Combustion Engines Development

.

Gunter P. Merker � Christian SchwarzRudiger TeichmannEditors

Combustion EnginesDevelopment

Mixture Formation, Combustion,Emissions and Simulation

EditorsUniv.-Prof. Dr.-Ing. habil.Gunter P. MerkerSchoneckstr. 3088060 TettnangGermanyg.p.merker@t-online.de

Dr.-Ing. Rudiger TeichmannAVL List GmbHHans-List-Platz 18020 GrazAustriaruediger.teichmann@avl.com

Apl. Prof. Dr.-Ing. habil.Christian SchwarzBMW-GroupEA 31Hufelandstr. 8a80788 MunchenGermanychristian.schwarz@bmw.de

Original german edition published by Vieweg & Teubner, Wiesbaden, 2009.

ISBN 978-3-642-02951-6 e-ISBN 978-3-642-14094-5DOI 10.1007/978-3-642-14094-5Springer Heidelberg Dordrecht London New York

Library of Congress Control Number: 2011936001

# Springer-Verlag Berlin Heidelberg 2012This work is subject to copyright. All rights are reserved, whether the whole or part of the material isconcerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting,reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publicationor parts thereof is permitted only under the provisions of the German Copyright Law of September 9,1965, in its current version, and permission for use must always be obtained from Springer. Violationsare liable to prosecution under the German Copyright Law.The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply,even in the absence of a specific statement, that such names are exempt from the relevant protectivelaws and regulations and therefore free for general use.

Printed on acid-free paper

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Preface

Nowadays commercial computer programs are normally used for engine and vehicle

development for e.g. the simulation of the transient performance of vehicles or

of the complete power train as well as for the simulation of high-grade transient

processes in the engine combustion chamber.

As in general no source code for these computer programs is available and due to

time-consuming studies of the corresponding descriptions users often have insuffi-

cient knowledge concerning the physical and chemical contents of the models used

in these programs. Therefore it is our special concern to reveal different physical

and chemical approaches and to show options and limits of the models used. So the

focus of this book is definitely on the thermodynamical, fluid mechanical and

chemical base of modeling of motor-driven processes.

The book is composed of three parts. Part I describes the operation and the

thermodynamically base of combustion engines, the combustion and reaction

kinetics as well as emissions building in six chapters. This chapter is completed

by a proceeding concerning combustion measurement. Part II with Chaps. 7–9 is

dedicated to the operating process calculation, the charging process and the model-

ing of exhaust after-treatment systems. Part III contains Chaps. 10–15 and starts

with the overall process analysis. Part III is preferentially about the calculation

possibilities in the combustion engine for e.g. phenomenological combustion mod-

els, simulation of injection and combustion and 3D simulations for fluid flow and

supercharging.

We hope that we succeeded in showing a comprehensive and current description

of the simulation of motor-driven processes and we would appreciate if all academ-

ical and technical users will profit from this book.

We thank all authors for their constructive and diligent co-operation. All authors

and their employers or institutions as well as their responsibility for the proceedings

are mentioned in the prefix of the book. We say special thanks to AVL List GmbH

for their professional and substantial support during the compilation of this book.

We are much obliged to Mr. Gary Patterson who made the final correction of the

English translation and we are also very thankful for his critical remarks concerning

v

the precise terminology. Many thanks also to the Springer-Verlag especially to

Mrs. Ulrike Butz for the kind and good co-operation.

This book is a translation of the 4th German edition which was published by

the Vieweg-Teubner Verlag in 2009. For the present English edition the text was

updated and extended by an overview description regarding the 3D calculation

program FIRE which is developed and sold by AVL.

