Nuclear Reactor Physics and Engineering
Description
Essential guide to analyzing nuclear energy systems, with focus on reactor physics, fuel cycle, system dynamics, thermal-hydraulics, and economics.
Nuclear Reactor Physics and Engineering highlights efforts in utilizing low enrichment uranium fuel as a substitute for carbon-based fuels in energy generation and provides an overview of important aspects of nuclear reactor physics utilizing the neutron diffusion equation for major reactor designs and MATLAB software for system analysis, with exercises illustrating key points and design parameters as supplementary material.
This revised and updated Second Edition reflects key findings of the 2023 National Academy of Sciences (NAS) report and discusses physical and engineering characteristics of advanced nuclear reactors, especially in the form of small modular reactors that have the potential to provide enhanced safety and economics, as well as effective long-term management of used nuclear fuel in geological repositories.
Key topics explored in the updated edition of Nuclear Reactor Physics and Engineering include:
- Impact of the use of high-assay low enrichment uranium (HALEU) fuel as a new efficient nuclear fuel
- Advantages resulting from combined uses of light water reactor and sodium-cooled fast reactor with fuel reprocessing
- Fundamental nuclear reactor physics, nuclear reactor system analysis, and lattice physics analysis for reactor cores
- Nuclear fuel cycle analysis, nuclear plant simulation and control, and management of used nuclear fuel
- Economic analysis of nuclear electricity and thermal-hydraulic analysis of nuclear systems.
With a wealth of all-new information detailing the state of the art in the field, Nuclear Reactor Physics and Engineering is an invaluable reference on the subject for undergraduate and graduate students in nuclear engineering, as well as practicing engineers involved with nuclear power plants.
More details
Other editions
Additional editions
Person
John C. Lee, PhD, has been on the nuclear engineering faculty at the University of Michigan since 1974 and served as the department chair for six years. He has published two Wiley books, Risk and Safety Analysis of Nuclear Systems (with N.J. McCormick, 2011, 2017 second printing) and Nuclear Reactor Physics and Engineering (2020). He has served on two U.S. National Academy of Sciences committees, including the recent committee on advanced nuclear reactors and used nuclear fuel. Dr. Lee is a Fellow of the American Nuclear Society.
Content
List of Tables xv
List of Figures xvii
Preface xxix
Preface to the Second Edition xxxi
Permissions and Copyrights xxxiii
About the Companion Website xxxv
1 Nuclear Power Plants 1
1.1 History and Current Status of Nuclear Power Plants 1
1.2 Basic Features of Nuclear Power Plants 3
1.3 Pressurized Water Reactor Systems 4
1.4 Boiling Water Reactor Systems 10
1.5 Advanced Reactor Designs 17
References 30
Problems 32
2 Neutron-Nucleus Reaction and Neutron Cross Section 33
2.1 Neutron-Nucleus Reaction Probability and Neutron Cross Section 34
2.2 Mechanisms of Neutron-Nucleus Interaction 35
2.3 Nuclear Fission Process 38
2.4 Two-Body Collision Mechanics and Center-of-Mass System 44
2.5 Single-Level Breit-Wigner Formula for Resonance Reaction 48
2.6 Differential Scattering Cross Section and Scattering Kernel 51
2.7 Further Remarks on Neutron Cross Section 55
References 60
Problems 61
3 Neutron Flux, Reaction Rate, and Effective Cross Section 65
3.1 Neutron Flux and Current 66
3.2 Rate of Neutron-Nucleus Interaction 72
3.3 Neutron Energy Distribution and Effective Thermal Cross Section 75
3.4 Application to a 1/V-Absorber 79
References 80
