Nuclear reactor physics and engineering

Cover......Page 1
Title Page......Page 5
Copyright......Page 6
Contents......Page 7
Preface......Page 16
Permissions and Copyrights......Page 18
List of Tables......Page 20
List of Figures......Page 21
Chapter 1 Nuclear Power Plants......Page 27
 1.1 History and Current Status of Nuclear Power Plants......Page 28
 1.2 Basic Features of Nuclear Power Plants......Page 29
 1.3 Pressurized Water Reactor Systems......Page 31
 1.4 Boiling Water Reactor Systems......Page 37
 1.5 Advanced Reactor Designs......Page 43
 References......Page 50
 Problems......Page 51
Chapter 2 Neutron-nucleus Reaction and Neutron Cross Section......Page 53
 2.1 Neutron-nucleus Reaction Probability and Neutron Cross Section......Page 54
 2.2 Mechanisms of Neutron-nucleus Interaction......Page 55
 2.3 Nuclear Fission Process......Page 58
 2.4 Two-body Collision Mechanics and Center-of-mass System......Page 63
 2.5 Single-Level Breit-Wigner Formula for Resonance Reaction......Page 68
 2.6 Differential Scattering Cross Section and Scattering Kernel......Page 71
  2.6.1 Differential Microscopic Scattering Cross Section......Page 72
  2.6.2 Scattering Kernel for Isotropic Scattering in CM Frame......Page 73
 2.7 Further Remarks on Neutron Cross Section......Page 75
 References......Page 80
 Problems......Page 81
Chapter 3 Neutron Flux......Page 85
 3.1 Neutron Flux and Current......Page 86
 3.2 Rate of Neutron-Nucleus Interaction......Page 92
 3.3 Neutron Energy Distribution and Effective Thermal Cross Section......Page 95
 3.4 Application to a -Absorber......Page 99
 Problems......Page 100
Chapter 4 Derivation of the Neutron Diffusion Equation......Page 103
 4.1 Basic Assumptions for Neutron Balance Statement......Page 104
 4.2 Neutron Balance Equation......Page 105
 4.3 Neutron Source Term......Page 109
 4.4 Fick\'s Law of Neutron Current......Page 110
 4.5 Neutron Transport Equation and p1 Approximation......Page 114
 4.6 Remarks on Diffusion Coefficient......Page 118
 4.8 One-Group Neutron Diffusion Equation......Page 120
 References......Page 122
 Problems......Page 123
Chapter 5 Applications of the One-Group Neutron Diffusion Equation......Page 125
 5.1 Boundary Conditions for Diffusion Equation......Page 126
  5.2.1 Flux in Non-multiplying Media with Localized Sources......Page 130
  5.2.2 Flux in Non-multiplying Media with Distributed Sources......Page 138
 5.3 Neutron Flux in Multiplying Medium and Criticality Condition......Page 141
  5.3.1 Criticality and Buckling......Page 142
  5.3.2 Effective Multiplication Factor......Page 143
  5.3.3 Eigenfunctions of Diffusion Equation and Buckling......Page 145
 5.4 Four- and Six-Factor Formulas for Multiplication Factor......Page 150
 References......Page 152
 Problems......Page 153
Chapter 6 Numerical Solution of the Neutron Diffusion Equation......Page 157
 6.1 Finite Difference Form of Diffusion Equation......Page 158
 6.2 Flux Solution Algorithm: Inner Iteration......Page 162
 6.3 Boundary Conditions for Difference Equation......Page 164
 6.4 Source or Outer Iteration......Page 166
 6.5 Relative Power Distribution and Overall Flow Chart......Page 169
 6.6 Single-Channel Flux Synthesis......Page 171
  6.7.1 Two-Dimensional Matrix Formulation......Page 175
  6.7.2 Three-Dimensional Formulation......Page 177
  6.7.3 Convergence Properties of Matrix Iteration Schemes......Page 180
  6.8.1 Nodal Expansion Method......Page 181
  6.8.2 Pin-Power Reconstruction Algorithm......Page 183
 6.9 Krylov Subspace Method as a Diffusion Equation Solver......Page 184
 References......Page 188
 Problems......Page 189
Chapter 7 Applications of the Two-Group Neutron Diffusion Equation......Page 191
