Mathematical Methods In Nuclear Reactor Dynamics

Author : Ziya Akcasuh
Publisher : Elsevier
Page : 473 pages
File Size : 41,5 Mb
Release : 2012-12-02
Category : Science
ISBN : 9780323149082

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Mathematical methods in Nuclear reactor Dynamics by Ziya Akcasuh Pdf

Mathematical Methods in Nuclear Reactor Dynamics covers the practical and theoretical aspects of point-reactor kinetics and linear and nonlinear reactor dynamics. The book, which is a result of the lectures given at the University of Michigan, is composed of seven chapters. The opening chapter of the book describes various physical phenomena influencing the temporal behavior of neutrons to provide insights into the physics of reactor dynamics and the interrelationships between various diverse phenomena. The text then presents a set of equations, called point kinetic equation, which describes the time behavior of the total power generated in the medium. The book also provides a short discussion on Gyftopoulos modification and Becker’s formulation. The next chapters explore the exact methods for solving the feedback-free point kinetic equations for a number of reactivity insertions and the validity of the various approximate methods of solution. The book also examines the derivation of models for a certain reactor type and briefly discusses the validity of these models in certain cases against experimental data. A chapter focuses on a concise presentation of the stability theory of linear systems with feedback. Lastly, the concepts of stability in nonlinear reactor systems and the criteria for asymptotic stability in the large as well as in a finite domain of initial disturbances are covered in the concluding chapter. The text is an ideal source for nuclear engineers and for those who have adequate background in reactor physics and operational and applied mathematics.

Author : Santanu Saha Ray
Publisher : CRC Press
Page : 235 pages
File Size : 51,6 Mb
Release : 2015-07-29
Category : Mathematics
ISBN : 9781498727280

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Fractional Calculus with Applications for Nuclear Reactor Dynamics by Santanu Saha Ray Pdf

Introduces Novel Applications for Solving Neutron Transport Equations While 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 ways. Since fractional calculus represents a reactor more closely than classical integer order calculus, Fractional Calculus with Applications for Nuclear Reactor Dynamics focuses on the application of fractional calculus to describe the physical behavior of nuclear reactors. It applies fractional calculus to incorporate the mathematical methods used to analyze the diffusion theory model of neutron transport and explains the role of neutron transport in reactor theory. The author discusses fractional calculus and the numerical solution for fractional neutron point kinetic equation (FNPKE), introduces the technique for efficient and accurate numerical computation for FNPKE with different values of reactivity, and analyzes the fractional neutron point kinetic (FNPK) model for the dynamic behavior of neutron motion. The book begins with an overview of nuclear reactors, explains how nuclear energy is extracted from reactors, and explores the behavior of neutron density using reactivity functions. It also demonstrates the applicability of the Haar wavelet method and introduces the neutron diffusion concept to aid readers in understanding the complex behavior of average neutron motion. This text: Applies the effective analytical and numerical methods to obtain the solution for the NDE Determines the numerical solution for one-group delayed neutron FNPKE by the explicit finite difference method Provides the numerical solution for classical as well as fractional neutron point kinetic equations Proposes the Haar wavelet operational method (HWOM) to obtain the numerical approximate solution of the neutron point kinetic equation, and more Fractional Calculus with Applications for Nuclear Reactor Dynamics thoroughly and systematically presents the concepts of fractional calculus and emphasizes the relevance of its application to the nuclear reactor.

Author : Weston M. Jr. Stacey
Publisher : Elsevier
Page : 192 pages
File Size : 49,9 Mb
Release : 2012-12-02
Category : Technology & Engineering
ISBN : 9780323160438

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Variational Methods in Nuclear Reactor Physics by Weston M. Jr. Stacey Pdf

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.

Author : Gilberto Espinosa Paredes
Publisher : Woodhead Publishing
Page : 404 pages
File Size : 45,7 Mb
Release : 2020-10-22
Category : Technology & Engineering
ISBN : 9780128236666

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Fractional-Order Models for Nuclear Reactor Analysis by Gilberto Espinosa Paredes Pdf

Fractional-Order Models for Nuclear Reactor Analysis presents fractional modeling issues in the context of anomalous diffusion processes in an accessible and practical way. The book emphasizes the importance of non-Fickian diffusion in heterogeneous systems as the core of the nuclear reactor, as well as different variations of diffusion processes in nuclear reactors which are presented to establish the importance of nuclear and thermohydraulic phenomena and the physical side effects of feedback. In addition, the book analyzes core issues in fractional modeling in nuclear reactors surrounding phenomenological description and important analytical sub-diffusive processes in the transport neutron. Users will find the most innovative modeling techniques of nuclear reactors using operator differentials of fractional order and applications in nuclear design and reactor dynamics. Proposed methods are tested with Boltzmann equations and non-linear order models alongside real data from nuclear power plants, making this a valuable resource for nuclear professionals, researchers and graduate students, as well as those working in nuclear research centers with expertise in mathematical modeling, physics and control. Presents and analyzes a new paradigm of nuclear reactor phenomena with fractional modeling Considers principles of fractional calculation, methods of solving differential equations of fractional order, and their applications Includes methodologies of linear and nonlinear analysis, along with design and dynamic analyses

Author : Karl Otto Ott,Robert J. Neuhold
Publisher : Unknown
Page : 384 pages
File Size : 55,5 Mb
Release : 1985
Category : Technology & Engineering
ISBN : UCAL:B5012570

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Introductory Nuclear Reactor Dynamics by Karl Otto Ott,Robert J. Neuhold Pdf

This text presents the theory and methods of prediction that are the heart of nuclear reactor safety. Time-dependent reactor behavior is explained in both mathematical and physical terms. This book also explains the logic behind the working formulas and calculational methods for reactor transients and illustrates typical dynamic responses. The classical concept of point kinetics is developed in three steps, with discussion of various solutions to kinetics problems. Each chapter includes homework problems and review questions.

