1 Introduction ................................................. 1
1.1 Introductory Remarks .................................... 1
1.2 Classification of Models ................................ 2
1.2.1 Physical Modeling ................................ 2
1.2.2 Mathematical Modeling ............................ 3
1.3 General Strategy for Modeling Two-Phase Phenomena ....... 3
1.4 Basic Physical Situations of Relevance in Gas-Liquid
Processes ............................................... 4
1.4.1 Gas-Liquid Two-Phase Flows in Cylindrical Bath ... 4
1.4.2 Gas-Liquid Two-Phase Flows in Pipes ............. 10
1.4.3 Dimensionless Parameters ........................ 13
1.5 Closing Remarks ........................................ 15
References .................................................. 15
2 Turbulence Structure of Two-Phase Jets ...................... 19
2.1 Mean Flow Characteristics .............................. 19
2.1.1 Introduction .................................... 19
2.1.2 Experiment ...................................... 20
2.1.3 Experimental Results ............................ 23
2.2 Conditional Sampling ................................... 33
2.2.1 Introductory Remarks ............................ 33
2.2.2 Experimental Apparatus and Procedure ............ 34
2.2.3 Shape and Size of Helium Bubble ................. 34
2.2.4 Four-Quadrant Classification Method ............. 35
2.2.5 Experimental Results Based on Four-Quadrant
Classification Method ........................... 36
2.3 Summary ................................................ 40
2.3.1 Mean Flow Characteristics ....................... 40
2.3.2 Conditional Sampling ............................ 41
References .................................................. 42
3 The Coanda Effect ........................................... 45
3.1 General Features ....................................... 45
3.1.1 Overview ........................................ 45
3.1.2 Mechanism of Coanda Effect ...................... 46
3.2 Wall Interaction in Metallurgical Reactor .............. 47
3.2.1 Bubble Characteristics .......................... 47
3.2.2 Liquid Flow Characteristics ..................... 60
3.3 Interaction Between Two Bubbling Jets .................. 69
3.3.1 Critical Condition for Merging of Two Bubbling
Jets ............................................ 69
3.3.2 Merging Length of Two Bubbling Jets ............. 73
3.3.3 Bubble Characteristics .......................... 77
3.3.4 Liquid Flow Characteristics ..................... 85
3.3.5 Mixing Time ..................................... 90
References .................................................. 91
4 Interfacial Phenomena ....................................... 95
4.1 Single Bubble on Flat Plate ............................ 95
4.1.1 Overview ........................................ 95
4.1.2 Experimental Apparatus and Procedure ............ 96
4.1.3 Experimental Results ............................ 98
4.1.4 Summary ........................................ 106
4.2 Bubbling Jet Along Vertical Flat Plate ................ 107
4.2.1 Bubble Characteristics ......................... 107
4.2.2 Liquid Flow Characteristics .................... 123
4.3 Bubble Shape and Size ................................. 132
4.3.1 Experimental Apparatus and Procedure ........... 135
4.3.2 Experimental Results ........................... 137
4.4 Bubble Removal from Molten Metal ...................... 146
4.4.1 Experimental Apparatus and Procedure ........... 146
4.4.2 Experimental Results ........................... 148
4.5 Flow Distribution in Vertical Pipes ................... 157
4.5.1 Experimental Apparatus and Procedure ........... 158
4.5.2 Experimental Results ........................... 159
4.5.3 Bubble Velocity and Size ....................... 164
References ................................................. 172
5 Swirling Flow and Mixing ................................... 177
5.1 Rotary Sloshing of Liquid in Cylindrical Vessel ....... 177
5.1.1 Linear Theory .................................. 177
5.1.2 Nonlinear Theory ............................... 178
5.1.3 Summary ........................................ 179
5.2 Swirl Motion of Bubbling Jet .......................... 181
5.2.1 General Features ............................... 181
5.2.2 Operation Under Reduced Surface Pressure ....... 193
5.2.3 Mixing Time .................................... 202
5.2.4 Effect of Top Slag ............................. 210
5.2.5 Effect of Offset Gas Injection ................. 217
5.2.6 Effect of Dual Jet Sources ..................... 218
References ................................................. 220
6 Slag-Metal Interaction ..................................... 223
6.1 Shape and Size of Entrained Metal Layer ............... 223
6.1.1 Experiment ..................................... 224
6.1.2 Experimental Results ........................... 228
