Table Of ContentNuclear
Engineering
An Introduction
With 191 Figures
Springer-Verlag
Berlin Heidelberg New York
London Paris Tokyo
Hong Kong Barcelona Budapest
Additional material to this book can be downloaded from http://extras.springer.com
Contents
1 Introduction. . . . . . . . . . 1
1.1 The General and the Unique . 1
1.2 The Law of Laws . . . . . 2
1.3 A Neutron Population Balance . 7
2 NeutronlNuclei Balance - The Fission Source 12
2.1 Fission Process as an Example. . . . 12
2.1.1 Nuclear Binding Energy . . . . . . 13
2.1.2 Excited States or Energy Levels in Atoms and Nuclei. 19
2.1.3 The Compound Nucleus . . . . . . 23
2.1.4 The Fission Event. . . . . . . . . 26
2.1.5 Fissile, Fissionable, and Fertile Isotopes 31
2.2 Radioactive Decay . . . . . . . . 34
2.2.1 Number (Atomic/Molecular) Density, N 34
2.2.2 Statistical and Quantized Nature of Radioactivity 36
2.2.3 The General Radioactive Isotope Balance 40
2.2.4 Decay Constant, Half-Life, and Mean Life 43
2.2.5 Fission Products in Nuclear Reactor Cores 47
Problems ......... . 51
3 Neutron Interaction with MaUer 53
3.1 Macroscopic and Microscopic Cross Sections. 53
3.2 Neutron Fluxes, Currents, and Beams . . 57
3.3 Cross-Sections Type. . . . . . . . 59
3.4 Macroscopic Cross-Sections .... 61
3.5 Energy Dependence of Cross-Sections 63
3.6 The "Six Factor" Formula 67
3.7 The SIXFAC Program ..... . 72
3.8 Calculation of koo . . . . . . . . 75
3.9 Calculation of koo for a "fast reactor" 78
3.10 Effective multiplication factor, keff 79
Problems .......... . 80
4 Neutron Diffusion - Basic Concepts 83
4.1 Fick's Law ..... . 83
4.2 The Diffusion Coefficient. . 89
4.3 Fick's Law Analogues in Other Branches of Science 94
4.4 The One-group DitTusion Equation . . . . . 96
4.5 Boundary Conditions . . . . . . . . . . 104
4.6 Solution to the One-group Diffusion Equation 110
4.6.1 Solution for a Plane Source 110
4.6.2 Solution for a Point Source 113
PDob~s . . . . . . . . 116
5 Neutron Balance - Energy . 119
5.1 Neutron Moderation . 119
5.1.1 The Importance of the Scattering Interaction 119
5.1.2 Evaluation of the Neutron Energy After Scattering . 120
5.1.3 The COlLIDE and SCATEREL PDograms . . . . 127
5.2 Neutron Energy Distribution in the Epithermal Region 134
5.3 Properties and Classification of Moderators 139
5.4 Thermal Neutrons. . . . . 141
5.4.1 The Maxwellian Distribution . . . . . . . . . . 141
5.4.2 The Thermal Flux. . . . . . . . . . . . . . . 147
5.4.3 Non-1JVFactors . . . . . . . . . . . . . . . 150
5.4.4 Mathematical PDoperties of a Maxwellian Distribution 154
Prob~s . . . . . . . . . . . . . . . . . . 156
6 Criticality. . . . . . . . . . . . . . . . . . . 159
6.1 Criticality and the Neutron Balance Equation . . 159
6.2 Basic Relationships. The ''Thxt Book' Slab Core . 162
6.3 Criticality Condition for the Generic Bare Core . 170
6.4 Criticality for Multienergy Group Neutron Balances 183
6.5 Finite Difference Solution Methods. . . . . . 188
6.6 The MULTIDIF (MULTI-group DIF-usim) Code 200
PDoblems . . . . . . . . . . . . 206
7 Neutron Balance - Time. . . . . . . . . . . . . 209
7.1 Prompt and Delayed Neutrons . . . . . . . . 209
7.1.1 Steady State and TlIDe Dependent Neutron Balances 209
7.1.2 Characteristics of Delayed Neutrons 211
7.1.3 Neutron Generation TIme .. 213
7.1.4 Prompt and Delayed Criticality 215
7.1.5 Definition of Reactivity Units . 216
7.2 Solution of Kinetics Equations . 218
7.2.1 Basic Assumptions Made. . . 218
7.2.2 Single Neutron Group Kinetics 220
7.2.3 Kinetic Equation with Delayed Neutrons . 223
7.2.4 The Asymptotic Period . 227
7.2.5 The 'PDompt' Jump • • • • • • • • • 232
vn
Contents
7.2.6 Estimation of Small Reactivities 237
7.3 Reactor Control Methods . . 239
7.3.1 Types of Reactivity Control . . 239
7.3.2 PWR Pin Type Control Rods . 240
7.3.3 BWR (Crucifonn) Control Rods 242
7.3.4 Centrally Located Control Rod 244
7.4 Control Practice ...... 247
7.4.1 Control Rod Worth Curves . . 247
7.42 Impact of a Control-Rod on the Neutron Flux . 251