Tettnang, Germany Gunter P. Merker

Graz, Austria Rudiger Teichmann

vi Preface

Contents

Part I Foundations of Thermodynamics and Chemistry

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.1 Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2 Model-Building . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.3 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2 Reciprocating Engines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.1 Energy Conversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.2 Geometry of the Crankshaft Drive . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.3 Thermodynamics of the Internal Combustion Engine . . . . . . . . . . . . . . . . 15

2.3.1 Foundations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.3.2 Closed Cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.3.3 Open Comparative Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.4 Parameters and Characteristic Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

2.5 Engine Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

2.5.1 Spark Ignition Engines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

2.5.2 Diesel Engines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3 Combustion Diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.1 Basics of Pressure Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.1.1 Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.1.2 The Piezoelectric Measurement Chain . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.1.3 Assembly Variants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

3.1.4 Selection of the Measurement Location . . . . . . . . . . . . . . . . . . . . . . . . 63

3.1.5 Adjusting the Pressure Level: Zero Level

Correction (Pegging) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

3.1.6 Methods That Measure Absolute Pressure . . . . . . . . . . . . . . . . . . . . . 70

vii

3.1.7 Angle and Trigger Marking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

3.1.8 TDC Assignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

3.1.9 Pressure Indication in the Inlet and Outlet System . . . . . . . . . . . 78

3.1.10 Data Capture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

3.2 Pressure Trace Analysis and Loss Distribution . . . . . . . . . . . . . . . . . . . . . . . 81

3.2.1 Determination of the Heat Release Rate . . . . . . . . . . . . . . . . . . . . . . . 82

3.2.2 Loss Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

3.2.3 Case Study: Comparison of Various Combustion

Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

3.3 Optical Diagnostic Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

3.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

3.3.2 Optical Methods: An Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

3.3.3 Application Examples of Optical Methods . . . . . . . . . . . . . . . . . . . . . 93

3.3.4 Diesel Engines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

3.3.5 SI Engines Optical Diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

3.3.6 Laser Based Measurement Techniques . . . . . . . . . . . . . . . . . . . . . . . . 113

3.3.7 Optical Combustion Diagnostics: Status and Forecast . . . . . . . . 114

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

4 Engine Combustion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

4.1 Fuels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

4.1.1 Gasoline and SI Engine Fuels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

4.1.2 Diesel Fuels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

4.1.3 Alternative Fuels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

4.2 Diesel Engines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

4.2.1 Injection Methods and Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

4.2.2 Mixture Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

4.2.3 Autoignition and the Combustion Sequence . . . . . . . . . . . . . . . . . . 138

4.3 Spark Ignition Engines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

4.3.1 Differences Between Premixed Flame and Diffusion

Combustion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

4.3.2 Ignition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

4.3.3 Flame Front Propagation After Ignition, the Effect

of Turbulence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146

4.3.4 Information About Combustion Speed from the

Heat Release Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

4.3.5 Irregular Combustion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

4.3.6 Combustion Process, Mixture Formation, Modes

of Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

5 Reaction Kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169

5.1 Foundations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169

5.1.1 Chemical Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169

viii Contents

5.1.2 Reaction Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173

5.1.3 Partial Equilibrium and Quasi-Steady-State . . . . . . . . . . . . . . . . . . . 174

5.2 Reaction Kinetics of Hydrocarbons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176

5.2.1 Oxidation of Hydrocarbons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176

5.2.2 Ignition Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179

5.2.3 Reaction Kinetics in Engine Simulation . . . . . . . . . . . . . . . . . . . . . . 185

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191

6 Pollutant Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193

6.1 Exhaust Gas Composition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193

6.2 Carbon Monoxide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195

6.3 Unburned Hydrocarbons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196

6.3.1 Sources of HC Emissions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196

6.3.2 Non-limited Pollutant Components . . . . . . . . . . . . . . . . . . . . . . . . . . . 200

6.4 Particle Emission in the Diesel Engine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203

6.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203

6.4.2 Polycyclic Aromatic Hydrocarbons . . . . . . . . . . . . . . . . . . . . . . . . . . . 206

