Thermal-Hydraulic Analysis of NuclearReactors

Bahman Zohuri • Nima Fathi

Thermal-HydraulicAnalysis of NuclearReactors

Bahman ZohuriDepartment of Nuclear EngineeringUniversity of New MexicoAlbuquerque, NM, USA

Nima FathiDepartment of Mechanical EngineeringUniversity of New MexicoAlbuquerque, NM, USA

ISBN 978-3-319-17433-4 ISBN 978-3-319-17434-1 (eBook)DOI 10.1007/978-3-319-17434-1

Library of Congress Control Number: 2015060229

Springer Cham Heidelberg New York Dordrecht London# Springer International Publishing Switzerland 2015This work is subject to copyright. All rights are reserved by the Publisher, whether the whole orpart of the material is concerned, specifically the rights of translation, reprinting, reuse ofillustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way,and transmission or information storage and retrieval, electronic adaptation, computer software,or by similar or dissimilar methodology now known or hereafter developed.The use of general descriptive names, registered names, trademarks, service marks, etc. in thispublication does not imply, even in the absence of a specific statement, that such names areexempt from the relevant protective laws and regulations and therefore free for general use.The publisher, the authors and the editors are safe to assume that the advice and information inthis book are believed to be true and accurate at the date of publication. Neither the publisher northe authors or the editors give a warranty, express or implied, with respect to the materialcontained herein or for any errors or omissions that may have been made.

Printed on acid-free paper

Springer International Publishing AG Switzerland is part of Springer Science+Business Media(www.springer.com)

This book is dedicated to my familyBahman Zohuri

This book is dedicated first and foremost to my grandfather,General Siavash Rahimi, and to the rest of my family

Nima Fathi

Preface

The demand for clean, non-fossil-based electricity is growing; therefore, the

world needs to develop new nuclear reactors with higher thermal efficiency

in order to increase electricity generation and decrease the detrimental effects

of fossil-based energy on the environment. The current fleet of nuclear power

plants is classified as Generation III or lower. However, these models are not

as energy efficient as they should be because the operating temperatures are

relatively low. Currently, groups of countries have initiated a program of

international collaboration to develop the next generation of nuclear reactors

called Generation IV. The ultimate goal of developing such reactors is to

increase the thermal efficiency from the current range of 30–35 % to

45–50 %. This increase in thermal efficiency would result in a higher

production of electricity compared to current pressurized water reactor

(PWR) or boiling water reactor (BWR) technologies.

The Generation IV International Forum (GIF) program has narrowed

down the design options for nuclear reactors to six concepts. These concepts

are gas-cooled fast reactors (GFRs), very high temperature reactors

(VHTRs), sodium-cooled fast reactors (SFRs), lead-cooled fast reactors

(LFRs), molten salt reactor (MSRs), and super critical water-cooled reactors

(SCWRs). These nuclear-reactor concepts differ in their design with respect

to aspects such as the neutron spectrum, coolant, moderator, and operating

temperature and pressure.

There are many different types of power reactors. What is common to

them all is that they produce thermal energy that can be used for its own sake

or converted into mechanical energy and, ultimately, in the vast majority of

cases, into electrical energy. Thermal-hydraulic issues related to both

operating and advanced reactors are presented. Further, thermal-hydraulic

research and development is continuing in both experimental and computa-

tional areas for operating reactors, reactors under construction or ready for

near-term deployment, and advanced Generation IV reactors. As computing

power increases, fine-scale multiphysics computational models, coupled with

systems analysis code, are expected to provide answers to many challenging

problems in both operating and advanced reactor designs.

Those that practice the art of nuclear engineering must have a physical and

intuitive understanding of the mechanisms and balances of forces that control

the transport of heat and mass in all physical systems. This understanding

vii

starts at the molecular level, with intermolecular forces and the motion of

molecules, and continues to the macroscopic level, where gradients of

velocity, temperature, and concentration drive the diffusion of momentum,

heat, and mass, and the forces of pressure, inertia, and buoyancy balance to

drive fluid convection.

All professors believe that there is no ideal textbook for the courses they

teach. In the case of courses related to the present subject, this is actually true.

Traditionally, during the years in which the authors taught courses on the

present subject matter, the text has been Transport Phenomena by Bird,

Stewart, and Lightfoot. Though this is an excellent text on the fundamentals

of transport phenomena, it lacks specific examples in nuclear engineering, as

well as information on two-phase flows, boiling, condensation, and forced

and natural convection. In writing this book, the authors have drawn heavily

on materials from Convective Heat and Mass Transfer by Kays and

Crawford, Convective Boiling and Condensation by Collier, and NuclearSystems by Todreas and Kazimi.

