Two-Phase Heat Transfer [Kõva köide]

Preface xvii

1 Introduction 1

1.1 Scope and Objectives of the Book 1

1.2 Basic Definitions 1

1.3 Various Models 2

1.3.1 Homogeneous Model 2

1.3.2 Separated Flow Models 2

1.3.3 Flow Pattern-Based Models 3

1.4 Classification of Channels 3

1.4.1 Based on Physical Dimensions 3

1.4.2 Based on Condensation Studies 3

1.4.3 Based on Boiling Flow Studies 4

1.4.4 Based on Two-Component Flow 4

1.4.5 Discussion 5

1.4.6 Recommendation 5

1.5 Flow Patterns in Channels 5

1.5.1 Horizontal Channels 5

1.5.1.1 Description of Flow Patterns 5

1.5.1.2 Flow Pattern Maps 6

1.5.2 Vertical Channels 7

1.5.3 Inclined Channels 7

1.5.4 Annuli 8

1.5.5 Minichannels 8

1.5.6 Horizontal Tube Bundles with Crossflow 9

1.5.7 Vertical Tube Bundles 10

1.5.8 Effect of Low Gravity 10

1.5.9 Recommendations 12

1.6 Heat Transfer in Single-Phase Flow 12

1.6.1 Flow Inside Channels 12

1.6.2 Vertical Tube/Rod Bundles with Axial Flow 13

1.6.3 Various Geometries 14

1.6.4 Liquid Metals 14

1.7 Calculation of Pressure Drop 14

1.7.1 Single-Phase Pressure Drop in Pipes 14

1.7.2 Two-Phase Pressure Drop in Pipes 15

1.7.3 Annuli and Vertical Tube Bundles 17

1.7.4 Horizontal Tube Bundles 17

1.7.5 Recommendations 17

1.8 Calculation of Void Fraction 17

1.8.1 Flow Inside Pipes 17

1.8.2 Flow in Tube Bundles 18

1.8.3 Recommendations 18

1.9 CFD Simulation 18

1.10 General Information 19

Nomenclature 19

References 20

2 Heat Transfer During Condensation 25

2.1 Introduction 25

2.2 Condensation on Plates 25

2.2.1 Nusselt Equations 25

2.2.2 Modifications to the Nusselt Equations 26

2.2.3 Condensation with Turbulent Film 27

2.2.4 Condensation on Underside of a Plate 27

2.2.5 Recommendations 28

2.3 Condensation Inside Plain Channels 28

2.3.1 Laminar Condensation in Vertical Tubes 28

2.3.2 The Onset of Turbulence 28

2.3.3 Prediction of Heat Transfer in Turbulent Flow 29

2.3.3.1 Analytical Models 29

2.3.3.2 CFD Models 30

2.3.3.3 Empirical Correlations 30

2.3.3.4 Correlations Applicable to Both Macro and Minichannels 34

2.3.4 Recommendation 41

2.4 Condensation Outside Tubes 41

2.4.1 Single Tube 41

2.4.1.1 Stagnant Vapor 41

2.4.1.2 Moving Vapor 42

2.4.2 Bundles of Horizontal Tubes 42

2.4.2.1 Vapor Entry from Top 42

2.4.2.2 Vapor Entry from Side 44

2.4.3 Recommendations 44

2.5 Condensation with Enhanced Tubes 44

2.5.1 Condensation on Outside Surface 44

2.5.1.1 Single Tubes 44

2.5.1.2 Tube Bundles 46

2.5.2 Condensation Inside Enhanced Tubes 47

2.5.3 Recommendations 49

2.6 Condensation of Superheated Vapors 49

2.6.1 Stagnant Vapor on External Surfaces 49

2.6.2 Forced Flow on External Surfaces 49

2.6.3 Flow inside Tubes 50

2.6.4 Plate-Type Heat Exchangers 50

2.6.5 Recommendations 51

2.7 Miscellaneous Condensation Problems 51

2.7.1 Condensation on Stationary Cone 51

2.7.2 Condensation on a Rotating Disk 51

2.7.3 Condensation on Rotating Vertical Cone 52

2.7.4 Condensation on Rotating Tubes 52

2.7.5 Plate-Type Condensers 53

2.7.5.1 Recommendation 54

2.7.6 Effect of Oil in Refrigerants 54

2.7.6.1 Recommendation 55

2.7.7 Effect of Gravity 55

2.7.7.1 Some Formulas for Zero Gravity 55

2.7.7.2 Experimental Studies 55

2.7.7.3 Conclusion 55

2.7.8 Effect of Non-condensable Gases 56

2.7.8.1 Prediction Methods 56

2.7.8.2 Recommendation 57

2.7.9 Flooding in Upflow 57

