Cover
Half Title
Title Page
Copyright Page
Dedication
Table of Contents
Preface to the Third Edition
Preface to the First Edition
Acknowledgments
Authors
Chapter 1 Principal Characteristics of Power Reactors
1.1 Introduction
1.2 Power Cycles
1.3 Primary Coolant Systems
1.4 Reactor Cores
1.5 Fuel Assemblies
1.5.1 LWR Fuel Bundles: Square Arrays
1.5.2 PHWR and AGR Fuel Bundles: Mixed Arrays
1.5.3 SFR Fuel Bundles: Hexagonal Arrays
1.6 Advanced Water- and Gas-Cooled Reactors (Generations III and III+)
1.7 Advanced Thermal and Fast Neutron Spectrum Reactors (Generation IV)
1.8 Small Modular Reactors
Problems
References
Chapter 2 Thermal Design Principles and Application
2.1 Introduction
2.2 Overall Plant Characteristics Influenced by Thermal Hydraulic Considerations
2.3 Energy Production and Transfer Parameters
2.4 Thermal Design Limits
2.4.1 Fuel Pins with Metallic Cladding
2.4.2 Graphite-Coated Fuel Particles
2.5 Thermal Design Margin
2.6 Figures of Merit for Core Thermal Performance
2.6.1 Power Density
2.6.2 Specific Power
2.6.3 Power Density and Specific Power Relationship
2.6.4 Specific Power in Terms of Fuel Cycle Operational Parameters
2.7 The Inverted Fuel Array
2.8 The Equivalent Annulus Approximation
Problems
References
Chapter 3 Reactor Energy Distribution
3.1 Introduction
3.2 Energy Generation and Deposition
3.2.1 Forms of Energy Generation
3.2.2 Energy Deposition
3.3 Fission Power and Calorimetric (Core Thermal) Power
3.4 Energy Generation Parameters
3.4.1 Energy Generation and Neutron Flux in Thermal Reactors
3.4.2 Relation between Heat Flux, Volumetric Energy Generation and Core Power
3.4.2.1 Single Pin Parameters
3.4.2.2 Core Power and Fuel Pin Parameters
3.5 Power Profiles in Reactor Cores
3.5.1 Homogeneous Unreflected Core
3.5.2 Homogeneous Core with Reflector
3.5.3 Heterogeneous Core
3.5.4 Effect of Control Rods
3.6 Energy Generation Rate within a Fuel Pin
3.6.1 Fuel Pins of Thermal Reactors
3.6.2 Fuel Pins of Fast Reactors
3.7 Energy Deposition Rate within the Moderator
3.8 Energy Deposition in the Structure
3.8.1 γ-Ray Absorption
3.8.2 Neutron Slowing Down
3.9 Decay Energy during Operation and Post Shutdown
3.9.1 Fission Power by Delayed Neutron after Reactivity Insertion
3.9.2 Power from Fission Product Decay
3.9.3 ANS Standard Decay Power
3.9.3.1 UO[sub(2)] in Light Water Reactors
3.9.3.2 Alternative Fuels in Light Water and Fast Reactors
3.10 Stored Energy Sources
3.10.1 The Zircaloy−Water Reaction
3.10.2 The Sodium−Water Reaction
3.10.3 The Sodium–Carbon Dioxide Reaction
3.10.4 The Corium–Concrete Interaction
Problems
References
Chapter 4 Transport Equations for Single-Phase Flow
4.1 Introduction
4.1.1 Equation Forms
4.1.2 Intensive and Extensive Properties
4.2 Mathematical Relations
4.2.1 Time and Spatial Derivatives
4.2.2 Gauss’s Divergence Theorem
4.2.3 Leibnitz’s Rules
4.3 Integral Lumped Parameter Approach
4.3.1 Control Mass Formulation
4.3.1.1 Mass
4.3.1.2 Momentum
4.3.1.3 Energy
4.3.1.4 Entropy
4.3.2 Control Volume Formulation
4.3.2.1 Mass
4.3.2.2 Momentum
4.3.2.3 Energy
4.3.2.4 Entropy
4.4 Integral Distributed Parameter Approach
4.5 Differential Conservation Equation Approach