 7.1 Derivation of Multi-Group Neutron Diffusion Equation......Page 192
 7.2 Steady-State Multi-Group Diffusion Equation......Page 196
 7.3 Two-Group Form of Effective Multiplication Factor......Page 198
 7.4 General Two-Group Diffusion Analysis......Page 202
 Problems......Page 204
Chapter 8 Nuclear Reactor Kinetics......Page 207
  8.1.1 Representation of Delayed Neutron Production......Page 208
  8.1.2 Point Kinetics Approximation......Page 210
  8.1.3 One-Group Delayed Neutron Model......Page 212
  8.2.1 Step Insertion of Reactivity......Page 213
  8.2.2 Prompt Jump or Zero-Lifetime Approximation......Page 216
  8.2.3 Inhour Equation......Page 218
  8.2.4 Linearized Kinetics Equation and Transfer Function......Page 221
  8.2.5 Infinite Delayed Approximation......Page 223
 8.3 State Space Representation of Point Kinetics Equation......Page 224
 8.4 Point Kinetics Equation with Feedback......Page 227
  8.4.1 The Ergen-Weinberg Model......Page 228
  8.4.2 The Nordheim-Fuchs Model......Page 231
 8.5 Reactivity Measurements......Page 233
 8.6 System Stability Analysis......Page 236
 8.7 Point Reactor and Space-Dependent Reactor Kinetics......Page 239
 References......Page 241
 Problems......Page 242
Chapter 9 Fast Neutron Spectrum Calculation......Page 245
 9.1 Neutron Balance Equation and Slowing Down Density......Page 247
 9.2 Elastic Scattering and Lethargy Variable......Page 250
  9.3.1 Slowing Down in the First Collision Interval......Page 253
  9.3.2 Slowing Down below the First Collision Interval......Page 257
  9.4.1 Effective Resonance Integral......Page 262
  9.4.2 Energy Self-Shielding Factor......Page 264
  9.4.3 Wide Resonance Approximation......Page 265
  9.4.4 Probability Table or Subgroup Method......Page 266
  9.5.1 Qualitative Description of Doppler Broadening......Page 269
  9.5.2 Analytical Treatment of Doppler Broadening......Page 270
 9.6 Fermi Age Theory......Page 274
 9.7 Comments on Lattice Physics Analysis......Page 278
 References......Page 279
 Problems......Page 280
Chapter 10 Perturbation Theory and Adjoint Flux......Page 281
 10.1 Operator Notation for Neutron Diffusion Equation......Page 282
 10.2 Adjoint Operator and Adjoint Flux......Page 283
 10.3 First-Order Perturbation Theory......Page 285
 10.4 Adjoint Flux for Control Rod Worth Calculation......Page 287
 10.5 Adjoint Flux for Variational Formulation......Page 289
 10.6 Adjoint Flux for Detector Response Calculation......Page 290
 10.7 Adjoint Formulation for Flux Perturbation Calculation......Page 292
 10.8 Concluding Remarks on Adjoint Flux......Page 295
 Problems......Page 296
Chapter 11 Lattice Physics Analysis of Heterogeneous Cores......Page 299
 11.1 Material Heterogeneity and Flux Distribution in Unit Cell......Page 301
 11.2 Neutronic Advantages of Fuel Lumping......Page 303
 11.3 Diffusion Theory Model for Thermal Utilization......Page 307
 11.4 Improved Method for Thermal Disadvantage Factor......Page 312
  11.4.2 Amouyal-Benoist-Horowitz Method......Page 313
  11.5.1 Spatial Self Shielding for Heterogeneous Unit Cell......Page 317
  11.5.2 Engineering Approaches for Resonance Integral......Page 321
  11.5.3 Implementation in the CPM-3 Code......Page 325
  11.6.1 Wigner-Wilkins Model......Page 326
  11.6.2 Qualitative Behavior of Thermal Neutron Spectrum......Page 327
 11.7 Integral Transport Methods......Page 329
 11.8 B1 Formulation for Spectrum Calculation......Page 332
  11.8.1 Basic Structure of B1 Formulation......Page 333
  11.8.2 Numerical Solution of B1 Equations......Page 335
  11.9.1 Bondarenko Formulation for Self-Shielding Factor......Page 338
  11.9.3 ERANOS System......Page 340
