Nuclear Thermal Hydraulics (eBook)

Series Aims and Scopes 6
Preface 8
Contents 11
Part I: Thermodynamics 19
Chapter 1: The First Law of Thermodynamics 20
1.1 Heat and Work 20
1.1.1 Temperature and Specific Heat 20
1.1.2 Absolute Work 21
1.1.3 p-V Diagram 22
1.2 First Law of Thermodynamics 23
1.3 Work by Fluids 25
1.3.1 Open Flow System 25
1.3.2 Steady Flow 28
1.3.3 Low-Speed Flow 29
1.3.4 Adiabatic Flow 29
1.4 Enthalpy 30
Chapter 2: Ideal Gas and Steam 32
2.1 Ideal Gas 32
2.1.1 Equation of State for an Ideal Gas 32
2.1.1.1 Boyle´s Law 32
2.1.1.2 Charles´s Law (Gay-Lussac´s Law) 32
2.1.2 State Change of an Ideal Gas 35
2.1.2.1 Isothermal Change 35
2.1.2.2 Constant-Pressure Change 36
2.1.2.3 Constant-Volume Change 37
2.1.2.4 Adiabatic Change 37
2.1.2.5 Polytropic Change 38
2.2 Steam 39
2.2.1 Basic Nature of Steam 39
2.2.2 State Quantity of Steam 41
2.2.3 Steam Tables and Steam Diagrams 43
Chapter 3: Second Law of Thermodynamics 56
3.1 Second Law of Thermodynamics 56
3.2 Reversible Change and Irreversible Change 57
3.3 Thermal Engine 58
3.4 Carnot Cycle 60
3.5 Entropy 62
Chapter 4: Gas Turbine Cycles and Steam Cycles 66
4.1 Gas Turbine Cycles 66
4.1.1 Brayton Cycle 67
4.1.2 Regenerating Brayton Cycle 70
4.1.3 Actual Cycles 72
4.2 Steam Cycles 73
4.2.1 Method of Generating Steam 73
4.2.2 Rankine Cycle 73
4.2.3 Reheating Cycle 77
4.2.4 Other Cycles 79
Part II: Fluid Dynamics 81
Chapter 5: Fundamental Equations of Flow 82
5.1 Physical Properties of Fluids 82
5.1.1 Continuum 82
5.1.2 Forces Exerted on a Fluid 85
5.1.3 Ideal Fluid and Viscous Fluid 86
5.1.4 Newtonian and Non-Newtonian Fluids 87
5.1.5 Compressible and Incompressible Fluids 88
5.1.6 Steady and Unsteady States 88
5.1.7 Developed Flow and Flow in an Entrance Region 88
5.2 Derivation of Fundamental Equations of Flow 89
5.2.1 Methods to Describe Flow Motion 89
5.2.2 Mass Conservation Equation of the Continuum (Equation of Continuity) 91
5.2.3 Motion Equation of the Continuum (Navier-Stokes Equation) 93
5.2.4 Mechanical Energy Conservation Equation 98
5.3 Boundary Conditions 100
5.3.1 Initial Condition 100
5.3.2 Boundary Conditions 101
5.3.2.1 Solid Surface 101
5.3.2.2 Solid Surface (in the Case of Viscous Fluid) 101
Chapter 6: Bernoulli´s Equation (Mechanics of Ideal Fluids) 104
6.1 Euler´s Equations of Motion 104
6.2 Equation of Motion Along a Streamline 105
6.3 Bernoulli´s Theorem and Its Application 106
6.3.1 Pitot Tube 107
6.3.2 Torricelli´s Theorem 108
6.3.3 Venturi Tube 110
Chapter 7: Law of Momentum 113
7.1 Law of Momentum 113
7.2 Application of the Law of Momentum 117
7.2.1 Forces Exerted on a Wall Surface by a Free Jet 117
7.2.1.1 Force Exerted on a Fixed Flat Plate 117
7.2.1.2 Force Exerted on a Moving Flat Plate 119
7.2.1.3 Force Exerted on a Fixed Curved Plate 120
7.2.1.4 Force Exerted on a Moving Curved Plate 122
7.2.2 Force Exerted on a Curved Tube 123
7.2.3 Losses at an Sudden Expansion Area of a Tube 124
7.2.4 Drag Exerted on an Object and Momentum Flux 126
7.2.5 Reaction of a Jet 128
7.2.5.1 Thrust Exerted on a Water Tank 128
7.2.5.2 Thrust of Rockets 129
7.2.5.3 Impulse Turbine 129
Chapter 8: Hydrodynamics of Viscous Fluid 133
8.1 Exact Solution of Navier-Stokes Equations 133
