases feature a broad range of bowl sizesand geometries.

• By choosing an optimal combustion chamber design from the high-load opti-mization study and varying swirl ratio, injection timing and pressure, excellentperforming designs were also found using the high-load optimal chambergeometry for the low-load condition. This, taken with the second conclusionsuggests that engine optimization studies for all operating loads should start withan optimization study of piston geometry, spray targeting for the high-loadcondition. Then further optimization on the spray injection event and swirl ratioshould be conducted for the low-load condition.

6.1.3 Optimization of a DDC Heavy-Duty Diesel Engine

In this example, a heavy-duty diesel engine produced by Detroit Diesel Company(DDC) was investigated. Similar to the example in Sect. 6.1.2, a multi-objectivegenetic algorithm methodology was coupled with the KIVA3v2 code and auto-mated mesh generator. Three different operating conditions, which represent low-load, mid-load, and full-load conditions, were considered. The input parameterranges were determined using a design of experiments methodology. The NSGA IIwas used for the optimization and the KIVA3v2 code with improved ERC sub-models was used. The characteristic time combustion model and Shell ignitionmodel were employed to improve computational efficiency. Three individualoptimizations were performed. SOI, spray angle, hole size, and the number ofholes were optimized. The optimizations are subject to design constraintsincluding peak cylinder pressure and the temperature at exhaust valve opening.The sensitivity of engine performance to the design parameters of interest was

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evaluated using a K-nearest neighbor regression method (c.f., Sect. 2.3) and aresponse surface analysis method. The KIVA3v2 code was integrated with com-mercial optimization software, modeFRONTIERTM (ESTECO).

As a compromise between the run time and the model requirements, the meshcell size was specified at 2 mm.

6.1.3.1 Engine Description and Operating Conditions

The base engine has an open bowl piston design. The basic features of the engineare listed in Table 6.17. Three different modes A25, B50, and A100, were opti-mized in the present work. They represent low-load, mid-load, and full-loadconditions, respectively. The operating conditions are listed in Table 6.18.


Numerical simulation was first validated by comparing with available experi-mental data (Ge et al. 2009a). Figure 6.28 shows the measured pressure and heatrelease rate (indicated by symbols) and the corresponding numerical results(indicated by lines). The numerical results are in reasonable agreement with theexperimental data.

Figure 6.29 shows the comparison of measured and simulated NOx and sootemissions. The NOx emissions were well predicted using the present models. Thepredicted soot emissions were in reasonable agreement with the measurements.

Table 6.17 Baseline enginespecifications

Combustion chamber Direct injection

Swirl ratio 0.5Bore 9 Stroke (mm) 133 9 168Displacement (L) 2.334Connection rod length (mm) 269.3Geometric compression ratio 16.1:1Fuel injector nozzles 6 holes, equally spacedSpray pattern included angle 146Nozzle orifice diameter (mm) 0.2304

Table 6.18 Operatingconditions of Mode A25,B50, and A100

A25 B50 A100

Boost pressure (bar) 1.59 2.45 3.45Boost temperature (K) 402.7 398.45 350.86Fuel injected (mg) 68.62 131.34 246.07DOI (�) 5.5 15 27RPM 1,265 1,558 1,266EGR (%) 40.5 29.5 25.54


The trend of predicted soot emission with SOI for Mode A25 matches the trend ofthe measurement very well.

The optimization search space is detailed in Table 6.19. The resolution is thetotal number of discrete steps in the search space for each parameter. The opti-mizations are subject to physical constraints including peak in-cylinder pressure(\22 MPa) and exhaust temperature (\1,180 K).

Figure 6.30 shows all of the citizens including Pareto citizens, and the baselinedesign for all three operating conditions A25, B50, and A100. Normal citizens,Pareto citizens, and the baseline design are indicated by red circles, black triangles,and blue squares, respectively. Also shown on the A25 and B50 plots are alter-native designs (green inverted triangle), which have superior performance com-pared to the baseline design. Note that the Pareto citizens are determined from theperspective of three objectives. Therefore, some Pareto solutions are not optimal in2D plots (c.f., right column of Fig. 6.30). At A25 the alternative design has a 19%NOx reduction, 32% soot reduction, and 2.7% GISFC reduction compared to thebaseline design. At B50 the alternative design has a 14.5% NOx reduction, 46%soot reduction, and a 1% GISFC increase compared to the baseline design. Thebaseline design is on the Pareto front for A100. For Mode A100, the pollutantemissions of the baseline engine are nearly optimal.

Figure 6.31 shows the response surfaces of GISFC, soot, and NOx emissionsfor SOI versus nozzle flow rate, number of holes, and the spray angle for modeA25. Also shown is the baseline design (black circle). The base design has aSOI of -7.25 �ATDC, spray angle of 73� (half angle), 6 nozzle holes, and a1.75 L/min. nozzle flow rate. The alternate nozzle design has a SOI of 4 �ATDC,spray angle of 77�, 11 nozzle holes, and a 1.9 L/min. nozzle flow rate. The retardedinjection timing is the most influential parameter in achieving the reduced NOxemissions. The increased spray angle and the increased number of holes led to thereduced soot and GISFC.

Figure 6.32 shows the response surfaces of GISFC, soot, and NOx emissionsfor SOI versus nozzle flow rate, number of holes, and the spray angle for modeB50. Also shown is the baseline design (black circle). The base design has a SOI of-3.0 �ATDC, spray angle of 73� (half angle), 6 nozzle holes, and a 1.75 L/min.nozzle flow rate. The alternate nozzle design has a SOI of 0 �ATDC, spray angleof 76�, 7 nozzle holes, and a 1.45 L/min. nozzle flow rate. The retarded injectiontiming is the most influential parameter in achieving the reduced NOx emissions.The increased spray angle led to the reduced soot emissions.

Table 6.19 Search space ofnozzle optimization

Parameter Min. Max. Resolution

Spray angle 140� 160� 11#holes 5 12 8Flow rate (L/min) 1.65 2.05 5SOI (A25) (�ATDC) -10� 8� 10SOI (B50) -10� 8� 10SOI (A100) -10� 6� 9

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Figure 6.33 shows the response surfaces of GISFC, soot, and NOx emissionsfor SOI vs. nozzle flow rate, number of holes, and the spray angle for mode A100.Also shown is the baseline design (black circle). The base design is nearly optimalat A100.

Fig. 6.28 Pressure and heat release rate of: a Mode A25; b B50; and c A100

Fig. 6.29 Engine-out NOx and soot emissions. Experimental soot data of the A25 case (lines) isfrom laser diagnostic measurement (right axis). The remaining experimental data is from smokemeter and shown on the left axis


Overall, the number of nozzle holes is the most important parameter for fueleconomy and pollutant emissions. A number of nozzle holes within the rangebetween 5 and 9 gives better fuel economy and pollutant reduction for full loadcase. For mid-load and low-load cases, the number of nozzle holes is equally asimportant as the SOI. More nozzle holes result in better fuel consumption. For thelow load case, more nozzle holes result in lower soot emissions, too. More nozzleholes and lower flow rate implies smaller nozzle hole area and smaller initial dropsize. Smaller drops have higher evaporation rates and this leads to a shorter spray

Fig. 6.30 All citizens and Pareto citizens from optimization, and baseline design of nozzleoptimization. Top row: Mode A25; middle row: Mode B50; bottom row: Mode A100

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penetration distance. For the full load case, the in-cylinder temperature andpressure is higher. Thus, the droplets evaporate much faster than the lower loadcases. In fact, the larger droplets generated by the larger nozzle hole have longerpenetration without wall impingement, which will benefit the mixing of the fuelvapor and oxygen. The same size of nozzle hole may result in significant wallimpingement in the mid- or low-load cases. Therefore, a smaller nozzle hole ispreferred in these cases. The effects of the flow rate are not as significant as thenumber of nozzle holes, because its relative change is smaller than the number ofnozzle holes: the ratio of maximum and minimum is 1.25 and 2.4 for flow rate andhole number, respectively.

For NOx emissions, SOI is the first or second most important parameter. NOxformation is relatively slower than many other elementary reactions and the totalNOx emission is proportional to the total lifetime of the high temperaturemixtures. Early injection usually has earlier ignition, which provides longer timefor NOx formation. Thus, an early injection usually has higher NOx emissionsthan a late injection. For fuel economy and soot, the spray angle is slightlymore important. A medial spray angle is not favored. A wide spray angle leadsto better fuel economy, while NOx reduction requires a narrow one. In general, a

Fig. 6.31 Response surfaces of SOI and flow rate, SOI and nozzle hole number, SOI and sprayangle for mode A25. Left column: GISFC; middle column: soot; right column: NOx. Black circle:baseline engine


wide spray angle gives better soot reduction. Under certain conditions, a narrowone also gives lower soot emission, especially for the full load case. Thecombustion efficiency strongly depends on the mixing of fuel and oxygen. Mostof the oxygen is located in the squish region, especially during the expansionstroke. If the spray is led to the squish region (with wide spray angle), bettermixing can be expected. That is why a wide spray angle usually has better fueleconomy and lower soot. With a medial spray angle, the risk of spray wallimpingement is higher. Therefore, a medial spray angle is not favored forall cases, especially for mid- and low-load cases. For the full load case, spraywall impingement is not severe. Due to the long injection duration, the effects onfuel economy and soot emissions are relatively small.

Assuming equal weighting of the different operating conditions, mode-averagedresponse surfaces can be generated (c.f., Fig. 6.34). Comparing with Figs. 6.31,6.32, and 6.33, the mode-averaged response surfaces are closer to the full load case(Mode A100, c.f., Fig. 6.33) than to the others. Therefore, the full load case is themost representative case for nozzle design optimization. Shi and Reitz (2008b)drew a similar conclusion from their work.

Fig. 6.32 Response surfaces of SOI and flow rate, SOI and nozzle hole number, SOI and sprayangle for mode B50. Left column: GISFC; middle column: soot; right column: NOx. Black circle:baseline engine

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6.1.3.3 Summary

In the present section, a multi-dimensional CFD code was integrated with acommercial optimization software—mode FRONTIER. Using the multi-objectivegenetic algorithm (NSGA-II), the nozzle design parameters of a heavy dutydiesel engine were optimized. The following conclusions can be drawn from thework:

• MOGA is an efficient and feasible tool for engine optimization. Response sur-faces of the MOGA results clearly quantify the influences of the designparameters on the optimal objectives.

• At low load a higher number of nozzle holes and a wider spray angle werefavored for reducing the soot emissions and fuel consumption.

• The mode-averaged response surfaces have closer pattern with the ones of highload. Therefore, the high load case is the most representative case for engineoptimization.

Fig. 6.33 Response surfaces of SOI and flow rate, SOI and nozzle hole number, SOI and sprayangle for mode A100. Left column: GISFC; middle column: soot; right column: NOx. Blackcircle: baseline engine


6.1.4 Optimization of a High-Speed Direct-Injection Diesel Engine


Growing concern over environmental issues has prompted regulatory authorities toincrease already stringent emission standards for the automobile industry. Mean-while, the international crude oil price is increasing, and Green House Gases(GHG) are becoming more concerned. Thus, fuel economy is becoming more andmore important from both a customer’s and a regulator’s perspective. The dieselengine is a promising option for passenger cars due to its high fuel conversionefficiency, which can be 40% more than that of modern SI engines (Cowland et al.2004).

In this example, a high-speed direct-injection (HSDI) diesel engine sized forpassenger cars was optimized using the MOGA and KIVA3v2 code discussed above.Spray targeting, swirl, and 11 parameters describing the piston bowl geometry weresimultaneously optimized for a full-load case. The results were analyzed using theCOSSO non-parametric regression analysis method. Sensitivities of the design

Fig. 6.34 Mode-averaged response surfaces of SOI and flow rate, SOI and nozzle hole number,SOI and spray angle with the same weight for Mode A25, B50, and A100. Left column: GISFC;middle column: soot; right column: NOx

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parameters on the fuel economy and pollutant emissions are illustrated inresponse surfaces. Some of the optimal designs were further analyzed for moreinsights. Physical mechanisms that explain correlations between design param-eters under certain operating conditions are explained based on the regressionanalysis results.

6.1.4.2 Mathematical Models and Numerical Methods

The improved version of the KIVA3v2 code discussed in earlier chapters was usedfor the multi-dimensional CFD modeling of the engine combustion processes. Theclosed-valve period of the engine cycle was considered. The gas jet model (Abaniand Reitz 2007) and radius-of-influence collision model (Munnannur and Reitz2009) were employed to reduce mesh dependency.

All the optimization tasks were conducted using a high-throughput computing(HTC) technique. The HTC software CONDOR (Thain et al. 2005) was designedto fully utilize distributively owned, heterogeneous computing resources, whichare available in university campus or other research communities. For instance, thecondor pool at the University of Wisconsin-Madison consists of more than 4,000computers. Like other full-featured batch systems, CONDOR provides a jobqueuing mechanism, scheduling policy, priority scheme, resource monitoring, andresource management. CONDOR is configured to only use idle desktop machines.When the machine is no longer available, CONDOR transparently produces acheckpoint and migrates the running job to another idle machine. A shared filesystem is not necessary for CONDOR. Based on these features, CONDOR andsimilar HCT systems are ideal for massive computer optimization.

6.1.4.3 Engine Description and Operating Conditions

The engine investigated in the present work is a production diesel engine forpassenger cars. Table 6.20 lists the specifications and the operating conditionsconsidered. The present case represents a full-load condition.

6.1.4.4 Optimization Parameters and Objectives

Engine operated under the three modes was optimized separately. However, exceptfor the SOI timing, the optimizations of the three modes had the same searchspace, as shown in Table 6.21. In the current study, the bowl shape was charac-terized using eleven parameters, including five outline parameters (the height ofthe central pedestal of the piston, Az; position of the bowl bottom, Bx; radius ofbowl, Cx and Dx; height of point C, Cz), and 6 other parameters for Bezier curvesthat connect the control points (Xab, Xba, Xbc, Xcb, Ycb, Ycd). The other featuresof the piston geometry were kept as the same as a baseline engine design. When


the piston bowl geometry is optimized, the computational mesh should be gen-erated automatically for efficiency using Kwickgrid methodology (Wickman 2003)that is described in Sect. 4.1. Figure 6.35 gives an example of grids generated byKwickgrid. The numbers 1- 6 indicate the Bezier curve control points, whichcorrespond to the parameters Xab, Xba, Xbc, Xcb, Ycb, and Ycd, respectively.As a compromise between computation efficiency and the model accuracy, thecell size was specified as 1 mm in this work (note the engine is smaller thanpreviously investigated heavy-duty engines). This resolution has been shown togive adequately mesh independent results by Abani et al. (2008a, b).

The KIVA3v2 code and Kwickgrid were integrated with the NSGA-II code. Allof the parameters were set as real variables except for the number of nozzle holes,which had to be an integer. The integer (binary) variable was limited to a finite

Table 6.20 Enginespecification and operatingconditions

Bore 9 Stroke (mm) 81.0 9 88.0Connection rod length (mm) 160.0Effective compression ratio 12.75:1Fuel injector nozzles 8 holes, equally spacedSpray pattern included angle 153�Nozzle orifice diameter (mm) 0.121IVC (�ATDC) -129.5EVO (�ATDC) 120.0Swirl ratio 2.0IMEP (bar) 18.0Fuel injected (mg) 55.6RPM 4,000SOI (�ATDC) -16DOI (�) 42.4EGR (%) 0.16

Table 6.21 Optimizationsearch space

Minimum Maximum

Spray angle (�) 140 160Nozzle hole number 5 12Swirl ratio 0.5 2.5Az 0.5 0.8Bx 0.8 1.0Cx 0.45 0.65Cz 0.60 0.85Dx 0.45 0.70Xab 0.1 0.7Xba 0.3 0.9Xbc 0.5 3.5Xcb 0.5 3.5Ycb 0.3 0.9Ycd 0.3 0.9SOI (�ATDC) -20 -5

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number of choices. In the present optimization, the total number of possibilities innozzle hole number is 8 (5–12 holes), however, the number of nozzle holes varies,the amount of injected fuel, injection velocity and injection duration was kept thesame as the baseline engine. Thus, the total flow area of the nozzle holes is kept thesame as the original value. With fewer nozzle holes, the size of nozzle hole islarger and so is the initial droplet size. To fully understand the influence of thedesign parameters, extensive search spaces were employed in the present work.

Since plenty of computer nodes were available on Condor pool, many jobs wererun simultaneously. A large population size for the genetic algorithm was thenpreferred. In the present work, the population size was set to 32, which showedgood performance in the study of Shi and Reitz (2008a). Typical computer timeswere about 6–12 h to complete one generation.

Fig. 6.35 Example of grids generated by Kwickgrid

Fig. 6.36 Fired and motoredin-cylinder pressure ofbaseline case



The baseline case was simulated using both the CTC and KIVA-CHEMKINmodels. The pressure traces are plotted in Fig. 6.36, which includes the motoredcase. Both the CTC and KIVA-CHEMKIN models match experimental data verywell. NOx and soot emissions predicted by the CTC and KIVA-CHEMKINmodels, which are shown in Fig. 6.37, are also close. This implies that the resultsof the CTC model are reliable for the present engine full-load operating conditionof interest. Since the computational cost of the CTC model is much less than theKIVA-CHEMKIN model, and many cases need to be computed to cover thedesign space, the CTC model was used in optimization.