 11.11 Overall Reactor Physics Analysis......Page 341
 References......Page 343
 Problems......Page 345
Chapter 12 Nuclear Fuel Cycle Analysis and Management......Page 349
 12.1 Nuclear Fuel Management......Page 350
 12.2 Key Nuclide Chains for Nuclear Fuel Cycle......Page 353
  12.3.1 Fuel Depletion Equation......Page 356
  12.3.2 Solution of Pointwise Depletion Equation......Page 357
  12.3.3 Fuel Depletion Equation in Global MGD Calculation......Page 359
  12.3.4 Simple Model for Fuel Burnup Estimation......Page 362
 12.4 Equilibrium Cycle and Mass Balance......Page 363
  12.4.1 Nuclide Balance Statement......Page 364
  12.4.2 Material Flow Sheet......Page 365
  12.4.3 REBUS Equilibrium Inventory Calculation......Page 367
  12.5.1 Reactivity-Based Instant Cycling Method......Page 369
  12.5.2 Application of Instant Cycling Method......Page 370
 12.6 Fission Product Xenon Buildup......Page 375
  12.6.1 Mechanism for 135Xe Production and Balance Equation......Page 376
  12.6.2 Time-Domain Solution of Xe-I Balance Equation......Page 377
  12.6.3 Effect of Samarium Buildup......Page 380
  12.7.1 Reactivity Variation over Fuel Cycle......Page 381
  12.7.2 Thermal-Hydraulic Feedback and Power Distribution......Page 382
  12.7.3 Control Requirements for Light Water Reactor......Page 383
  12.7.4 Power Distribution Control......Page 385
  12.8.1 Classification of Radioactive Waste......Page 386
  12.8.2 Characteristics of Radioactive Waste......Page 388
  12.8.3 Status of Used Nuclear Fuel Inventory......Page 390
  12.8.4 Partition and Transmutation of Waste......Page 391
 References......Page 394
 Problems......Page 397
Chapter 13 Thermal-Hydraulic Analysis of Reactor Systems......Page 399
  13.1.1 Fourier’s Law of Heat Conduction......Page 401
  13.1.2 Newton’s Law of Viscosity......Page 402
  13.1.3 Newton’s Law of Cooling......Page 403
  13.2.1 Equation of Continuity......Page 404
  13.2.2 Equation of Motion and Navier-Stokes Equation......Page 405
  13.2.3 Equations of Energy Conservation......Page 407
  13.2.4 Comments on Fluid Conservation Equations......Page 411
 13.3 Simple Solutions of Fluid Conservation Equations......Page 0
  13.3.1 Heat Conduction in Cylindrical Fuel Rod......Page 419
  13.3.2 Heat Conduction through Composite Wall......Page 421
  13.3.3 Forced Convection in Laminar Flow......Page 424
  13.3.4 Velocity Distribution in Turbulent Flow......Page 427
  13.3.5 Friction Factor and Hydraulic Diameter......Page 429
  13.4.2 Equation of Motion and Pressure Drop......Page 430
 13.5 Axial Temperature Distribution in Reactor Core......Page 432
  13.5.1 Power Distribution and Heat Flux in Reactor Core......Page 433
  13.5.2 Axial Temperature Profile in PWR Core......Page 435
  13.5.3 Axial Temperature Profile in BWR Core......Page 437
  13.5.4 Hot Channel Factors......Page 439
 13.6 Boiling Heat Transfer and Two-Phase Flow......Page 442
  13.6.1 Pool Boiling Regimes......Page 443
  13.6.2 Flow Boiling Regimes and Two-Phase Flow Patterns......Page 444
  13.6.3 Homogeneous Equilibrium Flow Model......Page 446
  13.6.4 Slip Flow Model......Page 447
  13.6.5 Drift Flux Model......Page 454
 13.7 Thermal Hydraulic Limitations and Power Capability......Page 456
  13.7.1 DNB Ratio and Number of Fuel Rods Reaching DNB......Page 457
  13.7.2 Non-Uniform Heat Flux Correction......Page 458
  13.7.3 Iterative Determination of DNB Ratio......Page 461
  13.7.4 Power Capability Determination......Page 462
  13.8.1 Light Water Reactor System Modeling Codes......Page 464
  13.8.2 Subchannel Analysis Codes......Page 469
  13.8.4 Containment Analysis Codes......Page 471
  13.8.5 Computational Fluid Dynamics Codes......Page 472
 13.9 Comments on Thermal-Hydraulic Models......Page 473
