Fluid Dynamics and Transport of Droplets and Sprays

Title......Page 5
Copyright......Page 6
Contents......Page 9
Preface......Page 13
Nomenclature......Page 16
1.1 Overview......Page 21
1.2 Droplet-Size Determination......Page 24
2 Isolated Spherically Symmetric Droplet Vaporization and Heating......Page 28
2.1 Theory of Spherically Symmetric Droplet Vaporization and Heating......Page 31
2.1.1 Gas-Phase Analysis......Page 32
2.1.2 Liquid-Phase Analysis......Page 39
2.1.3 Chemical Reaction......Page 44
2.2 Radiative Heating of Droplets......Page 46
3 Convective Droplet Vaporization, Heating, and Acceleration......Page 50
3.1 Convective Droplet Vaporization......Page 51
3.1.1 Evaluation of Reynolds Number Magnitude......Page 53
3.1.2 Physical Description......Page 55
3.1.3 Approximate Analyses for Gas-Phase Boundary Layer......Page 60
3.1.4 Approximate Analyses for Liquid-Phase Flows......Page 67
3.1.5 Droplet Drag Coefficients......Page 76
3.1.6 Results from Approximate Analyses......Page 77
3.1.7 Exact Analyses for Gas-Phase and Liquid-Phase Flows......Page 84
3.1.8 Free Convection......Page 91
3.2 Low Reynolds Number Behavior......Page 93
3.3 Droplet Vaporization in an Oscillating Gas......Page 96
3.4 Individual Droplet Behavior in an Unsteady Flow......Page 99
4 Multicomponent-Liquid Droplets......Page 110
4.1 Spherically Symmetric Diffusion......Page 113
4.1.1 Continuous-Thermodynamics Models......Page 117
4.2.1 Approximate Analyses......Page 118
4.2.2 Exact Analyses......Page 126
4.3 Metal-Slurry Droplet Vaporization and Combustion......Page 127
4.3.1 Burning of a Fuel Droplet Containing a Single Metal Particle......Page 128
4.3.2 Liquid Vaporization from Fine-Metal-Slurry Droplets......Page 136
4.3.3 Metal-Particle Combustion with Oxide Condensation......Page 149
4.4 Emulsified-Fuel-Droplet Vaporization and Burning......Page 150
5 Droplet Behavior under Near-Critical, Transcritical, and Supercritical Conditions......Page 154
5.1 High-Pressure Droplet Behavior in a Quiescent Environment......Page 156
5.2 Convective Effects and Secondary Atomization......Page 163
5.3 Molecular-Dynamics Simulation of Transcritical Droplet Vaporization......Page 167
6 Droplet Arrays and Groups......Page 170
6.1 Heating and Vaporization of Droplet Arrays......Page 173
6.2 Group Vaporization and Combustion......Page 185
6.3.1 Basic Formulation......Page 188
6.3.2 Analysis of Vaporization Without Combustion......Page 190
6.3.3 Combustion Analysis......Page 193
6.3.4 Array Combustion with Nonunitary Lewis Number......Page 199
6.3.5 Array Vaporization with Multicomponent Liquids......Page 209
6.4 Droplet Collisions......Page 212
6.4.1 Droplet–Droplet Collisions......Page 213
6.4.2 Droplet–Wall Collisions......Page 216
7 Spray Equations......Page 219
7.1 Averaging Process for Two-Continua Formulations......Page 220
7.1.1 Averaging of Dependent Variables......Page 224
7.1.2 Averaging of Derivatives......Page 227
7.1.3 Averaged Gas-Phase Equations......Page 230
7.1.4 Averaged Vorticity and Entropy......Page 234
7.1.5 Averaged Liquid-Phase Partial Differential Equations......Page 236
7.1.6 Averaged Liquid-Phase Lagrangian Equations......Page 238
7.1.7 The Microstructure......Page 240
7.2.1 Continuity Equations......Page 243
7.2.2 Momentum Conservation......Page 246