This text covers the fundamentals of thermodynamics required to under-

stand electrical power generation systems. It then covers the application of

these principles to nuclear reactor power systems. It is not a general thermo-

dynamics text but a thermodynamics text aimed at explaining the

fundamentals and applying them to the challenges facing actual nuclear

power systems. It is written at an undergraduate level but should also be

useful to practicing engineers.

The book also concentrates on the fundamentals of fluid dynamics and

heat transfer, thermal and hydraulic analysis of nuclear reactors, two-phase

flows and boiling, compressible flows, stress analysis, and energy conversion

methods.

It starts with fundamental definitions of units and dimensions then moves

on to thermodynamic variables such as temperature, pressure, and specific

volume. It then goes into thermal hydraulic analysis, with topics from that

field covered in Chaps. 2 through 16, where it finishes off with the design of a

heat exchanger and shells and tubes using various techniques of verification

and validation (V&V) in computational mechanics and the application of

their basic principles to Brayton and Rankine cycles for power generation.

Brayton cycle compressors, turbines, and recuperators are covered in gen-

eral, along with the fundamentals of heat exchanger design. Rankine steam

generators, turbines, condensers, and pumps are also discussed. Reheaters

and feed water heaters are also covered. Ultimate heat rejection by

circulating water systems is also discussed. Chapter 17 covers the analysis

of reactor accidents, which is independent of other chapters and can be

assigned as a standalone reading chapter for students or taught separately.

The third part of the book covers current and projected reactor systems

and how thermodynamic principles are applied to their design, operation, and

safety analyses.

viii Preface

Detailed appendices cover metric and English system units and

conversions, present detailed steam and gas tables, discuss heat transfer

properties, and describe nuclear reactor systems.

Albuquerque, NM, USA Bahman Zohuri

Nima Fathi

Preface ix

Acknowledgments

The authors would like to acknowledge all those individuals who lent their

help, encouragement, and support. We have decided not to name them all

since some of them may not be around to see the end result of their

encouragement, but we hope they can at least read this acknowledgment

wherever they may be.

Last but not least, special thanks go to our parents, wives, children, and

friends for their constant encouragement, without which this book could not

have been written. We especially appreciate their patience and understanding

for the authors’ frequent absence from home and long hours in front of the

computer during the preparation of this book.

xi

Contents

1 An Introduction to the Thermal-Hydraulic Aspects

of Nuclear Power Reactors . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Basics Understanding of Thermal-Hydraulic Aspects . . . 3

1.3 Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.3.1 Fundamental Units . . . . . . . . . . . . . . . . . . . . 4

1.3.2 Thermal Energy Units . . . . . . . . . . . . . . . . . . 5

1.3.3 Unit Conversion . . . . . . . . . . . . . . . . . . . . . . 6

1.4 System Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.4.1 Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.4.2 Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.4.3 Temperature . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.5 Properties of the Atmosphere . . . . . . . . . . . . . . . . . . . . 10

1.6 The Structure of Momentum, Heat,

and Mass Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

1.7 Common Dimensionless Parameters . . . . . . . . . . . . . . . 12

1.8 Computer Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

1.8.1 Probabilistic Risk Assessment Codes . . . . . . . 13

1.8.2 Fuel Behavior Codes . . . . . . . . . . . . . . . . . . . 13

1.8.3 Reactor Kinetics Codes . . . . . . . . . . . . . . . . . 13

1.8.4 Thermal-Hydraulic Codes . . . . . . . . . . . . . . . 13

1.8.5 Severe Accident Codes . . . . . . . . . . . . . . . . . 14

1.8.6 Design-Basis Accident (DBA) Codes . . . . . . . 15

1.8.7 Emergency Preparedness

and Response Codes . . . . . . . . . . . . . . . . . . . 15

1.8.8 Health Effects/Dose Calculation Codes . . . . . . 15

1.8.9 Radionuclide Transport Codes . . . . . . . . . . . . 16

Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2 Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.2 Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.3 First Law of Thermodynamics . . . . . . . . . . . . . . . . . . . 29

