FUNDAMENTALS OF TURBULENT AND MULTIPHASE COMBUSTION Fundamentals of Turbulent and Multiphase Combustion Kenneth K. Kuo and Ragini Acharya Copyright © 2012 John Wiley & Sons, Inc. FUNDAMENTALS OF TURBULENT AND MULTIPHASE COMBUSTION KENNETH K. KUO RAGINI ACHARYA JOHN WILEY & SONS, INC. This book is printed on acid-free paper. Copyright © 2012 by John Wiley & Sons, Inc. 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Some material included with standard print versions of this book may not be included in e-books or in print-on-demand. If this book refers to media such as a CD or DVD that is not included in the version you purchased, you may download this material at http://booksupport.wiley.com. For more information about Wiley products, visit www.wiley.com. Library of Congress Cataloging-in-Publication Data: Kuo, Kenneth K. KuFundamentals of turbulent and multiphase combustion / Kenneth K. Kuo, Ragini Acharya. — 1st ed. Ragini p. cm. RaIncludes bibliographical references and index. RagiISBN 978-0-470-22622-3 (hardback); 978-111-8-09929-2 (ebk.); 978-111-8-09931-5 (ebk.); 978-111-8-09932-2 (ebk.); 978-111-8-10767-6 (ebk.); 978-111-8-10768-3 (ebk.); 978-111-8-10770-6 (ebk.) R1. Combustion engineering. 2. Turbulence. 3. Combustion—Mathematical models. I. Acharya, Ragini. II. Acharya, Ragini. III. Title. RaQD516.K858 2012 Ra541  .361—dc23 2011024787 ISBN: 978-0-470-22622-3 Printed in the United States of America 10987654321 Ken Kuo would like to dedicate this book to his wife, Olivia (Jeon-lin), and their daughters, Phyllis and Angela, for their love, understanding, patience, and support, and to his mother, Mrs. Wen-Chen Kuo, for her love and encouragement. Ragini Acharya would like to dedicate this book to her parents, Meenakshi and Krishnama Acharya, for their love, patience, and support and for having endless faith in her. CONTENTS Preface xix 1 Introduction and Conservation Equations 1 1.1 Why Is Turbulent and Multiphase Combustion Important?, 3 1.2 Different Applications for Turbulent and Multiphase Combustion, 3 1.2.1 Applications in High Rates of Combustion of Materials for Propulsion Systems, 5 1.2.2 Applications in Power Generation, 7 1.2.3 Applications in Process Industry, 7 1.2.4 Applications in Household and Industrial Heating, 7 1.2.5 Applications in Safety Protections for Unwanted Combustion, 7 1.2.6 Applications in Ignition of Various Combustible Materials, 8 1.2.7 Applications in Emission Control of Combustion Products, 8 1.2.8 Applications in Active Control of Combustion Processes, 8 1.3 Objectives of Combustion Modeling, 8 1.4 Combustion-Related Constituent Disciplines, 9 1.5 General Approach for Solving Combustion Problems, 9 vii viii CONTENTS 1.6 Governing Equations for Combustion Models, 11 1.6.1 Conservation Equations, 11 1.6.2 Transport Equations, 11 1.6.3 Common Assumptions Made in Combustion Models, 11 1.6.4 Equation of State, 12 1.6.4.1 High-Pressure Correction, 13 1.7 Definitions of Concentrations, 14 1.8 Definitions of Energy and Enthalpy Forms, 16 1.9 Velocities of Chemical Species, 19 1.9.1 Definitions of Absolute and Relative Mass and Molar Fluxes, 20 1.10 Dimensionless Numbers, 23 1.11 Derivation of Species Mass Conservation Equation and Continuity Equation for Multicomponent Mixtures, 23 1.12 Momentum Conservation Equation for Mixture, 29 1.13 Energy Conservation Equation for Multicomponent Mixture, 33 1.14 Total Unknowns versus Governing Equations, 40 Homework Problems, 41 2 Laminar Premixed Flames 43 2.1 Basic Structure of One-Dimensional