Combustion Engines Development - Springer978-3-642-14094-5/1 · Gu¨nter P. Merker Christian...
Transcript of Combustion Engines Development - Springer978-3-642-14094-5/1 · Gu¨nter P. Merker Christian...
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 [email protected]
Dr.-Ing. Rudiger TeichmannAVL List GmbHHans-List-Platz 18020 [email protected]
Apl. Prof. Dr.-Ing. habil.Christian SchwarzBMW-GroupEA 31Hufelandstr. 8a80788 [email protected]
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.
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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, [email protected] www.uni-hannover.de
Dr.-Ing. Rudiger Teichmann Section 3.1, 3.3
AVL LIST GmbH, Graz, Austria, [email protected] www.avl.com
Ao.Univ.-Prof. Dr. techn. Andreas Wimmer Section3.1
Technical University Graz, [email protected], www.tugraz.at
apl. Prof. Dr.-Ing. habil. Christian Schwarz Chapter 7,10; Section 3.2
BMW AG, Munchen, [email protected], www.bmw.de
Dr. Ernst Winklhofer Section 3.3
AVL LIST GmbH, Graz, Austria, [email protected], www.avl.com
Dr.-Ing. Sebastian Rakowski Chapter 6; Section 4.1,4.2,11.3
WABCO Development GmbH, [email protected],
www.wabco.de
Dr.-Ing. Peter Eckert Chapter 6; Section 4.2, 5.2, 11.3
IAV GmbH, Berlin, [email protected], www.iav.de
Prof. Dr. techn. Andreas Witt Section 4.3
BMW AG, Munchen, [email protected], www.bmw.de
Prof. Dr.-Ing. habil. Gunnar Stiesch Section 5.1, 5.2, 11.2
MAN Diesel SE, Augsburg, [email protected], www.mandiesel.com
Dr.-Ing. Claus Reulein Chapter 8
BMW AG, Munchen, [email protected], www.bmw.de
Dr. Reinhard Tatschl Chapter 9; Appendix
AVL LIST GmbH, Graz, Austria, [email protected], www.avl.com
Dr. Johann Wurzenberger Chapter 9
AVL LIST GmbH, Graz, Austria, [email protected], www.avl.com
xv
Dr. rer. nat. Frank Otto Chapter 12, 13, 14
Daimler AG, Stuttgart, [email protected], www.daimler.de
Dr.-Ing. Christian Kruger Chapter 12, 13, 14
Daimler AG, Stuttgart, [email protected], www.daimler.de
Dr.-Ing. Bodo Durst Chapter 15
BMW AG, Munchen, [email protected], 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
.