4.5.1 Conservation of Mass
4.5.2 Conservation of Momentum
4.5.3 Conservation of Energy
4.5.3.1 Stagnation Internal Energy Equation
4.5.3.2 Stagnation Enthalpy Equation
4.5.3.3 Kinetic Energy Equation
4.5.3.4 Thermodynamic Energy Equations
4.5.3.5 Special Forms
4.5.4 Summary of Equations
4.6 Turbulent Flow
Problems
References
Chapter 5 Transport Equations for Two-Phase Flow
5.1 Introduction
5.1.1 Macroscopic versus Microscopic Information
5.1.2 Multicomponent versus Multiphase Systems
5.1.3 Mixture versus Multi fluid Models
5.2 Averaging Operators for Two-Phase Flow
5.2.1 Phase Density Function
5.2.2 Volume-Averaging Operators
5.2.3 Area-Averaging Operators
5.2.4 Local Time-Averaging Operators
5.2.5 Commutativity of Space- and Time-Averaging Operations
5.3 Volume-Averaged Properties
5.3.1 Void Fraction
5.3.1.1 Instantaneous Space-Averaged Void Fraction
5.3.1.2 Local Time-Averaged Void Fraction
5.3.1.3 Space- and Time-Averaged Void Fraction
5.3.2 Volumetric Phase Averaging
5.3.2.1 Instantaneous Volumetric Phase Averaging
5.3.2.2 Time Averaging of Volume-Averaged Quantities
5.3.3 Static Quality
5.3.4 Mixture Density
5.4 Area-Averaged Properties
5.4.1 Area-Averaged Phase Fraction
5.4.2 Flow Quality
5.4.3 Mass Fluxes
5.4.4 Volumetric Fluxes and Flow Rates
5.4.5 Velocity (Slip) Ratio
5.4.6 Mixture Density over an Area
5.4.7 Volumetric Flow Ratio
5.4.8 Flow Thermodynamic Quality
5.4.9 Summary of Useful Relations for One-Dimensional Flow
5.5 Mixture Equations for One-Dimensional Flow
5.5.1 Mass Continuity Equation
5.5.2 Momentum Equation
5.5.3 Energy Equation
5.6 Control-Volume Integral Transport Equations
5.6.1 Mass Balance
5.6.1.1 Mass Balance for Volume V[sub(k)]
5.6.1.2 Mass Balance in the Entire Volume V
5.6.1.3 Interfacial Jump Condition
5.6.1.4 Simplified Form of the Mixture Equation
5.6.2 Momentum Balance
5.6.2.1 Momentum Balance for Volume V[sub(k)]
5.6.2.2 Momentum Balance in the Entire Volume V
5.6.2.3 Interfacial Jump Condition
5.6.2.4 Common Assumptions
5.6.2.5 Simplified Forms of the Mixture Equation
5.6.3 Energy Balance
5.6.3.1 Energy Balance for Volume V[sub(k)]
5.6.3.2 Energy Equations for Total Volume V
5.6.3.3 Jump Condition
5.7 One-Dimensional Space-Averaged Transport Equations
5.7.1 Mass Equations
5.7.2 Momentum Equations
5.7.3 Energy Equations
Problems
References
Chapter 6 Thermodynamics of Nuclear Energy Conversion Systems—Nonflow and Steady Flow: Applications of the First and Second Law of Thermodynamics
6.1 Introduction
6.2 Nonflow Process
6.2.1 A Fuel–Coolant Thermal Interaction
6.2.1.1 Step I: Coolant and Fuel Equilibration at Constant Volume
6.2.1.2 Step II-A: Coolant and Fuel Expanded as Two Independent Systems, Isentropically
6.2.1.3 Step II-B: Coolant and Fuel Expanded as One System in Thermal Equilibrium, Isentropically
6.3 Thermodynamic Analysis of Nuclear Power Plants
6.4 Thermodynamic Analysis of a Simplified PWR System
6.4.1 First Law Analysis of a Simplified PWR System
6.4.2 Combined First and Second Law or Availability Analysis of a Simplified PWR System
6.4.2.1 Turbine and Pump
6.4.2.2 Steam Generator and Condenser
6.4.2.3 Reactor Irreversibility
6.4.2.4 Plant Irreversibility