The optimization was terminated at the 72nd generation, which results in about2,300 designs. The convergence metric of this optimization was then calculatedusing Eqs. 4.8 to 4.10. Figure 6.38 shows the history of the normalized conver-gence. As can be seen, convergence was reached by the 30th generation. But GAgenerations were allowed to continue after the 30th generation to fill morediversified solutions to the Pareto front.

All the citizens together with highlighted Pareto solutions and the baseline case,are plotted in Fig. 6.39. Normal citizens, Pareto citizens, and the baseline designare indicated by black hollow squares, blue triangles, and the red circle, respec-tively. The baseline engine performance is seen to be improved upon significantlyin terms of all the objectives.

Figures 6.40, 6.41, and 6.42 summarize the response functions of all the designparameters, as evaluated using the COSSO method. Their effects on the GISFC,soot and NOx are illustrated in Figs. 6.40, 6.41, and 6.42, respectively. Theabsolute error values of these response functions are about 10 g/kW h, 0.7 g/kgf,and 1.2 g/kgf for GISFC, soot, and NOx, respectively. In general, the number ofnozzle holes, which ranges from 5 to 12, has the most significant impact on theGISFC and soot emission. A nozzle with 6–8 holes benefits combustion efficiency

Fig. 6.37 NOx (left) and soot (right) emissions computed using the CTC and KIVA-CHEMKIN(CK) models

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and soot reduction. A nozzle with fewer holes gives lower NOx emissions. TheAFR (air to fuel ratio) of the full-load case is about 20 (corresponding globalequivalence ratio of 0.75). Therefore, it is essential to deliver the fuel to eachcorner of the combustion chamber to achieve good combustion efficiency. Plus, thepressure and temperature in this case are very high, so the droplets evaporate veryfast. If the initial droplet size is too small, the spray penetration will be too shortfor the fuel to reach the near wall squish region (which has more oxygen than thecylinder center).

A nozzle with more holes produces smaller droplets, which have shorter spraypenetrations. In this case, it becomes very difficult for the fuel to mix with theoxygen near the wall and results in poor combustion efficiency.

On the other hand, if the initial droplet size is too large, it presents the risk ofspray wall impingement, which will lead to poor combustion efficiency and high

Fig. 6.38 Normalizedconvergence history of theoptimization

Fig. 6.39 All citizens and Pareto solutions from optimization, and the baseline


soot and UHC emissions. Thus, the key issue for combustion efficiency of the full-load case lies in keeping spray penetration as long as possible while avoiding spraywall impingement. These effects of nozzle hole number (hole size) on the GISFCand pollutant emissions are clearly reflected in the response functions.

SOI is the most critical parameter for NOx emissions. The NOx formationreactions are relatively slow as compared to many other elementary reactionsinvolved in the heat release. Therefore, the total NOx emission is proportionalto the total lifetime of the high temperature mixtures. Early injection usuallyhas earlier ignition, which provides more time for NOx formation. Thus, a lateinjection consistently gives lower NOx emissions.

SOI also has a strong impact on the combustion efficiency. With different SOI,different percentages of fuel are injected into the bowl or squish regions. If too

Fig. 6.40 Response functions of individual design parameters on GISFC (g/kW h)

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much fuel is injected into one region, it is very difficult to transport the abundantfuel into the other region. In this sense, the effects of SOI and spray angle on theGISFC are the same: to deliver the appropriate amount of fuel to the squish andbowl regions. A SOI around -15 �ATDC is seen to gives the best GISFC. Thisimplies that, with this SOI, the ratio of the fuel delivered into the squish region andthe bowl region is the same as the ratio of the amount of available oxygen in thesetwo regions.

The response functions of spray angle show that a wider spray angle simulta-neously reduces fuel consumption and pollutant emissions. A wider spray deliversmore fuel into the squish region where there is more oxygen. Swirl adds a tan-gential velocity to the flow. Therefore, it enhances the mixing in the tangentialdirection and this enhances the evaporation of droplets. Consequently, it furtherreduces the spray penetration. Thus, for the same reason as the effects of nozzle

Fig. 6.41 Response functions of individual design parameters on soot emission (g/kgf)


hole number, strong swirl reduces GISFC. Too weak a swirl leads to poor mixingbetween fuel and oxygen in the tangential direction, and eventually to deterioratecombustion efficiency. The best fuel consumption is achieved when the swirl ratiois around 1.8. Note that strong swirl always benefits the soot reduction. However, aclear tradeoff between fuel consumption and NOx formation is observed in termsof the effects of the swirl flow.

The design parameters of the piston bowl can be separated into two categories:(1) outline parameters; and (2) Bezier curvature parameters. Among the fiveoutline parameters (Az, Bx, Cx, Cz, and Dx), Cx is the most important one interms of its impact on GISFC and pollutant emissions. Cx is the primary parameterdefining the radius of the piston bowl. It can be seen that Cx & 0.6 gives the best

Fig. 6.42 Response functions of individual design parameters on NOx emission (g/kgf)

226 6 Applications

GISFC and soot emissions, while keeping NOx emissions at an acceptable level.Since the position of point C is very important at full-load, the bowl curvatureabout point C becomes very important as well. One of its curvature parameters,Xbc, is seen to be the most important Bezier curvature parameter for GISFC andpollutant emissions. The curvature parameters have strong effects on the flowpattern in the piston bowl, especially the tumble flows. Therefore, their impactson soot emission are more evident than on the fuel economy and NOx. Ingeneral, the influences of these curvature parameters are proportional to the areasthey cover. According to Fig. 6.35, the curvature parameters Xbc, Xcb, and Ycbcover the largest surface of the piston bowl. They are also the most influentialcurvature parameters under the most operating conditions. The other outlineparameters play relatively less important roles in terms of the combustion effi-ciency and pollutant emissions. Some parameters almost have no influence onGISFC or pollutant emissions, for instance, Xab for soot, Xba for NOx and soot,Ycd for GISFC and NOx. Thus, it is concluded that the effects of someparameters on GISFC or pollutant emissions can be neglected, for instance, Az,Cz, Xab, Ycb.

The response curves in Figs. 6.40, 6.41, and 6.42 provide information about therelative importance of each design parameter. In addition, the response surfaces, as

Fig. 6.43 Selected response surfaces of GISFC


shown in Figs. 6.43 and 6.44, illustrate the joint effects of two design parameterson the objectives. The correlation between two design parameters can also beeasily observed from the response surfaces. If one parameter is more importantthan another and these two are strongly correlated, the important one should bedetermined first, and then the less important one can be optimized based on theirresponse surfaces.

Figures 6.43 and 6.44 show some selected response surfaces of GISFC andsoot emission, respectively. Only the response surfaces of strongly correlatedparameters are presented. Because SOI has a dominant influence on NOx emis-sion, response surfaces of NOx emission are not presented. It can be seen from

Fig. 6.44 Selected response surfaces of soot emission

228 6 Applications

Fig. 6.43a that the effects of SOI and spray angle on GISFC are strongly corre-lated. A wide spray prefers an early injection, while a narrow spray prefers aninjection a bit later. As mentioned above, the function of SOI is to inject adequateamount of fuel into piston bowl and squish regions. With the same SOI, if the sprayangle gets narrow, more fuel will be injected into the piston bowl. Since theinjection occurs mainly before TDC, a delay in the injection reduces the amount offuel heading to the piston bowl and this retains lower GISFC.

As observed from Fig. 6.40, the number of nozzle holes has a more importantinfluence on GISFC than the spray angle and swirl ratio. However, their responsesurfaces (c.f., Fig. 6.43b, c) show that these two parameters are correlated with thenumber of nozzle holes. With high swirl ratio, a nozzle with fewer holes (i.e.,larger initial droplet sizes) is preferred. This is consistent with the discussion aboutFigs. 6.40, 6.41, and 6.42. A long spray penetration without wall impingementhelps the fuel to mix with the available oxygen. Strong swirl reduces spray pen-etration, while a large initial droplet size increases the spray penetration. There-fore, a nozzle with fewer holes coupled with a strong swirl provides very good fueleconomy. In addition, the distance between spray plumes is also larger with fewerholes, and thus the higher swirl would not cause significant plume interaction todeteriorate fuel economy. The spray angle is also clearly correlated with thenumber of nozzle holes. When the spray angle is small, the spray is targeted at thepiston bowl. Therefore, the risk of spray wall impingement is high. A short spraypenetration is preferred. When the spray angle is large, the spray is targeted at thesquish region. Spray wall impingement is then not a problem any longer. A longspray penetration will benefit the mixing of fuel and oxygen. Thus, as seen inFig. 6.43, a narrow spray with a 7-hole nozzle, or a wide spray with a 5-holenozzle, has the best fuel economy. Some design parameters of the piston bowl arealso strongly correlated, for instance, Xab and Xba for GISFC, as shown inFig. 6.43d. Their response surface shows a saddle-like shape.

For soot emissions, a correlation between the number of nozzle holes and swirlratio can be seen from Fig. 6.44a. This response surface shows a very similarshape to their response surface of GISFC (c.f., Fig. 6.43b). The art of tuning thenumber of nozzle holes and swirl ratio is to avoid spray wall impingement whilekeeping long spray penetration. Soot emission is very sensitive to spray wallimpingement and the local mixing conditions. As with fuel economy, a weakerswirl works well with a medial hole size, while stronger swirl prefers a larger holesize (fewer holes). Overall, it is seen that strong swirl always enhances the mixingof fuel and oxygen and reduces soot emissions.

The geometry of the piston bowl has a significant effect on the soot emissions.It can be seen from Fig. 6.44b–d that the geometric parameters are strongly cor-related with the spray parameters and swirl. As the most important parameter forpiston bowl design, Cx shows distinct interactions with SOI, spray angle, and swirlratio. For an early injection, the effects of Cx can be neglected, because more ofthe fuel goes to the squish region and the combustion in the piston bowl is rela-tively less important. Retarding SOI, more fuel enters piston bowl. The shape ofthe piston bowl then plays a very important role for soot formation and oxidation.


An appropriate design of piston bowl coupled with an appropriate injection eventcan generate a strong tumble flow component, which can significantly reduce sootemissions. The response surface of Cx and spray angle, as well as the one of Cxand swirl ratio, shows that a moderate bowl throat radius works well with a narrowspray angle and a weak swirl, and a big bowl throat radius with a wide spray angleand a strong swirl. The interactions of geometric parameters are also evident interms of soot emissions, for instance, Cx and Cz (Fig. 6.44e), Xbc and Cx(Fig. 6.44f).

Three interesting designs were selected from the optimization results for furtheranalysis. Table 6.22 lists the performance of these designs compared with thebaseline engine at full-load. According to the numerical results, these designssimultaneously and significantly improve the baseline engine performance in termsof GISFC and pollutant emissions.

Figure 6.45 shows the comparison of in-cylinder pressure, heat release rate, andpollutant emissions between the baseline engine and these three selected designs.During the expansion stroke, the three designs have higher combustion efficienciesthan the baseline engine, which is indicated by the higher heat release rates in thisperiod. The baseline engine has a higher peak pressure than the optimal engines.The in-cylinder averaged temperature of the baseline engine is therefore higher.Additionally, because the injection of the baseline engine is earlier, the final NOxemission of the baseline engine is much higher than the optimal engines.

Figures 6.46, 6.47, 6.48, and 6.49 show contour plots on a cut-plane alongthe spray axis. Figure 6.46 shows the fuel vapor distribution as well as a vectorplot of the gas velocity of the baseline engine and the optimal designs atCA = 30 �ATDC. It can be seen that the baseline engine fails to deliver enoughfuel into the squish region, while for all the optimal designs more fuel enters thesquish region and mixes well with the oxygen. Geometry-generated tumble flows inthe bowl regions of the optimal designs are stronger than that of the baseline engine,which enhances the mixing in the piston bowl and benefits soot oxidation. Design 2has the strongest tumble flow, which makes this design the best one for sootreduction. Figure 6.47 shows the fuel vapor distribution and gas velocity field of thebaseline engine and optimal designs at CA = 100 �ATDC, which is close to EVO.For the baseline engine, there is still a lot of fuel left in the piston bowl region, andthis confirms that too much fuel is directed into the piston bowl and cannot mix withthe leftover oxygen in the squish region. Much less fuel is left in the optimalengines, i.e., the combustion in these optimal engines is more complete.

The distribution of oxygen also supports this fact. Figure 6.48 shows the oxygendistribution of the baseline engine and optimal designs at CA = 100 �ATDC. It can

Table 6.22 Comparison of the performance of baseline engine and three optimal engines

Design Baseline 1 2 3

GISFC (g/kW h) 249.8 229.7 (8%;) 236.2 (5%;) 241.2 (3%;)Soot (g/kgf) 2.68 1.22 (54%;) 0.66 (75%;) 1.08 (60%;)NOx (g/kgf) 29.23 19.46 (33%;) 13.93 (52%;) 8.71 (70%;)

230 6 Applications

be seen that there is a lot of oxygen left near the cylinder wall in the baseline engine.Considering that the mass of flow in the cylinder increases linearly with the radius(Dm ¼ 2prqDrDh, r is the radius and h is the depth), oxygen near the cylinder walloccupies a much larger region than oxygen near the axis. The gradient of theoxygen concentration is also very large. The left-over oxygen in the combustionchamber at EVO of baseline engine and optimal engines are about 0.0769, 0.0662,0.0654, 0.0657 g, respectively. Combining with the observations from Fig. 6.47 wecan conclude that the poor fuel economy of the baseline engine is due to the factthat the fuel in the piston bowl fails to mix and react with the oxygen nearthe cylinder wall. The optimal engines have a much more homogeneous distribu-tion of oxygen in the cylinder. Especially, the oxygen near the cylinder wallis well utilized. Comparing to designs 2 and 3, the peak pressure of design 1 ishigher (c.f., Fig. 6.45) being due to its earlier ignition. Therefore, the design 1 hashigher GISFC, even though its left-over oxygen is more than the other optimaldesigns.

Figure 6.49 shows the soot distribution of the baseline engine and optimaldesigns at CA = 100 �ATDC. The baseline engine has much higher soot emis-sions than the optimal engines. The main reason is the inappropriate amount of fueldelivered into the piston bowl. Geometry-generated tumble flow is also a plus.

Fig. 6.45 In-cylinder pressure and heat release rate (top), and pollutant emissions (bottom) of thebaseline engine and three selected designs (see Table 6.22)

Fig. 6.46 Fuel vapor distribution and velocity field of the baseline engine and optimal designs atCA = 30� ATDC


Thanks to the good mixing of fuel and oxygen and strong tumble flow, design 2has the lowest soot emissions. There is some soot left near the cylinder head andcrevice region in both designs 1 and 3.

6.1.4.6 Summary

In this example, a HSDI diesel engine for passenger cars was optimizedusing the multi-dimensional CFD code and multi-objective genetic algorithm

Fig. 6.47 Fuel vapor distribution and velocity field of the baseline engine and optimal designs atCA = 100� ATDC

Fig. 6.48 Oxygen distribution of the baseline engine and optimal designs at CA = 100� ATDC

232 6 Applications

methodology. Bowl geometry, spray targeting, and swirl ratio were optimizedsimultaneously. The following conclusions can be drawn from the presentwork:

• The full-load case should be optimized to deliver the fuel into each corner ofthe combustion chamber and to mix with the available oxygen. It is crucialto distribute the appropriate amount of fuel into the squish and bowl regions toachieve good fuel economy and pollutant reduction. Optimizations of the nozzlehole layout, bowl radius, and swirl ratio should be focused on.

• SOI is always the key parameter for NOx reduction.• When one bowl shape outline parameter becomes more important, the influ-

ences of the Bezier curvature parameters about this point increases as well. Thecorrelation between them usually cannot be ignored.

• In general, the influence of a Bezier curvature parameter is proportional to thetotal area of the surface that it covers.

6.2 Engine Optimization with AdvancedCombustion Models

This section provides several examples of engine optimizations that use detailedfuel chemistry for better accuracy, especially for engine premixed combustionmodes. To accelerate the simulations, an efficient chemistry solver with the AMCmodel and the DAC scheme (c.f., Chap. 3) was employed.

Fig. 6.49 Soot distribution of the baseline engine and optimal designs at CA = 100� ATDC


6.2.1 Optimization of a Heavy-Duty Compression-Ignition EngineFueled with Diesel and Gasoline-Like Fuels


Homogeneous Charge Compression-Ignition (HCCI) engines have received muchattention in recent decades due to their clean and efficient combustion. However,in practical engines, it is difficult to achieve a fully premixed air-fuel charge usingan in-cylinder direct injection system, and the fully premixed air-fuel charge alsousually results in unacceptable engine noise that accompanies the very fast pres-sure rise rate under mid- to high-load operating conditions. There is also no in-cycle control over combustion phasing in HCCI engines so that engine controlbecomes very difficult. The concept of Partially Premixed Combustion (PPC) incompression-ignition engines promises to avoid these difficulties faced by HCCIengines while attaining clean combustion.

