Resonance Self-Shielding Calculation Methods in Nuclear Reactors (Woodhead Publishing Series in Energy) PDF
Preview Resonance Self-Shielding Calculation Methods in Nuclear Reactors (Woodhead Publishing Series in Energy)
RESONANCE SELF-SHIELDING CALCULATION METHODS IN NUCLEAR REACTORS This page intentionally left blank Woodhead Publishing Series in Energy RESONANCE SELF-SHIELDING CALCULATION METHODS IN NUCLEAR REACTORS LIANGZHI CAO Professor, School of Nuclear Science and Technology, Xi’an Jiaotong University, Peoples Republic of China HONGCHUN WU Professor, School of Nuclear Science and Technology, Xi’an Jiaotong University, Peoples Republic of China QIAN ZHANG Distinguished Research Fellow, Department of Physics, Zhejiang University, Peoples Republic of China QINGMING HE Associate Professor, School of Nuclear Science and Technology, Xi’an Jiaotong University, Peoples Republic of China TIEJUN ZU Professor, School of Nuclear Science and Technology, Xi’an Jiaotong University, Peoples Republic of China WoodheadPublishingisanimprintofElsevier 50HampshireStreet,5thFloor, Cambridge,MA02139,UnitedStates TheBoulevard,Langford Lane,Kidlington,OX5 1GB,UnitedKingdom Copyright©2023ElsevierLtd.Allrightsreserved. Nopart ofthispublicationmay bereproduced ortransmittedinanyform orbyany means, electronicormechanical, including photocopying,recording,orany information storageandretrieval system,without permissioninwritingfrom the publisher.Details onhowtoseekpermission, furtherinformation aboutthe Publisher’spermissions policies andourarrangementswithorganizations suchasthe CopyrightClearanceCenterandtheCopyrightLicensingAgency,canbefoundatour website:www.elsevier.com/permissions. Thisbookandtheindividual contributionscontainedinitareprotected under copyrightbythePublisher (otherthanasmaybenotedherein). Notices Knowledgeandbestpracticeinthisfieldareconstantlychanging. Asnew research andexperiencebroadenourunderstanding, changesinresearch methods,professional practices,ormedical treatment maybecomenecessary. Practitionersandresearchersmustalwaysrelyontheir ownexperience andknowledge inevaluating andusingany information,methods,compounds,orexperiments describedherein. Inusingsuchinformation ormethods theyshouldbemindfulof theirown safetyandthesafetyofothers,includingpartiesforwhomthey havea professionalresponsibility. Tothefullestextentofthelaw,neither thePublishernortheauthors,contributors, or editors,assume anyliabilityforanyinjury and/ordamagetopersonsorproperty asa matterofproductsliability,negligence orotherwise,or fromanyuseor operationof anymethods,products, instructions,or ideascontainedinthematerialherein. ISBN:978-0-323-85872-4 Forinformation onallWoodhead Publishingpublications visitour website athttps://www.elsevier.com/books-and-journals Publisher:Charlotte Cockle Acquisitions Editor: CharlotteCockle EditorialProjectManager:Elaine D.MarieDesamero ProductionProjectManager:Prasanna Kalyanaraman CoverDesigner: Christian J.Bilbow TypesetbyTNQTechnologies Contents Foreword vii Preface ix 1 Introduction 1 1.1 Background 1 1.2 Someelementsforresonanceself-shielding calculation 3 1.3 Developmentofresonanceself-shieldingcalculation methods 5 1.4 Layoutofthisbook 12 References 13 2 Resonance cross-section processing 17 2.1 Evaluated nucleardatalibrary 17 2.2 Resonancereconstruction 20 2.3 Dopplerbroadening 30 2.4 Unresolvedresonancetreatment 35 2.5 Resonanceintegral table 40 2.6 Resonanceelastic scattering 42 2.7 Goldstein-Cohenfactor 59 References 61 3 Equivalence theory method 63 3.1 Approximatespectrumofhomogeneoussystems 63 3.2 Approximatespectrumofheterogeneoussystems 71 3.3 Theestablishment ofclassicalequivalence theory 75 3.4 Thecalculationoftheeffectivecross-section 85 3.5 Equivalence theoryoflattice systems 90 3.6 Discrepancy analysis 103 References 117 4 Subgroup method 121 4.1 Introduction 121 4.2 Methodologyofsubgroup method 122 4.3 Practicalapplication ofsubgroup method 145 4.4 Improvements ofsubgroup method 156 References 162 v vi Contents 5 Ultrafine group method 165 5.1 Introduction 165 5.2 Neutronslowing-down equation 166 5.3 Collisionprobability calculationandacceleration 171 5.4 Couplingwithmethodofcharacteristic (MOC) 178 References 192 6 Wavelet expansion method 195 6.1 Introduction 195 6.2 Theoreticalmethod 197 6.3 Numericalresults 210 6.4 Acouplingmethodofsubgroup andwaveletexpansion 220 6.5 Numericalresultsforthecouplingmethod 224 6.6 Conclusions 229 References 230 7 Resonance treatment in Monte Carlo method 233 7.1 Overview 233 7.2 TheMonteCarlomethod 234 7.3 OverviewoftheMonteCarlocodes 239 7.4 Temperaturetreatmentoftheresolvedresonance 246 7.5 Temperaturetreatmentoftheunresolvedresonance 254 7.6 Treatmentoftheresonanceelastic scatteringeffect 254 References 257 8 High-fidelity resonance self-shielding calculation 261 8.1 Overview 261 8.2 Continuous-energy quasi-one-dimensionalslowing-down based method 262 8.3 Pin-basedpointwiseenergyslowing-downmethod 267 8.4 Global-localself-shielding calculationscheme 275 References 327 9 Resonance treatment for double heterogeneity 331 9.1 Chordlengthsamplingforstochasticmedia 331 9.2 Theanalytical dancofffactorapproach 335 9.3 Thedisadvantage factorapproach 340 9.4 TheSanchez-Pomraningapproach 356 References 388 Index 391 Foreword Piero Ravetto Politecnico di Torino, Torino, Italy The study of resonance effects is one of the classic topics in reactor physics since the early stages of the history of nuclear energy. Resonance absorption plays an important role in establishing the equilibrium and sta- bility of the neutron field and, therefore, it constitutes a central point for the design and assessment of multiplying systems in both steady-state and transient conditions. The evaluation of resonance self-shielding is a key