8.1.1 Flow Between Parallel Flat Plates 133
8.1.2 Flow in a Round Tube 135
8.1.3 Flow on a Flat Plate That Instantaneously Starts Moving 138
8.2 Flow with a Small Reynolds Number 140
8.2.1 Stokes´s Approximation 141
8.2.2 Oseen´s Approximation 142
8.3 Flow with a Large Reynolds Number 144
8.3.1 Boundary Layer Equation 144
8.3.2 Laminar Boundary Layer Along a Flat Plate (Blasius´s Solution) 147
8.3.3 Boundary Layer Thickness (Displacement Thickness and Momentum Thickness) 148
8.3.3.1 Displacement Thickness 149
8.3.3.2 Momentum Thickness 150
8.3.4 Separation of Boundary Layer 150
8.3.5 Boundary Layer Momentum Equation 152
Chapter 9: Laminar Flow and Turbulent Flow (The Similarity Rule) 157
9.1 Similarity 157
9.1.1 Dimensionless Numbers in a Flow Field 157
9.1.2 Reynolds Similarity 158
9.1.3 Characteristic Length 159
9.1.4 Transition from Laminar Flow to Turbulent Flow 159
9.2 Reynolds Stress 160
9.2.1 The Reynolds Equations 160
9.2.2 Reynolds Stress Modeling 160
9.3 Flow in a Tube 161
9.4 Turbulent Boundary Layer 163
Chapter 10: Pressure Propagation and Critical Flow (Compressible Fluid Flow) 166
10.1 Compressible Fluids 166
10.2 General Fundamental Equations and Influencing Factors for One-Dimensional Steady Flow 168
10.2.1 Equation of Continuity 169
10.2.2 Equation of Momentum 170
10.2.3 Equation of Energy 171
10.3 Isentropic Flow 174
10.3.1 Isentropic Flow in a Tapered Nozzle 177
10.3.2 Isentropic Flow in and From a Divergent Nozzle 181
Chapter 11: Two-Phase Flow 186
11.1 Basic Concept of Gas-Liquid Two-Phase Flow 186
11.1.1 Flow Patterns 186
11.1.2 Heat Transfer Regime 187
11.1.3 Void Fraction and Quality 188
11.1.4 Slip Ratio 191
11.1.5 Pressure Loss 191
11.2 Modeling of Two-Phase Flow 193
11.2.1 Homogeneous Model 193
11.2.2 Drift-Flux Model 194
11.2.3 Two-Fluid Model 196
11.3 Pressure Loss and Void Fraction in Two-Phase Flow 197
11.3.1 Evaluation of Frictional Pressure Loss 197
11.3.1.1 Homogeneous Flow Model 197
11.3.1.2 Separated Flow Model 198
11.3.2 Evaluation Methods of Void Fraction 199
11.3.2.1 Homogeneous Flow Model 199
11.3.2.2 Slip Flow Model 199
11.3.2.3 Drift-Flux Model 200
11.4 Critical Flow 200
11.4.1 Pressure Wave in Two-Phase Flow 200
11.4.2 Two-Phase Critical Flow 202
11.4.2.1 HEM (Homogeneous Equilibrium Model) 202
11.4.2.2 Moody Model 202
Chapter 12: Flow Oscillations 205
12.1 Vortex-Induced Vibration 205
12.2 Fluid-Elastic Oscillation 208
12.3 Unstable Flows in Boiling Two-Phase Flow 209
12.3.1 Ledinegg Instability 209
12.3.2 Density Wave Oscillation 210
12.4 Nuclear-Coupled Stability of BWRs 212
12.4.1 Core Stability 212
12.4.1.1 Reactor Power 213
12.4.1.2 Core Coolant Flow Rate 214
12.4.1.3 Void Reactivity Coefficient 214
12.4.1.4 Axial Power Distribution 214
12.4.1.5 Pressure Losses at the Inlet Orifice and Spacers 214
12.4.2 Regional Stability 214
Part III: Heat Transfer 218
Chapter 13: Reactor Heat Production 219
13.1 Nuclear Reactions 219
13.1.1 Composition of Atoms 219
13.1.2 Binding Energy 220
13.1.3 Radioactive Decay 222
13.1.4 Nuclear Reactions 222
13.1.4.1 Nuclear Fission 223
13.1.4.2 Non-fissile Absorption Reactions 226
13.2 Neutrons 226
13.2.1 Types of Neutrons 226
13.2.2 Thermal Neutrons 227