6.5 More Complex Rankine Cycles: Superheat, Reheat, Regeneration and Moisture Separation
6.6 Simple Brayton Cycle
6.7 More Complex Brayton Cycles
6.8 Supercritical Carbon Dioxide Brayton Cycles
6.8.1 Simple S-CO[sub(2)] Brayton Cycle
6.8.2 S-CO[sub(2)] Brayton Cycle with Ideal Components and Regeneration
6.8.3 S-CO[sub(2)] Recompression Brayton Cycle with Ideal Components
6.8.4 S-CO[sub(2)] Recompression Brayton Cycle with Real Components and Pressure Losses
Problems
References
Chapter 7 Thermodynamics of Nuclear Energy Conversion Systems— Nonsteady Flow First Law Analysis
7.1 Introduction
7.2 Containment Pressurization Process
7.2.1 Analysis of Transient Conditions
7.2.1.1 Control Mass Approach
7.2.1.2 Control Volume Approach
7.2.2 Analysis of Final Equilibrium Pressure Conditions
7.2.2.1 Control Mass Approach
7.2.2.2 Control Volume Approach
7.2.2.3 Governing Equations for Determination of Final Conditions
7.2.2.4 Individual Cases
7.3 Response of a PWR Pressurizer to Load Changes
7.3.1 Equilibrium Single-Region Formulation
7.3.2 Analysis of Final Equilibrium Pressure Conditions
Problems
Chapter 8 Thermal Analysis of Fuel Elements
8.1 Introduction
8.2 Heat Conduction in Fuel Elements
8.2.1 General Equation of Heat Conduction
8.2.2 Thermal Conductivity Approximations
8.3 Thermal Properties of UO[sub(2)] and MOX
8.3.1 Thermal Conductivity
8.3.1.1 Temperature Effects
8.3.1.2 Porosity (Density) Effects
8.3.1.3 Oxygen-to-Metal Atomic Ratio
8.3.1.4 Plutonium Content
8.3.1.5 Effects of Pellet Cracking
8.3.1.6 Burnup
8.3.2 Fission Gas Release
8.3.3 Melting Point
8.3.4 Specific Heat
8.3.5 The Rim Effect
8.4 Temperature Distribution in Plate Fuel Elements
8.4.1 Heat Conduction in Fuel
8.4.2 Heat Conduction in Cladding
8.4.3 Thermal Resistances
8.4.4 Conditions for Symmetric Temperature Distributions
8.5 Temperature Distribution in Cylindrical Fuel Pins
8.5.1 General Conduction Equation for Cylindrical Geometry
8.5.2 Solid Fuel Pellet
8.5.3 Annular Fuel Pellet (Cooled Only on the Outside Surface R[sub(fo)])
8.5.4 Annular Fuel Pellet (Cooled on Both Surfaces)
8.5.5 Solid versus Annular Pellet Performance
8.5.6 Annular Fuel Pellet (Cooled Only on the Inside Surface R[sub(v)])
8.6 Temperature Distribution in Restructured Fuel Elements
8.6.1 Mass Balance
8.6.2 Power Density Relations
8.6.3 Heat Conduction in Zone 3
8.6.4 Heat Conduction in Zone 2
8.6.5 Heat Conduction in Zone 1
8.6.6 Solution of the Pellet Problem
8.6.7 Two-Zone Sintering
8.6.8 Design Implications of Restructured Fuel
8.7 Thermal Resistance between the Fuel and Coolant
8.7.1 Gap Conductance Models
8.7.1.1 As-Fabricated Gap
8.7.1.2 Gap Closure Effects
8.7.2 Cladding Corrosion: Oxide Film Buildup and Hydrogen Consequences
8.7.3 Overall Thermal Resistance
Problems
References
Chapter 9 Single-Phase Fluid Mechanics
9.1 Approach to Simplified Flow Analysis
9.1.1 Solution of the Flow Field Problem
9.1.2 Possible Simplifications
9.2 Inviscid Flow
9.2.1 Dynamics of Inviscid Flow
9.2.2 Bernoulli’s Integral
9.2.2.1 Time-Dependent Flow-General
9.2.2.2 Steady-State Flow
9.2.3 Compressible Inviscid Flow
9.2.3.1 Flow in a Constant-Area Duct