6.4.3 Soot Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208

6.4.4 Particle Emission Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211

6.5 Nitrogen Oxides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214

6.5.1 Thermal NO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214

6.5.2 Prompt NO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218

6.5.3 NO Formed via N2O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220

6.5.4 Fuel Nitrogen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220

6.5.5 Reactions Forming NO2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221

Part II Simulation of the Overall Process

7 Calculation of the Real Working Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227

7.1 Single-Zone Cylinder Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228

7.1.1 Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228

7.1.2 Mechanical Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230

7.1.3 Determination of the Mass Flow Through

the Valves/Valve Lift Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230

7.1.4 Heat Transfer in the Cylinder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234

7.1.5 Heat Transfer in the Exhaust Manifold . . . . . . . . . . . . . . . . . . . . . . . 243

7.1.6 Wall Temperature Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244

7.1.7 The Heat Release Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248

7.1.8 Knocking Combustion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261

7.1.9 Internal Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264

7.2 The Two-Zone Cylinder Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272

7.2.1 Modeling the High Pressure Range According

to Hohlbaum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272

Contents ix

7.2.2 Modeling the High Pressure Phase According

to Heider . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275

7.2.3 Results of NOx Calculation with Two-Zone Models . . . . . . . . . 279

7.2.4 Modeling the Gas Exchange for a Two-Stroke Engine . . . . . . . 279

7.3 Modeling the Gas Path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283

7.3.1 Modeling Peripheral Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284

7.3.2 Model Building . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285

7.3.3 Integration Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287

7.4 Gas Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288

7.4.1 Basic Equations of One-Dimensional Gas Dynamics . . . . . . . . . 288

7.4.2 Numerical Solution Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292

7.4.3 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295

7.5 Fuel System Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301

7.5.1 Modeling the Basic Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301

7.5.2 Application Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306

8 Charging of Internal Combustion Engines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309

8.1 Charging Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309

8.1.1 Pressure-Wave Charging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310

8.1.2 Mechanical Supercharging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313

8.1.3 Turbocharging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319

8.2 Simulation of Charging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332

8.2.1 Turbo Compressor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332

8.2.2 The Positive Displacement Charger . . . . . . . . . . . . . . . . . . . . . . . . . . . 341

8.2.3 The Flow Turbine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341

8.2.4 Turbochargers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353

8.2.5 Charge Air Cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362

9 Exhaust Aftertreatment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363

9.1 Modeling and Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364

9.2 Catalytic Converters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365

9.2.1 Basis Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365

9.2.2 Types of Catalytic Converters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 368

9.3 Diesel Particulate Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373

9.3.1 Basic Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374

9.3.2 Soot Loading and Pressure Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377

9.3.3 Regeneration and Temperature Distribution . . . . . . . . . . . . . . . . . . 379

9.4 Dosing Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380

9.5 System Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383

x Contents

Part III Simulation of Combustion and Charging

10 Total System Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387

10.1 General Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387

10.2 Thermal Engine Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 388

10.2.1 Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 388

10.2.2 Coolant System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 388

10.2.3 The Oil System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389

10.3 Engine Friction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 390

10.3.1 Friction Method for the Warm Engine . . . . . . . . . . . . . . . . . . . . 390

10.3.2 Friction Method for the Warm-up . . . . . . . . . . . . . . . . . . . . . . . . . 392

10.4 Stationary Simulation Results (Parameter Variations) . . . . . . . . . . . . 394

10.4.1 Load Variation in the Throttled SI Engine . . . . . . . . . . . . . . . . 394

10.4.2 Influence of Ignition and Combustion Duration . . . . . . . . . . 396

10.4.3 Variation of the Compression Ratio, Load,

and Peak Pressure in Large Diesel Engine . . . . . . . . . . . . . . . . 398

10.4.4 Investigations of Fully Variable Valve Trains . . . . . . . . . . . . 399

10.4.5 Variation of the Intake Pipe Length and the

Valve Durations (SI Engine, Full Load) . . . . . . . . . . . . . . . . . . 400

10.4.6 Exhaust Gas Recirculation in the Turbocharged

Passenger Car Diesel Engine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 401