Premixed Laminar Flames, 46 2.2 Conservation Equations for One-Dimensional Premixed Laminar Flames, 47 2.2.1 Various Models for Diffusion Velocities, 49 2.2.1.1 Multicomponent Diffusion Velocities (First-Order Approximation), 49 2.2.1.2 Various Models for Describing Source Terms due to Chemical Reactions, 54 2.2.2 Sensitivity Analysis, 66 2.3 Analytical Relationships for Premixed Laminar Flames with a Global Reaction, 68 2.3.1 Three Analysis Procedures for Premixed Laminar Flames, 77 2.3.2 Generalized Expression for Laminar Flame Speeds, 80 2.3.2.1 Reduced Reaction Mechanism for HC-Air Flame, 81 CONTENTS ix 2.3.3 Dependency of Laminar Flame Speed on Temperature and Pressure, 82 2.3.4 Premixed Laminar Flame Thickness, 84 2.4 Effect of Flame Stretch on Laminar Flame Speed, 86 2.4.1 Definitions of Stretch Factor and Karlovitz Number, 86 2.4.2 Governing Equation for Premixed Laminar Flame Surface Area, 94 2.4.3 Determination of Unstretched Premixed Laminar Flame Speeds and Markstein Lengths, 95 2.5 Modeling of Soot Formation in Laminar Premixed Flames, 103 2.5.1 Reaction Mechanisms for Soot Formation and Oxidation, 104 2.5.1.1 Empirical Models for Soot Formation, 106 2.5.1.2 Detailed Models for Soot Formation and Oxidation, 108 2.5.1.3 Formation of Aromatics, 109 2.5.1.4 Growth of Aromatics, 110 2.5.1.5 Migration Reactions, 112 2.5.1.6 Oxidation of Aromatics, 113 2.5.2 Mathematical Formulation of Soot Formation Model, 114 Homework Problems, 124 3 Laminar Non-Premixed Flames 125 3.1 Basic Structure of Non-Premixed Laminar Flames, 128 3.2 Flame Sheet Model, 129 3.3 Mixture Fraction Definition and Examples, 130 3.3.1 Balance Equations for Element Mass Fractions, 134 3.3.2 Temperature-Mixture Fraction Relationship, 138 3.4 Flamelet Structure of a Diffusion Flame, 142 3.4.1 Physical Significance of the Instantaneous Scalar Dissipation Rate, 145 3.4.2 Steady-State Combustion and Critical Scalar Dissipation Rate, 147 3.5 Time and Length Scales in Diffusion Flames, 151 3.6 Examples of Laminar Diffusion Flames, 153 3.6.1 Unsteady Mixing Layer, 153 x CONTENTS 3.6.2 Counterflow Diffusion Flames, 155 3.6.3 Coflow Diffusion Flame or Jet Flames, 165 3.7 Soot Formation in Laminar Diffusion Flames, 172 3.7.1 Soot Formation Model, 173 3.7.1.1 Particle Inception, 174 3.7.1.2 Surface Growth and Oxidation, 174 3.7.2 Appearance of Soot, 175 3.7.3 Experimental Studies by Using Coflow Burners, 176 3.7.3.1 Sooting Zone, 178 3.7.3.2 Effect of Fuel Structure, 182 3.7.3.3 Influence of Additives, 183 3.7.3.4 Coflow Ethylene/Air Laminar Diffusion Flames, 186 3.7.3.5 Modeling of Soot Formation, 191 Homework Problems, 204 4 Background in Turbulent Flows 206 4.1 Characteristics of Turbulent Flows, 210 4.1.1 Some Pictures, 212 4.2 Statistical Understanding of Turbulence, 213 4.2.1 Ensemble Averaging, 214 4.2.2 Time Averaging, 215 4.2.3 Spatial Averaging, 215 4.2.4 Statistical Moments, 215 4.2.5 Homogeneous Turbulence, 216 4.2.6 Isotropic Turbulence, 217 4.3 Conventional Averaging Methods, 217 4.3.1 Reynolds Averaging, 218 4.3.1.1 Correlation Functions, 222 4.3.2 Favre Averaging, 225 4.3.3 Relation between Time Averaged-Quantities and Mass-Weighted Averaged Quantities, 227 4.3.4 Mass-Weighted Conservation and Transport Equations, 228 4.3.4.1 Continuity and Momentum Equations, 228 4.3.4.2 Energy Equation, 230 4.3.4.3 Mean Kinetic Energy Equation, 231 CONTENTS xi 4.3.4.4 Reynolds-Stress Transport Equations, 232 4.3.4.5 Turbulence-Kinetic-Energy Equation, 234 4.3.4.6 Turbulent Dissipation Rate Equation, 236 4.3.4.7 