Detailed coverage of advanced combustion topics from the author of Principles of Combustion, Second Edition
Turbulence, turbulent combustion, and multiphase reacting flows have become major research topics in recent decades due to their application across diverse fields, including energy, environment, propulsion, transportation, industrial safety, and nanotechnology. Most of the knowledge accumulated from this research has never been published in book form—until now. Fundamentals of Turbulent and Multiphase Combustion presents up-to-date, integrated coverage of the fundamentals of turbulence, combustion, and multiphase phenomena along with useful experimental techniques, including non-intrusive, laser-based measurement techniques, providing a firm background in both contemporary and classical approaches. Beginning with two full chapters on laminar premixed and non-premixed flames, this book takes a multiphase approach, beginning with more common topics and moving on to higher-level applications.
In addition, Fundamentals of Turbulent and Multiphase Combustion:
-
Addresses seven basic topical areas in combustion and multiphase flows, including laminar premixed and non-premixed flames, theory of turbulence, turbulent premixed and non-premixed flames, and multiphase flows
-
Covers spray atomization and combustion, solid-propellant combustion, homogeneous propellants, nitramines, reacting boundary-layer flows, single energetic particle combustion, and granular bed combustion
-
Provides experimental setups and results whenever appropriate
Supported with a large number of examples and problems as well as a solutions manual, Fundamentals of Turbulent and Multiphase Combustion is an important resource for professional engineers and researchers as well as graduate students in mechanical, chemical, and aerospace engineering.
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 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 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 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
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 Damkohler'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 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 5.11 Geometrical Description of Turbulent Premixed Flames and G
-Equation, 368 5.11.1 Level Set Approach for the Corrugated Flamelets Regime,
371 5.11.2 Level Set Approach for the Thin Reaction Zone Regime, 374 5.12
Scales in Turbulent Combustion, 376 5.13 Closure of Chemical Reaction Source
Term, 380 5.14 Probability Density Function Approach to Turbulent Combustion,
381 5.14.1 Derivation of the Transport Equation for Probability Density
Function, 386 5.14.2 Moment Equations and PDF Equations, 391 5.14.3
Lagrangian Equations for Fluid Particles, 392 5.14.4 Gradient Transport Model
in Composition PDF Method, 395 5.14.5 Determination of Overall Reaction Rate,
397 5.14.6 Lagrangian Monte Carlo Particle Methods, 398 5.14.7 Filtered
Density Function Approach, 398 5.14.8 Prospect of PDF Methods, 399 Homework
Problems, 400 Project No. 1, 400 Project No. 2, 401 6 Non-premixed Turbulent
Flames 402 6.1 Major Issues in Non-premixed Turbulent Flames, 404 6.2
Turbulent Damkohler number, 406 6.3 Turbulent Reynolds Number, 407 6.4 Scales
in Non-premixed Turbulent Flames, 407 6.4.1 Direct Numerical Simulation and
Scales, 411 6.5 Turbulent Non-premixed Combustion Regime Diagram, 414 6.6
Turbulent Non-premixed Target Flames, 418 6.6.1 Simple Jet Flames, 419
6.6.1.1 CH4/H2/N2 Jet Flame, 420 6.6.1.2 Effect of Jet Velocity, 430 6.6.2
Piloted Jet Flames, 432 6.6.2.1 Comparison of Simple Jet Flame and Sandia
Flames D and F, 448 6.6.3 Bluff Body Flames, 452 6.6.4 Swirl Stabilized