10.5 Transient Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404

10.5.1 Acceleration of a Commercial Vehicle

from 0 to 80 km/h . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404

10.5.2 Turbocharger Intervention Possibilities . . . . . . . . . . . . . . . . . . . 406

10.5.3 Part Load in the ECE Test Cycle . . . . . . . . . . . . . . . . . . . . . . . . . 409

10.5.4 The Warm-up Phase in the ECE Test Cycle . . . . . . . . . . . . . . 409

10.5.5 Full Load Acceleration in the Turbocharged SI Engine . . 412

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414

11 Phenomenological Combustion Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415

11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415

11.2 Diesel Engine Combustion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417

11.2.1 Zero-Dimensional Heat Release Function . . . . . . . . . . . . . . . . 417

11.2.2 Stationary Gas Jet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 418

11.2.3 Packet Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423

11.2.4 Time Scale Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 430

11.3 SI Engine Combustion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433

11.3.1 Laminar and Turbulent Flame Front Speed . . . . . . . . . . . . . . . 433

11.3.2 Heat Release . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435

11.3.3 Ignition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 438

11.3.4 Knocking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 440

Contents xi

12 Three-Dimensional Flow Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443

12.1 Basic Fluid Mechanical Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443

12.1.1 Mass and Momentum Transport . . . . . . . . . . . . . . . . . . . . . . . . . . 443

12.1.2 Transport of Internal Energy and Species . . . . . . . . . . . . . . . . 447

12.1.3 Passive Scalars and the Mixture Fraction . . . . . . . . . . . . . . . . . 449

12.1.4 Conservative Formulation of the Transport Equations . . . 450

12.2 Turbulence and Turbulence Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 450

12.2.1 The Phenomenology of Turbulence . . . . . . . . . . . . . . . . . . . . . . . 450

12.2.2 Modeling Turbulence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 451

12.2.3 The Turbulent Law of the Wall . . . . . . . . . . . . . . . . . . . . . . . . . . . 455

12.2.4 Modeling the Turbulent Mixture State . . . . . . . . . . . . . . . . . . . . 457

12.2.5 The Validity of Turbulence Models: Alternative

Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 461

12.3 Numerics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465

12.3.1 The Finite Volume Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465

12.3.2 Discretization of the Diffusion Term:

Central Differences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 466

12.3.3 Discretization of the Convection Term:

The Upwind Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467

12.3.4 Discretization of the Time Derivation: Implicit

Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 469

12.3.5 Discretization of the Source Term . . . . . . . . . . . . . . . . . . . . . . . . 471

12.3.6 The Operator Split Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 472

12.3.7 Discretization and Numerical Solution of the

Momentum Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 472

12.4 Computational Meshes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473

12.5 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475

12.5.1 Simulation of Flow Structures in the Cylinder:

The SI Engine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475

12.5.2 Simulation of Flow Structures in the Cylinder:

Diesel Engines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 477

12.5.3 Internal Nozzle Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 479

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 482

13 Simulation of Injection Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483

13.1 Single-Droplet Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483

13.1.1 Momentum Exchange . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484

13.1.2 Mass and Heat Exchange (Single-Component Model) . . . 485

13.1.3 Mass and Heat Exchange in Multicomponent

Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 488

13.1.4 Flashboiling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 492