2.7.10 Condensation in Thermosiphons 58

2.7.11 Condensation in Helical Coils 58

2.8 Condensation of Vapor Mixtures 59

2.8.1 Physical Phenomena 59

2.8.2 Prediction Methods 60

2.8.3 Recommendation 61

2.9 Liquid Metals 61

2.9.1 Stagnant Vapors 61

2.9.2 Interfacial Resistance 62

2.9.3 Moving Vapors 62

2.9.4 Recommendation 62

2.10 Dropwise Condensation 63

2.10.1 Prediction of Mode of Condensation 63

2.10.2 Theories of Dropwise Condensation 63

2.10.3 Methods to Get Dropwise Condensations 63

2.10.4 Some Experimental Studies 64

2.10.5 Prediction of Heat Transfer 64

2.10.6 Recommendations 66

Nomenclature 66

References 67

3 Pool Boiling 77

3.1 Introduction 77

3.2 Nucleate Boiling 77

3.2.1 Mechanisms of Nucleate Boiling 77

3.2.1.1 Bubble Agitation 77

3.2.1.2 VaporLiquid Exchange 77

3.2.1.3 Evaporative Mechanism 78

3.2.2 Bubble Nucleation 78

3.2.2.1 Inception of Boiling 78

3.2.2.2 Bubble Nucleation Cycle 79

3.2.2.3 Active Nucleation Site Density 81

3.2.2.4 Recommendations 81

3.2.3 Correlations for Heat Transfer 81

3.2.3.1 Conclusion and Recommendation 83

3.2.4 Multicomponent Mixtures 83

3.2.4.1 Physical Phenomena 83

3.2.4.2 Prediction of Heat Transfer 84

3.2.4.3 Recommendation 86

3.2.5 Liquid Metals 86

3.2.5.1 Physical Phenomena 86

3.2.5.2 Prediction of Heat Transfer 87

3.2.5.3 Recommendations 88

3.3 Critical Heat Flux 90

3.3.1 Models of Mechanisms 90

3.3.1.1 Bubble Interference Model 90

3.3.1.2 Hydrodynamic Instability Model 90

3.3.1.3 Macrolayer Dryout Model 91

3.3.1.4 Dry Spot Model 91

3.3.1.5 Interfacial Lift-off Model 92

3.3.2 Correlations for Inclined Surfaces 92

3.3.3 Various Correlations 93

3.3.4 Effect of Subcooling 93

3.3.5 Various Other Factors Affecting CHF 94

3.3.6 Evaluation of CHF Prediction Methods 94

3.3.7 Recommendations 94

3.3.8 Multicomponent Mixtures 95

3.3.8.1 Physical Phenomena and Prediction Methods 95

3.3.8.2 Recommendation 95

3.3.9 Liquid Metals 95

3.3.9.1 Physical Phenomena 97

3.3.9.2 Prediction of CHF 98

3.3.9.3 Recommendations 102

3.4 Transition Boiling 102

3.5 Minimum Film Boiling Temperature 104

3.5.1 Prediction Methods 104

3.5.1.1 Analytical Models 104

3.5.1.2 Empirical Correlations 105

3.5.2 Recommendations 106

3.6 Film Boiling 106

3.6.1 Methods for Predicting Heat Transfer 106

3.6.1.1 Vertical Plates 106

3.6.1.2 Horizontal Cylinders 107

3.6.1.3 Horizontal Plates 108

3.6.1.4 Inclined Plates 108

3.6.1.5 Spheres 109

3.6.2 Liquid Metals 109

3.6.3 Recommendations 110

3.7 Various Topics 110

3.7.1 Effect of Gravity 110

3.7.1.1 Scaling Method of Raj et al. 110

3.7.1.2 Scaling for Hydrogen 112

3.7.1.3 Some Other Studies 112

3.7.1.4 Recommendations 113

3.7.2 Effect of Oil in Refrigerants 113

3.7.2.1 Mechanisms 114

3.7.2.2 Correlations 114

3.7.2.3 Recommendation 115

3.7.3 Thermosiphons 115

3.7.4 Effect of Some Organic Additives 115

Nomenclature 115

References 116

4 Forced Convection Subcooled Boiling 123

4.1 Introduction 123

4.2 Inception of Boiling in Channels 123

4.2.1 Analytical Models and Correlations 123

4.2.2 Minichannels 125

4.2.3 Effect of Dissolved Gases 126

4.2.4 Recommendations 126

4.3 Prediction of Subcooled Boiling Regimes in Channels 126

4.3.1 Recommendation 127

4.4 Prediction of Void Fraction in Channels 127

4.4.1 Recommendations 129

4.5 Heat Transfer in Channels 129

4.5.1 Visual Observations and Mechanisms 129

