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Fluid Dynamics and Transport of Droplets and Sprays Second Edition

Fluid Dynamics and Transport of Droplets and Sprays Second Edition

By William A. Sirignano

Fluid Dynamics and Transport of Droplets and Sprays Second Edition discusses the theoretical foundations of spray and droplet applications relevant to the technology for active control of sprays applied to new products and applications, improved product performance, cost reductions, and improved environmental outcomes. It also covers theory related to power and propulsion; materials processing and manufacturing technologies including droplet-based net form processing, coating, and painting; medication; pesticides and insecticides; and other consumer uses.

Fluid Dynamics and Transport of Droplets and Sprays Second Edition serves as both a graduate text and a reference for engineers and scientists exploring the theoretical and computational aspects of the fluid dynamics and transport of sprays and droplets. Attention is given to the behavior of individual droplets, including the effects of forced convection due to relative droplet-gas motion, Stefan convection due to the vaporization or condensation of the liquid, multicomponent liquids (and slurries), and internal circulation of the liquid. This second edition contains more information on droplet-droplet interactions, the use of the mass-flux potential, conserved scalar variables, spatial averaging and the formulation of the multi-continua equations, the confluence of spatial averaging for sprays and filtering for turbulence, direct numerical simulations and large-eddy simulations for turbulent sprays, and high-pressure vaporization processes. Two new chapters introduce liquid-film vaporization as an alternative to sprays for miniature applications and a review of liquid-stream distortion and break-up theory, which is relevant to spray formation.