Flames, 455 6.7 Turbulence-Chemistry Interaction, 456 6.7.1 Infinite
Chemistry Assumption, 456 6.7.1.1 Unity Lewis Number, 457 6.7.1.2 Nonunity
Lewis Number, 458 6.7.2 Finite-Rate Chemistry, 458 6.8 Probability Density
Approach for Turbulent Non-premixed Combustion, 462 6.8.1 Physical Models,
465 6.8.2 Turbulent Transport in Velocity-Composition Pdf Methods, 466
6.8.2.1 Stochastic Mixing Model, 467 6.8.2.2 Stochastic Reorientation Model,
468 6.8.3 Molecular Transport and Scalar Mixing Models, 469 6.8.3.1
Interaction by Exchange with the Mean Model, 471 6.8.3.2 Modified Curl Mixing
Model, 471 6.8.3.3 Euclidean Minimum Spanning Tree Model, 472 6.9 Flamelet
Models, 476 6.9.1 Laminar Flamelet Assumption, 477 6.9.2 Unsteady Flamelet
Modeling, 478 6.9.3 Flamelet Models and PDF, 479 6.10 Interactions of Flame
and Vortices, 480 6.10.1 Flame Rolled Up in a Single Vortex, 482 6.10.2 Flame
in a Shear Layer, 483 6.10.3 Jet Flames, 483 6.10.4 K'arm'an Vortex
Street/V-Shaped Flame Interaction, 484 6.10.5 Burning Vortex Ring, 484 6.10.6
Head-on Flame/Vortex Interaction, 485 6.10.7 Experimental Setups for
Flame/Vortex Interaction Studies, 486 6.10.7.1 Reaction Front/Vortex
Interaction in Liquids, 486 6.10.7.2 Jet Flames, 487 6.10.7.3 Counterflow
Diffusion Flames, 488 6.11 Generation and Dissipation of Vorticity Effects,
492 6.12 Non-premixed Flame-Vortex Interaction Combustion Diagram, 493 6.13
Flame Instability in Non-premixed Turbulent Flames, 496 6.14 Partially
Premixed Flames or Edge Flames, 500 6.14.1 Formation of Edge Flames, 501
6.14.2 Triple Flame Stabilization of Lifted Diffusion Flame, 502 6.14.3
Analysis of Edge Flames, 503 Homework Problems, 506 Project No. 6.1, 506
Project No. 6.2, 507 Project No. 6.3, 507 7 Background in Multiphase flows
with Reactions 509 7.1 Classification of Multiphase Flow Systems, 512 7.2
Practical Problems Involving Multiphase Systems, 514 7.3 Homogeneous versus
Multi-component/Multiphase Mixtures, 515 7.4 CFD and Multiphase Simulation,
516 7.5 Averaging Methods, 520 7.5.1 Eulerian Average-Eulerian Mean Values,
522 7.5.2 Lagrangian Average-Lagrangian Mean Values, 523 7.5.3 Boltzmann
Statistical Average, 524 7.5.4 Anderson and Jackson's Averaging for Dense
Fluidized Beds, 525 7.6 Local Instant Formulation, 533 7.7 Eulerian-Eulerian
Modeling, 536 7.7.1 Fluid-Fluid Modeling, 536 7.7.1.1 Closure Models, 538
7.7.2 Fluid-Solid Modeling, 540 7.7.2.1 Closure Models, 541 7.7.2.2 Dense
Particle Flows, 547 7.7.2.3 Dilute Particle Flows, 549 7.8
Eulerian-Lagrangian Modeling, 550 7.8.1 Fluid-Solid Modeling, 551 7.8.1.1
Fluid Phase, 551 7.8.1.2 Solid Phase, 552 7.9 Interfacial Transport (Jump
Conditions), 555 7.10 Interface-Tracking/Capturing, 561 7.10.1 Interface
Tracking, 563 7.10.1.1 Markers on Interface (Surface Marker Techniques), 564
7.10.1.2 Surface-Fitted Method, 567 7.10.2 Interface Capturing, 568 7.10.2.1
Markers in Fluid (MAC Formulation), 568 7.10.2.2 Volume of Fluid Method, 569
7.11 Discrete Particle Methods, 573 Homework Problems, 575 8 Spray
Atomization and Combustion 576 8.1 Introduction to Spray Combustion, 578 8.2
Spray-Combustion Systems, 580 8.3 Fuel Atomization, 582 8.3.1 Injector Types,
582 8.3.2 Atomization Characteristics, 584 8.4 Spray Statistics, 584 8.4.1
Particle Characterization, 584 8.4.2 Distribution Function, 585 8.4.2.1
Logarithmic Probability Distribution Function, 588 8.4.2.2 Rosin-Rammler
Distribution Function, 588 8.4.2.3 Nukiyama-Tanasawa Distribution Function,
589 8.4.2.4 Upper-Limit Distribution Function of Mugele and Evans, 589 8.4.3
Transport Equation of the Distribution Function, 590 8.4.4 Simplified Spray
Combustion Model for Liquid-Fuel Rocket Engines, 591 8.5 Spray Combustion
