Fundamentals of Turbulent and Multiphase Combustion

by Kuo, Kenneth Kuan-yun; Acharya, Ragini

• ISBN13: 9780470226223
• ISBN10: 0470226226
• Edition: 1st
• Format: Hardcover
• Copyright: 2012-04-24
• Publisher: Wiley

Summary

This book is a follow-on to the author's bestseller, Principles of Combustion, Second Edition published in 2005. The text covers advanced topics of combustion and flame that are not covered anywhere else. Kuo provides a multiphase systems approach beginning with more common topics and moving to higher level applications such as reacting boundary layer flows, ignition of homogeneous mixtures, flame extinction phenomena, and detonation processes in condensed phase materials. As with Kuo's earlier book, large numbers of examples and problems and a solutions manual are provided.

Author Biography

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.

Table of Contents

Preface	p. xix
Introduction and Conservation Equations	p. 1
Why Is Turbulent and Multiphase Combustion Important?	p. 3
Different Applications for Turbulent and Multiphase Combustion	p. 3
Applications in High Rates of Combustion of Materials for Propulsion Systems	p. 5
Applications in Power Generation	p. 7
Applications in Process Industry	p. 7
Applications in Household and Industrial Heating	p. 7
Applications in Safety Protections for Unwanted Combustion	p. 7
Applications in Ignition of Various Combustible Materials	p. 8
Applications in Emission Control of Combustion Products	p. 8
Applications in Active Control of Combustion Processes	p. 8
Objectives of Combustion Modeling	p. 8
Combustion-Related Constituent Disciplines	p. 9
General Approach for Solving Combustion Problems	p. 9
Governing Equations for Combustion Models	p. 11
Conservation Equations	p. 11
Transport Equations	p. 11
Common Assumptions Made in Combustion Models	p. 11
Equation of State	p. 12
High-Pressure Correction	p. 13
Definitions of Concentrations	p. 14
Definitions of Energy and Enthalpy Forms	p. 16
Velocities of Chemical Species	p. 19
Definitions of Absolute and Relative Mass and Molar Fluxes	p. 20
Dimensionless Numbers	p. 23
Derivation of Species Mass Conservation Equation and Continuity Equation for Multicomponent Mixtures	p. 23
Momentum Conservation Equation for Mixture	p. 29
Energy Conservation Equation for Multicomponent Mixture	p. 33
Total Unknowns versus Governing Equations	p. 40
Homework Problems	p. 41
Laminar Premixed Flames	p. 43
Basic Structure of One-Dimensional Premixed Laminar Flames	p. 46
Conservation Equations for One-Dimensional Premixed Laminar Flames	p. 47
Various Models for Diffusion Velocities	p. 49
Multicomponent Diffusion Velocities (First-Order Approximation)	p. 49
Various Models for Describing Source Terms due to Chemical Reactions	p. 54
Sensitivity Analysis	p. 66
Analytical Relationships for Premixed Laminar Flames with a Global Reaction	p. 68
Three Analysis Procedures for Premixed Laminar Flames	p. 77
Generalized Expression for Laminar Flame Speeds	p. 80
Reduced Reaction Mechanism for HC-Air Flame	p. 81
Dependency of Laminar Flame Speed on Temperature and Pressure	p. 82
Premixed Laminar Flame Thickness	p. 84
Effect of Flame Stretch on Laminar Flame Speed	p. 86
Definitions of Stretch Factor and Karlovitz Number	p. 86
Governing Equation for Premixed Laminar Flame Surface Area	p. 94
Determination of Unstretched Premixed Laminar Flame Speeds and Markstein Lengths	p. 95
Modeling of Soot Formation in Laminar Premixed Flames	p. 103
Reaction Mechanisms for Soot Formation and Oxidation	p. 104
Empirical Models for Soot Formation	p. 106
Detailed Models for Soot Formation and Oxidation	p. 108
Formation of Aromatics	p. 109
Growth of Aromatics	p. 110
Migration Reactions	p. 112
Oxidation of Aromatics	p. 113
Mathematical Formulation of Soot Formation Model	p. 114
Homework Problems	p. 124
Laminar Non-Premixed Flames	p. 125