7.2.3 Energy Conservation......Page 248
7.2.4 Hyperbolic Character of Liquid-Phase Equations......Page 250
7.2.5 Subgrid Models for Heat, Mass, and Momentum Exchange......Page 252
7.3 Discrete-Particle Formulation......Page 253
7.4 Probabilistic Formulation......Page 254
8.1 Efficient Algorithms for Droplet Computations......Page 257
8.2 Numerical Schemes and Optimization for Spray Computations......Page 265
8.2.1 Two-Phase Laminar Axisymmetric Jet Flow......Page 266
Solution Procedure......Page 268
Explicit Predictor–Corrector Scheme......Page 269
Block-Implicit Scheme......Page 270
Operator-Splitting Method......Page 271
Results......Page 272
8.2.2 Axisymmetric Unsteady Sprays......Page 275
Liquid-Phase Equations......Page 277
Numerical Aspects and Solution Procedure......Page 278
Numerical Results......Page 279
8.3 Point-Source Approximation in Spray Calculations......Page 289
Interpolation for Phase-Exchange Source Terms......Page 290
Spherically Symmetric Case......Page 291
Convective Case......Page 295
9 Spray Applications......Page 305
9.1 Spherically Symmetric Spray Phenomena......Page 307
9.2 Counterflow Spray Flows......Page 309
9.3 One-Dimensional Planar Spray Ignition and Flame Propagation......Page 316
9.4 Vaporization and Combustion of Droplet Streams......Page 321
9.5 Flame Propagation Through Metal-Slurry Sprays......Page 325
9.6 Liquid-Fueled Combustion Instability......Page 328
9.7 Spray Behavior in Near-Critical and Supercritical Domains......Page 330
9.8 Influence of Supercritical Droplet Behavior on Combustion Instability......Page 331
10 Spray Interactions with Turbulence and Vortical Structures......Page 334
10.1 Vortex--Spray Interactions......Page 338
10.2 Time-Averaged Turbulence Models......Page 341
10.3 Direct Numerical Simulation......Page 344
10.4 Large-Eddy Simulations......Page 349
10.4.1 Proper Two-Way Coupling for LES Closure......Page 352
10.4.2 Gas-Phase Equations......Page 353
10.4.3 Liquid-Phase Equations......Page 355
10.4.4 Vortex–Droplet Interactions......Page 356
11.1 Introduction......Page 360
11.2 Miniature Film-Combustor Concept......Page 362
11.3 Analysis of Liquid-Film Combustor......Page 367
11.3.1 Assumptions and Governing Equations......Page 368
11.3.2 Liquid-Phase Thermal Analysis......Page 369
11.3.3 Fluid-Dynamics Analysis......Page 370
11.3.4 Scalar Analysis......Page 371
11.3.5 Results......Page 374
11.4 Concluding Remarks......Page 380
12.1 Introduction......Page 381
12.2 Formulation of Governing Equations......Page 384
12.3 Round Jet Analyses......Page 386
12.3.1 Temporal Stability Analysis......Page 387
12.3.2 Surface Energy......Page 388
12.3.3 Spatial Stability Analysis......Page 390
12.3.4 Nonlinear Effects......Page 391
12.3.6 Cavitation......Page 396
12.4.1 Linear Theory......Page 401
12.4.3 Nonlinear Theory......Page 405
12.5 Annular Free Films......Page 416
12.5.1 Linear Theory......Page 417
12.5.2 Nonlinear Theory......Page 419
12.5.3 Effect of Swirl......Page 421
12.6 \"Conical\" Free Films......Page 422
12.7 Concluding Remarks......Page 426
Appendix A: The Field Equations......Page 429
Axisymmetric Formulation......Page 432
Spherically Symmetric Formulation......Page 433
Appendix B: Conserved Scalars......Page 435
Appendix C: Droplet-Model Summary......Page 442
Bibliography......Page 447
Index......Page 480