2.4 Enthalpy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

2.5 Energy Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

xiii

2.6 Carnot Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

2.7 Entropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

2.8 Waste Heat Recovery . . . . . . . . . . . . . . . . . . . . . . . . . . 40

2.8.1 Recuperator . . . . . . . . . . . . . . . . . . . . . . . . . 40

2.8.2 Heat Recovery Steam Generator . . . . . . . . . . 40

2.8.3 Reheater . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

2.8.4 Feedwater Heaters . . . . . . . . . . . . . . . . . . . . . 42

2.9 Power Plant and Thermal Cycle . . . . . . . . . . . . . . . . . . 44

2.9.1 Rankine Cycle for Power Plants . . . . . . . . . . . 47

2.9.2 Brayton Cycle for Power Plants . . . . . . . . . . . 48

2.9.3 Combined Brayton–Rankine Cycle . . . . . . . . . 49

2.10 Raising the Boiler Pressure . . . . . . . . . . . . . . . . . . . . . . 50

2.11 Superheat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

2.12 Regeneration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

2.13 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

3 Transport Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

3.2 Theory of Viscosity and Newtonian

and Non-Newtonian Fluids . . . . . . . . . . . . . . . . . . . . . . 58

3.3 Gas Viscosity at Low Density . . . . . . . . . . . . . . . . . . . . 61

3.4 Liquid Viscosity (Newtonian) . . . . . . . . . . . . . . . . . . . . 67

3.5 Liquid Viscosity (Non-Newtonian) . . . . . . . . . . . . . . . . 68

3.6 Thermal Conductivity Theory . . . . . . . . . . . . . . . . . . . . 69

3.7 Fundamental Modes of Heat Transfer . . . . . . . . . . . . . . 72

3.7.1 Conduction . . . . . . . . . . . . . . . . . . . . . . . . . . 72

3.7.2 Convection . . . . . . . . . . . . . . . . . . . . . . . . . . 73

3.7.3 Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

3.8 Theory of Thermal Conductivity of Gases

at Low Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

3.9 Theory of Thermal Conductivity of Liquids . . . . . . . . . 78

3.10 Theory of Mass Diffusion . . . . . . . . . . . . . . . . . . . . . . 78

Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

4 General Conservation Equations . . . . . . . . . . . . . . . . . . . . . . 89

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

4.2 Conservation of Mass . . . . . . . . . . . . . . . . . . . . . . . . . . 90

4.3 Conservation of Momentum . . . . . . . . . . . . . . . . . . . . . 96

4.4 Momentum Flux Expression . . . . . . . . . . . . . . . . . . . . . 98

4.5 Dimensionless Formulation of Momentum Equation . . . 100

4.6 Equation of Mechanical Energy . . . . . . . . . . . . . . . . . 104

4.7 Conservation of Energy . . . . . . . . . . . . . . . . . . . . . . . . 105

4.8 Dimensionless Formulation for Energy Equation . . . . . . 106

4.9 Control Volume Analysis . . . . . . . . . . . . . . . . . . . . . . . 108

Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

xiv Contents

5 Laminar Incompressible Forced Convection . . . . . . . . . . . . . 117

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

5.2 Fully Developed Laminar Flow . . . . . . . . . . . . . . . . . . 118

5.2.1 Convective Heat Transfer, Second

Edition, by Sadik Kakac

and Yaman Yener [5] . . . . . . . . . . . . . . . . . . 119

5.3 Transient Laminar Forced Convection in Ducts . . . . . . . 120

5.4 Fully Developed Laminar Flow in Other

Cross-Sectional Shape Tubes . . . . . . . . . . . . . . . . . . . . 127

5.5 Non-Newtonian Tube Flow . . . . . . . . . . . . . . . . . . . . . 133

5.6 Countercurrent Liquid–Vapor Flow in a Tube . . . . . . . . 134

5.7 Sudden Motion of Flow at a Wall . . . . . . . . . . . . . . . . . 136

5.8 Stagnation Point Flow . . . . . . . . . . . . . . . . . . . . . . . . . 138

5.9 Boundary-Layer Theory . . . . . . . . . . . . . . . . . . . . . . . . 144

5.10 Similarity Solutions for Boundary Layers . . . . . . . . . . . 150

5.11 Integral Solutions for Boundary Layers . . . . . . . . . . . . . 158

5.12 Creeping and Potential Flow . . . . . . . . . . . . . . . . . . . . 159

5.12.1 Creeping Flow or Stokes Flow Theory . . . . . . 161

5.12.2 Potential Flow Theory . . . . . . . . . . . . . . . . . . 166

5.13 Flow in Porous Media . . . . . . . . . . . . . . . . . . . . . . . . . 169

Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180

6 Turbulent Forced Convection . . . . . . . . . . . . . . . . . . . . . . . . 183

6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183

