Modelling of Nuclear Reactor Multi-physics

Modelling of Nuclear Reactor Multi-physics

From Local Balance Equations to Macroscopic Models in Neutronics and Thermal-Hydraulics

1st Edition - November 18, 2019

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  • Author: Christophe Demazière
  • Paperback ISBN: 9780128150696
  • eBook ISBN: 9780128150702

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Modelling of Nuclear Reactor Multiphysics: From Local Balance Equations to Macroscopic Models in Neutronics and Thermal-Hydraulics is an accessible guide to the advanced methods used to model nuclear reactor systems. The book addresses the frontier discipline of neutronic/thermal-hydraulic modelling of nuclear reactor cores, presenting the main techniques in a generic manner and for practical reactor calculations.The modelling of nuclear reactor systems is one of the most challenging tasks in complex system modelling, due to the many different scales and intertwined physical phenomena involved. The nuclear industry as well as the research institutes and universities heavily rely on the use of complex numerical codes. All the commercial codes are based on using different numerical tools for resolving the various physical fields, and to some extent the different scales, whereas the latest research platforms attempt to adopt a more integrated approach in resolving multiple scales and fields of physics. The book presents the main algorithms used in such codes for neutronic and thermal-hydraulic modelling, providing the details of the underlying methods, together with their assumptions and limitations. Because of the rapidly expanding use of coupled calculations for performing safety analyses, the analysists should be equally knowledgeable in all fields (i.e. neutron transport, fluid dynamics, heat transfer).The first chapter introduces the book’s subject matter and explains how to use its digital resources and interactive features. The following chapter derives the governing equations for neutron transport, fluid transport, and heat transfer, so that readers not familiar with any of these fields can comprehend the book without difficulty. The book thereafter examines the peculiarities of nuclear reactor systems and provides an overview of the relevant modelling strategies. Computational methods for neutron transport, first at the cell and assembly levels, then at the core level, and for one-/two-phase flow transport and heat transfer are treated in depth in respective chapters. The coupling between neutron transport solvers and thermal-hydraulic solvers for coarse mesh macroscopic models is given particular attention in a dedicated chapter. The final chapter summarizes the main techniques presented in the book and their interrelation, then explores beyond state-of-the-art modelling techniques relying on more integrated approaches.

Key Features

  • Covers neutron transport, fluid dynamics, and heat transfer, and their interdependence, in one reference
  • Analyses the emerging area of multi-physics and multi-scale reactor modelling
  • Contains 71 short videos explaining the key concepts and 77 interactive quizzes allowing the readers to test their understanding


M.Sc. or Ph.D. students in nuclear engineering, complex system modelling or computational physics. Engineers and scientists from the nuclear industry who use simulation tools for modelling core-follow and reactor transients

Table of Contents

  • List of Abbreviations 
    1. Introduction 
        1.1 Topics covered in the book 
        1.2 Structure of the book 
             1.2.a Contents 
             1.2.b Pedagogical approach 
        1.3 Notations and conventions used in the book 
        1.4 Reminder about some useful mathematical concepts 
             1.4.a Calculus on scalars, vectors and tensors 
             1.4.b Spherical coordinates and solid angles 
             1.4.c Gauss divergence theorems 
    2. Transport phenomena in nuclear reactors 
        2.1 Nuclear reactors as multi-physics and multi-scale systems 
              2.1.a Multi-physics  aspects 
              2.1.b Multi-scale aspects 
        2.2 Neutron transport 
              2.2.a Introduction 
              2.2.b Derivation of the neutron transport equation 
        2.3 Fluid dynamics 
              2.3.a Mathematical  formalism 
              2.3.b Generic differential conservation laws 
              2.3.c Mass and momentum differential conservation equations 
       2.4 Heat transfer
             2.4.a Heat transfer by conduction 
             2.4.b Heat transfer by convection 
       2.5 Overview of the modelling strategies 
       2.6 Deterministic and macroscopic modelling of nuclear systems 
             2.6.a Equations governing the neutron flux 
             2.6.b Equations governing the temperature and flow fields 
             2.6.c Coupling between the neutron kinetic and thermal- hydraulic modellings 
       2.7 Conclusions
    3. Neutron transport calculations at the cell and assembly levels 
        3.1 Representation of the energy dependence 
              3.1.a Multi-group formalism 
              3.1.b Nuclear data libraries 
        3.2 Treatment of resonances 
              3.2.a Introduction 
              3.2.b Neutron slowing-down without absorption 
              3.2.c Neutron slowing-down with absorption 
        3.3 Resolving the energy dependence 
        3.4 One-dimensional micro-group pin cell calculations 
              3.4.a Introduction 
              3.4.b Transport correction 
              3.4.c Method of collision probabilities 
              3.4.d Properties of the probabilities 
              3.4.e Application of the method of collision probabilities 
              3.4.f Rational approximation 
       3.5 Two-dimensional macro-group lattice calculations 
             3.5.a Introduction
             3.5.b Method of characteristics
             3.5.c Discrete ordinates (SN) method
             3.5.d Interface current method
             3.5.e Acceleration  methods
       3.6 Criticality spectrum calculations 
             3.6.a Introduction 
             3.6.b Properties of integral operators in infinite and homogeneous  media 
             3.6.c Integral operators in critical systems 
             3.6.d Homogeneous B1 method 
             3.6.e Homogeneous P1 method 
             3.6.f Fundamental mode method 
       3.7 Cross-section homogenization and condensation 
       3.8 Depletion calculations 
       3.9 Cross-section preparation for core calculations 
       3.10 Conclusions 
    4. Neutron transport calculations at the core level 
        4.1 Angular discretization of the neutron transport equation 
              4.1.a Spherical harmonics (PN) method 
              4.1.b Diffusion theory 
              4.1.c Simplified PN  method (SPN) 
              4.1.d Boundary  conditions 
        4.2 Spatial discretization of the neutron transport equation 
              4.2.a Introduction 
              4.2.b Finite difference methods 
              4.2.c Nodal methods 
              4.2.d Finite elements 
        4.3 Determination of the steady-state core-wise solution 
              4.3.a Introduction 
              4.3.b Direct methods 
              4.3.c Iterative methods 
        4.4 Determination of the non-steady-state core-wise solution 
              4.4.a Introduction 
              4.4.b Analysis of the balance equations with respect to the prompt neutrons 
              4.4.c Analysis of the balance equations with respect to the delayed neutrons 
              4.5 Conclusions 
    5. One-/two-phase flow transport and heat transfer 
        5.1 Tools required for flow transport modelling 
               5.1.a Introduction 
               5.1.b Two-phase flow regimes 
               5.1.c Mathematical  tools 
         5.2 Derivation of the space- and time-averaged conservation equations for flow transport
               5.2.a Introduction
               5.2.b Space-averaging of the local conservation equations
               5.2.c Time-averaging of the space-averaged conservation equations
               5.2.d Equations to be solved
         5.3 Flow models 
               5.3.a Two-fluid model
               5.3.b Mixture models with specified drift velocities
               5.3.c Homogeneous equilibrium model
         5.4 Spatial and temporal discretizations of the flow models 
         5.5 Modelling of heat conduction in solid structures 
         5.6 Conclusions 
    6. Neutronic/thermal-hydraulic coupling 
        6.1 Introduction 
        6.2 Modelling of the dependencies of the nuclear material data 
              6.2.a Introduction 
              6.2.b Data functionalization on base and partial values 
              6.2.c Tree-leaf representation 
              6.2.d Polynomial fitting 
         6.3 Spatial coupling 
               6.3.a Thermal-hydraulic to neutronic coupling 
               6.3.b Neutronic to thermal-hydraulic coupling 
               6.3.c Coupling coefficients
        6.4 Temporal coupling 
              6.4.a Introduction 
              6.4.b Operator Splitting approaches 
              6.4.c Integrated approaches 
        6.5 Conclusions 
    7. Conclusions 
        7.1 Summary 
        7.2 Outlook 