Due to the low volatility of diesel fuel, it is required to significantly advance theinjection timing to obtain a partially premixed charge prior to the auto-ignition ofthe fuel. However, such early injection can result in combustion chamber wall-wetting due to spray impingement with the walls. The resulting fuel film can be asource of high UHC emissions and low fuel economy. Also, injecting diesel fuelearly will cause heat release to occur during the compression stroke which is alsoundesirable. An alternative method to achieve a premixed charge is to suppressfuel auto-ignition and thus to increase the time allowed for air-fuel mixing. Onesuch application is the modulated kinetics (MK) combustion engine (Kimura et al.1999, 2001). MK combustion features a late injection timing in order to shorten thespray penetration (due to the high gas density) and also uses ultra-high EGR levelsto suppress ignition. The studies of Kimura et al. (1999, 2001) indicated that MKcombustion significantly reduces NOx and soot emissions without sacrificing fueleconomy. But due to the late injection, the operating range of MK combustion islimited to low- to mid-load conditions.

Clearly fuels with high volatility and low ignitability are desirable to achieve amore premixed air-fuel charge, and conventional gasoline is a good candidate fuel.However, until recently, gasoline has only been used in spark ignition engines,mainly due to the limitation of available control mechanisms of the injectionsystem in CI engines. Kalghatgi et al. (2006, 2007) are among the pioneers whoinvestigated the combustion processes of compression-ignition engines fueled withgasoline. Their studies pointed out that the gasoline CI engine effectively reducedNOx and soot emissions with acceptable heat release rates, as compared to dieselfuel under the same operating condition. The principle reason is that the longerauto-ignition time of gasoline separates the injection event and main heat releaseand thus minimizes the heat release in the diffusion flame regime. They also foundthat a dual-injection strategy is an effective way to achieve partially premixedcharge and to reduce the maximum heat release rate and cyclic variations in aCI engine fueled with gasoline. However, as indicated by Shi et al. (2010 d), in

234 6 Applications

general CI engines fueled with gasoline-like fuels have higher in-cylinder gaspressure rise rate (thus engine noise) and unburned hydrocarbons (UHC) emissionsthan those of conventional diesel engines. An injection system that is calibrated oroptimized for a CI engine fueled with diesel requires modifications for gasoline-like fuels due to their distinct spray characteristics and fuel reactivity. Therefore, itis of much interest to compare optimal injection parameters of a CI engine fueledwith diesel and gasoline-like fuels, to provide guidance for engine design. Theobjective of this work is to seek for optimal combinations of injection parametersfor a heavy-duty compression ignition engine fueled with diesel and gasoline-likefuels (gasoline and 10% ethanol blended gasoline E10) and operated under mid-and high-load conditions. The results are then discussed for both non-parametricand parametric studies in order to reveal guidelines for optimal engine design withthe different fuels.

In modern engines, the vast number of variables that control the combustionprocess results in a large number of iterations to achieve optimal designs. Obvi-ously, the use of simple combustion models is not applicable in the presentresearch, because the focus of this study is to compare the influence of differentfuels on engine optimal designs. This necessitates the use of more computationallyexpensive engine CFD tools with detailed fuel chemistry. Since with detailedchemistry over 90% of the computational time is spent on the chemistry solver,acceleration of the solver is critically important. The efficiency, feasibility, andreliability of the AMC model for engine optimization was validated by Ge et al.(2010b). As discussed in Chap. 3 in detail, the Adaptive Multi-grid Chemistry(AMC) model Shi et al. (2009a) and the Extended Dynamic Adaptive Chemistry(EDAC) scheme (Shi et al. 2010b) were both employed to achieve more efficientcalculations with detailed fuel chemistry for the present optimization problem.

6.2.1.2 Engine Description and Operating Condition

The studied engine is the same Caterpillar heavy-duty engine as described inSect. 6.1.2. The main engine specifications are listed in Table 6.6. The engineoperating conditions are listed in Table 6.23.

Table 6.23 Operating conditions of the Caterpillar DICI engine

Mid-load High-Load

Speed (rev/min) 1,300 1,300Fuel amount (g/cycle) 0.135 (0.141 for E10) 0.270 (0.282 for E10)IMEP (bar) 11 21EGR (%) 30 30Global equivalence ratio 0.6 0.8IVC temperature (K) 435 435Boost pressure (bar) 2.0 3.0IVC (�ATDC) -85 -85EVO (�ATDC) 130 130

6.2 Engine Optimization with Advanced Combustion Models 235

6.2.1.3 Model Validation

The present work adopted a modified version of the KIVA3v2 code with anefficient chemistry to evaluate the performance of a CI heavy-duty engine fueledwith diesel, gasoline and E10 under mid- and high-load conditions. The CFD toolwith detailed fuel chemistry (the reduced Primary Reference Fuel (PRF) mecha-nism by Ra and Reitz (2008) and reduced ethanol mechanism from the LLNLdetailed mechanism by Marinov (1999)) was validated against the experimental databy Hanson et al. (2009) on the same engine. Figure 6.50 compares the pressure tracesand emissions for a SOI sweep from -8 to -2 �ATDC. Figure 6.51 shows thecomparison for an EGR sweep study. It is seen that the CFD simulations agree withthe experimental trends fairly well, especially the major emission trends are cap-tured. This strengthens the confidence of using both the AMC and EDAC models inthe present optimization study.


The optimization studies were conducted using a multi-objective genetic algo-rithm, NSGA II. The NSGA II related parameters were set according to Shi andReitz (2008a, b) and a population size of 32 was used. Six tasks (two operatingconditions and three fuels) were conducted, which used 192 computer nodesrunning in parallel on the University of Wisconsin Condor system (Thain et al.2005). The entire optimization was completed in approximately six weeks(estimated time would be more than six months with the original chemistrysolver).

The optimization focused on selecting injection system parameters with thedifferent fuels. In-cylinder air motion due to swirl was also considered due to itslarge impact on the air-fuel mixing process. Therefore, eight parameters wereoptimized, which are summarized in Table 6.24 together with their lower andupper bounds. Six objective functions were selected: soot, NOx, UHC, and COemissions, fuel consumption (indicated by GISFC), as well as an engine noiseindicator, the Peak Pressure Rise Rate (PPRR). In addition, three feasibility con-straints were defined: maximum cylinder pressure and PPRR of 20 MPa and30 bar/CA, respectively, and lowest maximum average temperature of 1,200 K,below which the engine would misfire. If one or more of the constraints wereviolated, a penalty was assigned to its objectives, and thus the design was given thelowest priority for selection in the evolution. This simple penalty mechanismproved to be very effective to remove infeasible designs.

The optimization was terminated at the 25th generation (i.e., 32 (popula-tion) 9 25 (generation) = 800 individual evaluations for each fuel) based on theconvergence metric (as discussed in Chap. 4) shown in Fig. 6.52a. The figureshows that further GA evolutions only produce more cases to fill the existingPareto front (optimal solution set). Since it is impossible to visualize Paretosolutions with 6 objectives in a single plot, the values of the six objectives of the

236 6 Applications

Pareto solutions are mapped onto three plots, as shown in Fig. 6.52b–d for sootand NOx, UHC and CO, as well as GISFC and PPRR, respectively.

Figure 6.52b shows the trade-off relation of soot and NOx emissions for diesel(squares), while for gasoline (circles) and E10 (triangles), most of the Paretosolutions have extremely low soot emissions, as well as NOx. As seen inFig. 6.52c, the optimal diesel solutions tend to produce more CO emissions while

Fig. 6.50 Comparison of simulation and experiment (Hanson et al. 2009) (gasoline main SOIsweep (70% injected fuel) with 0% EGR and 30% pilot injection at -137�CA). a Pressure traces.b Soot. c NOx. d UHC. e CO


gasoline and E10 generate more UHC emissions. CO indicates the combustioncompleteness with diesel, but UHC is the indicator for gasoline and E10 under thepresent operating condition. The optimal diesel fuel designs have lower PPRRsthan those of gasoline and E10 and the fuel consumption of the optimal designswith the three fuels is distributed widely in Fig. 6.52d. In general, designs withhigher PPRR have better fuel economy, and for gasoline and E10 it is moredifficult to obtain a good compromise between fuel economy and PPRR.

Fig. 6.51 Comparison of simulation and experiment (Hanson et al. 2009) (EGR sweep).a Experimental pressure traces. b Simulated pressure traces. c Soot. d NOx. e UHC. f CO

238 6 Applications

The EPA on-highway HD 2010 emissions regulations mandate dramaticallylow engine exhaust PM, NOx, and non-methane HC (NMHC) levels, which are0.0136, 0.27, 0.19 g/kW h, respectively (http://www.dieselnet.com/standards/).Searching all Pareto solutions reveals that relatively few optimal diesel fueldesigns satisfy the NOx regulation, and none meets the PM and NMHC standards.For gasoline and E10, 95% of the optimal designs are below the soot limit, and afew designs with both soot and NOx emissions lower than the standards are also

Table 6.24 Optimizationparameters and their ranges

Parameter Range

Pilot SOI (�ATDC) -85.0 to -55.0Injection pressure of pilot injection (bar) 300 to 2,000Amount of pilot injection (%) 0 to 50Main SOI (�ATDC) -35.0 to 10.0Injection pressure of main injection (bar) 500 to 2,000Spray included angle (�) 60.0 to 85.0Swirl ratio 0.0 to 2.0Number of holes 6 to 12

Fig. 6.52 Convergence metric and Pareto solutions for mid-load. a Convergence metric.b Pareto solutions (Soot and NOx). c Pareto solutions (UHC and CO). d Pareto solutions (GISFCand PPRR)


found. However, none of the optimal gasoline and E10 designs meets the NMHClimit, which indicates that further oxidation of the exhaust gases is needed. Asimilar conclusion was reached by Manente et al. (2009) whose experimentssuggested that a conventional oxidation catalyst should be used to oxidize UHCand CO emissions when a CI engine is fueled with gasoline-like fuels.

Benchmark designs (i.e., Case 1 in all parametric studies) for further regressionanalysis were set to be designs with central values of the investigated ranges of thedesign parameters listed in Table 6.25, except that the main SOI was advanced to-25 �ATDC instead of its central value -12.5 �ATDC (since the E10 engine wasfound to misfire). The results of the benchmark designs for the three fuels areindicated by stars in Fig. 6.52b–d. Due to the early injection timing, the peakpressure rise rate of E10 for the benchmark design is very high.

The effects of each individual parameter on the objectives are summarized inTable 6.26. In the table each symbol designates the predicted change of anobjective as a function of a design parameter. Vertical arrows indicate primaryinfluences and the tilted arrows represent secondary effects. An upward directedarrow indicates that the value of the objective increases with the design parameter,and downward arrows indicate a monotonic decrease. Horizontal arrows representnegligible influences, while arc signs indicate that there is either a minimum value(downward) or a maximum value (upward) of objectives in the range of the designvariables. A combination of downward and upward arcs means that both a localminimum and a maximum value were found. Filled arcs are for primary effects asopposed to hollow arcs for the secondary effects.

The numbers represent the mean values of the design parameters and objectivesof all the Pareto solutions, which provide the general performance for eachfuel. The tabulated results are consistent with the observations of Fig. 6.52b–d.Gasoline and E10 fuels significantly favor the reduction of soot and NOx, whileproducing more UHC emissions than diesel, but with slightly lower CO emissions.It is also seen that the PPRR level increases with the fuel octane number as theoptimal designs with E10 fuel have the highest PPRR, followed by gasoline anddiesel fuel.

Interestingly but not surprisingly, the primary design parameter with diesel fuelis the amount of fuel in the first injection pulse, as four objectives show a strongdependency on this parameter, followed by the second injection timing. This isdifferent from the engine with gasoline and E10, where the second injection timingpredominantly affects engine performance and emissions, followed by the secondinjection pressure and spray included angle. The principle reason is that thecombustion phasing with diesel fuel is controlled by both the pilot injection andthe main injection due to the high reactivity of diesel. However, as in the study ofShi et al. (2010d), a rich mixture and a high ambient pressure are both important toignite gasoline and E10 within a reasonable time scale to avoid engine misfire.Under the mid-load condition of this study, the amount of the first injection gas-oline and E10 is not able to form locally a rich enough mixture. Therefore, it is thesecond injection that triggers the combustion and affects the subsequent emissionformation. It is also found that E10 needs a very early main injection timing as

240 6 Applications

Tab

le6.

25R

epre

sent

ativ

eop

tim

alde

sign

sfo

rth

em

id-l

oad

cond

itio

n

Die

sel

Gas

olin

eE

10

Cas

e1

Cas

e2

Cas

e3

Cas

e4

Cas

e1

Cas

e2

Cas

e3

Cas

e4

Cas

e1

Cas

e2

Cas

e3

Cas

e4

(a)

Des

ign

para

met

ers

SO

I 1(�

AT

DC

)-

70.0

-78

.0-

84.6

-64

.2-

70.0

-55

.2-

56.1

-79

.3-

70.0

-80

.0-

67.0

-78

.0P

ress

ure 1

(bar

)1,

150

699

578

1,35

21,

150

1,92

61,

798

1,87

31,

150

648

883

1,65

8F

irst

puls

e(%

)25

.031

.05.

06.

625

.049

.946

.90.

1725

.00.

524

.020

.9S

OI 2

(�A

TD

C)

-25

.06.

8-

10.7

-9.

3-

25.0

-8.

4-

7.7

-17

.5-

25.0

-33

.6-

33.8

-28

.9P

ress

ure 2

(bar

)1,

250

954

965

648

1,25

01,

238

974

1,11

31,

250

1,67

01,

783

1,16

6S

pray

angl

e(�

)72

.560

.476

.376

.672

.566

.066

.073

.772

.579

.773

.981

.0S

wir

lra

tio

1.0

0.4

1.6

1.8

1.0

0.7

0.5

1.7

1.0

1.5

0.7

0.0

Hol

enu

mbe

r9

107

89

610

119

87

8(b

)Si

mul

atio

nre

sult

sS

oot

(g/k

Wh)

0.05

50.

124

0.04

90.

046

0.00

60.

003

0.00

30.

000

0.00

00.

004

0.00

40.

006

NO

x(g

/kW

h)8.

491

0.36

81.

961

2.26

03.

583

0.51

50.

810

2.32

12.

432

0.16

90.

144

0.16

3U

HC

(g/k

Wh)

7.58

13.

876

1.14

61.

151

1.53

212

.33

2.33

94.

437

9.10

07.

630

4.70

36.

978

CO

(g/k

Wh)

11.6

09.

947

4.36

02.

836

4.51

612

.59

3.53

94.

422

4.03

87.

616

4.06

19.

051

GIS

FC

(g/k

Wh)

226.

122

3.6

187.

518

1.7

180.

621

8.5

183.

218

3.2

189.

720

6.6

200.

821

1.6

PP

RR

(bar

/CA

)30

.14

4.98

210

.42

8.17

969

.04

4.18

912

.49

29.4

230

.39

3.13

64.

208

2.09

9E

OI 1

(�C

A)

-66

.8-

72.8

-78

.9-

63.4

-66

.3-

49.5

-50

.6-

59.3

-66

.1-

79.0

-63

.5-

75.3

EO

I 2(�

CA

)-

15.7

16.6

2.8

6.8

-14

.4-

1.2

0.9

-5.

0-

13.9

-20

.8-

24.3

-16

.8C

A50

(AT

DC

)-

13.0

19.5

2.8

5.0

3.3

18.3

12.5

10.7

10.4

19.4

18.4

23.1


compared to gasoline due to its lower reactivity under the mid-load condition. Thisis also indicated by the averaged values in Table 6.26.

Since the amount of fuel in the first injection is critically important, its timingalso plays a role in diesel fuel performance. Retarding the first injection timingwith diesel reduces UHC and CO emissions, as well as GISFC and PPRR. Forgasoline and E10, a higher injection pressure of the main injection shortens theinjection duration with promoted premixed combustion, which is found to benefit

Table 6.26 Effect of individual design parameters on objectives for mid-load

(a) Diesel

Soot NOx UHC CO GISFC PPRR

0.116 1.582 2.716 10.22 206 8.58

SOI1 –68.0

Pressure1 1070

First pulse 0.102

SOI2 –2.66

Pressure2 982

Spray angle 73.0

Swirl ratio 1.39

Hole number 8.61

(b) Gasoline 0.00335 0.882 14.35 8.61 215.0 9.94

SOI1 –69.1

Pressure1 1260

First pulse 0.319

SOI2 –12.3

Pressure2 1280

Spray angle 70.6

Swirl ratio 1.47

Hole number 8.80

(c) E10 0.00578 0.6909 11.06 6.363 205.0 11.0

SOI1 –68.6

Pressure1 1120

First pulse 0.301

SOI2 –29.9

Pressure2 1520

Spray angle 77.2

Swirl ratio 0.83

Hole number 9.27

242 6 Applications

the reduction of soot, UHC, CO and GISFC. Spray included angle, swirl ratio, andthe number of nozzle holes have only a moderate influence on the objectives forthe different fuels. The regression analysis reveals that there are complex rela-tionships between the design parameters and engine performance and emissions.To gain insightful understandings about the causes of the influences, in-cylinderimage processing and parametric studies are used to further verify and investigatethe optimal designs.