6.2 Time-Averaged Conservation Equations

for Turbulent Flow in Ducts . . . . . . . . . . . . . . . . . . . . . 187

6.2.1 Time Averaging of Equation of Motion . . . . . 188

6.3 Laminar Sublayer and Outer Turbulent Region . . . . . . . 190

6.4 Turbulent Boundary Layer . . . . . . . . . . . . . . . . . . . . . . 191

6.5 Fully Developed Turbulent Flow in a Pipe . . . . . . . . . . 196

6.6 Turbulent Flow in Other Cross-Sectional Shapes . . . . . . 199

6.7 Effects of Surface Roughness . . . . . . . . . . . . . . . . . . . . 202

6.8 Numerical Modeling of Turbulence . . . . . . . . . . . . . . . 205

6.9 Friction Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206

6.10 Flow in Conduits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206

6.11 Flow Around Submerged Objects . . . . . . . . . . . . . . . . . 207

6.12 Turbulent Flow in Noncircular Tubes . . . . . . . . . . . . . . 208

6.13 Flow in Pipes and Ducts . . . . . . . . . . . . . . . . . . . . . . . . 209

6.14 Flow in Rod Bundles . . . . . . . . . . . . . . . . . . . . . . . . . . 217

6.15 Flow Parallel to Rod Bundles . . . . . . . . . . . . . . . . . . . . 218

6.16 Pressure Drop Across Spacers . . . . . . . . . . . . . . . . . . . 219

6.17 Flow Across Rod Bundles . . . . . . . . . . . . . . . . . . . . . . 223

Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229

Contents xv

7 Compressible Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231

7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231

7.2 Gas Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232

7.3 Speed of Sound in a Compressible Fluid . . . . . . . . . . . . 236

7.4 Critical Flow in a Compressible Fluid . . . . . . . . . . . . . . 239

7.5 Ideal Gas Relationships for Adiabatic

Compressible Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . 241

7.6 Rayleigh and Fanno Processes

for Compressible Flow . . . . . . . . . . . . . . . . . . . . . . . . . 242

7.7 Water Hammer (Hydraulic Shock) . . . . . . . . . . . . . . . . 244

7.7.1 Instantaneous Valve Closure . . . . . . . . . . . . . 246

7.7.2 Valve Closure Over Finite Time Periods . . . . . 248

Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252

8 Conduction Heat Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . 253

8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253

8.2 Basic Heat Conduction Equations . . . . . . . . . . . . . . . . . 254

8.2.1 A Compact Form of Basic Heat

Conduction Equations . . . . . . . . . . . . . . . . . . 255

8.2.2 Special Cases of Heat

Conduction Equations . . . . . . . . . . . . . . . . . . 255

8.2.3 Heat Conduction in a Cylinder

with a Uniform Heat Flux . . . . . . . . . . . . . . . 256

8.2.4 Heat Conduction in a Cylinder

with a Uniform Heat Flux (with Cladding) . . . 258

8.3 Composite Walls: Summed Resistance . . . . . . . . . . . . . 259

8.4 Conduction in Complex Systems: Fuel Elements . . . . . . 260

8.4.1 Thermal Properties of Fuels . . . . . . . . . . . . . . 261

8.5 Other Problems in Heat Conduction . . . . . . . . . . . . . . . 262

Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265

9 Forced Convection Heat Transfer . . . . . . . . . . . . . . . . . . . . . 267

9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267

9.2 Heat Transfer in Laminar Tube Flows . . . . . . . . . . . . . . 269

9.3 Heat Transfer in Laminar Boundary Layers . . . . . . . . . . 272

9.4 Heat Transfer in Turbulent Tube Flow . . . . . . . . . . . . . 276

9.5 Heat Transfer in High-Speed Laminar

Boundary-Layer Flow Along a Flat Plate . . . . . . . . . . . 280

Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285

10 Natural or Free Convection . . . . . . . . . . . . . . . . . . . . . . . . . . 287

10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287

10.2 Free Convection from a Vertical Plate . . . . . . . . . . . . . 290

10.3 Similarity Solution for Convection Boundary Layers . . . 293

10.4 Empirical Relationships for Free Convection . . . . . . . . . 295

xvi Contents

10.5 Natural Convection in Enclosure . . . . . . . . . . . . . . . . . 297

10.5.1 Enclosure Heated from the Side . . . . . . . . . . . 298

10.5.2 Enclosure Heated from Below . . . . . . . . . . . . 299

10.6 Natural Circulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 299

10.7 Laminar Film Condensation . . . . . . . . . . . . . . . . . . . . . 301

10.8 Characteristic Free Convection Velocity . . . . . . . . . . . . 303

Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308

11 Mass Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311