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Preface 
Nomenclature xiv
1 Introduction …………………………………. 1
1.1 Overview 1
1.2 Droplet-Size Determination 4
2 Isolated Spherically Symmetric Droplet Vaporization and Heating …. 8
2.1 Theory of Spherically Symmetric Droplet Vaporization and Heating 11
2.1.1 Gas-Phase Analysis 12
2.1.2 Liquid-Phase Analysis 19
2.1.3 Chemical Reaction 24
2.2 Radiative Heating of Droplets 26
3 Convective Droplet Vaporization, Heating, and Acceleration ……. 30
3.1 Convective Droplet Vaporization 31
3.1.1 Evaluation of Reynolds Number Magnitude 33
3.1.2 Physical Description 35
3.1.3 Approximate Analyses for Gas-Phase Boundary Layer 40
3.1.4 Approximate Analyses for Liquid-Phase Flows 47
3.1.5 Droplet Drag Coefficients 56
3.1.6 Results from Approximate Analyses 57
3.1.7 Exact Analyses for Gas-Phase and Liquid-Phase Flows 64
3.1.8 Free Convection 71
3.2 Low Reynolds Number Behavior 73
3.3 Droplet Vaporization in an Oscillating Gas 76
3.4 Individual Droplet Behavior in an Unsteady Flow 79
4 Multicomponent-Liquid Droplets ……………………. 90
4.1 Spherically Symmetric Diffusion 93
4.1.1 Continuous-Thermodynamics Models 97
4.2 Liquid-Phase Mass Diffusion with Convective Transport 98
4.2.1 Approximate Analyses 98
4.2.2 Exact Analyses 106
4.3 Metal-Slurry Droplet Vaporization and Combustion 107
4.3.1 Burning of a Fuel Droplet Containing a Single Metal Particle 108
4.3.2 Liquid Vaporization from Fine-Metal-Slurry Droplets 116
4.3.3 Metal-Particle Combustion with Oxide Condensation 129
4.4 Emulsified-Fuel-Droplet Vaporization and Burning 130
5 Droplet Behavior under Near-Critical, Transcritical, and
Supercritical Conditions …………………………. 134
5.1 High-Pressure Droplet Behavior in a Quiescent Environment 136
5.2 Convective Effects and Secondary Atomization 143
5.3 Molecular-Dynamics Simulation of Transcritical Droplet
Vaporization 147
6 Droplet Arrays and Groups ……………………….. 150
6.1 Heating and Vaporization of Droplet Arrays 153
6.2 Group Vaporization and Combustion 165
6.3 Generalized Theory for Droplet-Array Vaporization and Burning 168
6.3.1 Basic Formulation 168
6.3.2 Analysis of Vaporization Without Combustion 170
6.3.3 Combustion Analysis 173
6.3.4 Array Combustion with Nonunitary Lewis Number 179
6.3.5 Array Vaporization with Multicomponent Liquids 189
6.4 Droplet Collisions 192
6.4.1 Droplet–Droplet Collisions 193
6.4.2 Droplet–Wall Collisions 196
7 Spray Equations ……………………………… 199
7.1 Averaging Process for Two-Continua Formulations 200
7.1.1 Averaging of Dependent Variables 204
7.1.2 Averaging of Derivatives 207
7.1.3 Averaged Gas-Phase Equations 210
7.1.4 Averaged Vorticity and Entropy 214
7.1.5 Averaged Liquid-Phase Partial Differential Equations 216
7.1.6 Averaged Liquid-Phase Lagrangian Equations 218
7.1.7 The Microstructure 220
7.2 Two-Continua and Multicontinua Formulations 223
7.2.1 Continuity Equations 223
7.2.2 Momentum Conservation 226
7.2.3 Energy Conservation 228
7.2.4 Hyperbolic Character of Liquid-Phase Equations 230
7.2.5 Subgrid Models for Heat, Mass, and Momentum Exchange 232
7.3 Discrete-Particle Formulation 233
7.4 Probabilistic Formulation
8 Computational Issues …………………………… 237
8.1 Efficient Algorithms for Droplet Computations 237
8.2 Numerical Schemes and Optimization for Spray Computations 245
8.2.1 Two-Phase Laminar Axisymmetric Jet Flow 246
8.2.2 Axisymmetric Unsteady Sprays 255
8.2.3 Solution for Pressure 269
8.3 Point-Source Approximation in Spray Calculations 269
9 Spray Applications ……………………………. 285
9.1 Spherically Symmetric Spray Phenomena 287
9.2 Counterflow Spray Flows 289
9.3 One-Dimensional Planar Spray Ignition and Flame Propagation 296
9.4 Vaporization and Combustion of Droplet Streams 301
9.5 Flame Propagation Through Metal-Slurry Sprays 305
9.6 Liquid-Fueled Combustion Instability 308
9.7 Spray Behavior in Near-Critical and Supercritical Domains 310
9.8 Influence of Supercritical Droplet Behavior on Combustion
Instability 311
10 Spray Interactions with Turbulence and Vortical Structures …….. 314
10.1 Vortex–Spray Interactions 318
10.2 Time-Averaged Turbulence Models 321
10.3 Direct Numerical Simulation 324
10.4 Large-Eddy Simulations 329
10.4.1 Proper Two-Way Coupling for LES Closure 332
10.4.2 Gas-Phase Equations 333
10.4.3 Liquid-Phase Equations 335
10.4.4 Vortex–Droplet Interactions 336
11 Film Vaporization …………………………….. 340
11.1 Introduction 340
11.2 Miniature Film-Combustor Concept 342
11.3 Analysis of Liquid-Film Combustor 347
11.3.1 Assumptions and Governing Equations 348
11.3.2 Liquid-Phase Thermal Analysis 349
11.3.3 Fluid-Dynamics Analysis 350
11.3.4 Scalar Analysis 351
11.3.5 Results 354
11.4 Concluding Remarks 360
12 Stability of Liquid Streams ……………………….. 361
12.1 Introduction 361
12.2 Formulation of Governing Equations 364
12.3 Round Jet Analyses 366
12.3.1 Temporal Stability Analysis 367
12.3.2 Surface Energy
12.3.3 Spatial Stability Analysis 370
12.3.4 Nonlinear Effects 371
12.3.5 Viscous Effects 376
12.3.6 Cavitation 376
12.4 Planar Sheet Analyses 381
12.4.1 Linear Theory 381
12.4.2 Fan Sheets 385
12.4.3 Nonlinear Theory 385
12.5 Annular Free Films 396
12.5.1 Linear Theory 397
12.5.2 Nonlinear Theory 399
12.5.3 Effect of Swirl 401
12.6 “Conical” Free Films 402
12.7 Concluding Remarks 406
Appendix A The Field Equations ……………………… 409
Appendix B Conserved Scalars ………………………. 415
Appendix C Droplet-Model Summary …….
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