Modeling Multiphase Materials Processes (eBook)

Preface 6
Contents 8
1 Introduction 12
1.1 Introductory Remarks 12
1.2 Classification of Models 13
1.2.1 Physical Modeling 13
1.2.2 Mathematical Modeling 14
1.3 General Strategy for Modeling Two-Phase Phenomena 14
1.4 Basic Physical Situations of Relevance in Gas–Liquid Processes 15
1.4.1 Gas–Liquid Two-Phase Flows in Cylindrical Bath 15
1.4.1.1 Bubbling and Jetting 15
1.4.1.2 Characteristic Parameters 16
1.4.2 Gas–Liquid Two-Phase Flows in Pipes 21
1.4.2.1 Vertical Pipes 22
1.4.2.2 Horizontal Pipe 23
1.4.3 Dimensionless Parameters 24
1.4.3.1 Reynolds Number, Re 24
1.4.3.2 Froude Number, Fr 25
1.4.3.3 Weber Number, We 25
1.4.3.4 Mach Number, M 25
1.4.3.5 Strouhal Number, St 26
1.5 Closing Remarks 26
References 26
2 Turbulence Structure of Two-Phase Jets 29
2.1 Mean Flow Characteristics 29
2.1.1 Introduction 29
2.1.2 Experiment 30
2.1.2.1 Bubble characteristics 30
2.1.2.2 Liquid Flow Characteristics 32
2.1.3 Experimental Results 33
2.1.3.1 Bubble Characteristics 33
2.1.3.2 Liquid Flow Characteristics 39
2.2 Conditional Sampling 43
2.2.1 Introductory Remarks 43
2.2.2 Experimental Apparatus and Procedure 44
2.2.3 Shape and Size of Helium Bubble 44
2.2.4 Four-Quadrant Classification Method 45
2.2.5 Experimental Results Based on Four-Quadrant Classification Method 46
2.3 Summary 50
2.3.1 Mean Flow Characteristics 50
2.3.1.1 Bubble Characteristics 50
2.3.1.2 Liquid Flow Characteristics 50
2.3.2 Conditional Sampling 51
References 52
3 The Coanda Effect 54
3.1 General Features 54
3.1.1 Overview 54
3.1.2 Mechanism of Coanda Effect 55
3.2 Wall Interaction in Metallurgical Reactor 56
3.2.1 Bubble Characteristics 56
3.2.1.1 Experimental Apparatus and Procedure 56
3.2.1.2 Experimental Results 58
3.2.1.3 Summary on Bubble Characteristics 68
3.2.2 Liquid Flow Characteristics 69
3.2.2.1 Experimental Apparatus and Procedure 69
3.2.2.2 Experimental Results 70
3.2.2.3 Summary of Liquid Flow Characteristics 78
3.3 Interaction Between Two Bubbling Jets 78
3.3.1 Critical Condition for Merging of Two Bubbling Jets 78
3.3.1.1 Experimental Apparatus and Procedure 78
3.3.1.2 Experimental Results 80
3.3.2 Merging Length of Two Bubbling Jets 82
3.3.2.1 Experimental Apparatus and Procedure 82
3.3.2.2 Experimental Results 82
3.3.2.3 Summary 86
3.3.3 Bubble Characteristics 86
3.3.3.1 Experimental Apparatus and Procedure 87
3.3.3.2 Experimental Results 87
3.3.3.3 Summary of Bubble Characteristics 93
3.3.4 Liquid Flow Characteristics 94
3.3.4.1 Experimental Apparatus and Procedure 94
3.3.4.2 Experimental Results 94
3.3.4.3 Summary of Liquid Flow Characteristics 98
3.3.5 Mixing Time 99
References 100
4 Interfacial Phenomena 103
4.1 Single Bubble on Flat Plate 103
4.1.1 Overview 103
4.1.2 Experimental Apparatus and Procedure 104
4.1.3 Experimental Results 106
4.1.3.1 Bubble Shape Using Potential Method 106
4.1.3.2 Bubble Volume at Incipient Detachment Using Energy and Force Balance 108
4.1.3.3 Bubble Shape and Size and Critical Volume Using Laplace and Potential Methods 110
4.1.3.4 Measured and Predicted Aspect Ratio and Critical Bubble Volume 113
4.1.4 Summary 114
4.2 Bubbling Jet Along Vertical Flat Plate 115
