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Thermo-Hydraulics of Nuclear Reactors Thermo-Hydraulics of Nuclear Reactors Christopher Earls Brennen California Institute of Technology Pasadena, California Dankat Publishing Company Copyright c 2014 Christopher E. Brennen All rights reserved. No part of this publication may be reproduced, transmitted, transcribed, stored in a retrieval system, or translated into any language or computer language, in any form or by any means, without prior written permission from Christopher Earls Brennen. Library of Congress Card Number 05-??????? A catalogue record for this book is available from the British Library ISBN 0-9667409-8-X Preface This book presents an overview of the thermo-hydraulics of the nuclear reactors designed to produce power using nuclear fission. The book began many years ago as a series of notes prepared for a graduate student course at the California Institute of Technology. When, following the Three Mile Island accident in 1979, nuclear power became politically unpopular, demand and desire for such a course waned and I set the book aside in favor of other projects. However, as the various oil crises began to accentuate the need to explore alternative energy sources, the course and the preparation of this book was briefly revived. Then came the terrible Chernobyl accident in 1986 and the course and the book got shelved once more. However the pendulum swung back again as the problems of carbon emissions and global warming rose in our consciousness and I began again to add to the manuscript. Even when the prospects for nuclear energy took another downturn in the aftermath of the Fukushima accident (in 2011), I decided that I should finish the book whatever the future might be for the nuclear power industry. I happen to believe despite the accidents - or perhaps because of them - that nuclear power will be an essential component of electricity generation in the years ahead. The book is an introduction to a graduate level (or advanced undergraduate level) course in the thermo-hydraulics of nuclear power generation. Since the neutronics and thermo-hydraulics are closely linked a complete understanding of the thermo-hydraulics and the associated safety issues also requires knowledge of the neutronics of nuclear power generation and, in particular, of the interplay between the neutronics and the thermo-hydraulics that determines the design of the reactor core. This material necessarily leads into the critical issues associ- ated with nuclear reactor safety and this, in turn, would be incomplete without brief descriptions of the three major accidents (Three Mile Island, Chernobyl and Fukushima) that have influenced the development of nuclear power. Some sections in chapter 6 of this book were adapted from two of my other books, Cavitation and Bubble Dynamics and Fundamentals of Multiphase Flow and I am grateful to the publisher of those books, Cambridge University Press, for permission to reproduce those sections and their figures in the present text. Other figures and photographs reproduced in this book are acknowledged in their respective captions. I would also like to express my gratitude to the senior colleagues at the California Institute of Technology who introduced me to the topic of nuclear power generation, in particular Noel Corngold and Milton Ples- iii set. Milton did much to advance the cause of nuclear power generation in the United States and I am much indebted to him for his guidance. I also appreciate the interactions I had with colleagues in other institutions including Ivan Cat- ton, the late Ain Sonin, George Maise and the staff at the Nuclear Regulatory Commission. This book is dedicated to James MacAteer from whom I first heard the word neutron and to the Rainey Endowed School in Magherafelt where the physics Johnny Mac taught me stayed with me throughout my life. Christopher Earls Brennen California Institute of Technology, November 2013. iv Contents Preface iii Mathematical Nomenclature ix 1INTRODUCTION 1 1.1BackgroundandContext...................... 1 1.2ThisBook............................... 3 2 BASIC NUCLEAR POWER GENERATION 5 2.1Nuclearpower............................. 5 2.2Nuclearfuelcycle........................... 5 2.2.1 Thoriumfuelcycle...................... 7 2.2.2 Fuelchangesinthereactor................. 8 2.2.3 Thepost-reactorstages................... 8 2.3Nuclearphysics............................ 9 2.3.1 Basicnuclearfission..................... 9 2.3.2 Neutronenergyspectrum.................. 11 2.3.3 Cross-sectionsandmeanfreepaths............. 11 2.3.4 Delayedneutronsandemissions............... 13 2.4Radioactivityandradioactivedecay................ 14 2.4.1 Half-Life............................ 14 2.4.2 Decayinanuclearreactor.................. 15 2.5Radiation............................... 15 2.6Containmentsystems......................... 