7.4.3 Soluble Poison (Chemical Shim) Control 253
7.5 Temperature and Power Coefficients of Reactivity 256
7.5.1 Reactivity Coefficients . . . . . . . . . . . 256
7.5.2 The Fuel Temperature (Doppler) Reactivity Coefficient 259
7.5.3 The Moderator Reactivity Coefficient 265
7.5.4 The 'Void' Coefficient of Reactivity 268
7.5.5 The Power Coefficient of Reactivity 269
7.5.6 The SIXFACT Code. . 270
7.6 Fission Product Effects. . . . . . 271
7.6.1 Fission Product Types . • • • • • 271
7.6.2 High Cross Section Fission Products: Xe-135 . 273
7.6.3 Xe Transients . . 277
7.6.4 Sm-149 Poisoning. . . . . . . . 279
7.6.5 Fuel Depletion . . . . . . . . . 280
7.6.6 Long Tenn Fission Product Buildup 282
Problems . . . . . . . . . . . . . 286
8 Gamma and Neutron Radiation Effects 290
8.1 Importance of Gamma Rays. . . 290
8.1.1 Fundamental Gamma Ray-Matter Interaction Modes 292
8.1.2 Attenuation Coefficients 295
8.1.3 Energy Deposition . . . . . . 302
8.2 Radiation Units. . . . . . . . 303
8.2.1 From Source to Dose .. . . . 303
8.2.2 Units of Source Intensity. Activity 306
8.2.3 Units of the Radiation Field. Exposure 309
8.2.4 Units of Energy Deposition. Dose 312
8.3 Radiation Sources. . . . . 314
8.3.1 Natural Radiation Sources . 314
8.3.2 Manmade Radiation Sources 317
8.3.3 Effects of Radon . . . . . 319
8.4 Biological Effects of Radiation 323
8.4.1 Radiation Damage Mechanisms 323
8.4.2 Relative Biological Effectiveness. 325
8.4.3 Stochastic and Nonstochastic Effects 328
vm Contcn1S
8.4.4 Acute, Latent and Genetic Radiation Effects 331
8.4.5 Calculations. Effective Gamma Ray Doses 337
8.4.6 Calculation. External Neutron Doses 341
8.5 Radiation Protection Standards 346
8.5.1 Historical Overview . . . . . . . . 346
8.5.2 Current Standards. External Radiation . 347
8.5.3 Internal Radiations Sources. Calculations 352
8.5.4 Safeguard Standards for Internal Radiation 357
Problems 359
9 Shielding 362
9.1 Basic Concepts . 362
9.1.1 Characteristics of Shielding Problems 362
9.1.2 Spread of Radiation. Point Source . 363
9.1.3 Spread of Radiation. Sources Having Simple Geometries 365
9.2 Buildup Factors ............... 368
9.2.1 Uncolided and Scattered Radiation Beam Components 368
9.2.2 Definition of Buildup Factors . . . . . . . . . . 371
9.2.3 Example of the Use of Buildup Factors. Plane Source 373
9.3 Basic Shield Geometries . . 380
9.3.1 Shielded Infinite Plane Source 380
9.3.2 The Line Source . . . . . 386
9.3.3 Volumetric Radiation Sources 390
9.4 Computer Methods in Gamma Shield Design 391
9.4.1 Generalized Numerical Integration Methods (MathCAD) 391
9.4.2 Point Kernel Methods . . . . . . . 393
9.5 Reactor Shielding Problems . . . . . . . . . . . 400
9.5.1 Fission from the Shielding Perspective ... . . . 400
9.5.2 Overview of Radiation Types in an Operating Reactor 401
9.5.3 Energy Dependence of Core Radiation ...... 402
9.5.4 Neutron Shielding. The 'Removal' Cross Section . . 404
9.5.5 Methods for Estimating Effectiveness of Core Shields 408
9.5.6 Activation Induced Radiation . . 414
9.5.7 Coolant Activation . . . . . . . 416
9.6 Neutron Shielding. Exact Methods . 420
9.6.1 Transport Theory. Basic Definitions. 420
9.6.2 Transport Theory. Shielding Applications 424
9.6.3 Coupled Neutron-Gamma Cross Sections 426
9.6.4 Monte Carlo Theory . 428
Problems . . . . . 430
10 Core Heat Removal . 433
10.1 Core Energy Balance 433
10.1.1 Overview . . . . . 433
10.1.2 General Energy Balance . . . 434
10.1.3 Energy Balance ofPWR's .. 436
10.1.4 Energy Balance for BWR Cores 439
10.2 Energy Sources. . . . . . 442
10.2.1 Overview of Fission Energy . 442
10.2.2 Fuel Heat Sources. . . 444
10.2.3 Decay Heat . . . . . . . 447
10.3 The Heat Transfer Path. . . 449
10.3.1 Heat Conduction Equation . 449
10.3.2 Temperature Distribution Calculations for a Fuel Rod 454
10.3.3 Effect of Temperature Dependent Conductivity 459
10.3.4 Convective Heat Thmsfer Coefficients. 461
10.3.5 The FUELROD Program . . 466
10.4 DNB and CHF Ratios . . . 473
10.4.1 Boiling Correlations . . . . 477