11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311

11.2 Theory of Mass Diffusion . . . . . . . . . . . . . . . . . . . . . . 312

11.3 Noncondensable Gases and Evaporation . . . . . . . . . . . . 313

11.4 Noncondensable Gases and Condensation . . . . . . . . . . . 315

Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324

12 Thermal Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325

12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325

12.2 Radiation Absorption and Emission

at Solid Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327

12.3 Radiation Between Black Bodies . . . . . . . . . . . . . . . . . 329

12.4 Radiation Between Nonblack Bodies . . . . . . . . . . . . . . 331

12.5 Radiation Energy Transport in Absorbing Media . . . . . . 335

12.6 Increasing Heat Using Fins as Extensions

of Surface Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338

Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346

13 Multiphase Flow Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . 347

13.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347

13.1.1 Flow Patterns for Vertical Channels,

Upward Cocurrent Flow . . . . . . . . . . . . . . . . 348

13.1.2 Flow Patterns for Horizontal Channels . . . . . . 350

13.2 Standard Notation for Two-Phase Flow . . . . . . . . . . . . . 352

13.3 Governing Equations for Two-Phase Flow . . . . . . . . . . 353

13.4 Homogeneous Equilibrium Model . . . . . . . . . . . . . . . . 354

13.5 Homogeneous Flow Friction Pressure Drop . . . . . . . . . . 356

13.6 Separated Flow Model . . . . . . . . . . . . . . . . . . . . . . . . . 358

13.7 Separated Flow Friction Pressure Drop . . . . . . . . . . . . . 359

13.8 Sound Speed and Choking for Isentropic

Homogeneous Equilibrium Flows . . . . . . . . . . . . . . . . . 363

13.9 One-Dimensional Separated Internal Phase Flows . . . . . 365

13.9.1 Continuity Equations . . . . . . . . . . . . . . . . . . . 366

13.9.2 Momentum Equations . . . . . . . . . . . . . . . . . . 367

13.10 Flow with Phase Change . . . . . . . . . . . . . . . . . . . . . . . 368

Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373

Contents xvii

14 Convective Boiling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375

14.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375

14.1.1 Flow Patterns for Vertical

Convective Boiling . . . . . . . . . . . . . . . . . . . . 376

14.1.2 Flow Patterns for Horizontal

Convective Boiling . . . . . . . . . . . . . . . . . . . . 378

14.2 Vapor Bubble Equilibrium . . . . . . . . . . . . . . . . . . . . . . 379

14.3 Homogeneous Bubble Nucleation . . . . . . . . . . . . . . . . . 381

14.4 Bubble Growth Dynamics . . . . . . . . . . . . . . . . . . . . . . 382

14.5 Nucleate Pool Boiling from Surfaces . . . . . . . . . . . . . . 383

14.6 Subcooled Convective Boiling Heat Transfer . . . . . . . . 386

14.6.1 Onset of Nucleation . . . . . . . . . . . . . . . . . . . . 387

14.6.2 Heat Transfer in Partial Subcooled

Nucleate Boiling . . . . . . . . . . . . . . . . . . . . . . 392

14.7 Fully Developed Subcooled Nucleate Boiling . . . . . . . . 394

14.8 Saturated Convective Boiling Heat Transfer . . . . . . . . . 396

14.9 Flow Instability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 398

14.9.1 Static Flow Instability . . . . . . . . . . . . . . . . . . 398

14.9.2 Dynamic Flow Instability . . . . . . . . . . . . . . . 400

Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 401

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411

15 Thermal Stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413

15.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413

15.1.1 Materials for Reactor Construction . . . . . . . . . 414

15.2 An Introduction to Stress . . . . . . . . . . . . . . . . . . . . . . . 415

15.3 Stresses in Two Dimensions . . . . . . . . . . . . . . . . . . . . . 417

15.4 Stresses in Three Dimensions . . . . . . . . . . . . . . . . . . . . 420

15.5 An Introduction to Strain . . . . . . . . . . . . . . . . . . . . . . . 420

15.6 The Relationship Between Stress and Strain . . . . . . . . . 422

15.7 Plane-Strain Problems . . . . . . . . . . . . . . . . . . . . . . . . . 424

15.8 Plane-Stress Problems . . . . . . . . . . . . . . . . . . . . . . . . . 426

Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 428

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 432

16 Heat Exchangers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433

16.1 Types of Heat Exchanger . . . . . . . . . . . . . . . . . . . . . . . 433

16.2 Classification of Heat Exchanger