4.2.1 Bubble Characteristics 115
4.2.1.1 Overview 115
4.2.1.2 Experimental Apparatus and Procedure 117
4.2.1.3 Experimental Results 119
4.2.1.4 Summary 130
4.2.2 Liquid Flow Characteristics 131
4.2.2.1 Experimental Apparatus and Procedure 131
4.2.2.2 Results 132
4.2.2.3 Summary 140
4.3 Bubble Shape and Size 140
4.3.1 Experimental Apparatus and Procedure 143
4.3.2 Experimental Results 145
4.3.2.1 Bubble Attachment to Flat Plate 145
4.3.2.2 Bubble Collision with Flat Plate 148
4.3.2.3 Summary 154
4.4 Bubble Removal from Molten Metal 154
4.4.1 Experimental Apparatus and Procedure 154
4.4.2 Experimental Results 156
4.4.2.1 Behavior of Bubbling Jet Approaching Horizontal Cylinder 156
4.4.2.2 Behavior of Bubbles on Cylinder Surface 160
4.4.2.3 Stem Diameter and Stem Height of Trapped Bubble 161
4.4.2.4 Summary 165
4.5 Flow Distribution in Vertical Pipes 165
4.5.1 Experimental Apparatus and Procedure 166
4.5.2 Experimental Results 167
4.5.2.1 Flow Distribution 167
4.5.2.2 Bubbly Flow–Slug Flow Regime Boundary 169
4.5.2.3 Summary 171
4.5.3 Bubble Velocity and Size 172
4.5.3.1 Experimental Apparatus and Procedure 172
4.5.3.2 Experimental Results 172
4.5.3.3 Summary 179
References 180
5 Swirling Flow and Mixing 184
5.1 Rotary Sloshing of Liquid in Cylindrical Vessel 184
5.1.1 Linear Theory 184
5.1.2 Nonlinear Theory 185
5.1.3 Summary 186
5.2 Swirl Motion of Bubbling Jet 188
5.2.1 General Features 188
5.2.1.1 Classification of Swirl Motion 188
5.2.1.2 The First Kind of Swirl Motion 190
5.2.1.3 The Second Kind of Swirl Motion 195
5.2.1.4 Summary 199
5.2.2 Operation Under Reduced Surface Pressure 200
5.2.2.1 Experimental Apparatus and Procedure 201
5.2.2.2 Experimental Results and Discussion 202
5.2.2.3 Summary 209
5.2.3 Mixing Time 209
5.2.3.1 Experimental Apparatus and Procedure 210
5.2.3.2 Experimental Results 211
5.2.3.3 Summary 217
5.2.4 Effect of Top Slag 217
5.2.4.1 Experimental Apparatus and Procedure 218
5.2.4.2 Experimental Results 218
5.2.4.3 Summary 223
5.2.5 Effect of Offset Gas Injection 224
5.2.6 Effect of Dual Jet Sources 225
References 227
6 Slag–Metal Interaction 230
6.1 Shape and Size of Entrained Metal Layer 230
6.1.1 Experiment 231
6.1.2 Experimental Results 235
6.1.2.1 Total Holdup Distribution in the Slag Layer 235
6.1.2.2 Horizontal Distribution of Elevated Molten Metal Holdup 236
6.1.2.3 Height and Volume of Molten Metal in the Elevated Region 239
6.1.2.4 Accumulated Molten Metal Droplets 245
6.2 Characteristics of Metal Droplets 247
6.2.1 Experiment 248
6.2.2 Experimental Results 249
6.2.2.1 Mechanism of Metal Droplet Generation 249
6.2.2.2 Total Volume of Accumulated Molten Metal Droplets at Steady State, V 251
6.2.2.3 Birth Rate of Molten Metal Droplets 254
6.2.2.4 Lifetime of Molten Metal Droplet, 257
6.2.2.5 Death Rate of Molten Metal Droplets After Stoppageof Gas Injection 258
6.3 Summary 260
6.3.1 Shape and Size of Entrained Metal Layer 260
6.3.2 Characteristics of Metal Droplets 261
References 261
7 Surface Flow Control 263
7.1 Overview 263
7.2 Experiment 264
7.2.1 Experimental Apparatus and Procedure 264
7.2.2 Boundary Conditions on Bath Surface 265
7.2.3 Data Processing 265
7.3 Experimental Results 266
7.3.1 Mixing Time 266