Accordingly, in addition to the benchmark design, Case 1, three optimal designsfrom the Pareto solutions were reevaluated. They were chosen to further discussthe effects of primary design parameters on engine objective functions with eachfuel. The design parameters and simulation results of the selected optimal designsare shown in Table 6.25(a) and (b), respectively. In addition to the value of the 6objectives, Table 6.25(b) also lists the end-of-injection timings for the first andsecond injections, as well as the location of 50% accumulated heat release, CA50.

Results are visualized at four different representative timings during the enginecycle of each case in Fig. 6.53, 6.54, and 6.55 for the three fuels. The first image of

Fig. 6.53 In-cylinder images of representative diesel cases for mid-load. a Case 1. b Case 2.c Case 3. d Case 4. e Color bars


each case illustrates the contours of fuel mass fraction from 0 to 1% in a verticalcut-plane through the spray axis at the end of the first injection (EOI1). Thesecond image shows the fuel distribution (0–1%) at the time when 10% of the totalenergy is released (CA10). The third image visualizes temperature contours(1,000–2,500 K) on the cut-plane at CA50. The last image demonstrates the dis-tribution of CO mass fraction (0–1%) on the plane at CA90. The colored spheres inthe images represent spray droplets and their colors indicate the size distribution ofthe droplets from 0 to 100 lm diameter. In these images, blue (light) represents thelower boundary while red (dark) indicates the upper boundary. The superimposedarrows on the CA50 and CA90 images represent the directions of the bulk flow.

The regression analysis indicates that diesel combustion was most sensitive tothe amount of fuel injected in the first pulse. The reason is revealed by comparingCase 1 and Case 2 with Case 3 and Case 4 in Fig. 6.53. It is seen that a largeportion of the diesel fuel injected at early timings enters the crevice region inCases 1 and 2. The fuel resides in the crevice region and is released during theexpansion stroke. If the main combustion occurs before TDC (with higher like-lihood for diesel), the escaped fuel contributes to high UHC emissions and poorfuel economy. But if the combustion occurs late in the cycle, such as in Case 2with CA50 of 19.5 �ATDC, the escaped fuel can be oxidized further, as illustratedin the temperature distribution of Case 2 at CA50. This also explains why forgasoline and E10, a larger amount of fuel in the first injection does not necessarilylead to higher UHC emissions since they usually burn after TDC. If the firstinjection forms a combustible air-fuel mixture, the combustion phasing will belargely determined by its associated parameters, such as injection timing andpressure. For example, for cases with only a small amount of pilot fuel that is notable to trigger the ignition, the combustion characteristics are mainly determinedby the second injection, as for Cases 3 and 4 in Fig. 6.53.

Within a proper window of injection timings, a spray with included angle ofaround 75� results in a stagnation-point flow field in the combustion chamber, asindicated by the flow direction for Cases 1, 2, and 4 at CA50 for diesel inFig. 6.53. This benefits air-fuel mixing as the air in both squish and bowl regionsare better utilized, which is also consistent with the regression analysis. So, thelocation of CO formation and soot formation (not shown here) for these cases isclose to the stagnation point. The centrifugal effect of the swirling flow furtherconfines the stagnation flow. With a higher swirl ratio as for Case 4, the location ofCO and soot formation is closer to the piston bowl outer wall. For small sprayincluded angles, the air motion due to the spray jet is guided by the combustionchamber walls, as shown in Case 2 at CA50, which results in more CO and sootbeing directed into the squish region as it is not co-located with the high tem-perature region of the bowl.

Most of the optimal solutions of the gasoline and E10 cases had a relativelylarge amount of fuel in the first injection. The reason is that a locally rich mixtureis needed in order to ignite those two fuels. This is confirmed by observing thatmost cases start combustion in the region at the piston bowl edge and the squishregion where the first injection fuel and the second injection fuel overlap, as seen

244 6 Applications

in Figs. 6.54 and 6.55. Therefore, together with the regression analysis, the secondinjection timing is found to be the most influential parameter for gasoline-likefuels under the mid-load condition. According to the fuel distribution at CA10,most of the fuel is prepared (mixed) prior to combustion for gasoline and E10, andthe mixing level increases as the fuel reactivity decreases. Retarding the secondinjection timing results in higher UHC and CO emissions, as well as fuel con-sumption, but on the contrary, this benefits NOx reduction and also lowers PPRR.As a result of the premixed combustion, no stagnation-point flow field is foundin the studied cases at CA50. It is seen that the flow directions are primarilydetermined by the location of the highest volumetric heat release during thecombustion. At CA90, CO is distributed more widely for the gasoline and E10cases as compared to diesel. This favors CO oxidation with the ambient oxygen.The higher UHC emissions of gasoline and E10 are mainly attributed to their latercombustion phasing.

Overall, by filtering the optimal solutions with criteria, practical engine optimaldesigns are summarized in Table 6.27 for each fuel at mid-load in order to providedesign guidance. The diesel engine requires both late first (*-55 �ATDC) and

Fig. 6.54 In-cylinder images of representative gasoline cases for mid-load. a Case 1. b Case 2.c Case 3. d Case 4. e Color bars


second injection (*9 �ATDC) timings. In addition, the amount of fuel injected inthe first pulse should be limited below 10%. The preferred nozzle numbers arefrom 8 to 10 with narrow injection angles from 60� to 70�. For gasoline and E10,up to 50% first injected fuel is seen in the practical cases. The first injectiontimings of gasoline-like fuels are about 10� earlier (*-65 �ATDC) than thoseof diesel, and the second injection timings are about 20 (*-10 �ATDC) to 30(*-20 �ATDC) degree earlier. The number of holes for gasoline-like fuelsspreads widely in the studied range, i.e., from 6 to 12, and the injection angles arefrom 65� to 75�. Injection pressures and swirl ratios for these cases depend on thecombinations of the other design variables, which are distributed widely for allthree fuels.

An optimization study at high-load was also conducted following the sameprocedure as that used for the mid-load condition described previously. Thesimulations were again terminated at the 25th generation, based on the conver-gence metric shown in Fig. 6.56a.

Fig. 6.55 In-cylinder images of representative E10 cases for mid-load. a Case 1. b Case 2.c Case 3. d Case 4. e Color bars

246 6 Applications

Tab

le6.

27P

ract

ical

opti

mal

desi

gns

atm

id-l

oad

No.

Soo

tN

Ox

UH

CC

OG

ISF

CP

PR

RS

OI 1

Pre

1In

j%S

OI 2

Pre

2A

ngle

Sw

irl

Hol

e

(a)

Die

sel

(Soo

t<

0.06

8g/

kWh,

NO

x<

1.35

g/kW

h,P

PR

R<

10ba

r/C

A)

10.

050.

857.

6031

.77

250.

194.

30-

55.0

273

8.57

68.

921,

415.

068

.21

0.01

102

0.04

0.61

6.89

13.3

525

2.76

2.35

-65

.83

1,59

8.2

38.

961,

165.

160

.08

1.97

103

0.02

0.68

12.0

022

.93

275.

472.

36-

55.1

773

8.57

68.

921,

415.

068

.43

0.00

84

0.04

1.03

8.90

22.6

223

4.14

5.96

-55

.03

738.

576

8.92

1,41

5.0

68.4

31.

7610

50.

050.

935.

3125

.41

233.

4510

.11

-55

.17

1,52

5.6

68.

451,

415.

768

.42

0.00

9(b

)G

asol

ine

(Soo

t<

0.01

36g/

kWh,

NO

x<

1.35

g/kW

h,G

ISF

C<

210

g/kW

h,P

PR

R<

10ba

r/C

A)

10.

040.

3013

.77

13.3

319

7.39

4.90

-64

.75

351.

7849

-11

.55

1,43

1.8

72.6

61.

6612

20.

000.

9526

.34

11.1

720

5.26

9.20

-84

.54

825.

1846

-15

.69

1,65

0.6

74.6

11.

5010

30.

001.

0224

.68

11.4

420

6.84

9.29

-71

.07

1,39

5.4

49-

6.75

776.

9476

.21

1.00

114

0.00

1.06

19.9

213

.48

208.

246.

73-

70.1

71,

720.

443

-7.

441,

660.

664

.71

1.51

65

0.01

0.95

4.14

6.57

185.

029.

22-

56.5

11,

933.

147

-7.

7075

6.31

66.2

40.

5210

60.

000.

934.

326.

7418

5.70

7.51

-56

.51

1,93

3.1

47-

7.62

767.

3766

.41

0.52

107

0.01

0.95

7.94

7.79

207.

722.

34-

84.7

81,

949.

113

-16

.29

805.

6866

.38

0.53

7(c

)E

10(S

oot

<0.

0136

g/kW

h,N

Ox

<0.

27g/

kWh,

GIS

FC

<21

0g/

kWh,

PP

RR

<10

bar/

CA

)1

0.01

0.20

12.0

37.

9820

4.38

3.71

-68

.30

865.

0345

-34

.57

1,71

2.8

73.3

00.

728

20.

010.

1910

.88

10.3

720

0.99

5.00

-68

.24

1,17

3.0

49-

34.2

01,

409.

577

.57

0.06

103

0.00

0.20

7.76

7.80

199.

774.

62-

57.6

91,

180.

250

-17

.04

1,75

2.1

71.9

01.

6111

40.

010.

257.

545.

0318

9.70

8.38

-57

.29

854.

1634

-34

.97

1,75

2.1

71.5

01.

608


Similar to the mid-load case, it is seen in Fig. 6.56b that the optimal designswith diesel fuel show a trade-off between the soot and NOx emissions. Differentfrom the mid-load condition, some of the optimal designs for gasoline and E10produce high soot emissions that are comparable to the diesel fuel case. However,designs with simultaneously reduced soot and NOx are still found in Fig. 6.56b forgasoline and E10. As illustrated in Fig. 6.56c, the combustion completeness isrepresented by the higher CO emissions compared to the UHC for all three fuelsdifferent from the mid-load condition discussed previously. The high octanegasoline and E10 fuels have good fuel economy at high-load, as seen in Fig. 6.56cby the lower CO emissions and in Fig. 6.56d by the lower GISFC. However, thetrade-off between GISFC and PPRR becomes more problematic for the high-loadengine with gasoline and E10. None of the optimal diesel fuel designs was foundto have soot and NMHC emissions lower than the EPA 2010 regulations. About35% of the optimal designs had NOx levels below the limit, but they were alsoaccompanied with very high GISFC. For gasoline, only a few designs had bothsoot and NOx emissions lower than the regulated values. For E10, several optimaldesigns with soot emissions slightly higher than the regulated limit were seen and

Fig. 6.56 Convergence metric and Pareto solutions for high-load. a Convergence metric.b Pareto solutions (Soot and NOx). c Pareto solutions (UHC and CO). d Pareto solutions (GISFCand PPRR)

248 6 Applications

about 30% optimal designs had NOx emissions below the regulation. It should benoted that for gasoline and E10, low NOx does not necessarily indicate highGISFC, as in the case of diesel. However, the low NMHC emission regulation isstill not reachable with gasoline and E10 under the high-load condition.

Following the same convention as for the mid-load case, the influence of thedesign parameters on engine performance and emissions are listed in Table 6.28.The average values of CO and GISFC of all Pareto solutions confirm that theengine operating under high-load has better fuel economy with gasoline and E10than diesel although the engine noise level indicated by the PPRR is higher. This isprimarily due to the better mixing characteristics of the gasoline and E10 spraysbecause the air-fuel mixing process becomes more important as the engine loadincreases. However, for gasoline and E10, air-fuel mixing related parameters arenot as important as they are for diesel. For diesel, the fuel amount in the firstinjection is no longer the sole dominant parameter. As seen in Table 6.28(a), moreparameters, including the second injection timing, pressure, swirl ratio, and thenumber of holes that influence the air-fuel mixing process play more importantroles. This again confirms that focus needs to be placed on improving spray mixingat high-load. The second injection timing is found to be still critically significantfor gasoline and E10. In addition, the second injection pressure becomes moreimportant at high-load with gasoline, while E10 is more sensitive to the sprayincluded angle.

Again, four individual cases, including the benchmark case were selected for eachfuel and the design parameters and the corresponding results are given inTable 6.29(a) and (b), respectively. The regression analysis showed different effectsof each design parameter on engine performance and emissions, compared to at mid-load. The same as the mid-load cases, cases at four representative timings during theengine cycle were chosen to visualize the in-cylinder flow fields (the fuel massfraction range was increased to 2% and that of CO was changed to 3%).

Early injection of the diesel fuel pilot spray results in wall fuel films whicheventually enter the crevice region and are directly correlated with the UHCemissions. This was also previously found in the mid-load cases. Retarded maininjection is needed to prevent the engine from violating the peak pressure andPPRR constraints (20 MPa and 30 bar/CA, respectively). However, this deterio-rates fuel economy as the time allowed for air-fuel mixing shortens. Therefore,enhanced mixing is needed at high-load, as also pointed out in the regressionanalysis. Case 2 in Fig. 6.57 has 10 nozzle holes with the smallest hole area of thefour cases studied. Since the spray penetration scales linearly with the hole area(Shi and Reitz 2008c), Case 2 has the shortest spray penetration, although it alsohas the highest injection pressure (tip penetration scales as the � power). Thesmaller hole size produces smaller droplets downstream of the nozzle, as seen inFig. 6.57b at CA10, and consequently the fuel spray evaporates faster. Hence,decreasing nozzle size (increasing the number of holes) reduces soot, UHC, COemissions with improved fuel economy, as shown in Table 6.28(a). Comparedwith the mid-load results, a significant amount of CO is formed under the high-load condition, and the CO is distributed along the combustion chamber walls and


in the squish region. This highlights the importance of swirl for this operatingcondition. As in the mid-load cases, the flow patterns at CA50 again are found tobe driven by the spray injection in the CI engine with diesel fuel.

Table 6.28 Effect of individual design parameters on objectives for high-load

(a) Diesel

Soot NOx UHC CO GISFC PPRR

0.4473 0.4697 8.96 33.6 255 4.21

SOI1 –72.9

Pressure1 898

First pulse 0.14

SOI2 2.15

Pressure2 932

Spray angle 76.9

Swirl ratio 1.27

Hole number 8.06

(b) Gasoline

0.1876 0.5201 5.81 16.24 223 9.77

SOI1 –69.4

Pressure1 862

First pulse 0.264

SOI2 –1.03

Pressure2 1450

Spray angle 69.8

Swirl ratio 1.13

Hole number 8.53

(c) E10

0.217 0.4312 6.93 20.398 230.73 8.12

SOI1 –64.0

Pressure1 1039

First pulse 0.344

SOI2 2.58

Pressure2 1194

Spray angle 69.0

Swirl ratio 1.16

Hole number 8.46

250 6 Applications

Tab

le6.

29R

epre

sent

ativ

eop

tim

alde

sign

sfo

rth

ehi

gh-l

oad

cond

itio

n

Die

sel

Gas

olin

eE

10

Cas

e1

Cas

e2

Cas

e3

Cas

e4

Cas

e1

Cas

e2

Cas

e3

Cas

e4

Cas

e1

Cas

e2

Cas

e3

Cas

e4

(a)

Des

ign

para

met

ers

SO

I 1(�

AT

DC

)-

70.0

-65

.1-

75.4

-74

.2-

70.0

-62

.4-

71.3

-70

.8-

70.0

-66

.3-

58.1

-67

.1P

ress

ure 1

(bar

)1,

150

1,18

91,

866

1,52

31,

150

888

1,08

834

51,

150

744

1,17

01,

697

Fir

stpu

lse

(%)

25.0

13.2

23.0

19.1

25.0

8.5

15.3

23.6

25.0

31.6

37.1

37.0

SO

I 2(�

AT

DC

)-

25.0

1.5

-8.

85.

3-

25.0

-9.

7-

8.8

-3.

4-

25.0

-1.

51.

23.

3P

ress

ure 2

(bar

)1,

250

1,85

01,

301

1,11

91,

250

1,58

81,

891

1,88

31,

250

997

1,61

61,

748

Spr

ayan

gle

(�)

72.5

61.1

78.5

82.6

72.5

70.7

60.0

79.2

72.5

67.5

73.0

68.5

Sw

irl

rati

o1.

01.

71.

91.

61.

01.

60.

61.

51.

01.

21.

30.

9H

ole

num

ber

910

86

911

67

99

611

(b)

Sim

ulat

ion

resu

lts

Soo

t(g

/kW

h)0.

104

0.18

30.

120

0.27

70.

006

0.03

40.

032

0.06

30.

013

0.06

00.

060

0.10

7N

Ox

(g/k

Wh)

3.50

60.

375

1.77

30.

264

3.36

90.

988

0.64

80.

830

2.76

90.

411

0.52

30.

735

UH

C(g

/kW

h)12

.17

4.26

55.

051

9.39

40.

109

1.77

14.

309

4.09

20.

321

3.29

66.

081

3.09

6C

O(g

/kW

h)17

.96

24.3

98.

190

20.1

11.

185

27.0

97.

042

8.29

53.

611

7.00

76.

181

12.3

2G

ISF

C(g

/kW

h)22

7.5

227.

820

1.2

246.

819

0.3

206.

921

2.2

205.

919

1.0

215.

321

5.2

200.

9P

PR

R(b

ar/C

A)

27.3

84.

454

10.1

13.

706

174.

