Heat and Mass Transfer Series Editors: D. Mewes and F. Mayinger Carsten Baumgarten Mixture Formation in Internal Combustion Engines With 180Fi guresand 9 Tables Dr.-Ing. CarstenBau mgarten, MTU Friedrichshafen GmbH Maybachplatz 1 88045 Friedrichshafen Germany Series Editors Prof. Dr.-Ing. Dieter Mewes Prof. em. Dr.-Ing. E.h. Franz Mayinger Universität Hannover Technische Universität München Institut für Verfahrenstechnik Lehrstuhl für Thermodynamik Callinstr. 36 Boltzmannstr. 15 30167 Hannover, Germany 85748 Garching, Germany Library of CongressC ontrol Number: 2005937086 issn-1860-4846 isbn-103-540-30835-0 Springer-Verlag Berlin Heidelberg New York isbn-13978-3-540-30835-5 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifi cally the rights of translation, reprinting, reuse of illustrations, recitations, broadcasting, reproduction on microfi lm or in any other way, and storage in data banks. 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Typesetting: Digital data supplied by editor Cover design: deblik Berlin Printed on acid free paper 62/3020/SPI Publisher Services - 5 4 3 2 1 0 Preface A systematic control of mixture formation with modern high-pressure injection systems enables us to achieve considerable improvements of the combustion proc- ess in terms of reduced fuel consumption and engine-out raw emissions. However, because of the growing number of free parameters due to more flexible injection systems, variable valve trains, the application of different combustion concepts within different regions of the engine map, etc., the prediction of spray and mix- ture formation becomes increasingly complex. For this reason, the optimization of the in-cylinder processes using 3D computational fluid dynamics (CFD) becomes increasingly important. In these CFD codes, the detailed modeling of spray and mixture formation is a prerequisite for the correct calculation of the subsequent processes like ignition, combustion and formation of emissions. Although such simulation tools can be viewed as standard tools today, the predictive quality of the sub-models is con- stantly enhanced by a more accurate and detailed modeling of the relevant proc- esses, and by the inclusion of new important mechanisms and effects that come along with the development of new injection systems and have not been consid- ered so far. In this book the most widely used mathematical models for the simulation of spray and mixture formation in 3D CFD calculations are described and discussed. In order to give the reader an introduction into the complex processes, the book starts with a description of the fundamental mechanisms and categories of fuel in- jection, spray break-up, and mixture formation in internal combustion engines. They are presented in a comprehensive way using data from experimental investi- gations. Next, the basic equations needed for the simulation of mixture formation processes are derived and discussed in order to give the reader the basic knowl- edge needed to understand the theory and to follow the description of the detailed sub-models presented in the following chapters. These chapters include the model- ing of primary and secondary spray break-up, droplet drag, droplet collision, wall impingement, and wall film formation, evaporation, ignition, etc. Different model- ing approaches are compared and discussed with respect to the theory and underlying assumptions, and examples are given in order to demonstrate the capabilities of today’s simulation models as well as their shortcomings. Further on, the influence of the computational grid on the numerical computation of spray processes is discussed. The last chapter is about modern and future mixture formation and combustion processes. It includes a discussion of the potentials and future developments of high-pressure direct injection diesel, gasoline, and homogeneous charge compression ignition engines. VI Preface This book may serve both as a graduate level textbook for combustion engi- neering students and as a reference for professionals employed in the field of combustion engine modeling. The research necessary to write this book was carried out during my employ- ment as a postdoctoral scientist at the Institute of Technical Combustion (ITV) at the University of Hannover, Germany. The text was accepted in partial fulfillment of the requirements for the postdoctoral Habilitation-degree by the Department of Mechanical Engineering at the University of Hannover. There are many people who helped me in various ways while I was working on this book. First, I would like to thank Prof. Dr.