4.5.2 Prediction of Heat Transfer 130

4.5.2.1 Some Dimensional Correlations 130

4.5.2.2 The Shah Correlation 130

4.5.2.3 Various Correlations 132

4.5.2.4 Recommendations 135

4.6 Single Cylinder with Crossflow 135

4.6.1 Experimental Studies 135

4.6.2 Prediction of Heat Transfer 135

4.6.2.1 Shah Correlation 135

4.6.2.2 Other Correlations 137

4.6.3 Recommendation 138

4.7 Various Geometries 138

4.7.1 Tube Bundles with Axial Flow 138

4.7.2 Tube Bundles with Crossflow 138

4.7.3 Flow Parallel to a Flat Plate 138

4.7.4 Helical Coils 138

4.7.5 Bends 139

4.7.6 Rotating Tube 139

4.7.7 Jets Impinging on Hot Surfaces 141

4.7.7.1 Experimental Studies and Correlations 142

4.7.7.2 Recommendations 145

4.7.8 Spray Cooling 145

Nomenclature 146

References 146

5 Saturated Boiling with Forced Flow 151

5.1 Introduction 151

5.2 Boiling in Channels 151

5.2.1 Effect of Various Parameters 151

5.2.2 Prediction of Heat Transfer 152

5.2.2.1 Correlations for Macro Channels 152

5.2.2.2 Correlations for Minichannels 158

5.2.2.3 Correlations for Both Minichannels and Macrochannels 159

5.2.2.4 Recommendations 162

5.3 Plate-Type Heat Exchangers 162

5.3.1 Herringbone Plate Type 162

5.3.1.1 Longo et al. Correlation 163

5.3.1.2 Almalfi et al. Correlation 163

5.3.1.3 Ayub et al. Correlation 164

5.3.1.4 Recommendation 164

5.3.2 Plane Plate Heat Exchangers 164

5.3.3 Serrated Fin Plate Heat Exchangers 164

5.3.4 Plate Fin Heat Exchangers 165

5.4 Boiling in Various Geometries 166

5.4.1 Helical Coils 166

5.4.1.1 Correlations for Heat Transfer 166

5.4.1.2 Evaluation of Correlations 167

5.4.1.3 Discussion 167

5.4.1.4 Recommendation 167

5.4.2 Rotating Disk 168

5.4.3 Cylinder Rotating in a Liquid Pool 169

5.4.3.1 Recommendation 169

5.4.4 Bends 170

5.4.5 Spiral Wound Heat Exchangers (SWHE) 170

5.4.6 Falling Thin Film on Vertical Surfaces 171

5.4.6.1 Various Studies and Correlations 171

5.4.6.2 Recommendation 171

5.4.7 Vertical Tube/Rod Bundles with Axial Flow 172

5.4.8 Spiral Plate Heat Exchangers 172

5.5 Horizontal Tube Bundles with Upward Crossflow 172

5.5.1 Physical Phenomena 172

5.5.2 Prediction Methods for Heat Transfer 173

5.5.2.1 Shah Correlation 175

5.5.3 Conclusion and Recommendation 176

5.6 Horizontal Tube Bundles with Falling Film Evaporation 177

5.6.1 Flow Patterns/Modes 177

5.6.2 Heat Transfer 178

5.6.3 Conclusion and Recommendation 180

5.7 Boiling of Multicomponent Mixtures 180

5.7.1 Boiling in Tubes 180

5.7.2 Boiling in Various Geometries 182

5.7.3 Conclusions and Recommendations 182

5.8 Liquid Metals 182

5.8.1 Inception of Boiling 182

5.8.2 Heat Transfer 184

5.8.2.1 Sodium 184

5.8.2.2 Potassium 184

5.8.2.3 Mercury 186

5.8.2.4 Cesium and Rubidium 186

5.8.2.5 Mixtures of Liquid Metals 187

5.8.3 Conclusions and Recommendations 187

5.9 Effect of Gravity 187

5.9.1 Experimental Studies 188

5.9.2 Conclusions and Recommendation 189

5.9.3 Effect of Oil in Refrigerants 189

5.9.3.1 Heat Transfer with Immiscible Oils 189

5.9.3.2 Heat Transfer with Miscible Oils 190

5.9.3.3 Conclusions and Recommendations 190

Nomenclature 191

References 192

6 Critical Heat Flux in Flow Boiling 201

6.1 Introduction 201

6.2 CHF in Tubes 201

6.2.1 Types of Boiling Crisis and Mechanisms 201

6.2.2 Prediction Methods 201

6.2.2.1 Analytical Models 201

6.2.2.2 Lookup Tables of CHF 202