9.2.3.2 Flow through a Sudden Expansion or Contraction
9.3 Viscous Flow
9.3.1 Viscosity Fundamentals
9.3.2 Viscosity Changes with Temperature and Pressure
9.3.3 Boundary Layer
9.3.4 Turbulence
9.3.5 Dimensionless Analysis
9.3.6 Pressure Drop in Channels
9.3.7 Summary of Pressure Changes in Inviscid/Viscid and in Compressible/Incompressible Flows
9.4 Laminar Flow inside a Channel
9.4.1 Fully Developed Laminar Flow in a Circular Tube
9.4.2 Fully Developed Laminar Flow in Noncircular Geometries
9.4.3 Laminar Developing Flow Length
9.4.4 Form Losses in Laminar Flow
9.5 Turbulent Flow inside a Channel
9.5.1 Turbulent Diffusivity
9.5.2 Turbulent Velocity Distribution
9.5.3 Turbulent Friction Factors in Adiabatic and Diabatic Flows
9.5.3.1 Turbulent Friction Factor: Adiabatic Flow
9.5.3.2 Turbulent Friction Factor: Diabatic Flow
9.5.4 Fully Developed Turbulent Flow with Noncircular Geometries
9.5.5 Turbulent Developing Flow Length
9.5.6 Turbulent Friction Factors—Geometries for Enhanced Heat Transfer
9.5.6.1 Extended Surfaces
9.5.6.2 Twisted Tape Inserts
9.5.7 Turbulent Form Losses
9.6 Pressure Drop in Rod Bundles
9.6.1 Friction Loss along Bare Rod Bundles
9.6.1.1 Laminar Flow
9.6.1.2 Turbulent Flow
9.6.2 Pressure Loss at Fuel Pin Spacer and Support Structures
9.6.2.1 Grid Spacers
9.6.2.2 Wire Wrap Spacers
9.6.2.3 Grid versus Wire Wrap Pressure Loss
9.6.3 Pressure Loss for Cross Flow
9.6.3.1 Across Bare Rod Arrays
9.6.3.2 Across Wire-Wrapped Rod Bundles
9.6.4 Form Losses for Abrupt Area Changes
9.6.4.1 Method of Calculation
9.6.4.2 Loss Coefficient Values
Problems
References
Chapter 10 Single-Phase Heat Transfer
10.1 Fundamentals of Heat Transfer Analysis
10.1.1 Objectives of the Analysis
10.1.2 Approximations to the Energy Equation
10.1.3 Dimensional Analysis
10.1.4 Thermal Conductivity
10.1.5 Engineering Approach to Heat Transfer Analysis
10.2 Laminar Heat Transfer in a Pipe
10.2.1 Fully Developed Flow in a Circular Tube
10.2.2 Developed Flow in Other Geometries
10.2.3 Developing Laminar Flow Region
10.3 Turbulent Heat Transfer: Mixing Length Approach
10.3.1 Equations for Turbulent Flow in Circular Coordinates
10.3.2 Relation between ε[sub(M)],ε[sub(H)] and Mixing Lengths
10.3.3 Turbulent Temperature Profile
10.4 Turbulent Heat Transfer: Differential Approach
10.4.1 Basic Models
10.4.2 Transport Equations for the k[sub(T)]−ε[sub(T)] Model
10.4.3 One-Equation Model
10.4.4 Effect of Turbulence on the Energy Equation
10.4.5 Summary
10.5 Heat Transfer Correlations in Turbulent Flow
10.5.1 Nonmetallic Fluids—Smooth Heat Transfer Surfaces
10.5.1.1 Fully Developed Turbulent Flow
10.5.1.2 Entrance Region Effect
10.5.2 Nonmetallic Fluids—Geometries for Enhanced Heat Transfer
10.5.2.1 Ribbed Surfaces
10.5.2.2 Twisted Tape Inserts
10.5.3 Metallic Fluids—Smooth Heat Transfer Surfaces: Fully Developed Flow
10.5.3.1 Circular Tube
10.5.3.2 Parallel Plates
10.5.3.3 Concentric Annuli
10.5.3.4 Rod Bundles
Problems
References
Chapter 11 Two-Phase Flow Dynamics
11.1 Introduction
11.2 Flow Regimes
11.2.1 Regime Identicat fi ion
11.2.2 Flow Regime Maps
11.2.2.1 Vertical Flow
11.2.2.2 Horizontal Flow
11.2.3 Flooding and Flow Reversal