429

.011

.127

.015

9.0

8.06

017

.22

8.33

3E

OI 1

(�C

A)

-63

.5-

61.8

-70

.8-

69.9

-62

.6-

59.5

-66

.7-

58.0

-62

.3-

54.1

-46

.7-

57.6

EO

I 2(�

CA

)-

6.4

19.2

9.9

26.5

-3.

713

.310

.714

.3-

2.7

21.2

17.7

19.1

CA

50(�

AT

DC

)-

10.1

18.2

6.2

24.1

-0.

718

.918

.915

.13.

322

.816

.713

.5


For the high-load condition with high in-cylinder pressure and global equiva-lence ratio, auto-ignition is no longer a problem for both gasoline and E10. This isreflected by the location of the high temperature region at CA50 in Figs. 6.58 and6.59, which is not necessary to be the overlapping region of the first and secondspray plumes. Examination of all optimal solutions of the gasoline and E10 casesreveals that the second injection timing is around TDC for most cases, which isvery different from the mid-load cases. This is most likely driven by therequirement of meeting the peak pressure constraint of 20 MPa in the optimizationprocess. The larger area over which fuel is distributed at CA10 for gasoline andE10 signify the larger proportion of premixed combustion as compared to thediesel fuel case. But the difference at high-load is less than that for the mid-loadcase, as seen in Figs. 6.53, 6.54, and 6.55. This is obviously due to the late maininjection timing under this operating condition and also the longer injectionduration. However, optimal designs with low soot emissions are still found forgasoline and E10. Different from the diesel cases, the sensitivity of the gasolineand E10 cases to the main injection pressure is primarily through the injection

Fig. 6.57 In-cylinder images of representative diesel cases for high-load. a Case 1. b Case 2.c Case 3. d Case 4. e Color bars

252 6 Applications

parameters. In the optimization study, the total nozzle area was fixed, and thusincreasing injection pressure is equivalent to decreasing the injection duration,which increases the time for air-fuel mixing.

Distinguished from the mid-load cases where E10 required much earlier maininjection timing than gasoline, the main SOI of E10 for the high-load condition isslightly later than gasoline in general, as also shown by the averaged values inTable 6.28. Since auto-ignition of both E10 and gasoline is not an issue for thehigh-load condition, the main consideration in the GA evolutionary process of theoptimization study is meeting the constraints. Too-well-premixed air-fuel charge(CA50-EOI2 [ 5 �CA) and too early combustion phasing (CA50 \ 15 �ATDC)results in unacceptably high pressure rise rates. This trend can also be observedfrom Cases 1, 2, and 4 of gasoline and Cases 1 and 3 of E10 in Table 6.29 (b).Under the high-load condition the reactivity of E10 is slightly lower than gasoline,which allows for more time for the mixing processes. Therefore, it is necessary toretard the combustion phasing later than for gasoline in order to achieve similarPPRR levels. This also explains why, in general, E10 has lower fuel efficiency thangasoline.

Fig. 6.58 In-cylinder images of representative gasoline cases for high-load. a Case 1. b Case 2.c Case 3. d Case 4. e Color bars


Both spray-driven stagnation-point flow patterns and volumetric-heat-release-driven flow patterns are seen in Figs. 6.58 and 6.59. Due to the late CA50 of E10,the spray included angle and swirl ratio play more important roles than for gas-oline. As can be seen in Fig. 6.59, larger spray included angles ensure betterutilization of ambient air in both the piston bowl and squish regions and thusenhance combustion. However, smaller spray included angles help to slow downthe combustion and to lower PPRR levels, even though this sacrifices oxidation ofsoot, UHC and CO, as illustrated in Table 6.28(c). Spray targeting and the flowpatterns during the combustion profoundly influence the distribution of COand soot during the late engine cycle, as represented by the CO mass fractions inFig. 6.57, 6.58, and 6.59.

Again, practical engine optimal designs are summarized in Table 6.30 for eachfuel at high-load in order to facilitate engine design. For the diesel fuel, the firstinjection amount should be limited below 20%. The first injection timingsare from *-65 �ATDC to *-85 �ATDC, and the main injections rangefrom *-10 �ATDC to *0 �ATDC. High swirl level is required, which is seen to

Fig. 6.59 In-cylinder images of representative E10 cases for high-load a Case 1. b Case 2.c Case 3. d Case 4. e Color bars

254 6 Applications

be above 1.5 for many cases. Nozzle hole numbers range from 6 to 10 with wideinjection angles from *70� to *80�. For gasoline-like fuels, the first injectionamounts are between 30 and 40%, and the first injections are located between*-65 �ATDC and *-80 �ATDC. The swirl ratio is close to 1 for most cases.Nozzle hole numbers are from 8 to 11 with large injection angles from *70�to *80�. Similar to the mid-load cases, the injection pressure varies over a largerange for all three fuels, depending on other design variables.

The above optimization results indicate that it is possible to run a CI heavy-dutyengine with gasoline-like fuels and to achieve cleaner and more efficient com-bustion than with diesel-like fuels under mid- and high-load conditions. In addi-tion, it is noted that compared to GDI engines CI engines fueled with gasoline-likefuels have higher compression ratio, thus better thermal efficiency.

The combustion mode of gasoline-like fuels under the mid-load condition isPartially Premixed Combustion (PPC), which is advantageous over either HCCI orconventional diffusion combustion modes with diesel-like fuels. For the pureHCCI mode, control of the onset of auto-ignition is problematic. As seen in theoptimization study, the second injection timing with gasoline-like fuels at the mid-load condition provides a mechanism to control engine combustion. The highvolatility and low ignitability of gasoline-like fuels promote air-fuel mixing andallows a longer mixing time and late but still reasonable combustion phasing,which is essential for low soot and NOx emissions and high efficiency. However,this is hardly achievable for diesel-like fuels. The premixed combustion mode withdiesel fuel results in high UHC and CO emissions due to the fact that the earlyinjection leads to wall-wetting while the late injection has poor air-fuel mixing andcombustion efficiency, such as seen in PCCI combustion (Opat et al. 2007) andMK-type combustion (Kimura et al. 1999, 2001), respectively. In addition, con-ventional diesel diffusion combustion exhibits the well-known trade-off relation-ship between soot and NOx emissions, as also shown in the previous optimizationstudies of this chapter.

For the mid-load case, it was also found that both the fuel physical (e.g., vola-tility) and chemical (e.g., ignitability) properties are important. But the chemicalproperties are more influential, as seen in the comparison of gasoline and E10 cases.E10 has different preferred optimal injection variables than gasoline, especially thesecond injection timing. Furthermore, the higher octane number E10 more likelyfeatures unacceptably high pressure rise rates than gasoline and diesel. This sug-gests that lower octane number gasoline-like fuels (e.g., PRF80) may be better, ormore injection pulses may be needed. Nevertheless, the high volatility of gasoline-like fuels is very beneficial to achieve clean and efficient CI engine combustion,which indicates that the volatility requirement of fuels will most likely increase infuture, as discussed by Kalghatgi et al. (2007). Although, the optimal octanenumber of gasoline-like fuels in CI engines should be emphasized in future.

Compared to the mid-load condition, the high-load condition was found to beless sensitive to fuel reactivity. The second injection timings of optimal solutionswere all close to TDC with the different fuels. However, mixing-related parame-ters, such as injection pressure and swirl strength were found to be more important


Tab

le6.

30P

ract

ical

opti

mal

desi

gns

athi

gh-l

oad

No.

Soo

tN

Ox

UH

CC

OG

ISF

CP

PR

RS

OI 1

Pre

1In

j%S

OI 2

Pre

2A

ngle

Sw

irl

Hol

e

(a)

Die

sel

(Soo

t<

0.27

2g/

kWh,

NO

x<

1.35

g/kW

h,G

ISF

C<

220

g/kW

h,P

PR

R<

10ba

r/C

A)

10.

240.

833.

3426

.87

218.

865.

89-

75.4

31,

890.

81

-7.

361,

306.

273

.64

0.68

62

0.22

1.33

2.89

19.6

720

2.31

5.43

-63

.06

930.

538

-8.

4193

6.47

79.1

41.

596

30.

261.

093.

6124

.76

208.

083.

76-

83.2

71,

594.

57

-7.

3587

6.15

82.4

31.

197

40.

260.

783.

1028

.07

217.

607.

51-

68.1

236

4.73

10.

961,

794.

680

.89

1.77

105

0.20

1.03

4.51

10.3

320

7.70

3.89

-55

.81

305.

4720

-3.

2792

4.59

79.9

91.

607

60.

211.

211.

9519

.15

204.

614.

28-

83.0

91,

625.

65

-6.

601,

013.

781

.31

1.84

77

0.27

0.88

3.92

22.6

121

0.43

3.35

-68

.29

520.

238

-5.

1492

6.46

82.6

61.

188

80.

270.

634.

5423

.69

219.

943.

64-

82.2

71,

505.

510

4.11

1,56

3.0

82.0

61.

229

90.

230.

902.

5124

.92

213.

289.

53-

59.1

533

3.63

52.

131,

983.

879

.41

1.92

1010

0.24

1.11

9.57

15.5

921

2.05

3.60

-80

.35

1,32

8.6

25-

3.75

978.

7682

.61

1.57

711

0.24

0.89

2.18

16.7

421

0.96

3.61

-71

.12

834.

361

-5.

061,

085.

782

.39

1.45

8(b

)G

asol

ine

(Soo

t<

0.27

2g/

kWh,

NO

x<

1.35

g/kW

h,G

ISF

C<

210

g/kW

h,P

PR

R<

10ba

r/C

A)

10.

220.

9212

.81

17.5

020

9.12

5.06

-76

.19

1,00

4.3

343.

231,

543.

476

.34

1.75

82

0.25

0.72

6.98

17.6

420

7.87

7.88

-78

.39

1,17

6.2

346.

511,

543.

476

.27

0.96

113

0.26

1.16

5.38

23.4

820

0.50

5.61

-81

.86

1,17

5.2

340.

541,

543.

278

.39

0.96

104

0.21

0.72

5.25

22.3

520

2.42

6.85

-75

.59

819.

0234

-0.

681,

396.

160

.06

1.02

95

0.16

1.07

5.29

14.5

520

2.55

8.88

-76

.43

318.

4634

5.30

1,90

4.9

73.6

31.

2611

60.

230.

884.

5116

.75

201.

465.

76-

71.3

599

7.99

352.

071,

860.

273

.62

0.73

87

0.24

0.74

5.05

19.2

620

2.75

9.80

-72

.54

1,36

5.7

344.

931,

395.

778

.39

0.96

118

0.16

1.08

4.28

13.7

520

0.42

8.39

-75

.60

302.

9436

5.30

1,90

4.8

73.3

71.

2611

90.

200.

945.

1316

.16

205.

417.

43-

70.7

753

1.85

315.

181,

896.

874

.50

1.57

9(c

)E

10(S

oot

<0.

272

g/kW

h,N

Ox

<1.

35g/

kWh,

GIS

FC

<21

0g/

kWh,

PP

RR

<10

bar/

CA

)1

0.19

1.23

4.11

23.3

820

1.36

9.11

-57

.93

1,17

1.4

343.

231,

543.

472

.61

0.81

112

0.23

1.17

5.22

27.1

520

3.50

7.24

-66

.19

1,60

1.6

343.

301,

615.

872

.52

0.80

113

0.22

0.69

8.05

28.2

820

9.33

9.78

-69

.01

1,33

7.4

403.

081,

550.

063

.03

0.86

10

(con

tinu

ed)

256 6 Applications

Tab

le6.

30(c

onti

nued

)

No.

Soo

tN

Ox

UH

CC

OG

ISF

CP

PR

RS

OI 1

Pre

1In

j%S

OI 2

Pre

2A

ngle

Sw

irl

Hol

e

40.

150.

625.

1317

.72

209.

509.

72-

55.2

81,

202.

335

6.25

1,62

3.3

62.9

60.

899

50.

151.

155.

0111

.90

202.

928.

42-

64.8

684

2.69

373.

511,

622.

278

.24

1.03

116

0.19

1.02

3.17

17.6

420

2.78

7.39

-55

.38

1,13

4.0

343.

191,

416.

979

.29

0.87

117

0.12

1.29

4.20

14.9

219

8.53

9.61

-62

.82

1,10

3.2

393.

061,

610.

769

.99

0.38

11


for the high-load cases. It is noted that due to the long injection duration,diffusion combustion was not avoidable for all three fuels investigated at high-load. Also, considering the maximum pressure and peak pressure rise rateconstraints, the degree of premixed combustion should be limited. At high-load,the size of the nozzle holes and the injection pressure were found more influ-ential than for the mid-load case. The total area of the nozzle holes was fixed inthe present study, so the injection duration was only a function of injectionpressure. But the optimization study suggests that increasing the total nozzle holearea may be helpful for gasoline-like fuels since reduced injection duration wasfound to be beneficial.

Although optimization of a low-load condition was not conducted, generalguidance is offered from the results of the present study. Igniting gasoline-likefuels at low-load is difficult considering the low ignitability of lean mixtures.Therefore, the use of HCCI with advanced engine thermal management system(such as fuel reformation in the Negative Valve Overlap (NVO) period (Hirayaet al. 2002; Cao et al. 2008)) may be necessary to extend the operating limit tolow-load for a CI engine fueled with gasoline-like fuels. Also, the use of dual-fuelas proposed by Kokjohn et al. (2009) could extend the operating limit of gasolineCI engines. Finally, it should be pointed out that the high volatility of gasoline-likefuels is helpful for an HCCI engine in order to better prepare a fully premixedcharge.

6.2.1.5 Summary

This example presents a comprehensive optimization study of a heavy-duty CIengine operated under mid- and high-load conditions and fueled with diesel,gasoline, and E10. The focus was optimization of injection system parameters,including pilot and main injection timings, pressures, and amounts. Concludingremarks are as follows.

• Due to the large amount of individual engine CFD evaluations that are requiredfor optimization with detailed fuel chemistry, an efficient chemistry solver wasnecessary and was successfully applied in the research.

• Gasoline-like fuels exhibit great potential for cleaner combustion than withconventional diesel fuel. For the mid-load condition, the ignitability of gasoline-like fuels significantly influences the specification of the injection-related designparameters for engine performance and emissions. As a result, the engine perfor-mance with gasoline-like fuels is greatly affected by the second injection timing,while for the diesel fuel the first injection amount was found to be critical. For thehigh-load condition, mixing-related parameters dominate the family of optimaldesigns as the ignitability is no longer a major factor, and injection pressure, swirl,and nozzle designs are more influential. Consequently, higher injection pressure,swirl ratio and smaller nozzle holes that promote air-fuel mixing are desirable butthey are also subject to requirements of meeting the constraints.

258 6 Applications

• Different in-cylinder flow patterns were identified in the optimal engine designswith the different fuels. For example, due to the diffusion combustion, the dieselfuel exhibits stagnation-point flow fields in many optimal cases, while gasoline-like fuels show more volumetric-heat-release-driven flows due to the premixedcombustion. The results of the optimization study also indicate that lower octanenumber gasoline-like fuels may be more helpful to improve the controllability ofCI engines in PPC mode and reduce engine noise.

6.3 Strategies for Simultaneous Optimization of MultipleEngine Operating Conditions

It was found that different engine loads favor different nozzle design and piston bowlshapes. For instance, high load favors an injector with less nozzle holes, while lowload favors an injector with more nozzle holes (Ge et al. 2009a, b). Clearly, only oneuniform set of designs for the nozzle and piston bowl shape can be delivered to aproduction department. Thus, it raises a question: how can we use the state-of-the-artCFD tools to directly suggest an optimal design for engine production? This sectiondiscusses methodologies of simultaneous optimization for multiple operating con-ditions. Two methods, which are proposed by the authors, will be discussed. Both ofthem classify the design parameters into two categories: hardware design parametersand controllable design parameters. The controllable parameters indicate parametersthat can be changed during run-time, while hardware parameters cannot.

6.3.1 A Two-Step Method for Simultaneous Optimizationof Multiple Operating Conditions

The first method is based on optimization of full-load cases. The whole optimi-zation procedure is then divided into two steps:

1. determine the optimal design for the hardware parameters;2. determine the controllable parameters for each considered operating condition

with the optimal hardware design from Step 1.

The idea is illustrated in Fig. 6.60. Optimizations at different loads will give diff-erent sets of optimal hardware parameters. The first problem that needs to be addressedis to indicate at which engine load the hardware parameters should be optimized.Single case optimizations showed that full load is the most representative case (Shi andReitz 2008b; Ge et al. 2009b). Therefore, the hardware parameters were optimized atfull-load operating conditions. The controllable parameters were then optimized withthe optimal set of hardware parameters for each considered operating condition. In thepresent work, the hardware parameters include nozzle design and piston bowl shape,and the controllable parameters include SOI, swirl, boost pressure, and injectionpressure. Due to the large number of design parameters and optimization iterations in


Step 1, simplified combustion models—CTC model and shell model–were used. Themore accurate chemistry solver with the AMC model was used in Step 2.

As with the optimization in Sect. 6.1.4, the bowl shape was characterized usingeleven parameters. Computational meshes were automatically generated using theKwickgrid methodology. The present method was practiced on the same engine asthe one in Sect. 6.1.4. The engine specifications are listed in Table 6.20. Twofull-load operating conditions were considered in Step 1. Four other operatingconditions, including two mid-load cases and two low-load cases, were taken intoaccount in the second stage optimization.