6.2.2.3 Dimensional Correlations for Water 203

6.2.2.4 General Correlations 203

6.2.2.5 Fluid-to-Fluid Modeling 213

6.2.2.6 Non-uniform Heat Flux 214

6.2.3 Recommendations 216

6.3 CHF in Annuli 216

6.3.1 Vertical Annuli with Upflow 216

6.3.1.1 Dimensional Correlations for Water 216

6.3.1.2 General Correlations 217

6.3.1.3 Recommendations 220

6.3.2 Horizontal Annuli 221

6.3.3 Eccentric Annuli 221

6.4 CHF in Various Geometries 222

6.4.1 Single Cylinder with Crossflow 222

6.4.2 Horizontal Tube Bundles 224

6.4.2.1 Recommendation 226

6.4.3 Vertical Tube/Rod Bundles 227

6.4.3.1 Mixed Flow Analyses 227

6.4.3.2 Subchannel Analysis 228

6.4.3.3 Phenomenological Analyses 228

6.4.4 Falling Films on Vertical Surfaces 229

6.4.5 Flow Parallel to a Flat Plate 230

6.4.6 Helical Coils 230

6.4.6.1 Recommendation 232

6.4.7 Spiral Wound Heat Exchangers (SWHE) 232

6.4.8 Rotating Liquid Film 232

6.4.9 Bends 233

6.4.10 Jets Impinging on Hot Surfaces 234

6.4.10.1 Correlations for CHF in Free Stream Jets 234

6.4.10.2 Effect of Contact Angle 235

6.4.10.3 Multiple Jets 236

6.4.10.4 Effect of Heater Thickness 236

6.4.10.5 Confined Jets 236

6.4.10.6 Submerged Jets 236

6.4.10.7 Recommendations 236

6.4.11 Spray Cooling 236

6.4.12 Effect of Gravity 237

6.4.12.1 Terrestrial Studies 237

6.4.12.2 Experimental Studies at Low Gravities 238

6.4.12.3 CHF Prediction Methods 239

6.4.12.4 Recommendation 239

Nomenclature 239

References 240

7 Post-CHF Heat Transfer in Flow Boiling 247

7.1 Introduction 247

7.2 Film Boiling in Vertical Tubes 247

7.2.1 Physical Phenomena 247

7.2.2 Prediction of Dispersed Flow Film Boiling in Upflow 248

7.2.2.1 Empirical Correlations 248

7.2.2.2 Mechanistic Analyses 249

7.2.2.3 Phenomenological Correlations 249

7.2.2.4 Lookup Tables 254

7.2.2.5 Recommendations 256

7.2.3 Prediction of Inverted Annular Film Boiling in Upflow 256

7.2.3.1 Recommendations 257

7.2.4 Film Boiling in Downflow 257

7.3 Film Boiling in Horizontal Tubes 257

7.3.1 Prediction Methods 258

7.3.2 Recommendations 259

7.4 Film Boiling in Various Geometries 259

7.4.1 Annuli 259

7.4.2 Vertical Tube Bundles 260

7.4.3 Single Horizontal Cylinder 261

7.4.3.1 Recommendation 262

7.4.4 Spheres 262

7.4.5 Jets Impinging on Hot Surfaces 264

7.4.6 Bends 265

7.4.7 Helical Coils 265

7.4.8 Chilldown of Cryogenic Pipelines 266

7.4.9 Flow Parallel to a Plate 267

7.4.10 Spray Cooling 267

7.5 Minimum Film Boiling Temperature and Heat Flux 268

7.5.1 Flow in Channels 268

7.5.2 Jets Impinging on Hot Surfaces 268

7.5.3 Chilldown of Cryogenic Lines 269

7.5.4 Spheres 269

7.5.5 Spray Cooling 270

7.6 Transition Boiling 270

7.6.1 Flow in Channels 270

7.6.2 Jets on Hot Surfaces 271

7.6.3 Spheres 272

7.6.4 Spray Cooling 272

Nomenclature 273

References 274

8 Two-Component GasLiquid Heat Transfer 279

8.1 Introduction 279

8.2 Pre-mixed Mixtures in Channels 279

8.2.1 Flow Pattern-Based Prediction Methods 279

8.2.1.1 Bubbly Flow 279

8.2.1.2 Slug Flow 281

8.2.1.3 Annular Flow 282

8.2.1.4 Post-dryout Dispersed Flow 283

8.2.2 General Correlations 283

8.2.2.1 Horizontal Channels 283

8.2.2.2 Vertical Channels 286

8.2.2.3 Horizontal and Vertical Channels 288

8.2.2.4 Inclined Channels 289

8.2.3 Recommendations 289

8.3 Gas Flow through Channel Walls 290

8.3.1 Experimental Studies 290

8.3.2 Heat Transfer Prediction 292