Basic Structure of Non-Premixed Laminar Flames	p. 128
Flame Sheet Model	p. 129
Mixture Fraction Definition and Examples	p. 130
Balance Equations for Element Mass Fractions	p. 134
Temperature-Mixture Fraction Relationship	p. 138
Flamelet Structure of a Diffusion Flame	p. 142
Physical Significance of the Instantaneous Scalar Dissipation Rate	p. 145
Steady-State Combustion and Critical Scalar Dissipation Rate	p. 147
Time and Length Scales in Diffusion Flames	p. 151
Examples of Laminar Diffusion Flames	p. 153
Unsteady Mixing Layer	p. 153
Counterflow Diffusion Flames	p. 155
Coflow Diffusion Flame or Jet Flames	p. 165
Soot Formation in Laminar Diffusion Flames	p. 172
Soot Formation Model	p. 173
Particle Inception	p. 174
Surface Growth and Oxidation	p. 174
Appearance of Soot	p. 175
Experimental Studies by Using Coflow Burners	p. 176
Sooting Zone	p. 178
Effect of Fuel Structure	p. 182
Influence of Additives	p. 183
Coflow Ethylene/Air Laminar Diffusion Flames	p. 186
Modeling of Soot Formation	p. 191
Homework Problems	p. 204
Background in Turbulent Flows	p. 206
Characteristics of Turbulent Flows	p. 210
Some Pictures	p. 212
Statistical Understanding of Turbulence	p. 213
Ensemble Averaging	p. 214
Time Averaging	p. 215
Spatial Averaging	p. 215
Statistical Moments	p. 215
Homogeneous Turbulence	p. 216
Isotropic Turbulence	p. 217
Conventional Averaging Methods	p. 217
Reynolds Averaging	p. 218
Correlation Functions	p. 222
Favre Averaging	p. 225
Relation between Time Averaged-Quantities and Mass-Weighted Averaged Quantities	p. 227
Mass-Weighted Conservation and Transport Equations	p. 228
Continuity and Momentum Equations	p. 228
Energy Equation	p. 230
Mean Kinetic Energy Equation	p. 231
Reynolds-Stress Transport Equations	p. 232
Turbulence-Kinetic-Energy Equation	p. 234
Turbulent Dissipation Rate Equation	p. 236
Species Mass Conservation Equation	p. 242
Vorticity Equation	p. 243
Relationship between Enstrophy and the Turbulent Dissipation Rate	p. 246
Turbulence Models	p. 247
Probability Density Function	p. 249
Distribution Function	p. 250
Joint Probability Density Function	p. 252
Bayes’ Theorem	p. 254
Turbulent Scales	p. 256
Comment on Kolmogorov Hypotheses	p. 260
Large Eddy Simulation	p. 266
Filtering	p. 268
Filtered Momentum Equations and Subgrid Scale Stresses	p. 270
Modeling of Subgrid-Scale Stress Tensors	p. 274
Direct Numerical Simulation	p. 279
Homework Problems	p. 280
Turbulent Premixed Flames	p. 283
Physical Interpretation	p. 289
Some Early Studies in Correlation Development	p. 291
Damköhler’s Analysis (1940)	p. 292
Schelkin’s Analysis (1943)	p. 295
Karlovitz, Denniston, and Wells’s Analysis (1951)	p. 296
Summerfield’s Analysis (1955)	p. 297
Kovasznay’s Characteristic Time Approach (1956)	p. 298
Limitations of the Preceding Approaches	p. 299
Characteristic Scale of Wrinkles in Turbulent Premixed Flames	p. 304
Schlieren Photographs	p. 305
Observations on the Structure of Wrinkled Laminar Flames	p. 305
Measurements of Scales of Unburned and Burned Gas Lumps	p. 307
Length Scale of Wrinkles	p. 310
Development of Borghi Diagram for Premixed Turbulent Flames	p. 310
Physical Interpretation of Various Regimes in Borghi’s Diagram	p. 311
Wrinkled Flame Regime	p. 311
Wrinkled Flame with Pockets Regime (also Called Corrugated Flame Regime)	p. 311
Thickened Wrinkled Flames	p. 313
Thickened Flames with Possible Extinctions/Thick Flames	p. 314
Klimov-Williams Criterion	p. 314
Construction of Borghi Diagram	p. 316
Thick Flames (or Distributed Reaction Zone or Well-Stirred Reaction Zone)	p. 318
Wrinkled Flames	p. 318
Wrinkled Flamelets (Weak Turbulence)	p. 320
Corrugated Flamelets (Strong Turbulence)	p. 322
Measurements in Premixed Turbulent Flames	p. 324
Eddy-Break-up Model	p. 324
Spalding’s EBU Model	p. 335
Magnussen and Hjertager’s EBU Model	p. 336
Intermittency	p. 337
Flame-Turbulence Interaction	p. 339