6.2 Characteristics of Metal Droplets ..................... 240
6.2.1 Experiment ..................................... 241
6.2.2 Experimental Results ........................... 242
6.3 Summary ............................................... 253
6.3.1 Shape and Size of Entrained Metal Layer ........ 253
6.3.2 Characteristics of Metal Droplets .............. 254
References ................................................. 254
7 Surface Flow Control ....................................... 257
7.1 Overview .............................................. 257
7.2 Experiment ............................................ 258
7.2.1 Experimental Apparatus and Procedure ........... 258
7.2.2 Boundary Conditions on Bath Surface ............ 259
7.2.3 Data Processing ................................ 259
7.3 Experimental Results .................................. 260
7.3.1 Mixing Time .................................... 260
7.3.2 Fluid Flow Phenomena ........................... 261
7.4 Conclusions ........................................... 268
References ................................................. 270
8 Two-Phase Flow in Continuous Casting ....................... 271
8.1 Flow Characteristics .................................. 271
8.1.1 Overview ....................................... 271
8.1.2 Experiment ..................................... 272
8.1.3 Experimental Results ........................... 275
8.1.4 Summary ........................................ 285
8.2 Mold Powder Entrapment ................................ 286
8.2.1 Overview ....................................... 286
8.2.2 Experimental Apparatus and Procedure ........... 288
8.2.3 Some Aspects of Kelvin-Helmholtz Instability ... 290
8.2.4 Experimental Results ........................... 292
8.2.5 Summary ........................................ 300
References ................................................. 300
9 Modeling Gas-Liquid Flow in Metallurgical Operations ....... 303
9.1 Overview .............................................. 303
9.2 Review of Modeling Methods ............................ 303
9.3 Mathematical Models ................................... 308
9.3.1 Quasi-Single-Fluid (Momentum Balance) Models ... 309
9.3.2 Two-Fluid Model ................................ 319
9.3.3 Mathematical Models Based on Energy Balance .... 327
9.4 Boundary Conditions ................................... 329
9.5 Numerical Solution .................................... 331
References ................................................. 332
10 Numerical Modeling of Multiphase Flows in Materials
Processing ................................................. 337
10.1 Overview .............................................. 337
10.2 Control Volume-Based Finite Difference Method ......... 338
10.2.1 Continuum Mixture Model ........................ 338
10.2.2 Two-Fluid Models ............................... 345
10.3 The Finite Element Method ............................. 350
10.4 Multi-domain (Two-Region) Methods ..................... 358
10.5 Boundary Conditions ................................... 363
10.5.1 Boundary Conditions in Multiphase Models ....... 366
10.5.2 Boundary Conditions for Multi-region Method .... 367
References ................................................. 368
11 Review of Nanoscale and Microscale Phenomena in Materials
Processing ................................................. 375
11.1 Introduction .......................................... 375
11.1.1 Fundamentals ................................... 375
11.1.2 Applications ................................... 376
11.2 Definitions and Generation Method of Nanoscale and
Microscale ............................................ 376
11.2.1 Bubbles ........................................ 376
11.2.2 Generation Method .............................. 377
11.3 Removal of Gas from Gas-Liquid Mixture ................ 378
11.4 Flow Pattern of Gas-Liquid Two-Phase Flow in
Microchannels ......................................... 379
11.5 Flow Characteristics in Microchannels ................. 382
11.6 Heat Transfer in Microchannels ........................ 382
11.7 Numerical Simulation of Transport Phenomena ........... 383
11.8 Mixing in Microchannels and Microreactors ............. 383
11.9 Measurement Method .................................... 383
11.10 Enhancement of Gas Dissolution Rate .................. 383
11.11 Microfluidic Devices ................................. 384
11.12 Fuel Cell ............................................ 384
11.13 Closing Remarks ...................................... 384
References .................................................... 384
Appendix 1 .................................................... 389
Appendix 2 .................................................... 393
Index ......................................................... 411
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