Fluid dynamics and transport of droplets and sprays

This book 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.

Author Notes

William A. Sirignano is the Henry Samueli Professor of Mechanical and Aerospace Engineering and former Dean of the School of Engineering at the University of California, Irvine. Before that, he was the George Tallman Ladd Professor and Department Head at Carnegie-Mellon University and a professor at Princeton University. His major research and teaching interests include spray combustion, turbulent combustion and ignition, aerospace propulsion, fluid dynamics, and applied mathematics. Dr. Sirignano has written more than 450 research papers, book articles, and reports and has given more than 300 conference presentations and research seminars. He has been a formal consultant to 30 industrial organizations and federal laboratories.

Preface	p. xi
Nomenclature	p. xiv
1 Introduction	p. 1
1.1 Overview	p. 1
1.2 Dropiet-Size Determination	p. 4
2 Isolated Spherically Symmetric Droplet Vaporization and Heating	p. 8
2.1 Theory of Spherically Symmetric Droplet Vaporization and Heating	p. 11
2.1.1 Gas-Phase Analysis	p. 12
2.1.2 Liquid-Phase Analysis	p. 19
2.1.3 Chemical Reaction	p. 24
2.2 Radiative Heating of Droplets	p. 26
3 Convective Droplet Vaporization, Heating, and Acceleration	p. 30
3.1 Convective Droplet Vaporization	p. 31
3.1.1 Evaluation of Reynolds Number Magnitude	p. 33
3.1.2 Physical Description	p. 35
3.1.3 Approximate Analyses for Gas-Phase Boundary Layer	p. 40
3.1.4 Approximate Analyses for Liquid-Phase Flows	p. 47
3.1.5 Droplet Drag Coefficients	p. 56
3.1.6 Results from Approximate Analyses	p. 57
3.1.7 Exact Analyses for Gas-Phase and Liquid-Phase Flows	p. 64
3.1.8 Free Convection	p. 71
3.2 Low Reynolds Number Behavior	p. 73
3.3 Droplet Vaporization in an Oscillating Gas	p. 76
3.4 Individual Droplet Behavior in an Unsteady Row	p. 79
4 Multicomponent-Liquid Droplets	p. 90
4.1 Spherically Symmetric Diffusion	p. 93
4.1.1 Continuous-Thermodynamics Models	p. 97
4.2 Liquid-Phase Mass Diffusion with Convective Transport	p. 98
4.2.1 Approximate Analyses	p. 98
4.2.2 Exact Analyses	p. 106
4.3 Metal-Slurry Droplet Vaporization arid Combustion	p. 107
4.3.1 Burning of a Fuel Droplet Containing a Single Metal Particle	p. 108
4.3.2 Liquid Vaporization from Fine-Metal-Slurry Droplets	p. 116
4.3.3 Metal-Particle Combustion with Oxide Condensation	p. 129
4.4 Emulsified-Fuel-Droplet Vaporization and Burning	p. 130
5 Droplet Behavior under Near-Critical, Transcritical, and Supercritical Conditions	p. 134
5.1 High-Pressure Droplet Behavior in a Quiescent Environment	p. 136
5.2 Convective Effects and Secondary Atomization	p. 143
5.3 Molecular-Dynamics Simulation of Transcritical Droplet Vaporization	p. 147
6 Droplet Arrays and Groups	p. 150
6.1 Heating and Vaporization of Droplet Arrays	p. 153
6.2 Group Vaporization and Combustion	p. 165
6.3 Generalized Theory for Droplet-Array Vaporization and Burning	p. 168
6.3.1 Basic Formulation	p. 168
6.3.2 Analysis of Vaporization Without Combustion	p. 170
6.3.3 Combustion Analysis	p. 173
6.3.4 Array Combustion with Nonunitary Lewis Number	p. 179
6.3.5 Array Vaporization with Multicomponent Liquids	p. 189
6.4 Droplet Collisions	p. 192
6.4.1 Droplet-Droplet Collisions	p. 193