Effects of Flame on Turbulence	p. 341
Bray-Moss-Libby Model	p. 342
Governing Equations	p. 349
Gradient Transport	p. 353
Countergradient Transport	p. 354
Closure of Transport Terms	p. 357
Gradient Closure	p. 357
BML Closure	p. 358
Effect of Pressure Fluctuations Gradients	p. 361
Summary of DNS Results	p. 364
Turbulent Combustion Modeling Approaches	p. 368
Geometrical Description of Turbulent Premixed Flames and G-Equation	p. 368
Level Set Approach for the Corrugated Flamelets Regime	p. 371
Level Set Approach for the Thin Reaction Zone Regime	p. 374
Scales in Turbulent Combustion	p. 376
Closure of Chemical Reaction Source Term	p. 380
Probability Density Function Approach to Turbulent Combustion	p. 381
Derivation of the Transport Equation for Probability Density Function	p. 386
Moment Equations and PDF Equations	p. 391
Lagrangian Equations for Fluid Particles	p. 392
Gradient Transport Model in Composition PDF Method	p. 395
Determination of Overall Reaction Rate	p. 397
Lagrangian Monte Carlo Particle Methods	p. 398
Filtered Density Function Approach	p. 398
Prospect of PDF Methods	p. 399
Homework Problems	p. 400
Project No. 1	p. 400
Project No. 2	p. 401
Non-premixed Turbulent Flames	p. 402
Major Issues in Non-premixed Turbulent Flames	p. 404
Turbulent Damköhler number	p. 406
Turbulent Reynolds Number	p. 407
Scales in Non-premixed Turbulent Flames	p. 407
Direct Numerical Simulation and Scales	p. 411
Turbulent Non-premixed Combustion Regime Diagram	p. 414
Turbulent Non-premixed Target Flames	p. 418
Simple Jet Flames	p. 419
CH4/H2/N2 Jet Flame	p. 420
Effect of Jet Velocity	p. 430
Piloted Jet Flames	p. 432
Comparison of Simple Jet Flame and Sandia Flames D and F	p. 448
Bluff Body Flames	p. 452
Swirl Stabilized Flames	p. 455
Turbulence-Chemistry Interaction	p. 456
Infinite Chemistry Assumption	p. 456
Unity Lewis Number	p. 457
Nonunity Lewis Number	p. 458
Finite-Rate Chemistry	p. 458
Probability Density Approach for Turbulent Non-premixed Combustion	p. 462
Physical Models	p. 465
Turbulent Transport in Velocity-Composition Pdf Methods	p. 466
Stochastic Mixing Model	p. 467
Stochastic Reorientation Model	p. 468
Molecular Transport and Scalar Mixing Models	p. 469
Interaction by Exchange with the Mean Model	p. 471
Modified Curl Mixing Model	p. 471
Euclidean Minimum Spanning Tree Model	p. 472
Flamelet Models	p. 476
Laminar Flamelet Assumption	p. 477
Unsteady Flamelet Modeling	p. 478
Flamelet Models and PDF	p. 479
Interactions of Flame and Vortices	p. 480
Flame Rolled Up in a Single Vortex	p. 482
Flame in a Shear Layer	p. 483
Jet Flames	p. 483
K´arm´an Vortex Street/V-Shaped Flame Interaction	p. 484
Burning Vortex Ring	p. 484
Head-on Flame/Vortex Interaction	p. 485
Experimental Setups for Flame/Vortex Interaction Studies	p. 486
Reaction Front/Vortex Interaction in Liquids	p. 486
Jet Flames	p. 487
Counterflow Diffusion Flames	p. 488
Generation and Dissipation of Vorticity Effects	p. 492
Non-premixed Flame–Vortex Interaction Combustion Diagram	p. 493
Flame Instability in Non-premixed Turbulent Flames	p. 496
Partially Premixed Flames or Edge Flames	p. 500
Formation of Edge Flames	p. 501
Triple Flame Stabilization of Lifted Diffusion Flame	p. 502
Analysis of Edge Flames	p. 503
Homework Problems	p. 506
Project No. 6.1	p. 506
Project No. 6.2	p. 507
Project No. 6.3	p. 507
Background in Multiphase flows with Reactions	p. 509
Classification of Multiphase Flow Systems	p. 512
Practical Problems Involving Multiphase Systems	p. 514
Homogeneous versus Multi-component/Multiphase Mixtures	p. 515
CFD and Multiphase Simulation	p. 516
Averaging Methods	p. 520
Eulerian Average—Eulerian Mean Values	p. 522
Lagrangian Average—Lagrangian Mean Values	p. 523
Boltzmann Statistical Average	p. 524
Anderson and Jackson’s Averaging for Dense Fluidized Beds	p. 525
Local Instant Formulation	p. 533
Eulerian-Eulerian Modeling	p. 536
Fluid-Fluid Modeling	p. 536