17 2.6.1 Radioactiverelease...................... 17 2.6.2 Reactorshielding....................... 17 2.7Naturaluraniumreactors...................... 19 2.8Thermalreactors........................... 19 2.8.1 Moderator........................... 19 2.8.2 Neutronhistoryinathermalreactor............ 21 2.9Fastreactors............................. 22 2.10Criticality............................... 22 2.11Fuelcyclevariations......................... 23 v 3 CORE NEUTRONICS 27 3.1Introduction.............................. 27 3.2Neutrondensityandneutronflux.................. 27 3.3Discretizingtheenergyorspeedrange............... 28 3.4Averagingovermaterialcomponents................ 29 3.5Neutrontransporttheory...................... 30 3.6Diffusiontheory............................ 32 3.6.1 Introduction......................... 32 3.6.2 One-speedandtwo-speedapproximations......... 34 3.6.3 Steadystateone-speeddiffusiontheory.......... 35 3.6.4 Two-speeddiffusiontheory................. 36 3.6.5 Non-isotropicneutronfluxtreatments........... 38 3.6.6 Multigroup diffusion theories and calculations . 38 3.6.7 Latticecellcalculations................... 39 3.7Simplesolutionstothediffusionequation............. 40 3.7.1 Spherical and cylindrical reactors . ........ 40 3.7.2 Effectofareflectoronasphericalreactor......... 42 3.7.3 Effectofareflectoronacylindricalreactor........ 44 3.7.4 Effectofcontrolrodinsertion................ 45 3.8Steadystatelatticecalculations................... 48 3.8.1 Introduction......................... 48 3.8.2 Fuelrodlatticecell...................... 50 3.8.3 Controlrodlatticecell.................... 51 3.8.4 Otherlatticescales...................... 53 3.9Unsteadyorquasi-steadyneutronics................ 54 3.9.1 Unsteadyone-speeddiffusiontheory............ 55 3.9.2 Pointkineticsmodel..................... 56 3.10Moreadvancedneutronictheory.................. 57 3.11MonteCarlocalculations....................... 57 4 SOME REACTOR DESIGNS 59 4.1Introduction.............................. 59 4.2Currentnuclearreactors....................... 60 4.3Lightwaterreactors(LWRs).................... 61 4.3.1 Typesoflightwaterreactors(LWRs)........... 61 4.3.2 Pressurizedwaterreactors(PWRs)............. 62 4.3.3 Boiling water reactors (BWRs) ............... 64 4.3.4 FuelandcontrolrodsforLWRs............... 68 4.3.5 Smallmodularreactors................... 68 4.3.6 LWRcontrol......................... 70 4.4Heavywaterreactors(HWRs).................... 71 4.5Graphitemoderatedreactors.................... 73 4.6Gascooledreactors ......................... 74 4.7Fastneutronreactors(FNRs).................... 75 4.8Liquidmetalfastbreederreactors................. 75 4.9GenerationIVreactors........................ 79 vi 4.9.1 GenerationIVthermalreactors............... 79 4.9.2 GenerationIVfastreactors................. 80 5COREHEATTRANSFER 83 5.1Heatproductioninanuclearreactor................ 83 5.1.1 Introduction......................... 83 5.1.2 Heatsource.......................... 83 5.1.3 Fuelrodheattransfer.................... 84 5.1.4 Heattransfertothecoolant................. 87 5.2Coretemperaturedistributions................... 88 5.3 Core design - an illustrative LWR example . ........... 90 5.4Coredesign-anLMFBRexample................. 91 5.5 Boiling water reactor ......................... 91 5.5.1 Temperaturedistribution.................. 91 5.5.2 Massqualityandvoidfractiondistribution........ 92 5.6Criticalheatflux........................... 93 6MULTIPHASEFLOW 97 6.1Introduction.............................. 97 6.2Multiphaseflowregimes....................... 97 6.2.1 Multiphaseflownotation.................. 98 6.2.2 Multiphaseflowpatterns.................. 98 6.2.3 Flowregimemaps......................100 6.2.4 Flowpatternclassifications.................101 6.2.5 Limitsofdisperseflowregimes...............103 6.2.6 Limitsonseparatedflow...................104 6.3Pressuredrop.............................107 6.3.1 Introduction.........................107 6.3.2 Horizontaldisperseflow...................107 6.3.3 Homogeneousflowfriction..................108 6.3.4 Frictionallossinseparatedflow...............109 6.4Vaporization.............................113 6.4.1 Classesofvaporization....................113 6.4.2 Homogeneousvaporization.................113 6.4.3 Effectofinterfacialroughness................116 6.5Heterogeneousvaporization.....................117 6.5.1 Pool boiling . .........................117 6.5.2 Pool boiling on a horizontal surface . ...........117 6.5.3 Nucleate boiling . ..................120 6.5.4 Pool boiling crisis . ..................121 6.5.5 Film boiling . .........................123 6.5.6 Boiling on vertical surfaces . ...........125 6.6 Multiphase flow instabilities . ..................127 6.6.1 Introduction.........................127
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