10.4.2 CHF and DNB Calculations . 478
10.4.3 Hot Channel Factors . 481
Problems . . . . 484
11 Reactor Licensing 487
11.1 The Nuclear Regulatory Commission: Historical Background 487
11.2 The NRC: Organizational Structure and the ''Licensing Process" 489
11.2.1 Organizational Structure . . . . . . . . . . . . 489
11.2.2 The ''Licensing Process" . . . . . . . . . . . . 491
11.3 Title 10 of the Code of Federal Regulations (10 CPR) 494
11.4 The Design-Basis Accidents 495
11.4.1 Can Accidents be Designed? .......... 495
11.4.2 The Design Base (DB) Accidents ........ 497
11.4.3 The "Small Break" Loss ofCoo1ant Accident (SBLOCA) 501
11.5 The Multiple Barriers 504
11.5.1 The Fuel . . . . . 505
11.5.2 The Cladding ... 506
11.5.3 The Primary Coo1ant 506
11.5.4 Reactor Vessel . . . 506
11.5.5 The Containment Building 507
11.5.6 Large Dry Containment . 507
11.5.7 Pressure Suppression Containments . 510
11.6 Fission Product Release . . . . . 514
11.6.1 The "Source" Term . . . . . . . 514
11.6.2 Buildup of Fission Products Inventory. 516
11.6.3 Leakage from Buildings . . . . . . 519
11.7 Atmospheric Dispersion . . . . . . 521
11.7.1 Meteorology of Atmospheric Dispersion. 521
11.7.2 Diffusion Relationship . . . . . . . . 526
X Contents
11.8 Class Nine Accidents . . . . . . 531
11.8.1 Characteristics of a Class 9 Accident 531
11.8.2 The Class 9 Accident Scenario . 533
11.8.3 Generation of Hydrogen 536
11.9 Accident Risk Analysis 539
11.9.1 Society and Risk . . 539
11.9.2 Quantification of Risk 541
Problems 546
Appendix . 548
Subject Index . 559
1 Introduction
1.1 The General and the Unique
The knowledge which has to be acquired in every engineering field can be divided
roughly into two categories:
(a) "General" knowledge which is common to all engineers.
(b) "Unique" knowledge which distinguishes one engineering field from another.
At this point in your education process, you probably have taken courses which
dealt predominandy with knowledge belonging to the first category. With this class
you start a systematic sequence of courses that are going to present subjects which
distinguish a nuclear engineer from the other engineering fields. On a simple minded
level, the differences between the various engineering disciplines can be readily de
scribed. Thus, as you know, chemical engineers deal with chemical processes, elec
trical engineers with electricity, civil engineers with structures and so on. In this
simple classification scheme, the domain of nuclear engineers encompasses neu
trons, nuclear reactors and radiation processes. However, reality is in fact quite a bit
more complicated. You will find that as a nuclear engineer you will have to learn not
just about neutron interactioos with matter, but also about heat ttansfer, ftuid ftow,
chemical processes and even a little about meteorology. In practice, the differences
between the engineering disciplines turn out to be differences of emphasis rather
then substance.
Before starting out on the subjects which are emphasized in nuclear engineering,
it is worthwhile to consider a very basic physical principle which unifies all engi
neering fields, indeed all of science. That is the principle of conservation. It is the
assurance that an entity (e.g. mass), or some properties of this entity (e.g. momen
tum, charge) are conserved, which makes it possible to deal with these properties in
a quantitative way.
The principle owes its impor1ance to the circumstance that mass-energy (note
that we have combined these two propertiesl) and momentum are conserved. That is
also true ofc harge, parity, spin and a number ofo ther properties. It is the conservation
principle that makes it possible to write balance equations which state that in an
isolated volume the amount of the property stays constant. The "property" can have
various concentrations in different parts of that volume, these concentrations can
change with time, but their total sum must always add up to the same value. The
