Modelling of Nuclear Reactor Multi-physics

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 References 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 ConclusionsReferences 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 References 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 References 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 References 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 References 7. Conclusions 7.1 Summary 7.2 Outlook References Index