11.3 Flow Models
11.4 Overview of Void Fraction and Pressure Loss Correlations
11.5 Void Fraction Correlations
11.5.1 The Fundamental Void Fraction-Quality-Slip Relation
11.5.2 Homogeneous Equilibrium Model
11.5.3 Drift Flux Model
11.5.4 Chexal and Lellouche Correlation
11.5.5 Premoli Correlation
11.5.6 Bestion Correlation
11.6 Pressure–Drop Relations
11.6.1 The Acceleration, Friction and Gravity Components
11.6.2 Homogeneous Equilibrium Models
11.6.3 Separate Flow Models
11.6.3.1 Lockhart–Martinelli Correlation
11.6.3.2 Thom Correlation
11.6.3.3 Baroczy Correlation
11.6.3.4 Friedel Correlation
11.6.4 Two-Phase Pressure Drop
11.6.4.1 Pressure Drop for Zero Inlet Quality x= 0
11.6.4.2 Pressure Drop for Nonzero Inlet Quality
11.6.5 Relative Accuracy of Various Friction Pressure Loss Models
11.6.6 Pressure Losses across Singularities
11.7 Critical Flow
11.7.1 Background
11.7.2 Single-Phase Critical Flow
11.7.3 Two-Phase Critical Flow
11.7.3.1 Thermal Equilibrium Models
11.7.3.2 Thermal Nonequilibrium Models
11.7.3.3 Practical Guidelines for Calculations
11.8 Two-Phase Flow Instabilities in Nuclear Systems
11.8.1 Thermal-Hydraulic Instabilities
11.8.1.1 Ledinegg Instabilities
11.8.1.2 Density Wave Oscillations
11.8.2 Thermal-Hydraulic Instabilities with Neutronics Feedback
Problems
References
Chapter 12 Pool Boiling
12.1 Introduction
12.2 Nucleation
12.2.1 Equilibrium Bubble Radius
12.2.2 Homogeneous and Heterogeneous Nucleation
12.2.3 Vapor Trapping and Retention
12.2.4 Vapor Growth from Microcavities
12.2.5 Bubble Dynamics—Growth and Detachment
12.2.6 Nucleation Summary
12.3 The Pool Boiling Curve
12.4 Heat Transfer Regimes
12.4.1 Nucleate Boiling Heat Transfer (between Points B–C of the Boiling Curve of Figure 12.8)
12.4.2 Transition Boiling (between Points C–D of the Boiling Curve of Figure 12.8)
12.4.3 Film Boiling (between Points D–F of the Boiling Curve of Figure 12.8)
12.5 Limiting Conditions on the Boiling Curve
12.5.1 Critical Heat Flux (Point C of the Boiling Curve of Figure 12.8)
12.5.2 Minimum Stable Film Boiling Temperature (Point D of the Boiling Curve of Figure 12.8)
12.6 Surface Effects in Pool Boiling
12.7 Condensation Heat Transfer
12.7.1 Filmwise Condensation
12.7.1.1 Condensation on a Vertical Wall
12.7.1.2 Condensation on or in a Tube
12.7.2 Dropwise Condensation
12.7.3 The Effect of Noncondensable Gases
Problems
References
Chapter 13 Flow Boiling
13.1 Introduction
13.2 Heat Transfer Regions and Void Fraction/Quality Development
13.2.1 Heat Transfer Regions
13.2.1.1 Onset of Nucleate Boiling, Z[sub(ONB)]
13.2.1.2 Net Vapor Generation Point, Z[sub(NVG)]
13.2.1.3 Onset of Saturated Boiling, Z[sub(OSB)]
13.2.1.4 Location of Thermal Equilibrium, Z[sub(E)]
13.2.1.5 Void Fraction Profile, α(z)
13.3 Heat Transfer Coefficient Correlations
13.3.1 Correlations for Saturated Boiling
13.3.1.1 Early Correlations
13.3.1.2 Chen Correlation
13.3.1.3 Kandlikar Correlation
13.3.2 Correlations Applicable to Both Subcooled and Saturated Boiling
13.3.2.1 Early Correlations
13.3.2.2 Bjorge, Hall and Rohsenow Correlation
13.3.3 Correlations for Subcooled Boiling Only
13.3.3.1 Modification of the Chen Correlation