6.4.2 Droplet-Wall Collisions	p. 196
7 Spray Equations	p. 199
7.1 Averaging Process for Two-Continua Formulations	p. 200
7.1.1 Averaging of Dependent Variables	p. 204
7.1.2 Averaging of Derivatives	p. 207
7.1.3 Averaged Gas-Phase Equations	p. 210
7.1.4 Averaged Vorticity and Entropy	p. 214
7.1.5 Averaged Liquid-Phase Partial Differential Equations	p. 216
7.1.6 Averaged Liquid-Phase Lagrangian Equations	p. 218
7.1.7 The Microstructure	p. 220
7.2 Two-Continua and Multicontinua Formulations	p. 223
7.2.1 Continuity Equations	p. 223
7.2.2 Momentum Conservation	p. 226
7.2.3 Energy Conservation	p. 228
7.2.4 Hyperbolic Character of Liquid-Phase Equations	p. 230
7.2.5 Subgrid Models for Heat, Mass, and Momentum Exchange	p. 232
7.3 Discrete-Particle Formulation	p. 233
7.4 Probabilistic Formulation	p. 234
8 Computational Issues	p. 237
8.1 Efficient Algorithms for Droplet Computations	p. 237
8.2 Numerical Schemes and Optimization for Spray Computations	p. 245
8.2.1 Two-Phase Laminar Axisymmetric Jet Flow	p. 246
8.2.2 Axisymniptric Unsteady Sprays	p. 255
8.2.3 Solution for Pressure	p. 269
8.3 Point-Source Approximation in Spray Calculations	p. 269
9 Spray Applications	p. 285
9.1 Spherically Symmetric Spray Phenomena	p. 287
9.2 Counterflow Spray Flows	p. 289
9.3 One-Dimensional Planar Spray Ignition and Flame Propagation	p. 296
9.4 Vaporization and Combustion of Droplet Streams	p. 301
9.5 Flame Propagation Through Metal-Slurry Sprays	p. 305
9.6 Liquid-Fueled Combustion Instability	p. 308
9.7 Spray Behavior in Near-Critical and Supercritical Domains	p. 310
9.8 Influence of Supercritical Droplet Behavior on Combustion Instability	p. 311
10 Spray Interactions with Turbulence and Vortical Structures	p. 314
10.1 Vortex-Spray Interactions	p. 318
10.2 Time-Averaged Turbulence Models	p. 321
10.3 Direct Numerical Simulation	p. 324
10.4 Large-Eddy Simulations	p. 329
10.4.1 Proper Two-Way Coupling for LES Closure	p. 332
10.4.2 Gas-Phase Equations	p. 333
10.4.3 Liquid-Phase Equations	p. 335
10.4.4 Vortex-Droplet Interactions	p. 336
11 Film Vaporization	p. 340
11.1 Introduction	p. 340
11.2 Miniature Film-Combustor Concept	p. 342
11.3 Analysis of Liquid-Film Combustor	p. 347
11.3.1 Assumptions and Governing Equations	p. 348
11.3.2 Liquid-Phase Thermal Analysis	p. 349
11.3.3 Fluid-Dynamics Analysis	p. 350
11.3.4 Scalar Analysis	p. 351
11.3.5 Results	p. 354
11.4 Concluding Remarks	p. 360
12 Stability of Liquid Streams	p. 361
12.1 Introduction	p. 361
12.2 Formulation of Governing Equations	p. 364
12.3 Round Jet Analyses	p. 366
12.3.1 Temporal Stability Analysis	p. 367
12.3.2 Surface Energy	p. 368
12.3.3 Spatial Stability Analysis	p. 370
12.3.4 Nonlinear Effects	p. 371
12.3.5 Viscous Effects	p. 376
12.3.6 Cavitation	p. 376
12.4 Planar Sheet Analyses	p. 381
12.4.1 Linear Theory	p. 381
12.4.2 Fan Sheets	p. 385
12.4.3 Nonlinear Theory	p. 385
12.5 Annular Free Films	p. 396
12.5.1 Linear Theory	p. 397
12.5.2 Nonlinear Theory	p. 399
12.5.3 Effect of Swirl	p. 401
12.6 "Conical" Free Films	p. 402
12.7 Concluding Remarks	p. 406
Appendix A The Field Equations	p. 409
Appendix B Conserved Scalars	p. 415
Appendix C Droplet-Model Summary	p. 422
Bibliography	p. 427
Index	p. 460

Available:*

On Order

Summary

Summary

Author Notes

Table of Contents