pointinthegenerationofnuclearparametersforreactorsimulationsstarting from basic nuclear data. The most referenced classical monographies on the subject are already more than 40years old. The authors of this book have carried out a praiseworthyjobtocollectinasinglepieceofliteraturetheenormouswork that has been carried out over several decades on resonance self-shielding evaluations, all the way to the most recent advancements. It is particu- larlyusefulforareaderinterestedinthistopictohavethepossibilitytogain a broad general view on what has been done in the past and to perceive how the developments have taken place over the years going through the successive nine chapters of this book. While the classic approaches are properly reviewed and well-illustrated, the most recent developments, consistent with the enormous advances in computing power and capabil- itiesexperiencedinthelatesttimes,arealtogetherpresentedinanextensive way. The recent developments of nuclear reactors and the design of new advanced systems are posing new challenges to the generation of nuclear parameters. The authors are particularly careful to deepen the various as- pects of resonance self-shielding for multiplying systems featuring different neutron spectra and geometrical characteristics providing a useful physical insight into the methodologies. The book includes the relevant contributions in the development of dedicated numerical methods for resonance self-shielding evaluations given by the researchers of Xi’an Jaotong University. Of particular interest is the presentation of the innovative wavelet method, of the treatment of vii viii Foreword resonance effects within the stochastic Monte Carlo approach, of the techniques for high-fidelity simulations and of double heterogeneity problems. Inthisbookthereadercanalsofindausefulpresentationandasynthetic description of the most popular and widely used codes for neutronic sim- ulations throughout the world. Many illuminating paradigmatic numerical examples in various chapters allow the reader to well appreciate the quality of the performance of the methodologies presented. The bibliographies supplementing each chapter are really impressive for accuracy and completeness, always including many classic references together with the great deal of papers published in journals and in the proceedings of the numerousspecialists’conferencesandmeetingsheldaroundtheworld.The style of the presentation is concise and refreshing and it makes the reading easy and relaxing. The classic material is always presented in a clear and didactic fashion. For the characteristics of presenting both the standard information as wellastherecentadvancements,thisbookshouldconstituteaninteresting, enjoyable,andinformativereadingforbothstudentsdealingwithadvanced topics in nuclear engineering education, and young scientists and engineers who are keen to deepen their knowledge of a crucial theme for the neutronic simulations of nuclear reactors such as resonance physics and its modern numerical simulation. However, I must say that thereading of this book has been quite enjoyable and stimulating also for an old person like me. I am rather sure that the whole international reactor physics com- munity will welcome it and it will certainly be well appreciated for many years to come. Preface Driven by the increasing energy demand and carbon footprint worldwide, nuclear energy is playing a more significant role in the sustainable devel- opmentofmankind.Alotofinnovativenuclearreactorconceptualdesigns havebeenproposedforvariousapplicationsinthepastdecades.Thosenew designs are always featured with complex geometry, multinuclide compositionandspecialneutronspectrum,whichpresentsmanychallenges to reactor physics computational methods, especially resonance self- shielding calculation. The history of research on the resonance self-shielding calculation dates back to 1940s when Wigner developed the equivalence theory and then Carlvik and Roman improved it with the rational approximation method. After that, various methods have been proposed to deal with different resonance problems in different applications. Those methods can be roughly classified into three categories: equivalence theory method, sub- group (multiband) method, and continuous-energy method. The literature on those methods distribute in different journal papers and book chapters. However, there were only two books focusing on this topic. One was authored by Lawrence Dresner (Resonance Absorption in Nuclear Reactors, 1960781483222) and the other by A.A. Lukyanov (Moderation and Ab- sorption of Resonance Neutrons, 1974). In recent years, the classical resonance self-shielding methods, including equivalence theory, subgroup, and ultrafine-group, have been extended with higher precision and efficiency. Much work has been done on new topics like high-fidelity resonance treatment, resonance interference effect, multigroup equivalence, and so forth.Therefore,wethinkitisgoodtimingtopublishabookthatincludes those recent progresses in resonance self-shielding computational methods. Since 2004, the Nuclear Engineering Computational Physics (NECP) lab at Xi’an Jiaotong University started to work on various numerical methods for resonance self-shielding. Some traditional methods (equiva- lencetheorymethod,subgroupmethod,etc.)wererevisitedandimproved. Some advanced methods were programmed and implemented to reactor physics codes. Some new methods were proposed and evaluated. Based on those works, more than ten PhD and master students graduated from the lab. Each of them made their own contribution to progresses of the reso- nance self-shielding calculation. The primary motivation of this book is to ix
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