-Ing. habil. Günter P. Merker, the director of the Institute of Technical Combustion, for supporting my work in every possible respect. Prof. Dr.-Ing. Ulrich Spicher, the director of the Institute of Re- ciprocating Engines, University of Karlsruhe, and Prof. Dr.-Ing. habil. Dieter Mewes, the director of the Institute of Process Engineering, University of Han- nover, contributed to this work by their critical reviews and constructive com- ments. I would also like to thank my colleagues and friends at the University of Han- nover who gave me both, information and helpful criticism, and who provided an inspiring environment in which to carry out my work. Special thanks go to Mrs. Christina Brauer for carrying out all the schematic illustrations and technical drawings contained in this book. Hannover, October 2005 Carsten Baumgarten Contents Preface.................................................……………..........……….…………….. V Contents……………………………………………………..……………….... VII Nomenclature………………………………………………………………..… XI 1 Introduction………………………………………………………………….... 1 1.1 Modeling of Spray and Mixture Formation Processes………………...…. 1 1.2 Future Demands…………………………………………………...……... 3 2 Fundamentals of Mixture Formation in Engines…………………………… 5 2.1 Basics………………………………………………………………....…... 5 2.1.1 Break-Up Regimes of Liquid Jets……………………………....…… 5 2.1.2 Break-Up Regimes of Liquid Drops………………………………… 8 2.1.3 Structure of Engine Sprays…………………………………...……. 10 2.1.4 Spray-Wall Interaction…………………………………………...... 29 2.2 Injection Systems and Nozzle Types……………………………...……. 32 2.2.1 Direct Injection Diesel Engines………………………………....…. 32 2.2.2 Gasoline Engines………………………………………………...… 38 References……………………………………………………………...….... 43 3 Basic Equations…………………………………………………………....… 47 3.1 Description of the Continuous Phase………………………………...…. 47 3.1.1 Eulerian Description and Material Derivate…………………...…... 47 3.1.2 Conservation Equations for One-Dimensional Flows………...…… 49 3.1.3 Conservation Equations for Multi-Dimensional Flows…………..... 54 3.1.4 Turbulent Flows………………………………………………....…. 66 3.1.5 Application to In-Cylinder Processes…………………………...…. 79 3.2 Description of the Disperse Phase……………………………………… 81 3.2.1 Spray Equation…………………………………………………….. 81 3.2.2 Monte-Carlo Method…………………………………………….… 82 3.2.3 Stochastic-Parcel Method…………………………………....…….. 82 3.2.4 Eulerian-Lagrangian Description…………………………..…...…. 83 References…………………………………………………………….....….. 83 4 Modeling Spray and Mixture Formation………………………...……... 85 4.1 Primary Break-Up……………………………………………….……… 85 VIII Contents 4.1.1 Blob-Method……………………………………………………….. 86 4.1.2 Distribution Functions…………………………………………..…. 90 4.1.3 Turbulence-Induced Break-Up…………………………………….. 94 4.1.4 Cavitation-Induced Break-Up……………………………………… 98 4.1.5 Cavitation and Turbulence-Induced Break-Up………………..….. 100 4.1.6 Sheet Atomization Model for Hollow-Cone Sprays…………….... 109 4.2 Secondary Break-Up………………………………………………...…. 114 4.2.1 Phenomenological Models……………………………………...… 115 4.2.2 Taylor Analogy Break-Up Model……………………………….... 116 4.2.3 Droplet Deformation and Break-Up Model…………………...….. 122 4.2.4 Kelvin-Helmholtz Break-Up Model…………………………….... 125 4.2.5 Rayleigh-Taylor Break-Up Model……………………………...… 128 4.3 Combined Models……………………………………………………... 130 4.3.1 Blob-KH/RT Model……………………………………….……… 130 4.3.2 Blob-KH/DDB Model……………………………………….……. 131 4.3.3 Further Combined Models………………………………………... 132 4.3.4 LISA-TAB Model……………………………………………...…. 133 4.3.5 LISA-DDB Model…………………………………………...…… 135 4.4 Droplet Drag Modeling…………………………………………..……. 136 4.4.1 Spherical Drops……………………………………………….….. 136 4.4.2 Dynamic Drag Modeling………………………………….……… 136 4.5 Evaporation……………………………………………………...…….. 139 4.5.1 Evaporation of Single-Component Droplets…………………...…. 140 4.5.2 Evaporation of Multi-Component Droplets…………………...….. 144 4.5.3 Flash-Boiling…………………………………………………….... 158 4.5.4 Wall Film Evaporation………………………………….………… 162 4.6 Turbulent Dispersion……………………………………………….