8.3.3 Conclusions 292

8.4 Cooling by AirWater Mist 292

8.4.1 Single Cylinders in Crossflow 292

8.4.2 Flow over Tube Banks 294

8.4.3 Flow Parallel to Plates 294

8.4.4 Wedges 295

8.4.5 Jets 295

8.4.6 Sphere 297

8.5 Evaporation from Water Pools 297

8.5.1 Introduction 297

8.5.2 Empirical Correlations 297

8.5.3 Analytical Models 298

8.5.3.1 Shah Model 298

8.5.3.2 Other Models 300

8.5.4 CFD Models 301

8.5.5 Occupied Swimming Pools 301

8.5.6 Conclusions and Recommendations 301

8.6 Various Topics 301

8.6.1 Jets Impinging on Hot Surfaces 301

8.6.2 Vertical Tube Bundle 302

8.6.3 Effect of Gravity 302

8.7 Liquid MetalGas in Channels 303

8.7.1 Mercury 303

8.7.2 Various Liquid Metals 304

8.7.3 Discussion 305

Nomenclature 305

References 306

9 Gas-Fluidized Beds 311

9.1 Introduction 311

9.2 Regimes of Fluidization 311

9.2.1 Regime Transition Velocities 312

9.2.1.1 Minimum Fluidization Velocity 312

9.2.1.2 Various Regime Transition Velocities 312

9.2.2 Void Fraction and Bed Expansion 313

9.3 Properties of Solid Particles 313

9.3.1 Density 313

9.3.2 Particle Diameter 313

9.3.3 Particle Shape Factor 314

9.3.4 Classification of Particles 314

9.4 Parameters Affecting Heat Transfer to Surfaces 315

9.4.1 Gas Velocity 315

9.4.2 Particle Size and Shape 315

9.4.3 Pressure and Temperature 316

9.4.4 Heat Transfer Surface Diameter 317

9.4.5 Properties of Gas and Solid 317

9.4.6 Gas Distribution 317

9.4.7 Length and Location of Tube 317

9.4.8 Bed Diameter and Height 318

9.4.9 Tube Inclination 318

9.5 Theories of Heat Transfer 318

9.5.1 Film Theory 318

9.5.2 Penetration Theory 318

9.5.2.1 Particle Theory 319

9.5.2.2 Packet Theory 319

9.6 Prediction Methods for Single Tubes and Spheres 319

9.6.1 Analytical Models 319

9.6.1.1 Particle Models 319

9.6.1.2 Packet Models 320

9.6.2 Empirical Correlations 321

9.6.2.1 Maximum Heat Transfer 321

9.6.2.2 Correlations for the Entire Range 324

9.6.3 Recommendations 325

9.7 Tube Bundles 326

9.7.1 Horizontal Tube Bundles 326

9.7.2 Vertical Tube Bundles 328

9.7.3 Recommendations 328

9.8 Radiation Heat Transfer 329

9.8.1 Radiation Heat Transfer Coefficient and Effective Emissivity 329

9.8.2 Temperature for Significant Radiation Contribution 329

9.8.3 Conclusions and Recommendations 330

9.9 Heat Transfer to Bed Walls 330

9.9.1 Prediction Methods 330

9.9.2 Conclusions and Recommendations 331

9.10 Heat Transfer in Freeboard Region 331

9.10.1 Experimental Studies and Prediction Methods 332

9.10.2 Recommendation 332

9.11 Heat Transfer Between Gas and Particles 332

9.12 GasSolid Flow in Pipes 333

9.12.1 Regimes of GasSolid Flow 333

9.12.2 Experimental Studies of Heat Transfer 334

9.12.3 Prediction of Heat Transfer 334

9.12.3.1 Various Methods 334

9.12.3.2 Shah Correlation 336

9.12.4 Recommendation 337

9.13 Solar Collectors with Particle Suspensions 337

Nomenclature 338

References 340

Appendix 347

Index 357

Mirza Mohammed Shah, PhD, PE, has over 50 years experience of research and engineering. His more than 100 publications include his general predictive techniques for two-phase heat transfer which are widely used in the industry. He is Fellow of ASME and ASHRAE. Presently he is Director of Engineering Research Associates, an organization dedicated to promoting and performing research for developing practically useable solutions to problems.