13.3.3.2 Kandlikar Correlation
13.3.4 Post-CHF Heat Transfer
13.3.4.1 Both Film Boiling Regimes (Inverted and Dispersed Annular Flow)
13.3.4.2 Inverted Annular Flow Film Boiling (Only)
13.3.4.3 Dispersed Annular or Liquid Deficient Flow Film Boiling (Only)
13.3.4.4 Transition Boiling
13.3.5 Reflooding of a Core Which Has Been Uncovered
13.4 Critical Condition or Boiling Crisis
13.4.1 Critical Condition Mechanisms and Limiting Values
13.4.2 The Critical Condition Mechanisms
13.4.2.1 Models for DNB
13.4.2.2 Model for Dryout
13.4.2.3 Variation of the Critical Condition with Key Parameters
13.4.3 Correlations for the Critical Condition
13.4.3.1 Correlations for Tube Geometry
13.4.3.2 Correlations for Rod Bundle Geometry
13.4.4 Design Margin in Critical Condition Correlation
13.4.4.1 Characterization of the Critical Condition
13.4.4.2 Margin to the Critical Condition
13.4.4.3 Comparison of Various Correlations
13.4.4.4 Design Considerations
Problems
References
Chapter 14 Single Heated Channel: Steady-State Analysis
14.1 Introduction
14.2 Formulation of One-Dimensional Flow Equations
14.2.1 Nonuniform Velocities
14.2.2 Uniform and Equal Phase Velocities
14.3 Delineation of Behavior Modes
14.4 The LWR Cases Analyzed in Subsequent Sections
14.5 Steady-State Single-Phase Flow in a Heated Channel
14.5.1 Solution of the Energy Equation for a Single-Phase Coolant and Fuel Rod (PWR Case)
14.5.1.1 Coolant Temperature
14.5.1.2 Cladding Temperature
14.5.1.3 Fuel Centerline Temperature
14.5.2 Solution of the Energy Equation for a Single-Phase Coolant with Roughened Cladding Surface (Gas Fast Reactor)
14.5.3 Solution of the Momentum Equation to Obtain Single-Phase Pressure Drop
14.6 Heat Transfer and Associated Flow Condition Regions Which Can Exist in a Boiling Channel
14.7 Steady-State Two-Phase Flow in a Heated Channel under Fully Equilibrium (Thermal and Mechanical) Conditions
14.7.1 Solution of the Energy Equation for Two-Phase Flow (BWR Case with Single-Phase Entry Region)
14.7.2 Solution of the Momentum Equation for Fully Equilibrium Two-Phase Flow Conditions to Obtain Channel Pressure Drop (BWR Case with Single-Phase Entry Region)
14.7.2.1 P[sub(acc)]
14.7.2.2 P[sub(grav)]
14.7.2.3 P[sub(fric)]
14.7.2.4 P[sub(form)]
14.8 Steady-State Two-Phase Flow in a Heated Channel under Nonequilibrium Conditions
14.8.1 Solution of the Energy Equation for Nonequilibrium Conditions (BWR and PWR Cases)
14.8.1.1 Prescribed Wall Heat Flux
14.8.1.2 Prescribed Coolant Temperature
14.8.2 Solution of the Momentum Equation for Channel Nonequilibrium Conditions to Obtain Pressure Drop (BWR Case)
Problems
References
Appendix A: Selected Nomenclature
Appendix B: Physical and Mathematical Constants
Appendix C: Unit Systems
Appendix D: Mathematical Tables
Appendix E: Thermodynamic Properties
Appendix F: Thermophysical Properties of Some Substances
Appendix G: Dimensionless Groups of Fluid Mechanics and Heat Transfer
Appendix H: Multiplying Prefixes
Appendix I: List of Elements
Appendix J: Square and Hexagonal Rod Array Dimensions
Appendix K: Parameters for Typical BWR-5 and PWR Reactors
Appendix L: Acronyms and Abbreviations
Index