7.3.2 Fluid Flow Phenomena 267
7.3.2.1 Mean Velocity Components 267
7.3.2.2 Root-Mean-Square Turbulence Components and Reynolds Shear Stress 271
7.4 Conclusions 274
References 276
8 Two-Phase Flow in Continuous Casting 277
8.1 Flow Characteristics 277
8.1.1 Overview 277
8.1.2 Experiment 278
8.1.2.1 Experimental Apparatus 278
8.1.2.2 Dimensional Analysis 278
8.1.2.3 Experimental Procedure 280
8.1.3 Experimental Results 281
8.1.3.1 Dispersion of Bubbles and Mean Bubble Diameter 281
8.1.3.2 Mean Velocities and Root-Mean-Square Turbulence Components 281
8.1.3.3 Vertical Distribution of Axial Mean Velocity 283
8.1.3.4 Vertical Distribution of Root-Mean-Square Turbulence Components 283
8.1.3.5 Empirical Relations for Mean Velocity Components 285
8.1.4 Summary 291
8.2 Mold Powder Entrapment 292
8.2.1 Overview 292
8.2.2 Experimental Apparatus and Procedure 294
8.2.3 Some Aspects of Kelvin–Helmholtz Instability 296
8.2.3.1 Critical Velocity Difference for the Onset of Kelvin–Helmholtz Instability 296
8.2.3.2 Wavelength and Amplitude of Instability Wave 297
8.2.4 Experimental Results 298
8.2.4.1 Visualized Flow Field and Velocity Vectors 298
8.2.4.2 Critical Velocity Difference for the Onset of KHI 298
8.2.4.3 Comparison of Measured and Calculated Critical Salt Water Flow Velocity 299
8.2.4.4 Wavelength and Amplitude of KHI 304
8.2.4.5 KHI-Induced Mold Powder Entrapment in Continuous Casting Mold 305
8.2.5 Summary 306
References 306
9 Modeling Gas–Liquid Flow in Metallurgical Operations 309
9.1 Overview 309
9.2 Review of Modeling Methods 309
9.3 Mathematical Models 314
9.3.1 Quasi-Single-Fluid (Momentum Balance) Models 315
9.3.1.1 Two-Phase Zone Modeling 316
9.3.1.2 Turbulence Modeling 320
9.3.2 Two-Fluid Model 325
9.3.2.1 Eulerian–Eulerian Model 325
9.3.2.2 Eulerian–Lagrangian model 328
9.3.3 Mathematical Models Based on Energy Balance 333
9.4 Boundary Conditions 335
9.5 Numerical Solution 337
References 338
10 Numerical Modeling of Multiphase Flows in Materials Processing 342
10.1 Overview 342
10.2 Control Volume-Based Finite Difference Method 343
10.2.1 Continuum Mixture Model 343
10.2.2 Two-Fluid Models 350
10.3 The Finite Element Method 355
10.4 Multi-domain (Two-Region) Methods 363
10.5 Boundary Conditions 368
10.5.1 Boundary Conditions in Multiphase Models 371
10.5.2 Boundary Conditions for Multi-region Method 372
References 373
11 Review of Nanoscale and Microscale Phenomena in Materials Processing 379
11.1 Introduction 379
11.1.1 Fundamentals 379
11.1.2 Applications 380
11.2 Definitions and Generation Method of Nanoscale and Microscale 380
11.2.1 Bubbles 380
11.2.1.1 Nanobubble and Microbubble 380
11.2.2 Generation Method 381
11.3 Removal of Gas from Gas–Liquid Mixture 382
11.4 Flow Pattern of Gas–Liquid Two-Phase Flow in Microchannels 383
11.5 Flow Characteristics in Microchannels 386
11.6 Heat Transfer in Microchannels 386
11.7 Numerical Simulation of Transport Phenomena 387
11.8 Mixing in Microchannels and Microreactors 387
11.9 Measurement Method 387
11.10 Enhancement of Gas Dissolution Rate 387
11.11 Microfluidic Devices 388
11.12 Fuel Cell 388
11.13 Closing Remarks 388
References 388
Appendix 1 392
Appendix 2 396
Index 414