Table Of ContentModeling Engine Spray and Combustion Processes
Springer-Verlag BerlinHeidelberg GmbH
ONLINE lIBRARY
Engineering
http://www.springer.de/engine/
Gunnar Stiesch
Modeling Engine Spray
and Combustlon Processes
Springer
DR.-ING. GUNNAR STIESCH
Universtät Hannover
Instit. f. Technische Verbrennung
Welfengarten 1 A
30167 Hannover
Germany
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ISBN 978-3-642-05629-1 ISBN 978-3-662-08790-9 (eBook)
DOI 10.1007/978-3-662-08790-9
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Preface
The utilization of mathematical models to numerically describe the performance
of internal combustion engines is of great significance in the development of new
and improved engines. Today, such simulation models can already be viewed as
standard tools, and their importance is likely to increase further as available com
puter power is expected to increase and the predictive quality of the models is
constantly enhanced.
This book describes and discusses the most widely used mathematical models
for in-cylinder spray and combustion processes, which are the most important
subprocesses affecting engine fuel consumption and pollutant emissions. The
relevant thermodynamic, fluid dynamic and chemical principles are summarized,
and then the application of these principles to the in-cylinder processes is ex
plained. Different modeling approaches for the each subprocesses are compared
and discussed with respect to the governing model assumptions and simplifica
tions. Conclusions are drawn as to which model approach is appropriate for a
specific type of problem in the development process of an engine. Hence, this
book may serve both as a graduate level textbook for combustion engineering stu
dents and as a reference for professionals employed in the field of combustion en
gine modeling.
The research necessary for this book was carried out during my employment as
a postdoctoral scientist at the Institute of Technical Combustion (ITV) at the Uni
versity of Hannover, Germany and at the Engine Research Center (ERC) at the
University of Wisconsin-Madison, USA. The text was accepted in partial fulfill
ment of the requirements for the postdoctoral Habilitation-degree by the Depart
me nt of Mechanical Engineering at the University of Hannover.
Many individuals have assisted me in various ways while I have worked on this
book. First and foremost I would like to thank Prof. Günter P. Merker, the direc
tor of the ITV, for supporting my work in every possible respect. Many ideas for
this book were obtained from our numerous stimulating discussions about the sub
ject of engine modeling. I am also indebted to Prof. Rolf D. Reitz, the director of
the ERC, for inviting me to the University of Wisconsin-Madison and for teaching
me many aspects about multidimensional engine codes during my stay at the ERC.
Professor Dieter Mewes of the University of Hannover and Prof. Meinrad K.
Eberle of the ETH Zurich, Switzerland contributed to this work by their critical
reviews and constructive comments.
Special thanks are due to my colleagues and friends both at the University of
Hannover and at the University of Wisconsin-Madison for providing an inspiring
environment in which to carry out engine research.
VI Preface
I would like to acknowledge Mrs. Christina Brauer, the tracer at the ITV, for
her thoughtful assistance with the schematic illustrations and technical drawings
contained in this book.
Last but not least, I would like to thank my family for their constant support
and understanding while I was working on the manuscript.
Hannover, January 2003 Gunnar Stiesch
Contents
v
Preface ...•.........•.•.•...•.•.........•.•.•.....•..........•.•.•.....•.•...•.......•...•.....•.•.•......................
Contents ............................................................................................................. VII
Nomenclature ...................................................................................................... XI
1 Introduction ........................................................................................................ 1
1.1 Modeling of Combustion Processes ............................................................ 1
1.2 Direct Injection Combustion Engines .......................................................... 3
2 Thermodynamic Models .................................................................................... 5
2.1 Thermodynamic Fundamentals ................................................................... 5
2.2 Single-Zone Cylinder Model ....................................................................... 6
2.2.1 Mass and Energy Balances ................................................................... 6
2.2.2 Mass Fluxes ......................................................................................... 8
2.2.3 Mechanical Work ............................................................................... 12
2.2.4 Wall Heat Transfer ............................................................................. l4
2.2.5 Heat Release by Combustion ............................................................. 16
2.2.6 Ignition Delay .................................................................................... 21
2.2.7 Internal Energy ................................................................................... 23
2.3 Two-Stroke Scavenging Models ................................................................ 28
2.4 Empirical Two-Zone Combustion ModeL ............................................... 32
2.5 Typical Applications .................................................................................. 35
2.5.1 Heat Release Analysis ........................................................................ 35
2.5.2 Analysis of Complete Power Systems ............................................... 35
References ....................................................................................................... 37
3 Phenomenological Models ............................................................................... 41
3.1 Classification ............................................................................................. 41
3.2 Heat Release in Diesel Engines ................................................................. 43
3.2.1 Zero-Dimensional Buming Rate Function ......................................... 43
3.2.2 Free Gas Jet Theory ........................................................................... 47
3.2.3 Packet Models .................................................................................... 57
3.2.4 Time Scale Models ............................................................................. 67
3.3 Gas Composition and Mixing in Diesel Engines ....................................... 72
3.3.1 Two-Zone Cylinder Models ............................................................... 72
3.3.2 N-Zone Cylinder Models ................................................................... 75
VIII Contents
3.3.3 Packet Models .................................................................................... 76
3.4 Advanced Heat Transfer Models ............................................................... 77
3.4.1 Heat Transfer Mechanisms ................................................................ 77
3.4.2 Convective and Radiative Heat Transfer Model ................................ 78
3.5 SI Engine Combustion ............................................................................... 88
3.5.1 Buming Rate Calculation ................................................................... 88
3.5.2 Gas Composition ................................................................................ 91
3.5.3 Engine Knock ..................................................................................... 92
References ....................................................................................................... 96