 References......Page 474
 Problems......Page 477
Chapter 14 Power Coefficients of Reactivity......Page 481
 14.1 Physical Phenomena Affecting Core Reactivity......Page 482
 14.2 Relationship between Reactivity Coefficients......Page 484
 14.3 Two-Group Representation of Reactivity Feedback......Page 485
 14.4 Parametric Dependence of LWR Reactivity Coefficients......Page 487
 14.5 Reactivity Coefficients in Sodium-Cooled Fast Reactor......Page 489
 14.6 Reactivity Feedback Model for Sodium-Cooled Fast Reactor......Page 492
 References......Page 494
 Problems......Page 495
Chapter 15 Nuclear Energy Economics......Page 497
 15.1 Electrical Energy Cost......Page 498
 15.2 Overview of Engineering Economics......Page 500
  15.3.1 Capital Cost......Page 502
  15.3.2 Fuel Cost......Page 503
  15.3.4 Decommissioning Cost......Page 508
 15.4 Impact of Increased Capital and O&M Costs......Page 509
 References......Page 511
 Problems......Page 512
Chapter 16 Space-Time Kinetics and Reactor Control......Page 515
 16.1 Space-Time Reactor Kinetics......Page 516
  16.1.2 Direct Solution of Space-Time Kinetics Equation......Page 517
  16.1.3 Quasi-static Formulation of Kinetics Equation......Page 518
  16.1.4 Reactivity Determination from Multiple Detectors......Page 521
 16.2 Space-Time Power Oscillations due to Xenon Poisoning......Page 525
  16.2.1 Modal Analysis of Space-Time Xenon-Power Oscillations......Page 526
  16.2.2 Stability of Space-Time Xenon-Power Oscillations......Page 530
  16.2.3 Space-Time Xenon-Power Oscillations in X-Y plane......Page 536
  16.3.1 Optimal Control of Xenon-Induced Transients......Page 538
  16.3.2 Control of Spatial Xenon Oscillations......Page 542
  16.4.1 Linear Quadratic Regulator......Page 547
  16.4.2 H2 Controller......Page 549
  16.4.3 H∞ Controller......Page 551
  16.4.4 Augmented Plant Representation......Page 553
 16.5 Alternate Reactor Control Techniques......Page 555
 16.6 Kalman Filtering for Optimal System Estimation......Page 560
 References......Page 562
 Problems......Page 566
 17.1 Collision Probability Method......Page 569
  17.1.1 Integral Transport Equation......Page 570
  17.1.2 Reciprocity Relationship......Page 572
  17.1.3 Transport Kernel and Collision Probability......Page 573
 17.2 First-Flight Escape Probability and Dirac Chord Method......Page 575
  17.3.1 Escape Probability and Flux Depression Factor......Page 580
  17.3.2 Net Escape Probability and Collision Probability......Page 582
  17.3.3 Dancoff Factor for Fuel Lattice......Page 583
 17.4 Numerical Solution of Neutron Transport Equation......Page 585
  17.4.1 Collision Probability Calculation for Annular Geometry......Page 586
  17.4.2 Discrete Ordinates Method......Page 590
  17.4.3 Method of Characteristics......Page 592
  17.4.4 Monte Carlo Algorithm......Page 593
 References......Page 596
 Problems......Page 598
Appendix A Key Physical Constants......Page 601
Appendix B Comparison of Major Reactor Types......Page 603
 References......Page 604
 C.1 Gamma Function......Page 607
 C.2 Legendre Polynomial and Spherical Harmonics......Page 609
 C.3 Bessel Function......Page 611
 C.4 Dirac Delta Function......Page 613
 References......Page 614
 D.1 Laplace Transform......Page 617
 D.2 Fourier Transform......Page 618
 D.3 Jordan\'s Lemma......Page 619
 References......Page 620
 E.1 Euler-Lagrange and Hamilton Equations......Page 621
 E.2 Pontryagin\'s Maximum Principle......Page 623
 References......Page 628
 F.1 Linear Kalman Filter......Page 629
 F.2 Unscented Kalman Filter......Page 632
 References......Page 634
Answers to Selected Problems......Page 635
Index......Page 647
EULA......Page 658