by Construction Type . . . . . . . . . . . . . . . . . . . . . . . . . . 435

16.2.1 Tubular Heat Exchangers . . . . . . . . . . . . . . . . 436

16.2.2 Plate Heat Exchangers . . . . . . . . . . . . . . . . . . 436

16.2.3 Plate-Fin Heat Exchangers . . . . . . . . . . . . . . . 437

16.2.4 Tube-Fin Heat Exchangers . . . . . . . . . . . . . . . 437

16.2.5 Regenerative Heat Exchangers . . . . . . . . . . . . 439

16.3 Condensers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439

16.4 Boilers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 440

16.5 Classification by Compactness . . . . . . . . . . . . . . . . . . . 440

16.6 Types of Applications . . . . . . . . . . . . . . . . . . . . . . . . . 440

16.7 Cooling Towers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 440

xviii Contents

16.8 Regenerators and Recuperators . . . . . . . . . . . . . . . . . . . 441

16.9 Heat Exchanger Analysis: Use of LMTD . . . . . . . . . . . 446

16.10 Effectiveness-NTU Method for Heat

Exchanger Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 452

16.11 Special Operating Conditions . . . . . . . . . . . . . . . . . . . . 457

16.12 Compact Heat Exchangers . . . . . . . . . . . . . . . . . . . . . . 458

Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 461

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464

17 Analysis of Reactor Accident . . . . . . . . . . . . . . . . . . . . . . . . . 465

17.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465

17.2 Thermal Design Margin . . . . . . . . . . . . . . . . . . . . . . . . 466

17.3 Steady-State Heat Generation in Reactor Fuel . . . . . . . . 469

17.4 Homogeneous Unreflected Core . . . . . . . . . . . . . . . . . . 472

17.5 Reflectors and Heterogeneous Cores . . . . . . . . . . . . . . . 473

17.6 Heat Generation Following Shutdown . . . . . . . . . . . . . . 474

17.7 Loss-of-Coolant Accidents: Containment

Pressurization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 476

Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 477

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 478

18 Probabilistic Risk Assessment . . . . . . . . . . . . . . . . . . . . . . . . 479

18.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 479

18.2 What Is the Risk? . . . . . . . . . . . . . . . . . . . . . . . . . . . . 480

18.3 Risk Assessment Methods . . . . . . . . . . . . . . . . . . . . . . 481

18.4 Types of Risk Assessment . . . . . . . . . . . . . . . . . . . . . . 482

18.5 What Are the Benefits of PRA? . . . . . . . . . . . . . . . . . . 484

18.6 Abbreviation Used in PRA . . . . . . . . . . . . . . . . . . . . . . 485

Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 487

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 488

19 Nuclear Power Plants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 489

19.1 Fission Energy Generation . . . . . . . . . . . . . . . . . . . . . . 489

19.2 The First Chain Reaction . . . . . . . . . . . . . . . . . . . . . . . 490

19.3 Concepts in Nuclear Criticality . . . . . . . . . . . . . . . . . . . 492

19.4 Fundamentals of Fission Nuclear Reactors . . . . . . . . . . 493

19.5 Reactor Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . 494

19.6 Thermal Reactors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495

19.7 Nuclear Power Plants and Their Classifications . . . . . . . 497

19.8 Classification by Moderator Material . . . . . . . . . . . . . . 497

19.8.1 Light Water Reactors . . . . . . . . . . . . . . . . . . 497

19.8.2 Graphite-Moderated Reactors . . . . . . . . . . . . 497

19.8.3 Heavy Water Reactors . . . . . . . . . . . . . . . . . . 499

19.9 Classification by Coolant Material . . . . . . . . . . . . . . . . 500

19.9.1 Pressurized Water Reactors . . . . . . . . . . . . . . 500

19.9.2 Boiling Water Reactors . . . . . . . . . . . . . . . . . 502

19.9.3 Gas-Cooled Reactors . . . . . . . . . . . . . . . . . . . 503

19.10 Classification by Reaction Type . . . . . . . . . . . . . . . . . . 505

19.10.1 Fast Neutron Reactor . . . . . . . . . . . . . . . . . . . 505

19.10.2 Thermal Neutron Reactor . . . . . . . . . . . . . . . 506

19.10.3 Liquid Metal Fast Breeder Reactors . . . . . . . . 507

Contents xix

19.11 Nuclear Fission Power Generation . . . . . . . . . . . . . . . . 510

19.12 Generation IV Nuclear Energy Systems . . . . . . . . . . . . 511

19.13 Technological State of the Art and Anticipated

Developments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513

19.14 Next-Generation Nuclear Plant . . . . . . . . . . . . . . . . . . 515

