Neutronic Analysis For Nuclear Reactor Systems

672 Pages·2019·15.439 MB·English

by  Bahman Zohuri

Bahman Zohuri
Neutronic
Analysis For
Nuclear Reactor
Systems
Second Edition
Neutronic Analysis For Nuclear Reactor Systems

Bahman Zohuri
Neutronic Analysis
For Nuclear Reactor Systems
Second Edition
BahmanZohuri
GalaxyAdvancedEngineering,Inc.
UniversityofNewMexico
Albuquerque,NM,USA
Additionalmaterialtothisbookcanbedownloadedfromhttp://extras.springer.com.
ISBN978-3-030-04905-8 ISBN978-3-030-04906-5 (eBook)
https://doi.org/10.1007/978-3-030-04906-5
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This book is dedicated to Children, Natasha,
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Preface
Thistextdevelopsthetheoryofnuclearreactorsfromthefundamentalsoffissionto
theoperatingcharacteristicsofmodernreactors.Itisaimedatseniorundergraduate
orfirstyeargraduatestudentlevel.Itisdesignedasatwo-semestertextwiththefirst
half emphasizing reactor criticality analysis and all of the physics that goes into
moderncalculations.Itwillstartwithsimplifiedone-groupdiffusiontheorymodels
andextendintosophisticatedmulti-grouptransporttheorymodels.Eachchapterwill
haveatleastoneexamplecoveringtheissuesdiscussed.Desktopcalculationswillbe
discussed and demonstrated in examples. A small one-dimensional computer code
will be provided to demonstrate the models discussed. Resonance theory, thermal
scattering, and heterogeneous effects will be discussed and characterized. Detailed
data sets will be provided that will allow two, three, and four groups of desktop
calculations. Additional multi-group data sets will be provided with the
computerdisk.
The second half of the book will deal with the two main topics of interest to
operatingreactors–reactorkinetics/dynamicsandin-corefuelmanagement.Based
onthefundamentalphysicsdiscussedinthefirsthalfofthebook,reactivitymodels
will be developed using realistic reactor cross-section data and modern analytic
tools.Adjointmethodswillbeexplainedindetail.Perturbationtheorywillbeused
extensively to quantify reactivity effects. Both linear and nonlinear reactor kinetic
feedback models are included. Control system models will be mainly based on
linearization techniques. Fuel management analysis will be based on a linear reac-
tivitymodel.Codemodelingwillbediscussedandexampleproblemsincludedthat
canbeaddressedwithdesktopmethods.Thetheoryforextendingfuelmanagement
calculationstomodernlarge-scalecomputerswillbediscussed.
Some sections and chapters of the book reflect inputs and lecture notes from
Professor Emeritus William J. Garland, Department of Engineering Physics,
McMaster University, Professor Hiroshi Sekimoto of Tokyo Institute of Technol-
ogy,andProfessorH.VanDamofDelftUniversityofTechnologyaswellassome
of my own lectures and notes while consulting with the Department of Energy.
Some of my lecture notes from my class notes at the University of Illinois and
vii
viii Preface
UniversityofNewMexicowereusedaswellwhiletakingrelatedcourseasgraduate
student.
My many thanks also go to Dr. Stanley Thompson of Oregon State University
andhisrichnotesonthetopicsof“UnstableNuclearPower,”whichwereavailable
ontheInternet.
Itisanticipatedthatthefirsthalfofthebookwillbeusefultomanyprofessionals
in the nuclear industry. The second half of the book should be of use to nuclear
engineeringprofessionalsconcernedwithoperatingnuclearreactors.
Albuquerque,NM,USA BahmanZohuri
Acknowledgment
IwouldliketogivemyheartfeltthankstoProfessorPatrickMcDanielforhislecture
notes given at the University of New Mexico, Nuclear Engineering Department,
Professor Hiroshi Sekimoto of Tokyo Institute of Technology for his Nuclear
Reactor Theory book, Professor H. Van Dam of Delft University of Technology
for his nuclear reactor physics lecture notes AP3341, and Professor Emeritus
William J. Garland, Department of Engineering Physics, McMaster University,
who provided me some of his lectures and class notes and graciously gave me
permissiontousetheminsectionsorchaptersthroughoutthisbookwhereIsawitfit.
I also like to take this opportunity to thank Professor Emeritus Sydney Yip of
MassachusettsInstituteofTechnologyforhisgenerousandrichclasslecturesthathe
providedmeafterparticipatinginsomeofhislectureclasseswhenhewasactively
teachingintheNuclearEngineeringDepartmentofMIT.
ix
Contents
1 NeutronPhysicsBackground. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Nuclei:Sizes,Composition,andBindingEnergies. . . . . . . . . . 1
1.2 DecayofaNucleus. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.3 DistributionofNuclidesandNuclearFission/Nuclear
Fusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.4 Neutron-NucleusInteraction. . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.4.1 NuclearReactionsRatesandNeutronCross
Sections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . 13
1.4.2 EffectsofTemperatureonCrossSection. . . . . . . . . . . 19
1.4.3 NuclearCross-SectionalProcessingCodes. . . . . . . . . . 19
1.4.4 EnergyDependenceofNeutronCrossSections. . . . . . 24
1.4.5 TypesofInteractions. . . . . . . . . . . . . . . . . . . . . . . . . 27
1.5 MeanFreePath. . .. . . . . . .. . . . . .. . . . . .. . . . . .. . . . . . .. 29
1.6 NuclearCrossSectionandNeutronFluxSummary. . . . . . . . . . 30
1.7 Fission. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
1.8 FissionSpectra. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
1.9 TheNuclearFuel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
1.9.1 FertileMaterial. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
1.10 LiquidDropModelofaNucleus. . . . . . . . . . . . . . . . . . . . . . . 46
1.11 SummaryofFissionProcess. . . . . . . . . . . . . . . . . . . . . . . . . . 47
1.12 ReactorPowerCalculation. . . .. . . . . . .. . . . . . . .. . . . . . . .. 48
1.13 RelationshipBetweenNeutronFluxandReactorPower. . . . . . . 49
Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
2 ModelingNeutronTransportandInteractions. . . . . . . . . . . . . . . . 53
2.1 TransportEquations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
2.2 ReactionRates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
2.3 ReactorPowerCalculation. . . .. . . . . . .. . . . . . . .. . . . . . . .. 54
2.4 RelationshipBetweenNeutronFluxandReactorPower. . . . . . . 55
xi