13.2.3 Interaction Between Neutrons and Materials 228
13.3 Distribution of Thermal Neutron Flux in a Thermal Reactor 232
13.3.1 Critical State 232
13.3.2 Thermal Neutron Flux Distribution in the Thermal Reactor 235
13.4 Reactor Power 241
13.4.1 Reactor Full Power 241
13.4.2 Uranium Consumption 242
13.5 Heat Production in Fuel Elements 242
13.6 Heat Production in Moderator 243
13.6.1 Neutron Moderation 243
13.6.2 Heat Production in Moderator 244
13.7 Heat Production in Reflector, Thermal Barrier, and Reactor Vessel Wall 245
13.8 Heat Production at Nonsteady State 246
13.8.1 Delayed Neutron Effect 246
13.8.2 Thermal Power from Nuclear Fission 248
13.8.3 Thermal Power from Decay Heat 249
Chapter 14: Heat Conduction 252
14.1 Fundamental Explanation of Heat Conduction 252
14.1.1 Fourier´s Law 252
14.1.2 Basic Equations 253
14.1.3 Steady Heat Conduction 257
14.1.3.1 Heat Conduction in a Plane Wall 257
14.1.3.2 Heat Conduction in a Composite Wall 259
14.1.3.3 Heat Conduction in a Hollow Cylindrical Wall 261
14.1.4 Nonsteady-State Heat Conduction 262
14.2 Heat Conduction in the Reactor 264
14.2.1 Temperature Distribution in the Fuel Element 264
14.2.1.1 Temperature Distribution Inside the Platelike Fuel 265
14.2.1.2 Temperature Distribution inside the Cylindrical Fuel 268
14.2.1.3 Calculation of Temperature Distribution in the Cylindrical Fuel 272
14.2.1.4 Changes of Physical Properties of the Fuel Element 272
14.2.2 Temperature Distribution in a Plate Structure 275
14.2.3 Temperature Change in the Fuel Element in the Nonsteady State 278
Chapter 15: Convective Heat Transfer 281
15.1 Heat Transfer Coefficients 281
15.2 Basic Equations of Heat Convection 283
15.2.1 Derivation of Energy Conservation Equation 283
15.2.2 Dimensionless Numbers for Convective Heat Transfer 288
15.2.2.1 Similarity of Basic Equations and Dimensionless Numbers 288
15.2.2.2 Major Dimensionless Numbers 289
15.3 Forced Convective Laminar Heat Transfer 292
15.3.1 Forced Convective Laminar Heat Transfer on a Horizontal Plate 292
15.3.1.1 Basic Equations 292
15.3.1.2 Boundary Conditions 294
15.3.1.3 Derivation of Analytical Solution 294
15.3.1.4 Correlations of Heat Transfer 295
15.3.1.5 Film Temperature 298
15.3.2 Forced Convective Laminar Heat Transfer in Tube Flow 298
15.3.2.1 The Temperature Entrance Region and Developed Region 298
15.3.2.2 Developed Temperature Field 299
15.3.2.3 Heat Transfer in the Developed Temperature Field 301
15.3.2.4 Heat Transfer in the Thermal Entrance Region 302
15.3.2.5 Heat Transfer Coefficient and Reference Temperature of Material 304
15.4 Forced Convective Turbulent Heat Transfer 305
15.4.1 Forced Convective Turbulent Heat Transfer on a Horizontal Plate 305
15.4.1.1 Velocity Distribution in Turbulent Boundary Layer 306
15.4.1.2 Heat Transfer in the Turbulent Boundary Layer 308
15.4.2 Forced Convective Turbulent Heat Transfer in Tube Flow 311
15.4.2.1 Experimental Correlations of Heat Transfer 312
15.4.2.2 Influence of the Entrance Region 312
15.4.2.3 Influence of Variation of Fluid Physical Property 313
15.4.2.4 Heat Transfer of Different Shape Tube or Path from a Circular Tube 313
15.5 Natural Convective Heat Transfer 314