6.3.1.1 Optimization of Hardware Parameters Under Full-LoadOperating Conditions

Hardware parameters, including spray angle, number of nozzle holes, and pistonbowl design, were optimized together with swirl ratio and SOI under full-loadoperating conditions. Two full-load cases, Case A and Case B, were considered.The specific operating conditions are listed in Table 6.31. Engine operation underthese two modes was optimized separately and Table 6.32 lists the search space ofthe present optimization.

Since 15 design parameters were considered in these two optimizations, manygenerations are needed for the optimization to achieve convergence. Thus, sim-plified combustion models are preferred at this stage. The CTC model and theShell model have been proven to be reliable for conventional diesel combustionunder full-load conditions (Ge et al. 2009b). The same methodologies as used by

Fig. 6.60 Flowchart of multi-mode optimization

260 6 Applications

Ge et al. (2009b) were used in this section. The optimizations were stopped at the72nd generation, which resulted in about 2,300 valid designs for each case.

Figure 6.61 shows all citizens from the optimization of Cases A and B, as well asthe baseline designs. Pareto designs are indicated by blue triangles. Six designs, whichare indicated by arrows in Fig. 6.61, were selected from these Pareto designs andvalidated using the KIVA-CHEMKIN model. The piston shapes of these optimaldesigns were illustrated in Fig. 6.62. SOI sweeps of these six designs as well as thebaseline design were made for both Case A and B. GISFC and engine-out emissionsresults are shown in Fig. 6.63. It can be seen that Designs II and IV show goodperformance in both fuel consumption and engine-out emissions. Especially, DesignIV simultaneously reduces fuel consumption and pollutant emissions for both full-loadcases. Comparison of the performance of the baseline engine and Design IV is shownin Table 6.33. Significant improvements over the baseline engine were achieved forthe two full-load cases, with about 10% reduction in NOx emission, about 50%reduction in soot emission, and 1 * 5% improvement in fuel consumption. Thus, thehardware designs of Design IV was selected as the optimal hardware design and usedfor further optimization. Note that the results computed using the KIVA-CHEMKINmodel are slightly different from the ones computed using the CTC model. Therefore,the results in Fig. 6.61 are a little different from the data in Fig. 6.63 and Table 6.33.

6.3.1.2 Optimization of Controllable Parameters for All OperatingConditions

The above optimization of the two full-load cases eventually suggested an optimalhardware design, including the nozzle design and piston bowl shape. In thissection, controllable parameters, including SOI, swirl ratio, boost pressure, and

Table 6.31 Full-loadoperating conditions

Case A Case B

Speed (rev/min) 4,000 2,000IMEP (bar) 18.0 22.7Fuel injected (kg/h) 6.7 3.8SOI (�ATDC) -16.04 -7DOI (�) 42.4 28.5

Table 6.32 Optimization search space

Parameter Min. Max. Parameter Min. Max.

Spray angle (�) 140 160 Cz 0.60 0.5Nozzle hole number 5 12 Dx 0.45 0.70Swirl ratio 0.5 2.5 Xab 0.1 0.7SOI (�ATDC), Case A -20 -5 Xba 0.3 0.9SOI (�ATDC), Case B -25 10 Xbc 0.5 3.5Az 0.5 0.8 Xcb 0.5 3.5Bx 0.8 1.0 Ycb 0.3 0.9Cx 0.45 0.65 Ycd 0.3 0.9

6.3 Strategies for Simultaneous Optimization of Multiple Engine Operating Conditions 261

injection pressure, were optimized for each considered case. Since only 4 parameterswere considered in these optimizations, advanced combustion models could be usedfor more accurate prediction. Especially, the part-load cases are more kinetics-controlled and therefore use of a detailed reaction mechanism greatly improves the

Fig. 6.62 Piston bowl shapes of Designs I-VI: from left to right, from top to bottom

Fig. 6.61 All citizens and Pareto solutions from the optimization, and the baseline design forCase A (top) and B (bottom). Arrows indicated are the selected optimal designs

262 6 Applications

accuracy of the predictions (Ge et al. 2010a). Thus, instead of the CTC and Shellmodels, the AMC model (Shi et al. 2009b) with the ERC n-heptane mechanism (Patelet al. 2004) was used in the optimizations in this section. Other models are the same asthe ones in the previous section. The AMC model for optimization has been validatedin detail for the same baseline engine in a previous study (Ge et al. 2010b).

Fig. 6.63 SOI sweeps of the baseline design and selected optimal designs for Case A (left) and B(right)


The two full-load cases, Cases A and B, were optimized at first. Only GISFC wasconsidered as an objective.2 Performance and design parameters of Design IV andoptimal designs A1 and B1 are compared in Table 6.34. It can be seen that more than1% additional improvement in fuel consumption can be achieved by optimizingthe controllable design parameters. Note that the GISFC in Table 6.34 is based onthe computation using the AMC model, and therefore it is slightly different from thevalue in Table 6.33 which was computed using the KIVA-CHEMKIN model.

The same method was extended to optimize the controllable parameters for a newCase C. Case C represents a medium-load case whose engine speed is 2,400 rev/minand IMEP is about 15 bar. Objectives in this case include GISFC, NOx and sootemissions. Figure 6.64 shows all citizens and Pareto solutions from the optimization,and the baseline design. All data is based on computations using the AMC model.Selected optimal designs, which simultaneously reduce fuel consumption and pol-lutant emissions, as well as the baseline design are listed in Table 6.35. Optimaldesign C1 represents the best fuel consumption design which has 5% improvement inGISFC compared to the baseline design. Optimal design C2 has good NOx reductionwith acceptable fuel consumption and soot emission: 46% reduction in NOx emis-sion is achieved in Design C2. While optimal design C3 represents the lowest sootdesign, with 26% reduction in soot emission.

Case D is a medium-load case whose engine speed is 2,280 rev/min and IMEPis about 9 bar. The optimization objectives were set to GISFC, soot and NOxemissions. Figure 6.65 shows all citizens and Pareto solutions from the optimization,and the baseline design. Selected optimal designs as well as the baseline design are

Table 6.33 Comparison of the performance of baseline engine and Design IV

NOx (g/kgf) Soot (g/kgf) GISFC(g/kW h)

SOI

Case A Baseline 50.1 1.92 249.4 -16.Design IV 45.4 (9.5%;) 0.74 (65%;) 237.3 (5%;) -15.1

Case B Baseline 32.8 1.29 216.6 -7Design IV 28.4 (14%;) 0.80 (38%;) 213.8 (1.3%;) -7.1

Table 6.34 Optimal designs of full-load cases

GISFC (g/kW h) SOI (�ATDC) Swirl ratio (-) Pboost (bar) Pinj (bar)

Design IV Case A 232.3 -15.1 1.73 3.57 1,600Optimum A1 228.9 (1.5%;) -15.5 1.81 2.45 1,790Design IV Case B 217.9 -7.1 1.73 3.2 1,600Optimum B1 215.4 (1.1%;) -8.3 1.78 3.65 1,616

2 According to NEDC emission tests (Schmidt 2008), NOx emissions are not considered underfull-load conditions. Since soot emission is usually proportional to GISFC, only GISFC wasconsidered.

264 6 Applications

listed in Table 6.36. Optimal design D1 has very good fuel consumption and low sootemissions. Compared to the baseline design, 3% reduction in GISFC and 10%reduction in soot emissions were achieved. Optimal design D2 has very goodreduction in NOx emission, with 7% reduction compared with baseline engine. Bothof them simultaneously reduce fuel consumption and engine-out emissions.

Case E is a low-load case whose engine speed is 1,500 rev/min and IMEP isabout 7 bar. The same optimization was performed on Case E, with objectives ofGISFC, NOx and soot emissions. Figure 6.66 shows all citizens and Pareto

Fig. 6.64 All citizens and Pareto solutions from optimization and the baseline design: Case C(medium-load, 15 bar)

Table 6.35 Selected optimal designs of Case C (medium-load, 15 bar)

NOx (g/kgf) Soot (g/kgf) GISFC (g/kW h)

Baseline 32.5 1.28 217.2Optimum C1 28.0 (14%;) 1.15 (10%;) 206.6 (5%;)Optimum C2 17.4 (46%;) 1.23 (4%;) 213.2 (2%;)Optimum C3 30.4 (6.5%;) 0.95 (26%;) 210.3 (3%;)

Fig. 6.65 All citizens and Pareto solutions from optimization and the baseline design: Case D(medium-load, 9 bar)


solutions from the optimization, and the baseline design. Again, all data is basedon computations using the AMC model. Selected optimal designs, which simul-taneously reduce fuel consumption and pollutant emissions, as well as the baselinedesign are listed in Table 6.37. Optimal design E1 represents the best fuel con-sumption design, which has 10% reduction in GISFC compared to the baselinedesign. Optimal design E2 has the lowest soot emission, with 55% reductioncompared with the baseline engine. Optimal design E3 has good NOx reductionwith acceptable fuel consumption and soot emission: 46% reduction in NOxemission, and 1% reduction in GISFC and soot emission. Optimal design E4 hassimilar reduction in GISFC and soot emission as Design E2, but much better NOxreduction (8%).

Figure 6.67 shows some selected response surfaces from this optimization.It can be seen that SOI and boost pressure are the dominant parameters for both

Table 6.36 Selected optimal designs of Case D (medium-load, 9 bar)


Baseline 23.2 1.03 198.8Optimum D1 22.1 (5%;) 0.93 (10%;) 192.9 (3%;)Optimum D2 21.6 (7%;) 0.99 (4%;) 194.1 (2%;)

Table 6.37 Selected optimal designs of Case E (low-load, 7 bar)


Baseline 30.7 0.977 253.7Optimum E1 24.6 (20%;) 0.755 (23%;) 229.4 (10%;)Optimum E2 29.5 (4%;) 0.436 (55%;) 231.7 (9%;)Optimum E3 16.7 (46%;) 0.97 (1%;) 252.3 (1%;)Optimum E4 28.3 (8%;) 0.493 (50%;) 229.7 (9%;)

Fig. 6.66 All citizens and Pareto solutions from optimization and the baseline design: Case E(low-load, 7 bar)

266 6 Applications

GISFC and soot emissions. Correlations among the controllable parameters werenot found in the optimization of all these cases. This implies that these controllableparameters can also be optimized separately. These observations were also true forthe other cases whose response surfaces are not shown for brevity.

Finally, Case F is a very-low-load case whose engine speed is 1,500 rev/minand IMEP is about 4 bar. Besides GISFC, NOx and soot emissions, CO and UHCemissions were taken into account in objectives. Figure 6.68 shows all citizens andPareto solutions from the optimization, and the baseline design. It can be seenfrom Fig. 6.68 that the baseline engine represents one of the optimal designscompared to the citizens from the present optimization (c.f., plots of GISFC andNOx emission). Designs that simultaneously reduce GISFC and all pollutantemissions were not found in the present optimization. One of the major reasons isthat the hardware design was optimized under the full-load condition. As shownin (Shi and Reitz 2008b; Ge et al. 2009a, b), full-load conditions have differentpreferences from the low-load conditions. For instance, full-load cases prefer alarge bowl design while low-load cases prefer a small bowl design (Ge et al.2009b). Selected optimal designs, which simultaneously reduce fuel consump-tion and UHC and CO emissions, as well as the baseline design are listed inTable 6.38. Optimal design F1 represents the best fuel consumption design,which has 3% reduction in GISFC compared to the baseline design. Significantreductions in CO and UHC emissions were achieved—80% and 48% reductions

Fig. 6.67 Selected response surfaces: Case E (low-load, 7 bar)


in CO and UHC, respectively. Optimal design F2 has considerable reduction insoot, CO, and UHC emissions, with 22, 88, 93% reduction compared withbaseline engine, respectively. Besides, more than 2% improvement in GISFCwas obtained. Optimal design F3 has improved NOx emission with similarfuel consumption. CO and UHC emissions were reduced by around 60%.However, soot emission increased by 2 fold. Overall, the current hardwaredesign is good at CO and UHC reduction but not NOx reduction, indicatingthat other methods, such as the use of increased EGR levels might be needed atlow-load.

Figure 6.69 summarizes averaged design parameters as a function of engineload. The averaged values were evaluated by averaging over all the Pareto

Fig. 6.68 All citizens and Pareto solutions from optimization and the baseline design: Case F(low-load, 4 bar)

Table 6.38 Selected optimal designs of Case F (low-load, 4 bar)

NOx (g/kgf) Soot (g/kgf) CO (g/kgf) UHC (g/kgf) GISFC (g/kW h)

baseline 9.1 0.529 13.1 2.67 252.9Optimum F1 56.1 (516%:) 0.787 (48%:) 2.65 (80%;) 1.39 (48%;) 246.0 (3%;)Optimum F2 54.4 (498%:) 0.410 (22%;) 1.53 (88%;) 0.9 (93%;) 246.8 (2.4%;)Optimum F3 8.11 (11%;) 1.664 (215%:) 5.82 (56%;) 0.958 (64%;) 255.8 (1%:)

268 6 Applications

solutions for each operating condition. Since only GISFC was taken as theobjective in the optimizations of Cases A and B, there is no Pareto front fromthese two optimizations and therefore these two cases were not considered here.There is no evident trend in SOI, since either early injection or late injectionmay lead to certain benefits such as NOx and GISFC reduction. This is trueparticularly for the very low-load case (Case F, IMEP = 4 bar). The very lateinjection condition shows similar features as those of MK combustion, whichhas very low NOx emissions and good fuel consumption. Very early injectionmay lead to a similar combustion event as in HCCI combustion. Additionally,CO and UHC emissions and a wider search space of SOI were considered in theoptimization of Case F. Therefore, Case F has a large variance in SOI of thePareto designs. Case D also considered a wider search space of SOI than CasesC and E, which results in a larger variance in SOI, too. The boost pressureincreases with the engine load. Higher load requires more injected fuel, and thecorresponding amount of air, therefore necessitating higher boost pressure to

Table 6.39 Scaling laws for the specification of the 450 cc optimal and down-scaled 400 ccengines

Parameter 450 cc 400 cc Scaling factor

Bore (cm) 8.1 7.788 LStroke (cm) 8.8 8.461 LDisplacement volume (cm3) 453.23 402.88 L3

Volume@TDC (cm3) 31.66824 28.18 L3

Squish height (cm) 0.07 0.0673 LCompression Ratio 15.313 15.295 EqualConrod length (cm) 16 16 –Bowl diameter (cm) 4.836 4.65 LIVC (�ATDC) -129.5 EqualEVO (�ATDC) 120 EqualTwall/Thead/Tpiston (K) 379/385/441 Equal

Fig. 6.69 Averaged design parameters from Pareto solutions as a function of engine load


trap more air in cylinder. It can be seen that the averaged injection pressureincreases as engine load increases. The ambient density and temperature in thehigh-load cases are higher than the ones in the low-load cases. Plus the globalequivalence ratio is higher in the high-load cases. Therefore, mixing withavailable oxygen is essential for engine performance, and the key issue for spraycontrol lies in keeping spray penetration as long as possible while avoidingspray wall impingement. Higher injection pressure needed for the high-loadcondition increases spray penetration and enhances mixing with oxygen near thecylinder wall and piston bottom. There is no evident trend in the averaged swirlratio with engine load as well. Although the same search space was used for theswirl ratio, the variance in the Pareto designs is larger in the low-load cases thanthe high-load cases. This implies that the high-load cases have a clear prefer-ence in swirl, while engine performance is less sensitive to the swirl for thelow-load cases.

6.3.1.3 Summary

The following conclusions can be drawn from the present section:

• The present study demonstrated that the proposed hardware optimizationmethod is feasible for CFD-based engine optimization.

• With the fixed optimal hardware design and optimal sets of controllableparameters for each case, optimal designs which simultaneously reduce fuelconsumption and pollutant emissions were obtained in all cases except for thevery low load case. The reason is that different engine loads have differentpreferences in hardware design, for instance, bowl radius, which is smaller atlow load.

• Strong correlations among the controllable design parameters were notobserved, which implies that these controllable parameters can be optimizedseparately.

• Optimal injection pressure and boost pressure increase with engine load, but noevident trend in SOI and swirl ratio is observed.

With small modifications, the present method could be applied to other enginedevelopment procedures.

6.3.2 A Consistent Method for Simultaneous Optimizationof Multiple Operating Conditions

The second method is a general method for the optimization of multipleoperating conditions. Design parameters cover a common set of hardwareparameters, as well as sets of controllable parameters for each individual

270 6 Applications

condition. We take a computational optimization of IC engine with KIVA CFDcode and genetic algorithms for example. The optimization objectives includeGISFC and the pollutant emissions (soot and NOx emissions) of all the oper-ating conditions.

The concept of this optimization methodology as depicted in Fig. 6.70, indi-cates that each GA population invokes two KIVA runs (e.g., for 2,000 and4,000 rev/min cases, respectively). Each run generates a set of objectives thatinclude GISFC, NOx and soot emissions. Thus, there are six objectives in. Thisoptimization method avoids conflicts in hardware designs from independentoptimization for each individual case, and offers a systematic method forengine optimization. Considering that the computational cost of one optimizationis proportional to its total number of design parameters, the computational cost ofthe present method is

cos t / Nhw þ Ncase � Ncontr

which will usually be lower than the total cost of the conventional individualoptimization where cos t / Ncase � ðNhw þ NcontrÞ. Here Ncase is the total numberof considered operating conditions, and Nhw and Ncontr indicate the number ofhardware parameters and controllable parameters, respectively.