Species Mass Conservation Equation, 242 4.3.5 Vorticity Equation, 243 4.3.6 Relationship between Enstrophy and the Turbulent Dissipation Rate, 246 4.4 Turbulence Models, 247 4.5 Probability Density Function, 249 4.5.1 Distribution Function, 250 4.5.2 Joint Probability Density Function, 252 4.5.3 Bayes’ Theorem, 254 4.6 Turbulent Scales, 256 4.6.1 Comment on Kolmogorov Hypotheses, 260 4.7 Large Eddy Simulation, 266 4.7.1 Filtering, 268 4.7.2 Filtered Momentum Equations and Subgrid Scale Stresses, 270 4.7.3 Modeling of Subgrid-Scale Stress Tensors, 274 4.8 Direct Numerical Simulation, 279 Homework Problems, 280 5 Turbulent Premixed Flames 283 5.1 Physical Interpretation, 289 5.2 Some Early Studies in Correlation Development, 291 5.2.1 Damk ¨ ohler’s Analysis (1940), 292 5.2.2 Schelkin’s Analysis (1943), 295 5.2.3 Karlovitz, Denniston, and Wells’s Analysis (1951), 296 5.2.4 Summerfield’s Analysis (1955), 297 5.2.5 Kovasznay’s Characteristic Time Approach (1956), 298 5.2.6 Limitations of the Preceding Approaches, 299 5.3 Characteristic Scale of Wrinkles in Turbulent Premixed Flames, 304 5.3.1 Schlieren Photographs, 305 5.3.2 Observations on the Structure of Wrinkled Laminar Flames, 305 xii CONTENTS 5.3.3 Measurements of Scales of Unburned and Burned Gas Lumps, 307 5.3.4 Length Scale of Wrinkles, 310 5.4 Development of Borghi Diagram for Premixed Turbulent Flames, 310 5.4.1 Physical Interpretation of Various Regimes in Borghi’s Diagram, 311 5.4.1.1 Wrinkled Flame Regime, 311 5.4.1.2 Wrinkled Flame with Pockets Regime (also Called Corrugated Flame Regime), 311 5.4.1.3 Thickened Wrinkled Flames, 313 5.4.1.4 Thickened Flames with Possible Extinctions/Thick Flames, 314 5.4.2 Klimov-Williams Criterion, 314 5.4.3 Construction of Borghi Diagram, 316 5.4.3.1 Thick Flames (or Distributed Reaction Zone or Well-Stirred Reaction Zone), 318 5.4.4 Wrinkled Flames, 318 5.4.4.1 Wrinkled Flamelets (Weak Turbulence), 320 5.4.4.2 Corrugated Flamelets (Strong Turbulence), 322 5.5 Measurements in Premixed Turbulent Flames, 324 5.6 Eddy-Break-up Model, 324 5.6.1 Spalding’s EBU Model, 335 5.6.2 Magnussen and Hjertager’s EBU Model, 336 5.7 Intermittency, 337 5.8 Flame-Turbulence Interaction, 339 5.8.1 Effects of Flame on Turbulence, 341 5.9 Bray-Moss-Libby Model, 342 5.9.1 Governing Equations, 349 5.9.2 Gradient Transport, 353 5.9.3 Countergradient Transport, 354 5.9.4 Closure of Transport Terms, 357 5.9.4.1 Gradient Closure, 357 5.9.4.2 BML Closure, 358 5.9.5 Effect of Pressure Fluctuations Gradients, 361 5.9.6 Summary of DNS Results, 364 5.10 Turbulent Combustion Modeling Approaches, 368 [...]... the knowledge of the turbulent and multiphase combustion with application in different aspects, such as: • • • • 1.2.8 For reduction of pollutants generated from combustion Reduction of formation of NOx , SOx , and CO2 Reduction of formation of particulates such as soot and coke Control of the temperature and chemical compositions of combustion products Applications in Active Control of Combustion Processes... thermal energy by turbulent and multiphase combustion processes • Thermal energy generated by combustion: Used for heating of residences, factories, of ces, hospitals, schools, and various types of buildings; and heating of International Space Station (ISS) and many special facilities 1.2.5 Applications in Safety Protections for Unwanted Combustion Knowledge of turbulent and multiphase combustion is also... experimental setups and results are provided The first volume addresses eight basic topical areas