19.15 Why We Need to Consider the Future Role

of Nuclear Power Now . . . . . . . . . . . . . . . . . . . . . . . . . 516

19.16 Generation IV Roadmap Project . . . . . . . . . . . . . . . . . . 518

19.17 Licensing Strategy Components . . . . . . . . . . . . . . . . . . 519

19.18 Market and Industry Status and Potentials . . . . . . . . . . . 520

19.19 Barriers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 521

19.20 Needs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 522

19.21 Synergies with Other Sectors . . . . . . . . . . . . . . . . . . . . 522

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523

20 Nuclear Fuel Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 525

20.1 The Nuclear Fuel Cycle . . . . . . . . . . . . . . . . . . . . . . . . 525

20.2 Fuel Cycle Choices . . . . . . . . . . . . . . . . . . . . . . . . . . . 529

20.3 In-Core Fuel Management . . . . . . . . . . . . . . . . . . . . . . 531

20.4 Nuclear Fuel and Waste Management . . . . . . . . . . . . . . 532

20.4.1 Managing HLW from Used Fuel . . . . . . . . . . 533

20.4.2 Recycling Used Fuel . . . . . . . . . . . . . . . . . . . 534

20.4.3 Storage and Disposal of Used Fuel

and Other HLW . . . . . . . . . . . . . . . . . . . . . . 537

20.4.4 Regulation of Disposal . . . . . . . . . . . . . . . . . 539

20.5 Processing of Used Nuclear Fuel . . . . . . . . . . . . . . . . . 540

20.5.1 Reprocessing Policies . . . . . . . . . . . . . . . . . . 541

20.6 Back End of Fuel Cycle . . . . . . . . . . . . . . . . . . . . . . . . 542

Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 542

21 The Economic Future of Nuclear Power . . . . . . . . . . . . . . . . 543

21.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543

21.2 Overall Costs: Fuel, Operation,

and Waste Disposal . . . . . . . . . . . . . . . . . . . . . . . . . . . 544

21.2.1 Fuel Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . 545

21.2.2 Future Cost Competitiveness . . . . . . . . . . . . . 548

21.2.3 Major Studies on Future Cost

Competitiveness . . . . . . . . . . . . . . . . . . . . . . 549

21.2.4 Operations and Maintenance Costs . . . . . . . . . 553

21.2.5 Production Costs . . . . . . . . . . . . . . . . . . . . . . 555

21.2.6 Costs Related to Waste Management . . . . . . . 556

21.2.7 Life-Cycle Costs (US Figures) . . . . . . . . . . . . 558

21.2.8 Construction Costs . . . . . . . . . . . . . . . . . . . . 558

21.3 Comparing the Economics of Different Forms

of Electricity Generation . . . . . . . . . . . . . . . . . . . . . . . 560

21.4 System Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 561

21.5 External Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 561

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 564

xx Contents

22 Safety, Waste Disposal, Containment, and Accidents . . . . . . . 565

22.1 Safety . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 565

22.2 Nuclear Waste Disposal . . . . . . . . . . . . . . . . . . . . . . . . 567

22.3 Contamination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 567

22.4 Accidents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 569

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 571

Appendix A: Table and Graph Compilations . . . . . . . . . . . . . . . . 573

Appendix B: Physical Property Tables . . . . . . . . . . . . . . . . . . . . . 579

Appendix C: Units, Dimensions,

and Conversion Factors . . . . . . . . . . . . . . . . . . . . . . 603

Appendix D: Physical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . 627

Appendix E: Fluid Property Data . . . . . . . . . . . . . . . . . . . . . . . . . 635

Appendix F: Basic Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 641

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 647

Contents xxi

Authors

Bahman Zohuri is currently at Galaxy Advanced Engineering, Inc., a

consulting company he founded in 1991 when he left both the semiconductor

and defense industries after many years of working as a chief scientist. After

graduating from the University of Illinois in the field of physics and

applied mathematics, he joined Westinghouse Electric Corporation, where

he performed thermal hydraulic analysis and natural circulation for inherent

shutdown heat removal systems (ISHRS) in the core of a liquid metal fast

breeder reactor (LMFBR) as a secondary fully inherent shutdown system for

secondary loop heat exchanges. All these designs were used for nuclear

safety and reliability engineering for self-actuated shutdown systems.