This method will be practiced in the next section.

6.4 Coupling of Scaling Laws with Computational Optimization

The scaling laws discussed in Chap. 5 were applied to down-size an optimal designin Sect. 6.1.4 from 450 to 400 cc. The scaling laws were validated by comparingthe two engines under six operating conditions, which cover full-load, mid-load,

Fig. 6.70 Flowchart of consistent multi-mode optimization


and low-load conditions. The down-scaled optimal design is then taken as thestarting point for engine development of this class, and is further optimized usingthe second method described in Sect. 6.3.

6.4.1 Downsizing of a HSDI Diesel Engine

Scaling laws are desired to produce identical performance and emission levels ofengines of different sizes. However, it is very difficult to achieve this aim inreality. First of all, geometric similarity is needed, such that the two scaledengines have similar boundary conditions. This includes scaling the bore, stroke,squish height, and piston bowl shape. The resulting compression ratio should bethe same in the two engines. By setting the same boost pressure and tempera-ture,3 the same wall temperatures, and the same initial flow conditions, such asthe swirl ratio, similar initial thermodynamic and fluid dynamic conditions priorto spray injection can be achieved in the combustion chamber. Secondly, simi-larity in spray dynamics should be considered. Spray development has a primaryeffect on engine performance and pollutant emissions as it determines the mixingof the fuel and air. The aim is to have similar fuel distributions before thecombustion event. This is usually quantified in terms of spray penetration, whichis the essential parameter determining the fuel distribution. Finally, similarity inthe combustion characteristics in the scaled engines should be maintained inorder to provide similar engine performance and emissions. In the following, a450 cc HSDI engine is down-scaled to a 400 cc engine following the proceduresdescribed above.

The 450 cc HSDI diesel engine was optimized in a previous computationaloptimization study (Ge et al. 2009b, 2010). The scaling factor is based the ratio ofthe displacements:

V ¼ 400=450 ¼ 0:8889

and the corresponding length scaling factor is:

L ¼ ð400=450Þ1=3 ¼ 0:9615:

Based on the scaling relations listed in Table 5.1, the two scaled pistongeometries of the two engines are depicted in Fig. 6.71 and the engine specifica-tions are listed in Table 6.39. Valve opening and closing timings, wall temperatures,

3 In Chap. 5, different initial temperatures were used to take into account the different heattransfer between engines of different sizes. Since the scaling factor in this section is close tounity, the corresponding volume-to-area ratios of the two engines are similar and thus the sameinitial temperatures were used in this section.

272 6 Applications

boost pressures and temperatures were kept the same, so that the thermodynamicconditions before spray injection are similar between the two engines.

The scaling relations described in Chap. 5 were applied to the 450 cc and400 cc engines. Parameters concerning the nozzle design are listed in Table 6.40.Operating parameters, including engine speed, boost pressure and temperature,swirl ratio, injection timing and duration in crank angles, injected fuel mass,injection pressure, and EGR, are listed in Table 6.41 for two full-load operatingconditions. The same scaling laws can be applied for mid- and low-load operatingconditions as well (Ge et al. 2011). All of the six cases for both engines weresimulated using the same CFD code and include full-, mid- and low-load cases, atdifferent speeds. Pressure traces, HRR, averaged and peak temperatures, NOx andsoot emissions for the two full-load cases are plotted in Fig. 6.72. Since HRR isnot a volume-specific variable, the HRR of the down-scaled engine is multipliedby the scaling factor V. It is seen that all of these cylinder averaged quantitiesmatch very well, which implies the applicability of the scaling laws. Figure 6.73shows the comparison of the GISFC and engine-out emissions of the six operatingconditions between the two engines. Slight discrepancies are observed only in thetwo low-load cases.

Fig. 6.71 Schematic of thepiston geometries of the450 cc (left) and 400 cc(right) engines

Table 6.40 Scaling laws for the nozzle design of the 450 cc optimal and down-scaled 400 ccengine

450 cc 400 cc Scaling factor

Nozzle diameter (lm) 121 116 LNozzle hole number 8 8 Equal

Table 6.41 Scaling laws for full-load cases: 2,000 and 4,000 rev/min

450 cc 400 cc 450 cc 400 cc Scalingfactor

Engine speed (rev/min) 2,000 2,026.3 4,000 4,052.7 L�1=3

Temperature@IVC 358 482.42 EqualPressure@IVC (atm) 3.2012 3.57 EqualSwirl@IVC 1.73 1.73 EqualSOI -7.06 -15.1 EqualDOI 32.5 42.4 EqualInjected fuel mass (mg) 0.063 0.056 0.0556 0.0494 L3

Injection pressure (bar) 1,600 1,518 1,600 1,518 L4=3

EGR 0.13% 0.16% Equal

6.4 Coupling of Scaling Laws with Computational Optimization 273

6.4.2 Optimization of Downsized Engine

It was of interest to explore whether the 400 cc engine downsized from the pre-vious optimized 450 cc engine using the scaling laws could be further optimized.Thus, the downsized engine was further optimized using a multi-objective geneticalgorithm methodology. Since full-load cases are the more representative condi-tions, only the two full-load cases (2,000 and 4,000 rev/min) were considered in

Fig. 6.72 Pressure, heat release rate, average temperature, peak temperature, and NOx and sootemissions of the full-load cases: 2,000 (left) and 4,000 rev/min (right)

274 6 Applications

the optimization. The consistent optimization method described in Sect. 6.3.2 wasemployed to optimize the down-sized engine operating under two full-load con-ditions. The hardware parameters considered in the present optimization includenozzle design (spray angle and number of nozzle holes), 12 parameters describingthe piston bowl shape, and one parameter describing the relative bore size, Xb. AnXb of unity corresponds to the ratio of bore and stroke of the down-sized 450 ccengine design. When the bore size is changed, the volume at TDC and BDC is keptas the same, so that the compression ratio is the same, i.e.,:

VBDC ¼ Vbowl þ Vsquish þ Vcrevice þ Vdisplacement;

VTDC ¼ Vbowl þ Vsquish þ Vcrevice:

Thus, the corresponding thermodynamic conditions are guaranteed to be thesame, too. In this case, Vdisplacement ¼ p

4� Bore2 � Stroke and Vsquish ¼ p4 � Bore2 �

hsquish were kept the same. The stroke and squish height hsquish can then be determinedfrom the bore size. The width and depth of the piston-liner crevice were kept thesame. This implies that the crevice volume changes with the bore size as,

Vcrevice ¼ pðBore� dcreviceÞdcrevicehcrevice:

The difference in crevice volume was accounted for by adjusting the pistonbowl volume. The piston bowl shape was kept the same except that the radius anddepth of bowl were adjusted to match the volume at TDC and BDC (by keepingVbowl þ Vcrevice ¼ const:).

The mesh was generated using the automated mesh generator—Kwickgrid (c.f.,Sect. 4.1)—based on the inputs of these hardware parameters. Figure 6.75 showsan example of a mesh generated using Kwickgrid. Controllable parameters includeSOI and swirl ratio. Each population invokes two KIVA runs (for the 2,000 and4,000 rev/min cases, respectively). Each run generates a set of objectives that

Fig. 6.73 Fuel consumption and engine-out emissions of the 450 and 400 cc engines


include GISFC, NOx and soot emissions. Thus, there are in total six objectives inthe present work. This optimization method avoids conflicts in hardware designsfrom independent optimization for each individual case, and offers a systematicmethod for engine optimization.

All the optimizations were conducted through CONDOR–the high throughputcomputing system (Thain et al. 2005). In usual practice, the optimization startsfrom a set of randomly generated designs by default. In other words, the opti-mization starts from scratch. This implies that the down-scaled optimal design isnot utilized. To deal with this problem, one of the randomly generated designs inthe first generation was replaced by the down-scaled optimal design (c.f.,Fig. 6.75), which means that the evolution was seeded with the optimal design.Figure 6.76 shows a comparison of the early stage optimization results without andwith the seed of the down-scaled optimal design. The left plot in Fig. 6.76 showsthe distribution of initial citizens (1st generation) in terms of NOx and GISFC forthe two optimizations. The blue solid star indicates the down-scaled optimaldesign. The red hollow star indicates the citizen that is randomly generated in the

Fig. 6.74 Automated mesh generator. Bezier curvature parameters: 1 Xab; 2 Xba; 3 Xbc; 4 Xcb;5 Ycb; 6 Ycd

Fig. 6.75 Implementation of baseline design into optimization methodology

276 6 Applications

first optimization (without the seed) but is replaced by the down-scaled optimaldesign in the second optimization (with the seed), while the other citizens areretained. The right plot in Fig. 6.76 illustrates the Pareto designs from the twooptimizations at the 10th generation. Comparing to the optimal design, the randomone has higher GISFC and lower NOx emission ranges. This initial differencecauses the evident difference in the Pareto front at the 10th GA generation. ThePareto solutions from the optimization starting with random seeds in general havelower NOx emissions, while the optimal solutions from the optimization with aninitial optimal design have lower GISFC. Especially, it is seen that there are moredesigns near the optimal design (blue solid star). It then can be concluded that theinitial seeds are important for the evolution of optimization. The resulting citizenshave more good features that the initial seeds have, i.e., seeded with a design thathas good GISFC will lead to more citizens that have good GISFC.

Figure 6.77 shows the final response functions with respect to bore size. Theleft column is for the 2,000 rev/min case and the right column is for the 4,000 rev/min case. In general, the shapes of the response functions are similar and a sweetspot can be seen in the response function of GISFC for both cases. The optimalbore parameters are very close to unity, which indicates that the original bore/stroke ratio is in the range of the optimal design. The response functions of theNOx emissions are similar in shape but different in magnitude for the two cases.A smaller bore benefits NOx reduction in general. For the soot emissions, boththe shape and magnitude are quite close and a larger bore is preferred for sootreduction.

Figure 6.78 shows multi-parameter response surfaces indicating the effect ofbore size on GISFC for the 2,000 rev/min case. The correlation with SOI is seen tobe minor. However, the bore size strongly correlates with spray angle. When thebore size is changed, spray targeting needs to be changed to maintain the optimalfuel distribution in the bowl and squish regions. Thus bore size is found to becorrelated with the radius of the piston bowl and Xcb (the most influencingparameter for piston bowl shape). When bore size is changed, the absolute radiusand depth of the piston bowl are changed accordingly. This affects the flow

Fig. 6.76 Influence of initial design parameters. Left: 1st generation, right: 10th generationcitizens with and without seeded 400 cc case from the scaled 450 cc optimum


structures in the piston bowl and, consequently, the fuel and air mixing. Eventu-ally, it has an impact on engine performance.

Figure 6.79 shows multi-parameter response surfaces indicating the effect ofbore size on soot emissions for the 2,000 rev/min case. Similar to the GISFCresults, there is no correlation between SOI and bore size, but there are strongcorrelations between bore size and spray angle, bowl radius, and Xcb.

Figure 6.80 shows the corresponding response surfaces indicating the effect ofbore size on GISFC for the 4,000 rev/min case. The observations are similar tothose of the 2,000 rev/min case. Compared to the 2,000 rev/min case, GISFC ismore sensitive to SOI. For the high speed case, the real time per crank angle isshorter. Therefore, the time for mixing and reaction becomes more crucial,especially for chemical reactions, which mainly depend on the chemical propertiesof the reactants. Bore size is found to be correlated with the swirl ratio, e.g., small

Fig. 6.77 Response functions with respect to bore size. Left: 2,000 rev/min, right: 4,000 rev/min

278 6 Applications

Fig. 6.78 Response surfaces of GISFC as a function of bore size: 2,000 rev/min

Fig. 6.79 Response surfaces of soot as a function of bore size: 2,000 rev/min


bores prefer strong swirl and large bores favor low swirl ratio. As discussed in Geet al. (2009b), spray penetration should be as long as possible but without spraywall impingement for full load cases. Since swirl flow adds a tangential velocitycomponent to the spray and vapor trajectory and increases the relative velocitybetween the spray and air flows, swirl reduces spray and vapor penetration. Whenthe bore is small, the spray and vapor penetration should be reduced accordingly toensure a more homogeneous distribution of fuel vapor. Increasing swirl ratio canachieve this aim. Therefore, a high swirl ratio is preferred in this case, and a lowswirl is preferred when the bore is large.

6.5 Summary

In the present example, a HSDI diesel engine was downsized from 450 to 400 ccusing scaling laws based on spray penetration and flame lift-off length similitude.The scaling laws were validated by comparing the two engines’ performance.A consistent optimization method was applied that is able to simultaneouslyoptimize multiple operating conditions without conflict. The following conclusionswere drawn from the study:

Fig. 6.80 Response surfaces of GISFC as a function of bore size: 4,000 rev/min

280 6 Applications

• The extended scaling laws work well for a wide range of operating conditions.But it is noted that the range of scaling factor considered in the present work isrelatively small.

• Initial seeds have significant effects on the final citizens. Good features of theinitial seeds will be retained. Thus, seeded with optimal designs from previousoptimization will speed up convergence of optimization.

• The optimization results show that bore size can be correlated with spray angle,swirl ratio, radius of the piston bowl, and the bowl shape Bezier curvatureparameter Xbc (reentrancy).

• When the engine speed is high, fuel efficiency depends more on injectiontiming, because the time for mixing and chemical reaction becomes shorter andis thus more critical.

6.5 Summary 281

Chapter 7Epilogue

We began this book by stating the important role of internal combustion engines inthe transportation sector and the fact that this role is projected to not diminish inthe next few decades. However, increasing fuel prices and escalating environ-mental concerns due to vehicle emissions are forcing engineers to look for bettersolutions to improve existing IC engine designs. Modeling IC engines provides acost-effective and time-efficient way to study engine performance and pollutantformation. With increasing capacity and improved prediction accuracy of ICengine modeling tools, numerical simulations have become more important inassisting IC engine design and optimization. More than 30 representative papersthat focus on computational engine optimization were reviewed to describe therecent progress in the relevant research areas in Chap. 1.

In Chap. 2, the performance of non-evolutionary optimization, evolutionaryoptimization, single-objective and multi-objective optimization methods werecompared with several particularly designed mathematical test problems. It wasconcluded that multi-objective evolutionary optimization methods are more suit-able for real-world IC engine design problems, which are multi-objective opti-mization problems in nature. Another focus of Chap. 2 was an overview of enginecomputational fluid dynamics (CFD) modeling methods. A detailed review of eachsophisticated model is beyond the scope of this book. Instead, the framework ofengine CFD modeling and the basic concepts of the governing equations, physicalmodels, and numerical methods were covered. In addition, the applicable ranges,advantages and disadvantages of existing physical models were also briefly dis-cussed. The last part of Chap. 2, describes the fundamental ideas of severalregression methods. The component selection and smoothing operator (COSSO)method was discussed in more detail because it was the main regression analysistool used in this book.

How to improve the efficiency of engine CFD modeling tools remains one ofthe main challenges in computational optimization of IC engines. This issue wastackled in Chap. 3 with methods that fall into four categories. First, methods werepresented for reducing mesh- and timestep-dependency for spray modeling, whichenables engine simulations using coarser meshes and larger timesteps while


283

adequately resolving spatial and temporal information of the modeling withoutusing finer meshes and smaller timesteps. Second, reducing the size of reactionmechanisms has been an active subject in reacting flow simulations. An automaticapproach for mechanism reduction that is based on the directed relation graph witherror propagation (DRGEP) and principal component analysis (PCA) methods wasproposed. It was shown that reaction mechanisms of significantly reduced sizes areobtainable by performing a two-stage reduction approach to the detailed reactionmechanisms while maintaining their major characteristics. Third, multi-gridtechniques in reacting flow simulations were discussed. The idea is to approximatethe solution over the entire computational domain by grouping thermodynami-cally-similar computational cells to reduce the calling frequency of the CFD solverto the chemistry solver. An adaptive multi-grid chemistry (AMC) solver for enginesimulations was developed, and it showed significant speed-up in both homoge-neous charge compression ignition (HCCI) and direct-injection (DI) engine sim-ulations. The fourth approach is an extension to the mechanism reduction method,which dynamically applies efficient mechanism reduction methods, such as theDRGEP method, on-the-fly to engine CFD simulation so that each computationalcell solves a small reaction mechanism at every timestep. It was demonstrated thatcumulative benefits are achievable by combining all these approaches to furtherspeed-up engine simulations.

To extend the comparative study of optimization methods conducted in Chap. 2with mathematical test functions, three widely used multi-objective geneticalgorithms were compared, namely, micro-GA, non-dominated sorting geneticalgorithm II (NSGA II), and adaptive range multi-objective genetic algorithm(ARMOGA) for a real-world engine optimization problem in Chap. 4. To assesstheir performance, four quantities were defined to quantify the optimality anddiversity of the optimization methods. It was concluded that NSGA II performedthe best with a large population size, and it thus was extensively used in the casestudies of this book. Then, the NSGA II with different niching techniques wasfurther investigated and the convergence and diversity metrics were proposed toassess its performance. A dynamic learning strategy was proposed based on theassessment of regression methods for an engine optimization problem.