Product details

  • No. of pages: 368
  • Language: English
  • Copyright: © Academic Press 2019
  • Published: November 18, 2019
  • Imprint: Academic Press
  • Paperback ISBN: 9780128150696
  • eBook ISBN: 9780128150702

About the Author

Christophe Demazière

Christophe Demazière is a Full Professor at Chalmers University of Technology, Sweden, where he leads the DREAM (Deterministic REActor Modelling ) task force at the Department of Physics. DREAM is a multidisciplinary group with expertise in neutron transport, fluid dynamics, heat transfer, and numerical methods. The group tackles the modelling of nuclear reactors from an integrated viewpoint (taking the multi-physics and multi-scale aspects into account). He has more than 20 years of experience in nuclear reactor modelling, covering reactor statics, reactor dynamics, and neutron noise. He has been educating MSc students, PhD students and nuclear engineers in nuclear reactor modelling. He is a referee for various journals including Nuclear Science and Engineering, Nuclear Technology, Annals of Nuclear Energy, Progress in Nuclear Energy and Nuclear Engineering and Design. He is a member of the American Nuclear Society (ANS).

Affiliations and Expertise

Chalmers University of Technology, Sweden

Ratings and Reviews

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  • Rasmus A. Tue May 12 2020

    The reason I fell in love with computational physics

    I took Professor Demazière's courses in Physics and Modelling of Nuclear Reactors as a master student a few years back, when he taught using the lecture notes that preceded this book. From skimming the book, it looks like the presentation is broadly similar, although a bit more elaborated and polished in the book form. Back then I had no intention of becoming a computational physicist, but Prof. Demazière's crystal clear way of communicating the very complex subject matter of multi-scale and multi-physics modelling of nuclear reactors was incredibly inspirational, leading me to do a full year master thesis on reactor modelling in Prof. Demazière's group. If there had been any suitable PhD positions available at the time, I would have gladly stayed for a PhD project as well. As it happened, I ended up in battery modelling instead, but I don't think I would have pursued PhD studies if I hadn't fallen in love with physics modelling in Prof. Demazière's classes. I have never had a teacher before or since that can break down such a broad and deep field into a coherent whole in such an elegant manner. His presentation has enough detail and rigour to understand fully where the equations and approaches come from, while never getting bogged down in unnecessary details. He has a clear overarching framework that makes it easier for students to put the subject matter of each chapter into perspective, and his consistency of mathematical notation makes the context switching between neutron physics and thermal-hydraulics as facile as can reasonably be expected. This book dispenses with the artificial division between neutronics and thermal-hydraulics that has pervaded the field before. This book is a must-read for anyone looking to start a career in first principles physics and modelling of nuclear reactors, and I hope it inspires generations of reactor physicists to push the envelope of first principles-understanding and design of hte next generation of nuclear reactors.