15.5.1 Natural Convective Heat Transfer Around a Vertical Plate 314
15.5.1.1 Basic Equations 314
15.5.1.2 Analytical Solution in Laminar Flow 316
15.5.1.3 Transition from Laminar Flow to Turbulent Flow 317
15.5.1.4 Heat Transfer in Turbulent Flow 318
15.5.2 Natural Convective Heat Transfer Around a Horizontal Cylinder 318
Chapter 16: Boiling Heat Transfer and Critical Heat Flux 322
16.1 Pool Boiling Heat Transfer 322
16.1.1 Pool Boiling 322
16.1.2 Empirical Correlations of Pool Boiling Heat Transfer 325
16.1.2.1 Nucleate Boiling Heat Transfer 325
16.1.2.2 Film Boiling Heat Transfer 326
16.1.2.3 Critical Heat Flux 327
16.1.2.4 Minimum Heat Flux 328
16.2 Forced Convective Boiling Heat Transfer 329
16.2.1 Overview of Heat Transfer Regime 329
16.2.2 Heat Transfer in the Nucleate Boiling Region 332
16.2.2.1 Inception Point of Nucleate Boiling 332
16.2.2.2 Net Vapor Generation Point 333
16.2.2.3 Partial Nucleate Boiling Region 333
16.2.2.4 Developed Nucleate Boiling Region 333
16.2.3 Heat Transfer in Forced Convection Boiling Region 334
16.2.4 Heat Transfer in the Post Dryout Region 336
16.2.5 Critical Heat Flux 340
16.3 Critical Heat Flux in PWR Fuel Assemblies 341
16.3.1 W-3 Correlation 341
16.3.1.1 DNB Heat Flux Under Uniform Heat Generation 341
16.3.1.2 DNB Heat Flux Under Nonuniform Heat Generation 342
16.3.1.3 Other Correction Factors 345
16.3.2 Advanced DNB Equations 346
16.4 Critical Heat Flux in BWR Fuel Assemblies 346
16.4.1 Hench-Levy Correlation 348
16.4.2 Correlation Using the F Factor 348
16.4.3 Correlation Using Boiling Length and Critical Quality 349
Chapter 17: Condensation Heat Transfer 354
17.1 Filmwise and Dropwise Condensations 354
17.2 Filmwise Condensation on a Vertical Surface 355
17.3 Film-wise Condensation on the External Surface of a Horizontal Round Tube and Tube Bundle 359
17.3.1 Film-wise Condensation on the External Surface of a Horizontal Round Tube 359
17.3.2 Filmwise Condensation on the External Surface of a Horizontal Tube Bundle 361
17.4 Filmwise Condensation of the Vapor Containing Superheated Vapor and Noncondensable Gas 363
17.4.1 Condensation of Superheated Vapor 363
17.4.2 Condensation of the Vapor Containing Noncondensable gas 364
Chapter 18: Radiative Heat Transfer 367
18.1 Physical Properties of Thermal Radiation 367
18.1.1 Emission and Absorption of Thermal Radiation 367
18.1.1.1 Emission of Thermal Radiation 367
18.1.1.2 Absorption of Thermal Radiation 369
18.1.2 Radiation Intensity 371
18.2 Radiative Heat Transfer Between Two Solid Surfaces 372
18.2.1 Radiant Exchange Between Two Black Bodies and Geometrical Factor 372
18.2.2 Relation Among Geometrical Factors 374
18.2.3 Radiative Heat Transfer Between Two Black Body Surfaces 375
18.2.3.1 Radiative Heat Transfer Between Two Flat Surfaces 375
18.2.3.2 Radiative Heat Transfer in an Enclosed Region Formed of n Black Body Surfaces 376
18.2.4 Radiative Heat Transfer Between Two Non-Black Body Surfaces 378
18.2.4.1 Radiative Heat Transfer Between Two Flat Surfaces 378
18.2.4.2 Radiative Heat Transfer in an Enclosed Region Formed of n Gray Body Surfaces 380
Chapter 19: Thermal Hydraulics Inside the Reactor 381
19.1 Selection of Coolants 381
19.1.1 Characteristics of Gas Coolants 381
