Preface ........................................................ xi
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 ............................. 234
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 Axisymmetriс 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 ................................. 368
12.3.1 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 В Conserved Scalars ................................. 415
Appendix С Droplet-Model Summary ............................. 422
Bibliography .................................................. 427
Index ......................................................... 460
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