Problems 80
4 Derivation of the Neutron Diffusion Equation 83
4.1 Basic Assumptions for Neutron Balance Statement 84
4.2 Neutron Balance Equation 85
4.3 Neutron Source Term 89
4.4 Fick's Law of Neutron Current 90
4.5 Neutron Transport Equation and P1 Approximation 93
4.6 Remarks on Diffusion Coefficient 98
4.7 Limitations of Neutron Diffusion Theory 100
4.8 One-Group Neutron Diffusion Equation 100
4.9 Summary Discussion of Diffusion Equation 102
References 102
Problems 103
5 Applications of the One-Group Neutron Diffusion Equation 105
5.1 Boundary Conditions for Diffusion Equation 106
5.2 Solution of Steady-State Diffusion Equation 110
5.3 Neutron Flux in Multiplying Medium and Criticality Condition 120
5.4 Four- and Six-Factor Formulas for Multiplication Factor 129
5.5 Concluding Remarks 131
References 131
Problems 132
6 Numerical Solution of the Neutron Diffusion Equation 137
6.1 Finite Difference Form of Diffusion Equation 138
6.2 Flux Solution Algorithm: Inner Iteration 142
6.3 Boundary Conditions for Difference Equation 144
6.4 Source or Outer Iteration 146
6.5 Relative Power Distribution and Overall Flow Chart 148
6.6 Single-Channel Flux Synthesis 151
6.7 Multidimensional Finite Difference Formulation 154
6.8 Coarse-Mesh Diffusion Equation Solver 160
6.9 Krylov Subspace Method as a Diffusion Equation Solver 164
References 168
Problems 169
7 Applications of the Two-Group Neutron Diffusion Equation 171
7.1 Derivation of Multigroup Neutron Diffusion Equation 172
7.2 Steady-State Multigroup Diffusion Equation 176
7.3 Two-Group Form of Effective Multiplication Factor 178
7.4 General Two-Group Diffusion Analysis 181
References 184
Problems 184
8 Nuclear Reactor Kinetics 189
8.1 Derivation of Point Kinetics Equation 190
8.2 Solution of Point Kinetics Equation without Feedback 194
8.3 State Space Representation of Point Kinetics Equation 205
8.4 Point Kinetics Equation with Feedback 208
8.5 Reactivity Measurements 214
8.6 System Stability Analysis 217
8.7 Point Reactor and Space-Dependent Reactor Kinetics 221
References 223
Problems 223
9 Fast Neutron Spectrum Calculation 227
9.1 Neutron Balance Equation and Slowing Down Density 228
9.2 Elastic Scattering and Lethargy Variable 232
9.3 Neutron Slowing Down in Infinite Medium 234
9.4 Resonance Escape Probability 243
9.5 Doppler Broadening of Resonances 250
9.6 Fermi Age Theory 256
9.7 Comments on Lattice Physics Analysis 260
References 261
Problems 262
10 Perturbation Theory and Adjoint Flux 265
10.1 Operator Notation for Neutron Diffusion Equation 265
10.2 Adjoint Operator and Adjoint Flux 267
10.3 First-Order Perturbation Theory 269
10.4 Adjoint Flux for Control Rod Worth Calculation 271
10.5 Adjoint Flux for Variational Formulation 273
10.6 Adjoint Flux for Detector Response Calculation 274
10.7 Adjoint Formulation for Flux Perturbation Calculation 276
10.8 Concluding Remarks on Adjoint Flux 280
References 280
Problems 281
11 Lattice Physics Analysis of Heterogeneous Cores 283
11.1 Material Heterogeneity and Flux Distribution in Unit Cell 285
11.2 Neutronic Advantages of Fuel Lumping 287
11.3 Diffusion Theory Model for Thermal Utilization 291
11.4 Improved Method for Thermal Disadvantage Factor 296
11.5 Resonance Escape Probability for Heterogeneous Cell 300
11.6 Thermal Spectrum Calculation 310
11.7 Integral Transport Methods 313
11.8 B1 Formulation for Spectrum Calculation 316
11.9 Lattice Physics Methodology for Fast Reactor 322
11.10 Monte Carlo Lattice Physics Analysis 325
11.11 Overall Reactor Physics Analysis 326
References 327
Problems 330
12 Nuclear Fuel Cycle Analysis and Management 333
12.1 Nuclear Fuel Cycle Analysis 334
12.2 Nuclear Transmutation Formulation 337