19.1.2 Characteristics of Light Water as Coolant and Moderator 383
19.1.3 Characteristics of Heavy Water as Coolant and Moderator 384
19.1.4 Characteristics of Liquid Sodium as Coolant and Moderator 384
19.2 Thermal Hydraulics Inside a Pressurized Water Reactor 385
19.2.1 Flow Inside the Reactor Core 385
19.2.2 Pressure Drop Inside the Reactor Core 387
19.2.3 Temperature Distribution in the Fuel Assembly 388
19.2.3.1 Coolant Temperature Distribution in the Axial Direction 389
19.2.3.2 Fuel Rod Surface Temperature Distribution 390
19.2.3.3 Fuel Center Temperature Distribution 392
19.2.3.4 Hot Channel Factor 395
19.3 Thermal Hydraulics Inside the Boiling Water Reactor 398
19.3.1 Flow Inside the Reactor Core 398
19.3.2 Pressure Drop Inside the Reactor Core 401
19.3.2.1 Neutron Flux Distribution 401
19.3.2.2 Quality Distribution and Boiling Inception Point 401
19.3.2.3 Void Fraction 405
19.3.2.4 Pressure Drop Calculation 406
19.3.2.5 Pressure Drop in Actual Reactor 408
19.3.3 Temperature Distribution in the Fuel Assembly 408
19.3.3.1 Coolant Temperature Distribution 408
19.3.3.2 Fuel Rod Surface Temperature Distribution 409
19.3.3.3 Fuel Center Temperature Distribution 411
19.3.3.4 Hot Channel Factor 413
19.4 Thermal Changes Associated with the Burnup 413
19.4.1 Change of Power Distribution 413
19.4.2 Change of Thermal Properties Due to the Irradiation 414
19.4.3 Thermal Hydraulic Change Due to the Change of Clad Dimensions 414
19.4.4 Thermal Hydraulic Change Due to the Change of Fuel Rod Deformation 415
Chapter 20: Reactor Thermal Design 417
20.1 Limit Values for Thermal Design 417
20.1.1 Thermal Limit Values 417
20.1.2 Thermal Limit Values of the Light Water Reactor Core 417
20.1.2.1 Prevention of Fuel Melting 417
20.1.2.2 Prevention of Fuel Burnout 418
20.1.2.3 Prevention of Clad Corrosion 418
20.1.2.4 Prevention of Hydraulic Instability 419
20.1.3 Other Thermal Limit Values 419
20.2 Reactor Core Thermal Design Procedure 420
20.2.1 Relation Between Reactor Core Thermal Design and Other Designs 420
20.2.2 Example of Reactor Core Thermal Design Procedure 420
20.2.3 Example of Reactor Core Thermal Hydraulic Design 421
20.2.4 Reactor Core Geometry and Number of Fuel Assemblies 421
20.3 Fuel Element and Fuel Assembly Thermal Design 423
20.3.1 Fuel Element Thermal Design 423
20.3.2 Thermal Margin for Fuel Center Melting 423
20.3.3 Fuel Assembly Thermal Design 424
20.4 Mock-up Test for Reactor Thermal Hydraulic Characteristics 425
20.4.1 Mock-up Test 425
20.4.2 Flow and Heat Transfer in the Reactor Core and the Fuel Assembly 425
20.4.3 Control Rod Drop Velocity 426
20.4.4 Mechanical Capability and Performance Test for Incore Equipment and Structure 426
20.4.5 Flow and Heat Transfer Basic Experiments 426
20.5 Thermal Design to Prevent Fuel Burnout in the LWR 427
20.5.1 Criteria 427
20.5.2 Evaluation Method for PWR 427
20.5.2.1 Minimum DNBR 427
20.5.2.2 95x95 Standard 428
20.5.2.3 Sub-channel Analysis 429
20.5.2.4 Analyzed Example of Minimum DNBR 429
20.5.3 Evaluation Method for BWR 430
20.5.3.1 Minimum Critical Power Ratio (MCPR) 430
20.5.3.2 MCPR Analyzed Example 431
Answers for Exercises 433
Part I 433
Part II 439
Part III 453
Index 459