13.2 Spray Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493

13.2.1 The Boltzmann–Williams Equation . . . . . . . . . . . . . . . . . . . . . . . 494

xii Contents

13.2.2 The Numerical Solution of the Boltzmann–Williams

Equation; the Standard Model (Lagrange Formulation) . . . 496

13.2.3 Excursus: The Numerical Determination of Random

Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 498

13.2.4 Parcel Start Conditions at the Nozzle Exit . . . . . . . . . . . . . . 500

13.2.5 Modeling Breakup Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 501

13.2.6 Modeling Collision Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 506

13.2.7 Modeling Turbulent Dispersion in the Standard Model . . . 507

13.2.8 Describing Turbulent Dispersion with the

Fokker–Planck Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 508

13.2.9 Representing Diffusion with the Fokker–Planck

Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514

13.2.10 Problems in the Standard Spray Model . . . . . . . . . . . . . . . . . . 517

13.2.11 Application Example: Direct Gasoline Injection

for Stratified Charge with Centrally Arranged

Piezo-Actuated Outward-Opening Injector . . . . . . . . . . . . . 521

13.3 Euler Spray Models: Formulation of Spray Dynamics

with Observable Averages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523

13.3.1 Locally Homogeneous Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 525

13.3.2 The Embedding of 1D-Euler Methods and Other

Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 527

13.3.3 The 3D Euler Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 530

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 534

14 Simulation of Combustion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 537

14.1 Excursus: Combustion Regimes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 537

14.2 General Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 539

14.3 Diesel Combustion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 541

14.3.1 Simulation of Heat Release . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 542

14.3.2 Ignition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 549

14.3.3 NOx Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 550

14.3.4 Soot Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 551

14.3.5 HC and CO Emissions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 552

14.4 The Homogeneous SI Engine (Premixed Combustion) . . . . . . . . . . . 553

14.4.1 The Two-Phase Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 553

14.4.2 The Magnussen Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 556

14.4.3 Flame Surface Density Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 561

14.4.4 The G-Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 564

14.4.5 The Diffusive G-Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 568

14.4.6 Ignition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 569

14.4.7 Knocking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 569

14.4.8 Pollutant Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 570

14.5 The SI Engine with Stratified Charge (Partially

Premixed Flames) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 570

Contents xiii

14.6 Fluid-Mechanical Simulation of Charge Exchange,

Mixture Formation and Combustion: Future Prospects . . . . . . . . . . . 575

14.6.1 Mesh Movement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 576

14.6.2 Numerics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 577

14.6.3 Turbulence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 578

14.6.4 Modeling Injection Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 578

14.6.5 Modeling Combustion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 582

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 583

15 3D Supercharging Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 585

15.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 585

15.2 Foundations of the 3D Simulation of Turbo-Machines . . . . . . . . . . . 586

15.2.1 The Treatment of Different and Various Moving

Coordinate Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 586

15.2.2 Grid Generation for Turbo-Machines . . . . . . . . . . . . . . . . . . . . . 589

15.2.3 The Creation of Calculation Models and Boundary

Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 591