12.3 Equilibrium Cycle and Mass Balance 347
12.4 Simplified Cycling Model 353
12.5 Fission Product Xenon Buildup 359
12.6 General Incore Management Considerations 365
12.7 Fission Products and Radioactive Waste 371
12.8 Management of Used Nuclear Fuel 376
12.9 Key Considerations for Geological Disposal 396
References 404
Problems 409
13 Thermal-Hydraulic Analysis of Reactor Systems 413
13.1 Empirical Laws for Energy and Momentum Transport 415
13.2 Derivation of Fluid Conservation Equations 418
13.3 Simple Solutions of Fluid Conservation Equations 426
13.4 Conservation Equations for Channel Flow 443
13.5 Axial Temperature Distribution in Reactor Core 446
13.6 Boiling Heat Transfer and Two-Phase Flow 456
13.7 Thermal Hydraulic Limitations and Power Capability 471
13.8 Thermal-Hydraulic Models for Nuclear Plant Analysis 479
13.9 Advances in Nuclear Plant Modeling System 488
References 489
Problems 493
14 Power Coefficients of Reactivity 499
14.1 Physical Phenomena Affecting Core Reactivity 500
14.2 Relationship Between Reactivity Coefficients 502
14.3 Two-Group Representation of Reactivity Feedback 503
14.4 Parametric Dependence of LWR Reactivity Coefficients 505
14.5 Reactivity Coefficients in Sodium-Cooled Fast Reactor 508
14.6 Reactivity Feedback Model for Sodium-Cooled Fast Reactor 510
References 512
Problems 513
15 Nuclear Energy Economics 515
15.1 Electrical Energy Cost 516
15.2 Overview of Engineering Economics 519
15.3 Calculation of Nuclear Electricity Generation Cost 521
15.4 Impact of Increased Capital and O&M Costs 530
15.5 Energy Generation Efficiency of Various Technologies 533
References 536
Problems 539
16 Space-Time Kinetics and Reactor Control 541
16.1 Space-Time Reactor Kinetics 542
16.2 Space-Time Power Oscillations due to Xenon Poisoning 551
16.3 Time-Optimal Reactor Control 564
16.4 Model-Based Reactor Control 572
16.5 Alternate Reactor Control Techniques 581
16.6 Kalman Filtering for Optimal System Estimation 585
References 588
Problems 592
17 Elements of Neutron Transport Theory 595
17.1 Collision Probability Method 595
17.2 First-Flight Escape Probability and Dirac Chord Method 600
17.3 Flux Depression Calculation and Blackness 605
17.4 Numerical Solution of Neutron Transport Equation 610
References 621
Problems 623
Appendix A Key Physical Constants 627
Appendix B Comparison of Major Reactor Types 629
References 633
Appendix C Special Mathematical Functions 635
C.1 Gamma Function 635
C.2 Legendre Polynomial and Spherical Harmonics 637
C.3 Bessel Function 639
C.4 Dirac Delta Function 642
References 642
Appendix D Integral Transforms 643
D.1 Laplace Transform 643
D.2 Fourier Transform 645
D.3 Jordan's Lemma 645
References 647
Appendix E Calculus of Variation for Optimal Control Formulation 649
E.1 Euler-Lagrange and Hamilton Equations 649
E.2 Pontryagin's Maximum Principle 650
References 656
Appendix F Kalman Filter Algorithm 657
F.1 Linear Kalman Filter 657
F.2 Unscented Kalman Filter 660
References 662
Answers to Selected Problems 663
Index 679
List of Figures
Figure 1.1 Nuclear power plant evolution.
Figure 1.2 Overall layout of a PWR plant.
Figure 1.3 Schematic diagram of a PWR plant.
Figure 1.6 Cross-section view of PWR fuel assemblies for the AP1000 design.
Figure 1.8 Cutaway view of Mark I BWR containment structure.
Figure 1.10 BWR fuel bundle cluster illustrating the W-W and N-N gaps.
Figure 1.12 Sodium-cooled fast reactor plant.
Figure 1.13 Top view of the reactor core of a SFR plant.
Figure 1.14 Very high-temperature reactor plant.
Figure 1.15 Top view inside the reactor vessel of a VHTR plant.
Figure 1.16 TRISO particle, pin cell, and prismatic fuel assembly for the VHTR plant.
Figure 1.17 Molten-salt reactor plant.
