Nuclear Systems, Vol. 1: Thermal Hydraulic Fundamentals

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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