4 Fundamentals of Multidimensional CFD-Codes ......................................... 101
4.1 Conservation Equations ........................................................................... 101
4.2 Numerical Methodology .......................................................................... 104
4.3 Turbulence Models .................................................................................. 109
4.4 Boundary Layers and Convective Heat Transfer ..................................... 112
4.5 Application to In-Cylinder Processes ...................................................... 116
References ..................................................................................................... 117
5 Multidimensional Models of Spray Processes .............................................. 119
5.1 General Considerations ........................................................................... 119
5.1.1 Spray Processes in Combustion Engines ......................................... 119
5.1.2 Spray Regimes ................................................................................. 120
5.2 The Spray Equation ................................................................................. 122
5.2.1 Equations and Exchange Terms ....................................................... 122
5.2.2 Numerical Implementation ............................................................... 124
5.3 Droplet Kinematics .................................................................................. 126
5.3.1 Drop Drag and Deformation ............................................................ 126
5.3.2 Turbulent Dispersion / Diffusion ..................................................... 128
5.4 Spray Atomization ................................................................................... 130
5.4.1 Breakup Regimes ............................................................................. 131
5.4.2 Wave-Breakup Model ...................................................................... 135
5.4.3 Blob-Injection Model ....................................................................... 137
5.4.4 Turbulence and Cavitation Based Primary Breakup Model.. ........... 139
5.4.5 Sheet-Atomization Model for Hollow-Cone Sprays ........................ 146
5.5 Secondary Droplet Breakup ..................................................................... 153
5.5.1 Drop Breakup Regimes .................................................................... 153
5.5.2 The Reitz-Diwakar Model ............................................................... 154
5.5.3 The Taylor-Analogy Breakup ModeI... ............................................ 155
5.5.4 The Kelvin-Helmholtz Breakup ModeL ......................................... 158
5.5.5 The Rayleigh-Taylor Breakup Model .............................................. 159
5.6 DropletIDroplet and SpraylWall Interactions .......................................... 161
5.6.1 Droplet Collision and Coalescence .................................................. 161
5.6.2 Spray-Wall Impingement ................................................................. 165
5.7 Fuel Evaporation ..................................................................................... 171
5.7.1 Droplet Evaporation ......................................................................... 172
5.7.2 Multi-Component Fuels ................................................................... 174
Contents IX
5.7.3 Flash Boiling .................................................................................... 180
5.8 Grid Dependencies .................................................................................. 181
5.8.1 Problem Description ........................................................................ 181
5.8.2 Reduction of Grid Dependencies ..................................................... 183
References .......................................................... ,. ......................................... 186
6 Multidimensional Combustion Models ........................................................ 193
6.1 Combustion Fundamentals ...................................................................... 193
6.1.1 Chemical Equilibrium ...................................................................... 193
6.1.2 Reaction Kinetics ............................................................................. 196
6.1.3 Reaction Mechanisms for Hydrocarbon Flames .............................. 198
6.1.4 Combustion Regimes and Flame Types ........................................... 202
6.2 Ignition Processes .................................................................................... 205
6.2.1 Ignition Fundamentals ...................................................................... 205
6.2.2 Autoignition Modeling ..................................................................... 209
6.2.3 Spark-Ignition Modeling .................................................................. 213
6.3 Premixed Combustion ............................................................................. 222
6.3.1 The Flamelet Assumption ................................................................ 222
6.3.2 Eddy-Breakup Models ..................................................................... 222
6.3.3 Flame Area Evolution Models ......................................................... 224
6.3.4 The Fractal Model ............................................................................ 227
6.4 Diffusion Combustion ............................................................................. 228
6.4.1 The Characteristic Time Scale Model .............................................. 228
6.4.2 Flamelet Models ............................................................................... 230
6.4.3 pdf-Models ....................................................................................... 238
6.5 Partially Premixed Combustion in DISI Engines .................................... 241
6.5.1 Flame Structure ................................................................................ 241
6.5.2 A Formulation based on Lagrangian Flame Front Tracking ............ 242
6.5.3 A Formulation based on the G-Equation .......................................... 246
References ..................................................................................................... 249
7 Pollutant Formation ....................................................................................... 255
7.1 Exhaust Gas Composition. ....................................................................... 255
7.2 Nitrogen Oxides ....................................................................................... 257
7.2.1 Reaction Paths .................................................................................. 257
7.2.2 Thermal NO ..................................................................................... 258
7.2.3 Prompt NO ....................................................................................... 260
7.3 Soot. ......................................................................................................... 26.1
7.3.1 Phenomenology ................................................................................ 261
7.3.2 Semi-Global Mechanisms ................................................................ 264
7.3.3 Detailed Chemistry Mechanisms ..................................................... 269
References ..................................................................................................... 271
8 Conclusions ..................................................................................................... 275
Index ................................................................................................................... 279