in combustion and multiphase flows, including laminar premixed and nonpremixed flames; theory of turbulence; turbulent premixed and nonpremixed flames; background of multiphase flows; and spray atomization and combustion A deep understanding of these topics is necessary for researchers in the field of combustion The... turbulent and multiphase combustion as a major area of research for understanding and importance of solution of multiple challenging and interesting problems related to energy, environment, transportation, and chemical propulsion, among other fields The second topic provides a summary of the major conservation equations used by researchers in the combustion community 1.1 WHY IS TURBULENT AND MULTIPHASE COMBUSTION. .. is one of the most complex problems the scientific community faces Its complexity increases with chemical reactions and even more in the presence of multiphase flows A number of useful books have been published recently in the areas of theory of turbulence, multiphase fluid dynamics, turbulent combustion, and combustion of propellants These include Theoretical and Numerical Combustion by Poinsot and Veynante;... propellant combustion, thermal decomposition and combustion of nitramines burning behavior of homogeneous solid propellants, chemically reacting boundary-layer flows, ignition and combustion of combustion of single energetic solid particles, and combustion of solid particles in multiphase flows The major reason for including solid-propellant combustion here is to provide concepts for condensed-phase combustion. .. Veynante; Turbulent Flows by Pope; Introduction to Turbulent Flow by Mathieu and Scott; Turbulent Combustion by Peters; Multiphase Flow Dynamics by Kolev; Combustion Physics by Law; Fluid Dynamics and Transport of Droplet and Sprays by Sirignano; Compressible, Turbulence, and High-Speed Flow by Gatski and Bonnet; Combustion by Glassman and Yetter, among others Kenneth Kuo, the first author of this book,... 1.2 DIFFERENT APPLICATIONS FOR TURBULENT AND MULTIPHASE COMBUSTION There are various applications of turbulent and multiphase combustion associated closely with our daily life Some of these are: • Power generation from combustion (one example of two-phase turbulent combustion used for energy generation from coal-fired burners can be seen in Figure 1.1) 4 INTRODUCTION AND CONSERVATION EQUATIONS PFB Gasifier... manuscript, including Professors Andr´ L Boehman, James G e Brasseur, John H Mahaffy, Daniel C Haworth, and Richard A Yetter We both would like to acknowledge the generosity of Professor Peyman Givi of the University of Pittsburgh for granting us full permission to use some of his numerical simulation results of RANS, LES, and DNS of a turbulent jet flame on the jacket of Volume 1 For the cover of Volume 2, we... solutions of problems In these two new books, we have attempted to integrate the fundamental theories of turbulence, combustion, and multiphase phenomena as well as experimental techniques, so that readers can acquire a firm background in both contemporary and classical approaches The first book volume is called Fundamentals of Turbulent and Multiphase Combustion; the second is called Applications of Turbulent . FUNDAMENTALS OF TURBULENT AND MULTIPHASE COMBUSTION Fundamentals of Turbulent and Multiphase Combustion Kenneth K. Kuo and Ragini Acharya Copyright. limitations. VOLUME 1, FUNDAMENTALS OF TURBULENT AND MULTIPHASE COMBUSTION Chapter 1 introduces and stresses the importance of combustion and multiphase flows