Nuclear Science and Technology, Volume 3: Numerical Methods of Reactor Analysis presents the numerical analysis frequently used in the nuclear reactor field. This book discusses the numerical approximation for the multigroup diffusion method, which results in simple algebraic equations. Organized into six chapters, this volume starts with an overview of the simplified formulation of linear algebra by defining the matrices and operations with matrices. This text then discusses the properties of special matrices and reviews the elementary properties of finite difference equations. Other chapters consider a variety of methods of obtaining numerical solutions to the approximating equations. The final chapter deals with Monte Carlo method, which is a statistical method for solving statistical or deterministic problems. This book is a valuable resource for nuclear engineers. Students at the graduate level who had an introductory course in reactor physics and a basic course in differential equations will also find this book useful.
This book covers the entire spectrum of the science and technology of nuclear reactor systems, from underlying physics, to next generation system applications and beyond. Beginning with neutron physics background and modeling of transport and diffusion, this self-contained learning tool progresses step-by-step to discussions of reactor kinetics, dynamics, and stability that will be invaluable to anyone with a college-level mathematics background wishing to develop an understanding of nuclear power. From fuels and reactions to full systems and plants, the author provides a clear picture of how nuclear energy works, how it can be optimized for safety and efficiency, and why it is important to the future.
Introduces Novel Applications for Solving Neutron Transport EquationsWhile deemed nonessential in the past, fractional calculus is now gaining momentum in the science and engineering community. Various disciplines have discovered that realistic models of physical phenomenon can be achieved with fractional calculus and are using them in numerous way
An introductory text for broad areas of nuclear reactor physics Nuclear Reactor Physics and Engineering offers information on analysis, design, control, and operation of nuclear reactors. The author—a noted expert on the topic—explores the fundamentals and presents the mathematical formulations that are grounded in differential equations and linear algebra. The book puts the focus on the use of neutron diffusion theory for the development of techniques for lattice physics and global reactor system analysis. The author also includes recent developments in numerical algorithms, including the Krylov subspace method, and the MATLAB software, including the Simulink toolbox, for efficient studies of steady-state and transient reactor configurations. In addition, nuclear fuel cycle and associated economics analysis are presented, together with the application of modern control theory to reactor operation. This important book: Provides a comprehensive introduction to the fundamental concepts of nuclear reactor physics and engineering Contains information on nuclear reactor kinetics and reactor design analysis Presents illustrative examples to enhance understanding Offers self-contained derivation of fluid conservation equations Written for undergraduate and graduate students in nuclear engineering and practicing engineers, Nuclear Reactor Physics and Engineering covers the fundamental concepts and tools of nuclear reactor physics and analysis.
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. - 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
Nuclear Science and Technology, Volume 10: Variational Methods in Nuclear Reactor Physics presents the mathematical methods of a variational origin that are useful in obtaining approximate solutions to science and engineering problems. This book is composed of five chapters and begins with a discussion on the variation principles for physical systems described by both inhomogeneous and homogeneous equations to develop a generalized perturbation theory. Chapter 2 deals with the applications of variational estimates and generalized perturbation theory to neutron transport problems. Chapter 3 covers the variation principles of the Lagrangian form that are constructed for a general, linear- time-dependent process and for the specific case of the P1 neutron kinetics equations. Chapter 4 presents the general procedure for the variational derivation of synthesis approximations and their applications to problems in reactor physics. This chapter also examines the relationship of the spatial synthesis and finite-element method and a hybrid method that combines features of both methods. Chapter 5 describes the relationship of variation theory with the Hamilton-Jacobi theory and with the optimization theories of the maximum principle and dynamic programming. Nuclear physicists and researchers will find this text invaluable.
Classic textbook for an introductory course in nuclear reactor analysis that introduces the nuclear engineering student to the basic scientific principles of nuclear fission chain reactions and lays a foundation for the subsequent application of these principles to the nuclear design and analysis of reactor cores. This text introduces the student to the fundamental principles governing nuclear fission chain reactions in a manner that renders the transition to practical nuclear reactor design methods most natural. The authors stress throughout the very close interplay between the nuclear analysis of a reactor core and those nonnuclear aspects of core analysis, such as thermal-hydraulics or materials studies, which play a major role in determining a reactor design.
Physics of Nuclear Reactors presents a comprehensive analysis of nuclear reactor physics. Editors P. Mohanakrishnan, Om Pal Singh, and Kannan Umasankari and a team of expert contributors combine their knowledge to guide the reader through a toolkit of methods for solving transport equations, understanding the physics of reactor design principles, and developing reactor safety strategies. The inclusion of experimental and operational reactor physics makes this a unique reference for those working and researching nuclear power and the fuel cycle in existing power generation sites and experimental facilities. The book also includes radiation physics, shielding techniques and an analysis of shield design, neutron monitoring and core operations. Those involved in the development and operation of nuclear reactors and the fuel cycle will gain a thorough understanding of all elements of nuclear reactor physics, thus enabling them to apply the analysis and solution methods provided to their own work and research. This book looks to future reactors in development and analyzes their status and challenges before providing possible worked-through solutions. Cover image: Kaiga Atomic Power Station Units 1 - 4, Karnataka, India. In 2018, Unit 1 of the Kaiga Station surpassed the world record of continuous operation, at 962 days. Image courtesy of DAE, India. Includes methods for solving neutron transport problems, nuclear cross-section data and solutions of transport theory Dedicates a chapter to reactor safety that covers mitigation, probabilistic safety assessment and uncertainty analysis Covers experimental and operational physics with details on noise analysis and failed fuel detection
Manual of numerical methods in concrete aims to present a unified approach for the available mathematical models of concrete, linking them to finite element analysis and to computer programs in which special provisions are made for concrete plasticity, cracking and crushing with and without concrete aggregate interlocking. Creep, temperature, and shrinkage formulations are included and geared to various concrete constitutive models.