Closure Models	p. 538
Fluid-Solid Modeling	p. 540
Closure Models	p. 541
Dense Particle Flows	p. 547
Dilute Particle Flows	p. 549
Eulerian-Lagrangian Modeling	p. 550
Fluid-Solid Modeling	p. 551
Fluid Phase	p. 551
Solid Phase	p. 552
Interfacial Transport (Jump Conditions)	p. 555
Interface-Tracking/Capturing	p. 561
Interface Tracking	p. 563
Markers on Interface (Surface Marker Techniques)	p. 564
Surface-Fitted Method	p. 567
Interface Capturing	p. 568
Markers in Fluid (MAC Formulation)	p. 568
Volume of Fluid Method	p. 569
Discrete Particle Methods	p. 573
Homework Problems	p. 575
Spray Atomization and Combustion	p. 576
Introduction to Spray Combustion	p. 578
Spray-Combustion Systems	p. 580
Fuel Atomization	p. 582
Injector Types	p. 582
Atomization Characteristics	p. 584
Spray Statistics	p. 584
Particle Characterization	p. 584
Distribution Function	p. 585
Logarithmic Probability Distribution Function	p. 588
Rosin-Rammler Distribution Function	p. 588
Nukiyama-Tanasawa Distribution Function	p. 589
Upper-Limit Distribution Function of Mugele and Evans	p. 589
Transport Equation of the Distribution Function	p. 590
Simplified Spray Combustion Model for Liquid-Fuel Rocket Engines	p. 591
Spray Combustion Characteristics	p. 594
Classification of Models Developed for Spray Combustion Processes	p. 602
Simple Correlations	p. 602
Droplet Ballistic Models	p. 603
One-Dimensional Models	p. 603
Stirred-Reactor Models	p. 604
Locally Homogeneous-Flow Models	p. 605
Two-Phase-Flow (Dispersed-Flow) Models	p. 605
Locally Homogeneous Flow Models	p. 605
Classification of LHF Models	p. 606
Mathematical Formulation of LHF Models	p. 609
Basic Assumptions	p. 609
Equation of State	p. 609
Conservation Equations	p. 615
Turbulent Transport Equations	p. 619
Boundary Conditions	p. 620
Solution Procedures	p. 620
Comparison of LHF-Model Predictions with Experimental Data	p. 626
Two-Phase-Flow (Dispersed-Flow) Models	p. 634
Particle-Source-in-Cell Model (Discrete-Droplet Model)	p. 637
Models for Single Drop Behavior	p. 639
Drop Breakup Process and Mechanism	p. 654
Drop Breakup Process	p. 654
Multi-component Droplet Breakup by Microexplosion	p. 659
Deterministic Discrete Droplet Models	p. 662
Gas-Phase Treatment in DDDMs	p. 664
Liquid-Phase Treatment in DDDMs	p. 666
Results of DDDMs	p. 667
Stochastic Discrete Droplet Models	p. 669
Comparison of Results between DDDMs and SDDMs	p. 671
Dense Sprays	p. 682
Introduction	p. 682
Background	p. 684
Jet Breakup Models	p. 690
Impinging Jet Atomization	p. 699
Group-Combustion Models of Chiu	p. 700
Group-Combustion Numbers	p. 701
Modes of Group Burning in Spray Flames	p. 703
Droplet Collison	p. 706
Droplet-Droplet Collisions	p. 707
Droplet-Wall Collision	p. 708
Interacting Droplet in a Many-Droplet System	p. 710
Optical Techniques for Particle Size Measurements	p. 710
Types of Optical Particle Sizing Methods	p. 711
Single Particle Counting Methods	p. 711
Scattering Ratio Technique	p. 712
Intensity Deconvolution Method	p. 713
Interferometric Method (Phase-Shift Method)	p. 713
Visibility Method Using a Laser Doppler Velocimeter LDV	p. 713
Phase Doppler Sizing Anemometer	p. 713
Ensemble Particle Sizing Techniques	p. 714
Extinction Measurement Techniques	p. 714
Multiple Angle Scattering Technique	p. 714
Fraunhofer Diffraction Particle Analyzer	p. 715
Integral Transform Solutions for Near-Forward Scattering	p. 716
Effect of Droplet Spacing on Spray Combustion	p. 717
Evaporation and Combustion of Droplet Arrays	p. 717
Homework Problems	p. 720
Useful Vector and Tensor Operations	p. 723
Constants and Conversion Factors Often Used in Combustion	p. 751
Naming of Hydrocarbons	p. 755
Detailed Gas-Phase Reaction Mechanism for Aromatics Formation	p. 759
Particle Size–U.S. Sieve Size and Tyler Screen Mesh Equivalents	p. 795
Bibliography	p. 799
Index	p. 869
Table of Contents provided by Publisher. All Rights Reserved.