Fundamentals of Turbulent and Multiphase Combustion (eBook, PDF)
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Fundamentals of Turbulent and Multiphase Combustion (eBook, PDF)
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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,…mehr
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- Produktdetails
- Verlag: John Wiley & Sons
- Seitenzahl: 912
- Erscheinungstermin: 12. April 2012
- Englisch
- ISBN-13: 9781118099322
- Artikelnr.: 38240367
- Verlag: John Wiley & Sons
- Seitenzahl: 912
- Erscheinungstermin: 12. April 2012
- Englisch
- ISBN-13: 9781118099322
- Artikelnr.: 38240367
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 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 Damk
ohler 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
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 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 Damk
ohler 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