Figure 1.18 Top view inside a MSR reactor vessel.
Figure 1.19 Schematic illustration of the NuScale module.
Figure 1.20 Micro modular reactor.
Figure 2.1 A collimated beam of neutron incident on a slab.
Figure 2.2 Energy levels for a compound nucleus.
Figure 2.6 Energy spectrum of fission neutrons emitted for U, ENDF/B-VIII.0 MF = 5, MT = 18 and 455.
Figure 2.7 Velocities before and after the collision in Lab and CM systems.
Figure 2.9 Resonance cross section as a function of neutron energy.
Figure 2.10 Scattering of collimated beam into solid angle around in distance .
Figure 2.11 Solid angle with azimuthal symmetry.
Figure 2.12 Elastic scattering kernel as a function of outgoing neutron energy.
Figure 2.13 Total cross section of B, ENDF/B-VIII.
Figure 2.14 Total cross section of C, ENDF/B-VIII.
Figure 2.15 Radiative capture cross section for U, ENDF/B-VIII.
Figure 2.16 Radiative capture cross section for Pu, ENDF/B-VIII.
Figure 3.1 Differential volume elements in physical and velocity spaces.
Figure 3.2 Differential cylinder for visualizing angular flux as neutron current.
Figure 3.3 Neutron flux for a collimated neutron beam.
Figure 3.4 Projection of a unit cross-sectional area.
Figure 3.5 Relationship between vector current and net current .
Figure 3.6 Maxwell-Boltzmann distribution as a function of speed.
Figure 4.1 Unit cross-sectional area for the negative partial current.
Figure 4.2 Directional vector projected via polar and azimuthal angles.
Figure 4.3 Physical interpretation of transport mean free path .
Figure 5.1 Linear extrapolation of flux at a free surface.
Figure 5.2 Two material regions separated by vacuum.
Figure 5.3 Planar source in slab geometry.
Figure 5.4 Closed contour in the Fourier domain -space.
Figure 5.5 Extrapolated boundary for slab geometry.
Figure 5.6 Two-region slab with plane source.
Figure 5.7 Construction of a plane source from annular ring sources.
Figure 5.8 Three lowest-order flux modes for slab reactor of height .
Figure 5.9 Life cycle of neutrons illustrating the six-factor formula.
Figure 6.1 Discretization scheme for the flux and flux derivative.
Figure 6.2 Discretized flux distribution at the vacuum boundary.
Figure 6.3 Flux distribution near a reflecting boundary at .
Figure 6.4 Inner and outer iterations for solution of the diffusion equation.
Figure 6.5 Finite-difference mesh structure for .
Figure 6.6 2-D discretization scheme.
Figure 6.7 Two-dimensional finite-difference structure.
Figure 6.8 2-D line relaxation scheme.
Figure 6.9 Successive relaxation scheme.
Figure 6.10 NEM geometry for solution in the -direction.
Figure 6.11 Illustration of the homogenous and heterogeneous fluxes.
Figure 7.1 Lethargy variable and energy group structure.
Figure 8.1 Schematics of decay chains for fission product Br.
Figure 8.2 Transient and stable solutions of the point kinetic equations with dollar.
Figure 8.3 Reactivity versus roots of the inhour equation
Figure 8.4 Transfer function representing the output-to-input ratio.
Figure 8.5 Open-loop transfer function connecting control input to output together with controller .
Figure 8.6 Simulink setup for the pulse source solution of Example 8.2.
Figure 8.7 Simulink pulse source output of Example 8.2.
Figure 8.8 Phase plane solution of the Ergen-Weinberg model.
Figure 8.9 Time-domain behavior of the Ergen-Weinberg model.
Figure 8.10 Time-domain behavior of the Nordheim-Fuchs power excursion model.
Figure 8.11 Inverse multiplication as a function of fuel mass.
Figure 8.14 Nyquist diagram for , Example 8.4.
Figure 8.15 Bode diagram for , Example 8.4, indicating db and .
Figure 8.16 Bode diagram for open-loop reactor transfer function .
Figure 9.1 Phase volume representing the neutron balance.
Figure 9.2 Lethargy variable and average lethargy increase per collision.