15.3 Postprocessing: Analysis and Visualization of Results . . . . . . . . . . . 593

15.4 Examples of Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 595

15.4.1 Analysis of Compressor Behavior . . . . . . . . . . . . . . . . . . . . . . . . 595

15.4.2 Examination of Turbine Variants . . . . . . . . . . . . . . . . . . . . . . . . . 599

Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 601

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 631

xiv Contents

Chapters, Contributions and Authors

Univ.-Prof. Dr.-Ing. habil. Gunter P. Merker Chapter 1, 2

Leibniz Universitat, Hannover, g.p.merker@t-online.de www.uni-hannover.de

Dr.-Ing. Rudiger Teichmann Section 3.1, 3.3

AVL LIST GmbH, Graz, Austria, ruediger.teichmann@avl.com www.avl.com

Ao.Univ.-Prof. Dr. techn. Andreas Wimmer Section3.1

Technical University Graz, andreas.wimmer@lec.tugraz.at, www.tugraz.at

apl. Prof. Dr.-Ing. habil. Christian Schwarz Chapter 7,10; Section 3.2

BMW AG, Munchen, christian.schwarz@bmw.de, www.bmw.de

Dr. Ernst Winklhofer Section 3.3

AVL LIST GmbH, Graz, Austria, ernst.winklhofer@avl.com, www.avl.com

Dr.-Ing. Sebastian Rakowski Chapter 6; Section 4.1,4.2,11.3

WABCO Development GmbH, sebastian.rakowski.sr@googlemail.com,

www.wabco.de

Dr.-Ing. Peter Eckert Chapter 6; Section 4.2, 5.2, 11.3

IAV GmbH, Berlin, peter.eckert@iav.de, www.iav.de

Prof. Dr. techn. Andreas Witt Section 4.3

BMW AG, Munchen, andreas.witt@bmw.de, www.bmw.de

Prof. Dr.-Ing. habil. Gunnar Stiesch Section 5.1, 5.2, 11.2

MAN Diesel SE, Augsburg, gunnar.stiesch@man.eu, www.mandiesel.com

Dr.-Ing. Claus Reulein Chapter 8

BMW AG, Munchen, claus.reulein@bmw.de, www.bmw.de

Dr. Reinhard Tatschl Chapter 9; Appendix

AVL LIST GmbH, Graz, Austria, reinhard.tatschl@avl.com, www.avl.com

Dr. Johann Wurzenberger Chapter 9

AVL LIST GmbH, Graz, Austria, johann.wurzenberger@avl.com, www.avl.com

xv

Dr. rer. nat. Frank Otto Chapter 12, 13, 14

Daimler AG, Stuttgart, frank.otto@daimler.com, www.daimler.de

Dr.-Ing. Christian Kruger Chapter 12, 13, 14

Daimler AG, Stuttgart, christian.c.krueger@daimler.com, www.daimler.de

Dr.-Ing. Bodo Durst Chapter 15

BMW AG, Munchen, bodo.durst@bmw.de, www.bmw.de

xvi Chapters, Contributions and Authors

List of Companies and Universities

Companies

AVL LIST GmbH, Graz, Austria Dr. Reinhard Tatschl

Dr.-Ing. Rudiger Teichmann

Dr. Ernst Winklhofer

Dr. Johann Wurzenberger

BMW AG, Munchen Dr.-Ing. Bodo Durst

Dr.-Ing. Claus Reulein

apl. Prof. Dr.-Ing. habil. Christian Schwarz

Dr. techn. Andreas Witt

Daimler AG, Stuttgart Dr.-Ing. Christian Kruger

Dr. rer. nat. Frank Otto

IAV GmbH, Berlin Dr.-Ing. Peter Eckert

Dr.-Ing. Sebastian Rakowski

MAN Diesel SE, Augsburg apl. Prof. Dr.-Ing. habil. Gunnar Stiesch

WABCO Development GmbH Dr.-Ing. Sebastian Rakowski

Universities

Leibniz University Hannover Univ.-Prof. Dr.-Ing. habil. Gunter P. Merker

Technical University Graz, Austria Ao. Univ.-Prof. Dr. techn. Andreas Wimmer

xvii

.

The Editors

Univ.-Prof. Dr.-Ing. habil. Gunter P. Merker was born in Augsburg/Germany in

1942. He studied mechanical engineering at the Technical University in Munich

and received his diploma in 1969. He worked then as an assistant lecturer at this

Institute and got his PhD in 1974 with a thesis on free convection problems. From

1975 to 1976, he has been as a research fellow at the Californian Institute of

Technology in Pasadena/CA. Having returned to the Munich Technical University,

he qualified as a university lecturer in 1978. From 1978 to 1980, he was with

MTU GmbH in Munich. In 1980 he accepted an associate professorship for

refrigeration technology at the University of Karlsruhe. In 1986 he started work

at MTU Friedrichshafen, where he was head of the department analytics and engine

calculation. In 1994 he accepted a full professorship for combustion engines at the

University of Hannover. There he was head of the Institute of Technical Combus-

tion until he retired in 2005. He was adviser to 43 PhD students. He is editor and

co-editor of more than 140 technical scientific publications as well as six technical

books on thermal transmission, fluid mechanics and combustion engines. He is a

member of the Scientific Association in Braunschweig as well as of different

technical committees. In addition to that, he works as an independent adviser for

engine manufactories and service industries.