Characteristics, 594 8.6 Classification of Models Developed for Spray
Combustion Processes, 602 8.6.1 Simple Correlations, 602 8.6.2 Droplet
Ballistic Models, 603 8.6.3 One-Dimensional Models, 603 8.6.4 Stirred-Reactor
Models, 604 8.6.5 Locally Homogeneous-Flow Models, 605 8.6.6 Two-Phase-Flow
(Dispersed-Flow) Models, 605 8.7 Locally Homogeneous Flow Models, 605 8.7.1
Classification of LHF Models, 606 8.7.2 Mathematical Formulation of LHF
Models, 609 8.7.2.1 Basic Assumptions, 609 8.7.2.2 Equation of State, 609
8.7.2.3 Conservation Equations, 615 8.7.2.4 Turbulent Transport Equations,
619 8.7.2.5 Boundary Conditions, 620 8.7.2.6 Solution Procedures, 620 8.7.2.7
Comparison of LHF-Model Predictions with Experimental Data, 626 8.8
Two-Phase-Flow (Dispersed-Flow) Models, 634 8.8.1 Particle-Source-in-Cell
Model (Discrete-Droplet Model), 637 8.8.1.1 Models for Single Drop Behavior,
639 8.8.2 Drop Breakup Process and Mechanism, 654 8.8.2.1 Drop Breakup
Process, 654 8.8.2.2 Multi-component Droplet Breakup by Microexplosion, 659
8.8.3 Deterministic Discrete Droplet Models, 662 8.8.3.1 Gas-Phase Treatment
in DDDMs, 664 8.8.3.2 Liquid-Phase Treatment in DDDMs, 666 8.8.3.3 Results of
DDDMs, 667 8.8.4 Stochastic Discrete Droplet Models, 669 8.8.5 Comparison of
Results between DDDMs and SDDMs, 671 8.8.6 Dense Sprays, 682 8.8.6.1
Introduction, 682 8.8.6.2 Background, 684 8.8.6.3 Jet Breakup Models, 690
8.8.6.4 Impinging Jet Atomization, 699 8.9 Group-Combustion Models of Chiu,
700 8.9.1 Group-Combustion Numbers, 701 8.9.2 Modes of Group Burning in Spray
Flames, 703 8.10 Droplet Collison, 706 8.10.1 Droplet-Droplet Collisions, 707
8.10.2 Droplet-Wall Collision, 708 8.10.3 Interacting Droplet in a
Many-Droplet System, 710 8.11 Optical Techniques for Particle Size
Measurements, 710 8.11.1 Types of Optical Particle Sizing Methods, 711 8.11.2
Single Particle Counting Methods, 711 8.11.2.1 Scattering Ratio Technique,
712 8.11.2.2 Intensity Deconvolution Method, 713 8.11.2.3 Interferometric
Method (Phase-Shift Method), 713 8.11.2.4 Visibility Method Using a Laser
Doppler Velocimeter LDV, 713 8.11.2.5 Phase Doppler Sizing Anemometer, 713
8.11.3 Ensemble Particle Sizing Techniques, 714 8.11.3.1 Extinction
Measurement Techniques, 714 8.11.3.2 Multiple Angle Scattering Technique, 714
8.11.3.3 Fraunhofer Diffraction Particle Analyzer, 715 8.11.3.4 Integral
Transform Solutions for Near-Forward Scattering, 716 8.12 Effect of Droplet
Spacing on Spray Combustion, 717 8.12.1 Evaporation and Combustion of Droplet
Arrays, 717 Homework Problems, 720 Appendix A: Useful Vector and Tensor
Operations 723 Appendix B: Constants and Conversion Factors Often Used in
Combustion 751 Appendix C: Naming of Hydrocarbons 755 Appendix D:
Detailed Gas-Phase Reaction Mechanism for Aromatics Formation 759 Appendix
E: Particle Size-U.S. Sieve Size and Tyler Screen Mesh Equivalents 795
Bibliography 799 Index 869
Kenneth K. Kuo is Distinguished Professor of Mechanical Engineering and Director of the High Pressure Combustion Laboratory (HPCL) in the Department of Mechanical and Nuclear Engineering of the College of Engineering at Pennsylvania State University. Professor Kuo established the HPCL and is recognized as one of the leading researchers and experts in propulsion-related combustion. Ragini Acharya is Senior Research Scientist at United Technologies Research Center. She received her PhD from Pennsylvania State University in December, 2008. Dr. Acharya's research expertise includes development of multi-physics, multi-scale, multiphase models, fire dynamics, numerical methods, and scientific computing. She has authored or coauthored multiple technical articles in these areas.