….. 166 4.7 Collision and Coalescence………………………………………….….. 169 4.7.1 Droplet Collision Regimes…………………………………….….. 169 4.7.2 Collision Modeling…………………………………………….…. 172 4.7.3 Implementation in CFD Codes…………………………..……….. 178 4.8 Wall Impingement………………………………………………...…… 180 4.8.1 Impingement Regimes………………………………………….… 181 4.8.2 Impingement Modeling…………………………………………… 183 4.8.3 Wall Film Modeling………………………………………….…… 191 4.9 Ignition…………………………………………………………...……. 197 4.9.1 Auto-Ignition………………………………………………...……. 197 4.9.2 Spark-Ignition…………………………………………………….. 200 References…………………………………………………………………. 203 5 Grid Dependencies…………………………………………………………. 211 5.1 General Problem……………………………………………………..… 211 5.2 Improved Inter-Phase Coupling……………………………………..… 216 5.3 Improved Collision Modeling……………………………………….… 220 5.4 Eulerian-Eulerian Approaches……………………………………...….. 221 References…………………………………………………………………. 223 Contents IX 6 Modern Concepts…………………………………………………………... 225 6.1 Introduction……………………………………………………………. 225 6.2 DI Diesel Engines…………………………………………………..….. 226 6.2.1 Conventional Diesel Combustion………………………………… 226 6.2.2 Multiple Injection and Injection Rate Shaping……………...……. 230 6.2.3 Piezo Injectors……………………………………………………. 234 6.2.4 Variable Nozzle Concept…………………………………………. 236 6.2.5 Increase of Injection Pressure………………………………..…… 237 6.2.6 Pressure Modulation………………………………………...……. 239 6.2.7 Future Demands………………………………………………..…. 241 6.3 DI Gasoline Engines…………………………………………………… 242 6.3.1 Introduction…………………………………………………….…. 242 6.3.2 Operating Modes……………………………………………….… 244 6.3.3 Stratified-Charge Combustion Concepts……………………...….. 246 6.3.4 Future Demands………………………………………………..…. 251 6.4 Homogeneous Charge Compression Ignition (HCCI)………………… 253 6.4.1 Introduction……………………………………………………….. 253 6.4.2 HCCI Chemistry………………………………………………….. 256 6.4.3 Emission Behavior………………………………………...…….. 261 6.4.4 Basic Challenges………………………………………………….. 264 6.4.5 Influence Parameters and Control of HCCI Combustion……..….. 270 6.4.6 Transient Behavior – Control Strategies………………………..… 279 6.4.7 Future HCCI Engine Applications…………………………...…… 279 References…………………………………………………………………. 280 7 Conclusions…………………………………………………………………. 287 Index……………………………………………………………………………291 Nomenclature Abbreviations ATDC after top dead center B Spalding transfer number BMEP break mean effective pressure BTDC before top dead center CAI controlled auto-ignition CAN controlled auto-ignition number CFD computational fluid dynamics CI compression ignition CN cetane number, cavitation number CR compression ratio, common rail DDB droplet deformation and break-up model DDM discrete droplet model DI direct injection DISI direct injection spark ignition DNS direct numerical simulation EGR exhaust gas recirculation GDI gasoline direct injection HCCI homogeneous charge compression ignition HTO high temperature oxidation ICAS interactive cross-sectionally averaged spray IMEP indicated mean effective pressure K cavitation number KH Kelvin-Helmholtz model La Laplace number LES large eddy simulation LHF lower heating value LISA linearized instability sheet atomization model LTO low temperature oxidation M third body species in chemical reactions MEF maximum entropy formalism MW molecular weight NTC negative temperature coefficient Nu Nusselt number XII Nomenclature ON octane number PDF probability density function PFI port fuel injection PM particulate matter (soot) Pr Prandtl number RANS Reynolds averaged Navier-Stokes equations Re Reynolds number RT Rayleigh-Taylor model Sc Schmidt number Sh Sherwood number SI spark ignition SMD Sauter mean diameter SOC start of combustion SR swirl ratio St Stokes number T Taylor number TAB Taylor-analogy break-up model TDC top dead center UIS unit injector system UPS unit pump system VCO valve covered orifice VVT variable valve train We Weber number Z Ohnesorge number Symbols a sound speed [m/s], acceleration [m2/s2], thermal diffusivity [m2/s], major semi axis of ellipsoid [m] A area [m2], constant [ / ] b minor semi axis of ellipsoid [m], spray width [m] B non-dimensional impact parameter [ / ] c molar density, concentration [mol/m3] C constant [ / ] C contraction coefficient [ / ] c C discharge coefficient [ / ] d C drag coefficient [ / ] D c wall friction coefficient [ / ] f