Apl. Prof. Dr.-Ing. habil. Christian Schwarz was born in Regensburg in 1964. From1983 to 1988, he studied mechanical engineering at the Munich Technical Uni-

versity. From 1989 to 1993, he worked as an assistant lecturer at the chair of

internal combustion engines and vehicles at the Munich Technical University

(Prof. Woschni). During that time he worked on unsteady, 0-dimensional process

calculation for charged and quickly working diesel engines and got his PhD in 1993

on his thesis “Simulation of the transient reaction of charged diesel engines during

operation”. Still at the same university, he was head of a team that worked on a part

of the EU research project “Hybrid Zero Emission Mobility” (1993–1997). In 1998

he qualified as a university lecturer, his treatise was on “Theory and Simulation of

Charged Combustion Engines”. He was appointed private lecturer by the University

of Hannover in 1999, and he got the venia legendi in combustion engines. Since

xix

then he has been teaching the subject “simulation of processes in combustion

engines”. In 2004 the Hannover University conferred him the title “apl. Prof.”.

In 1997 he started work in the department for advance development at BMW

AG. In 2001 he was appointed head of this department and was responsible for the

development of new combustion techniques for spark ignition (SI) engines, such as

direct hydrogen ignition, as well as of new concepts for charged SI engines. Since

2004 he has been working in series development, being responsible for the devel-

opment of combustion techniques of the SI engines produced in series. He has

supervised several dissertations on combustion engines. Besides, he is the author

and co-author of several publications and lectures, as well as of a technical book

about combustion techniques and the charging of combustion engines.

In the research association about internal combustion engines, he is head of the

planning team for total processes, and he is also part of its scientific advisory board.

Dr.-Ing. Rudiger Teichmann was born in Nordhausen in 1960. He studied mechan-

ical engineering at the Technical University Dresden from 1982 till 1987. After his

study he became a research student and a scientific staff member till 1990. In 1991

he got his PhD with a thesis on combustion development for truck diesel engines.

In the same year he started his professional carrier in the department for advance

development at BMW AG in Munich. His special fields of work were thermody-

namic, combustion development, load exchange for gasoline engines and cali-

bration in series development as well. In 1999 he became the head of product

management for the complete indicating measurement chain at AVL List GmbH in

Graz. After 3 years he was nominated as segment leader “Indicating Measurement”

and global business segment leader for “Combustion Measurement” in 2005. In

addition to this responsibility he is in charge of the vehicle measurement activities

from AVL since 2007. Mr. Teichmann is author and co-author of several publica-

tions and tutor of diploma thesis.

xx The Editors

Abbreviations

BDC Bottom Dead Center

BMEP Brake mean effective pressure

BV Burning function

CNG Compressed Natural Gas

CR Common Rail

DI Direct injection

DME Dimethylether

EGR Exhaust gas recirculation

EV Injection valve

FAME Fatty Acid Methyl Ester

GDI Gasoline direct injection

HE Hydro-erosive (cavitation)

ID Ignition delay

IMEP Indicated mean effective pressure

IR Injection rate

IV Injection valve

LDA Laser Doppler Anemomentry

LIF Laser induced Fluorescence

LPG Liquified Petroleum Gas

MOZ Engine octan number

PAK Polycyclic aromatic hydrocarbons

PCV Pressure Control Valve

PDA Phase Doppler Anemometry

PIV Particle image velocimetry

RG Residual gas

RME Rape methylester

RoHR Rate of heat release

ROZ Research octan number

TC Turbo charged; Turbocharger

xxi

TDC Compression Top Dead Center

UV Ultraviolet

VI Unit injector

V-Soot Soot number based on flame analysis

ZZP Start of ignition

Symbols

A Flame front surface [m2]