Around 1978, Dr. Zohuri designed a mercury heat pipe and electromagnetic

pumps for large pool concepts of LMFBRs for heat rejection purpose in such

reactors, for which he received a patent. Subsequently, he was transferred to

the defense division of Westinghouse, where he was responsible for the

dynamic analysis and launch method and handling of MX missiles from

canisters. The results were applied to MX launch seal performance and

muzzle blast phenomena analysis (i.e., missile vibration and hydrodynamic

shock formation). Dr. Zohuri was also involved in conducting analytical

calculations and computations in the study of nonlinear ion waves in

rarefying plasma. The results were applied to the propagation of soliton

waves and the resulting charge collector traces in the rarefactions character-

istic of the corona of a laser-irradiated target pellet. As part of his graduate

research work at Argonne National Laboratory, he performed computations

and programming of multi-exchange integrals in surface physics and solid

state physics. Dr. Zohuri holds patents in areas such as diffusion processes

and the design of diffusion furnaces, which he obtained while working as a

senior process engineer for various semiconductor companies such as Intel

Corp., Varian Inc., and National Semiconductor. Later on he joined

Lockheed Missile and Aerospace Corporation as Senior Chief Scientist and

was responsible for research and development (R&D) and the study of

vulnerability, survivability, and both radiation and laser hardening of various

components of the Strategic Defense Initiative, also known as Star Wars.

This included of payload (i.e., IR sensors) for the Defense Support Program,

Boost Surveillance and Tracking Satellite, and Space Surveillance and

Tracking Satellite against laser or nuclear threats. While at Lockheed, he

also studied and analyzed how laser beams and nuclear radiation interact

xxiii

with materials and investigated transient radiation effects in electronics,

electromagnetic pulses, system-generated electromagnetic pulses, single-

event upsets, blasts, and thermomechanical, hardness assurance, mainte-

nance, device technologies.

He spent a few years consulting under the auspices of his company, Galaxy

Advanced Engineering, with Sandia National Laboratories, where he

supported the development of operational hazard assessments for the Air

Force SafetyCenter in collaborationwith other interested parties. The intended

use of the results of his consulting work was their eventual inclusion in Air

Force Instructions issued specifically for directed energy weapons operational

safety. Dr. Zohuri completed the first version of a comprehensive library of

detailed laser tools for airborne lasers, advanced tactical lasers, tactical high-

energy lasers, and mobile/tactical high-energy laser, for example.

He also oversaw SDI computer programs related to Battle Management

C3, artificial intelligence, and autonomous systems. He is the author of

several publications and holds various patents such as Laser Activated

Radioactive Decay and Results of Thru-Bulkhead Initiation.

Finally, Dr. Zohuri recently published two books with CRC/Francis

Taylor, Heat Pipe Design and Technology: A Practical Approach and

Directed Energy Weapons Technologies, and has published the following

book with Springer Publishing Company as listed below:

1. Dimensional Analysis and Self-Similarity Methods for Engineers and

Scientists, March 2015

2. Thermodynamics in Nuclear Power Systems with Dr. Patrick McDaniel,

June 2015

3. Combined Cycle Driven Efficiency for Next Generation Nuclear Power

Plants, May 2015

Nima Fathi holds an MSc in mechanical engineering, focusing on

multiphase-flow modeling for particle interaction in Stokes flow. He is an

expert in computational fluid dynamics (CFD) and verification and validation

(V&V) in computational mechanics. Nima has many years of experience in

industry, where he designed more than 86 different types of heat exchangers

and pressure vessels for the various projects in which he participated over the

years. His outstanding industrial and engineering experiences and

accomplishments include successful collaboration with various Asian and

U.S. companies on projects related to thermal, structural, and CFD analysis.

His technical experience includes design, industrial drafting, procure-

ment, and fabrication, all related to fluid dynamics and thermal hydraulic

analysis of multiphase flows. He also holds two patents pending in the

optimization of heat transfer in solar chimney power plants and increasing

thermal hydraulic performance in power plants.

Presently, Mr. Fathi is at the University of NewMexico in the Department

of Mechanical Engineering, where for the past several years he has been

teaching courses in heat transfer while pursuing his PhD in mechanical

engineering and his MSc in nuclear engineering.

xxiv Authors