Engine-size scaling is an efficient way to expedite prototype engine develop-ment and optimization by utilizing existing design information of either larger orsmaller-scale engines. In Chap. 5, such size-scaling relationship between ICengines of different dimensions is discussed. The scaling laws were proposedbased on the spray liquid penetration and flame lift-off lengths in diesel engines.The scaling laws were then applied in a light-duty and a heavy-duty productiondiesel engines. The engine simulation results illustrated that such scaling laws canindeed lead to similar performance and emissions between the two engines.

To demonstrate the applicability of the engine optimization tools that have beendeveloped, Chap. 6 summarizes seven cases that include optimization studies ofspark-ignition (SI) and compression-ignition (CI) engines, light-duty and heavy-duty engines, and engines fueled with gasoline and diesel. The use of CFD sim-ulations was first demonstrated with simple combustion models for engine

284 7 Epilogue

optimization within conventional combustion regimes. Then, a heavy-duty CIengine fueled with diesel and gasoline-like fuels was optimized using advancedcombustion models with efficient chemistry solvers. Strategies for simultaneousoptimization of multiple engine operating conditions were discussed. Inspired bythe engine size-scaling study in Chap. 5, engine size-scaling laws were alsoemployed in an engine optimization study and the results showed how thismethodology can be used for downsizing development of a high-speed direct-injection (HSDI) diesel engine.

Finally, it is noted that engine design and optimization is a sophisticated pro-cess that involves the optimization of different engine components and integratedsystem level optimization. The present book focuses on the in-cylinder combustionstrategy optimization only. But we believe that the optimization methodologiesand numerical models described throughout the entire book are generally appli-cable to other related areas.

7 Epilogue 285

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Index

AAcetylene, 46, 154, 174

see soot precursor, 44–46, 154Adaptive Multi-grid Chemistry (AMC), 14,

94–95, 99–102, 104, 116, 122–123,233, 235–236, 263–264, 266, 284

Arbitrary Lagrangian–Eulerian (ALE), 68Arc, 41Arrhenius equation, 29, 42, 45, 80Atomization, 46, 49, 60, 180, 187–188

BBezier, 126–128, 192, 219–220, 226–227, 233,

276, 281Bio-diesel, 79Boiling temperature, 60Bottom Dead Center (BDC), 114Boundary condition, 66Box-Cox transformation, 139Bray-Moss-Libby (BML), 40Breakdown, 41Breakup length, 50, 53–54Breakup time, 50, 53–54, 150Broyden–Fletcher–Goldfarb–Shanno

(BFGS), 15

CCarbon monoxide (CO), 5, 8, 42, 88, 102,

104–109, 189Caterpillar (CAT), 88, 126, 148, 153, 189Characteristic Time Combustion (CTC)

model, 22, 38, 127–128, 177, 189,199, 260–261, 263

CHEMKIN, 38, 80, 85, 95, 154, 222, 261, 264Chi-squared distribution, 48–49

Chrysler, 182Coalescence, 57Coherent flame model, 40Cold start, 6Collision, 56–58, 60, 70, 76–79, 101, 219Compression ratio (CR), 5, 88, 126–127,

148, 154, 158, 161, 168–169,183, 190–191, 211, 220, 255,269, 272, 275

Compression-Ignition (CI), 2, 14, 234, 284Computational Fluid Dynamics (CFD), 3, 27Computational Singular Perturbation

(CSP), 79Conditional Moment Closure (CMC), 41Continuous Droplet Model (CDM), 30Continuous Formulation Model (CFM), 30Contraction coefficient, 47Controlled Random Search (CRS), 9CONVERGE, 70Convergence metric, 134Courant–Friedrichs–Lewy (CFL), 69Crevice, 63–64, 168, 232, 244, 249, 275Crowding distance, 24–25, 132–133

DDepth First Search (DFS), 81Design of Experiments (DoE), 139, 210Detroit Diesel Company (DDC), 210Diesel Particulate Filters (DPF), viDiffusion combustion, 14, 39, 189

also see diffusion flame, 14, 39, 189Direct Injection (DI), 2, 5, 7, 9, 71, 79, 149,

178, 181–182, 218, 234, 284High Speed Direct Injection (HSDI), 9, 14,

71, 148, 218, 232, 272, 280, 285Direct Numerical Simulation (DNS), 32

305

D (cont.)Directed Relation Graph (DRG), 80–81Directed Relation Graph with Error

Propagation (DRGEP), 80–81Discharge coefficient, 46–47, 49Discrete Particle Ignition Kernel (DPIK)

model, 41–42, 180see ignition, 41

Dispersion, 50–51, 54Diversity metric, 135Downsizing, 148, 272Drag, 55Droplet deformation, 55Droplet size, 46, 48–49Dual fuel, vii, 258Dynamic Adaptive Chemistry (DAC), 105

Extended Dynamic AdaptiveChemistry (EDAC), 105

EEmissions

see Nox emission model, 43see Soot model, 44

Engine combustion phasing, 84Engine Research Center (ERC), 42–43, 46,

95, 101, 114–117, 123–124, 127,179, 210

Environmental Protection Agency (EPA), 1Equilibrium constant, 29equivalence ratio, 7, 10, 88, 94, 96–97,

104, 108–109, 113, 117, 126,162, 169, 172, 176, 190–191,205, 223, 235, 270

ESTECO, 15, 27, 211Evaporation Model, 58Exhaust Gas Recirculation (EGR), vi, 5, 9–10,

101–102, 104, 112, 117, 126, 154,162, 169, 176, 190–191, 211, 220,234–238, 268, 273

Exhaust Valve Opening (EVO), 5, 210Extended Dynamic Adaptive Chemistry

(EDAC), 105see Dynamic Adaptive Chemistry

(DAC), 105

FFederal Test Procedure (FTP), 88Fiat, 102–105FIRE, 70Finite volume, 68, 179Fitness value, 25Flame kernel, 41

Flame lift-off length, 147, 150–152, 175Flame propagation, 41–42Flame surface density model, 40, 180Flamelet, 39

Eulerian particle flamelet model(EPFM), 40

Representative Interactive Flamelet(RIF), 40

FLUENT, 70FORTé, 70Frossling correlation, 58Fuel consumption, 192

see Gross indicated specific fuelconsumption, 192

GG-equation, 40, 42, 70Gas jet model, 77Gasoline Direct Injection (GDI), 2, 5Genetic Algorithms (GA), 10–12, 20–22, 24,

26–27, 178, 181, 210, 217, 221, 232Adaptive Range Multi-objective Genetic

Algorithm (ARMOGA), 11, 22, 25,125, 128

Multi-objective genetic algorithm(MOGA), 22

Non-dominated Sorting Genetic Algorithm(NSGA), 11, 21, 24, 26, 125

Single-Objective GeneticAlgorithm (SOGA), 9, 20

Micro-Genetic Algorithm(micro-GA, l-GA), 11, 20, 125

Glow, 41GM, 102–105Gradient-based method, 8Gross Indicated Specific Fuel Consumption

(GISFC), 192see Fuel Consumption, 192

Grouping, 95–97Growth rate, 50–52

HHeat Release Rate (HRR), 106n-Heptane, 42, 46, 79High Throughput Computing (HTC), 219Homogeneous Charge Compression Ignition

(HCCI), vii, 2, 10, 13, 75, 79,84–88, 94–96, 99–101, 104–109,113–117, 162–165, 234, 284

Hydrocarbons (HC), 63, 102see Unburned Hydrocarbons (UHC),

63, 102

306 Index

IIgnition, 41

discrete particle ignition kernel model(DPIK), 41, 180

Shell auto-ignition model (Shell model), 42Ignition delay, 10, 163Indicated Mean Effective Pressure (IMEP), 88,

101, 104, 148, 154, 162, 169, 220,235, 261, 264–265, 267, 269

Indicated Specific Fuel Consumption (ISFC),148, 182, 185, 187–188

Gross Indicated Specific Fuel Consumption(GISFC), 125, 129, 139–144, 192,194–200, 206–207, 209, 212–213,215–218, 222–231, 236–237, 239,243, 248–249, 261, 264–269, 271,273, 276–280

Iso-octane, 79, 180Intake Valve Closing (IVC), 10, 88Internal Combustion Engines, 1, 2, 14Intrinsic Low-Dimensional Manifolds

(ILDM), 79

Kk-e model, 33, 35, 37

RNG k-e model, 37, 39K-nearest neighbors (KN), 13, 72, 125Kelvin-Helmholtz (KH) model, 51Knock, 42Kriging (KR), 13, 72, 125Kwickgrid, 126, 191, 193

LLagrangian-Drop Eulerian-Fluid (LDEF), 75Large Eddy Simulation (LES), 33–34, 38,

40, 70Latin Hypercube Sampling (LHS), 8Law-of-the-wall, 66Lawrence Livermore National Laboratory

(LLNL), 114–116, 122–124, 236Ligament diameter, 50Linearized Instability Sheet Atomization

(LISA) model, 49–50, 180Locally Homogeneous Flow (LHF), 30

MMaximum merit function (MMF)

see merit functionMean Deviation of the Distance between

Neighbor Pareto Solutions(MDDNPS), 129–132

Mean Distance between Extreme ParetoSolutions (MDEPS), 129–132

Mean Distance to the Pareto Front (MDPF),129–132

Mercedes Benz, 178Mercury Marine, 182Merit Function, 11, 20–22, 181, 183–184, 189

Maximum merit function (MMF), 184Method of Characteristics (MOC), 179Methyl Butanoate (MB), 79Methyl decanoate (MD), 79, 83, 87, 89Misfire, 236, 240ModeFRONTIER, 11, 16, 21, 27, 73, 128,

144, 211Modified Bessel function, 51–52Modulated Kinetics (MK), 13–14, 234,

255, 269Monte-Carlo, 34, 68Multi-component, 6, 60Multi-Objective Evolutionary Algorithms

(MOEA), 24Multi-step phenomenological soot model

see sootMulti-zone, 13, 94, 96, 99Multiple injection, 9–10

NNagle and Strickland-Constable, 45NEDC, 264Negative Valve Overlap (NVO), 258Neural Networks (NN), 13, 72, 125, 138, 140,

144–145Non-differentiable Interactive Multi-objective

BUndle-based optimization System(NIMBUS), 9

Non-Methane Hydrocarbons(NMHC), 239–240, 248–249

Non-Parametric Regression (NPR), 71, 210non-premixed combustion, 107, 117Niche, 25–26

Niching technique, 125, 131, 135, 284Nitrogen dioxide (NO2), 43, 154Nitrogen monoxide (NO), 3, 5, 10, 43–44, 107,

109, 112, 114, 154Nitrogen Oxide (NOx), 3–11, 43–44, 71,

101, 104–109, 114–115, 118–125,128–129, 176, 182, 185–218,222–230, 233–242, 245–251,255–257, 261, 264–277

Nozzle flow model, 46–48Number of Pareto Solutions (NPS), 129–130Nukiyama-Tanasawa distribution, 49Nusselt number, 59

Index 307

On-Octane, 79Ohnesorge number, 52OpenFOAM, 70Ordinary Differential Equations (ODE),

80, 95, 106–107

PPareto

Pareto front, 19, 21–26, 128–136, 193–195,212, 222, 236, 269, 277

Pareto design, 198, 261, 269–270, 277Partially Premixed Combustion (PPC), 2, 14,

40, 234, 255, 259Particulate Matter (PM), 1, 148, 239Particle Swarm Optimization (PSO), 9, 11Path Flux Analysis (PFA), 80–84, 106Peak Pressure Rise Rate (PPRR), 236–242,

245, 247–257Peclet number, 59Perfectly Stirred Reactor (PSR), 38Polycyclic Aromatic Hydrocarbons

(PAH), 46Port Fuel Injection (PFI), 6, 60Prandtl number, 36–37, 59Premixed Charge Compression Ignition

(PCCI), 10, 13, 102–105, 255Premixed combustion, 194, 233, 242, 245,

252, 255, 258Primary breakup, 48–51Primary Reference Fuel (PRF), 79, 101, 116,

236, 255Principal Component Analysis (PCA), 79–80,

85–93, 284Probability Density Function (PDF), 34, 40Progress equivalence ratio, 96–97, 108–113

QQuasi-Second-Order Upwind (QSOU), 68Quasi-Steady-State (QSS), 80, 82

RR-value-based breadth-first search (RBFS), 82Radial Basis Functions (RBF)

see Regression analysisRadius-of-Influence (ROI) model, 57–58, 219Rayleigh-Taylor (RT) model, 51–54, 70, 79,

101, 128Ranz-Marshall correlation, 59Reaction rate, 29, 38–40, 79–80, 107Reaction mechanism reduction, 13–14, 79–84

Reactivity Controlled Compression Ignition(RCCI), vii

Regression analysisCOmponent Selection and Smoothing

Operator (COSSO) method, 12,71–73, 189, 195–196, 210,218, 222, 283

k-nearest method, 13, 72–73, 125, 133,138, 144–145, 211

Kriging method, 8, 13, 72–73, 125,138, 144–145

Neural networks method, 13, 72–73, 125,138, 144

Radial Basis functions method, 13, 72–73,125, 138–141, 144–145

Remapping, 95, 98–99Representative Interactive

Flamelet (RIF)see flamelet

Response Surface Method (RSM), 7–8, 12–13,72, 138–140, 144, 195–200,211–219, 227–230, 266–267,277–278

Reynolds Stress Model (RSM), 34Reynolds Averaged Numerical Simulation

(RANS), 33–34, 38RNG k-e model

see k-e modelRosin-Rammler

distribution, 149, 180

SSauter mean diameter (SMD), 185Sauter Mean Radius (SMR), 48Scaling law, 147–177, 269, 271–274,

280–281, 284–285Schmidt number, 37, 58Secondary breakup, 51–54Selective Catalytic Reduction (SCR), viSemi-Implicit Method for Pressure-Linked

Equations (SIMPLE), 68SENKIN, 85Sequential Quadratic Programming

(SQP), 7Sharing function, 25Shell auto-ignition model

(Shell model)see ignition

Sherwood number, 58Single-cylinder research engine,

153, 178, 182Smoothing spline analysis of variance

(SS-ANOVA), 71–72

308 Index

Sootsoot emission, 3, 11, 71, 105, 115, 123, 125,

139, 152–156, 163, 165, 173–176,189–193, 196–198, 201–217,222–234, 237, 248, 252, 261,264–267, 271–278

soot formation, 10, 44–45, 150, 166,175–176, 189, 204, 230, 244

soot precursor, 44–46, 101, 128, 154,174–175

two-step soot model, 44–46, 101, 154multi-step phenomenological

soot model, 46Spalding mass transfer number, 58Spark Ignition (SI), 2, 5, 41, 177, 234, 284

spark-ignition direct injection (SIDI), 5Spray angle, 6, 46, 103, 137, 161, 168,

184, 191–192, 195–199, 201–203,205–206, 209–210, 212–213,215–218, 220, 225, 229–230,241–242, 250–251, 260–261, 275,277–278, 281

Spray equation, 32, 68, 75Spray tip penetration, 77–78, 147–152, 159,

164–165, 169, 175, 178, 203,207–208, 215, 223–226, 229,234, 249, 270, 272, 280, 284

Squish flow, 167, 170, 203Star-CD, 70Stratification, 5–6, 102, 178Subgrid-scale (SGS), 33, 70Surface-to-volume, 64, 163Swirl, 5–6, 10, 49–50, 68, 149, 151–153, 159,

176, 178, 180, 182, 195–200, 204,206–209, 225–226, 229–230, 236,244, 247, 250, 254–258, 270, 280

swirl ratio, 9, 11–12, 14, 125–128, 137,148, 151–154, 159, 161, 168, 176,189–199, 202–211, 220, 226,229–230, 241–246, 249–251,254–255, 258–261, 264,270–275, 278–281

TTaylor Analogy Breakup (TAB), 55, 180Taylor number, 52

Top Dead Center (TDC), 6, 149, 156–157,161, 168–173, 202, 252, 255, 275

Tumble flow, 5–6, 10, 149, 159–160, 178, 180,185, 227, 230–232

Turbulence, 4, 6, 11, 30, 32–42, 54, 67, 95,148, 151, 156, 158, 162–166, 171,175–176

Turbulence correlation time, 54Turbulent persistence time, 55Two-step soot model

see soot

UUnburned Hydrocarbons (UHC), 63, 102,

178–179, 187, 235Hydrocarbons (HC), 42, 63, 85, 87–88,

96, 102, 107–110, 178–179,182, 186–187, 235

VVariable Valve Timings (VVT), 5Vapor pressure, 47VECTIS, 70Vena contracta, 47–48Viscosity, 35, 38, 50–51, 53, 65

WWall film, 60–62Wall function, 67, 70Wall heat transfer, 3, 67, 102, 148, 156, 158,

175–176, 178, 182, 185–187Wall impingement, 60–63, 101, 128, 149,

178, 187, 191, 203, 205, 207–208,215–216, 224, 229, 234, 270, 280

Wavelength, 51–53, 100Wave number, 32, 50Wave stability theory, 49–53Weber number, 51, 52, 56, 60Well stirred reactor (WSR), 95

ZZel’dovich mechanism, 43, 128

Index 309