Bm, Bl Coefficient to laminar flame velocity

C Damkoehler-Coefficient

c Constant

cp Specific heat at constant pressure

cv Specific heat at constant volume

Cd Flow coefficient

cL, cT Integral length scale coefficient

cm Medium piston velocity [m/s]

E Energy

Ex Expansion factor describing heat release (premixed)

h Specific enthalpy [J/kg]

Hs Specific heating value [J/kg]

HU, Hu Lower heating value [J/kg]

K Cavitation number

k Turbulent kinetic energy [m2/s2]

Ki Cavitation index

lI Integrale length scale [m]

lT Taylor length scale

m Mass [kg]

n General parameter

p Pressure [bar]

Pme Mean effective pressure [bar]

Q Heat release [W]

s Flame velocity [m/s]

T Temperature [K]

t Time

u Turbulent velocity fluctuation[m/s]

V Volume [m3]; volume flow [m3/s]

X1, X2, X3 Parameters for Livengood–Wu Integral

�v Pipe flow coefficient

xxii Abbreviations

Indices

0 Quiescent condition; standard reference

1 inlet

2 exit

ad Adiabatic

crit critical

dif Diffusion

e or i Inlet

f Fuel

F Fuel

ID Ignition delay

iv Inlet valve

l Laminar

m, M Mean

nock If knocking occurs

p constant pressure

pre Pre-mixed

R or RG Residual gas

s isentropic

SOI Start of ignition

t Turbulent

u Environment; Unburned

v constant volume

vap Vapour pressure (in combination with pressure)

(Greek) Symbols

Dhi Reaction enthalpy of i-th reaction

Dpak Partial pressure difference across ash thickness

Dprk Partial pressure difference across soot filtration layer

Dprk Partial pressure difference across soot thickness

Dpw Partial pressure loss across the wall

AF,n Cross-section of pipe

ageo Geometric surface of monolith

cg Gas composition

cj,g Concentration of species j in gas

cL Surface concentration of species

cp,s Heat capacity of solid phase

Deff Effective diffusion coefficient

Abbreviations xxiii

dhyd Hydraulic diameter of the pipe

di Diameter of the pipe

Fn Friction coefficient

Gzh Graetz number for heat transfer

Gzm Graetz number to mass transfer

hj Enthalpy of species j under gaseous condition

kw,krt,kak,krk Permeability of considered layers

MGj Molar mass of species j

mruss,in Intake mass flow of soot

pg Gas pressure

pg,n Pressure in pipe

PS,n Circumference of channel

ri Reaction rate of species j

Sc Schmidt-number

Srk Soot filtration coefficient

t Characteristic time [s]

t Time

Tg Gas temperature

Ts Wall temperature

vg Gas phase velocity

vg,n Free flow velocity in pipe

vw Wall velocity

vw,n Normalized wall velocity

vw,n Velocity in porous wall

wg,1 Wall velocity

wj,g Mass fraction of species j

x Length coordinate

z Length coordinate

a Heat transfer coefficient between gaseous and solid condition

a General parameter

b General parameter

bj Mass transfer coefficient of species (j)

G Free surface

dak Ash thickness

drk Soot thickness

k Isentropic exponent

l Air/fuel ratio

lg Heat conductivity of the gas

ls Heat transfer coefficient of wall

m Dynamic viscosity; First viscosity coefficient [Ns/m2]

ni,j Stoichiometric coefficient of species (j) of i-th reaction

x Contraction number; pipe friction number

r Density [kg/m3]

xxiv Abbreviations

rg Density of the gas

rg,n Density in pipe

rs Density of solid phase

tfluid, tchem Physical and chemical mixing time [s]

j Crankshaft angle [�CA]Ф Ratio of equivalence

Abbreviations xxv

.