Author : G.S. Christensen,S.A. Soliman,R. Nieva
Publisher : Springer
Page : 236 pages
File Size : 54,6 Mb
Release : 2013-09-27
Category : Mathematics
ISBN : 1489936041

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Optimal Control of Distributed Nuclear Reactors by G.S. Christensen,S.A. Soliman,R. Nieva Pdf

This book is devoted to the mathematical optimization theory and modeling techniques that recently have been applied to the problem of controlling the shape and intensity of the power density distribution in the core of large nuclear reactors. The book has been prepared with the following purposes in mind: 1. To provide, in a condensed manner, the background preparation on reactor kinetics required for a comprehensive description of the main problems encountered in designing spatial control systems for nuclear reactor cores. 2. To present the work that has already been done on this subject and provide the basic mathematical tools required for a full understand ing of the different methods proposed in the literature. 3. To stimulate further work in this challenging area by weighting the advantages and disadvantages of the existing techniques and evaluating their effectiveness and applicability. In addition to coverage of the standard topics on the subject of optimal control for distributed parametersystems, the book includes, at amathemati cal level suitable for graduate students in engineering, discussions of con ceptsoffunctional analysis, the representation theory ofgroups, and integral equations. Although these topics constitute a requisite for a full understanding of the new developments in the area of reactor modeling and control, they are seidom treated together in a single book and, when they are, their presenta tion isoften directed to the mathematician.They are thus relatively unknown to the engineering community.

Author : Thomas W. Kerlin,Belle R. Upadhyaya
Publisher : Academic Press
Page : 402 pages
File Size : 41,5 Mb
Release : 2019-10-05
Category : Business & Economics
ISBN : 9780128152621

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Dynamics and Control of Nuclear Reactors by Thomas W. Kerlin,Belle R. Upadhyaya Pdf

Dynamics and Control of Nuclear Reactors presents the latest knowledge and research in reactor dynamics, control and instrumentation; important factors in ensuring the safe and economic operation of nuclear power plants. This book provides current and future engineers with a single resource containing all relevant information, including detailed treatments on the modeling, simulation, operational features and dynamic characteristics of pressurized light-water reactors, boiling light-water reactors, pressurized heavy-water reactors and molten-salt reactors. It also provides pertinent, but less detailed information on small modular reactors, sodium fast reactors, and gas-cooled reactors. Provides case studies and examples to demonstrate learning through problem solving, including an analysis of accidents at Three Mile Island, Chernobyl and Fukushima Daiichi Includes MATLAB codes to enable the reader to apply the knowledge gained to their own projects and research Features examples and problems that illustrate the principles of dynamic analysis as well as the mathematical tools necessary to understand and apply the analysis Publishers Note: Table 3.1 has been revised and will be included in future printings of the book with the following data: Group Decay Constant, li (sec-1) Delayed Neutron Fraction (bi) 1 0.0124 0.000221 2 0.0305 0.001467 3 0.111 0.001313 4 0.301 0.002647 5 1.14 0.000771 6 3.01 0.000281 Total delayed neutron fraction: 0.0067

Author : S R Shimjith,A P Tiwari,B Bandyopadhyay
Publisher : Springer
Page : 154 pages
File Size : 41,5 Mb
Release : 2012-08-10
Category : Technology & Engineering
ISBN : 9783642305894

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Modeling and Control of a Large Nuclear Reactor by S R Shimjith,A P Tiwari,B Bandyopadhyay Pdf

Control analysis and design of large nuclear reactors requires a suitable mathematical model representing the steady state and dynamic behavior of the reactor with reasonable accuracy. This task is, however, quite challenging because of several complex dynamic phenomena existing in a reactor. Quite often, the models developed would be of prohibitively large order, non-linear and of complex structure not readily amenable for control studies. Moreover, the existence of simultaneously occurring dynamic variations at different speeds makes the mathematical model susceptible to numerical ill-conditioning, inhibiting direct application of standard control techniques. This monograph introduces a technique for mathematical modeling of large nuclear reactors in the framework of multi-point kinetics, to obtain a comparatively smaller order model in standard state space form thus overcoming these difficulties. It further brings in innovative methods for controller design for systems exhibiting multi-time-scale property, with emphasis on three-time-scale systems.

Author : Henry Hurwitz
Publisher : Unknown
Page : 12 pages
File Size : 40,6 Mb
Release : 1950
Category : Nuclear reactors
ISBN : UOM:39015086415158

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Mathematical Methods in Pile Calculations by Henry Hurwitz Pdf

Author : British Nuclear Energy Society
Publisher : Thomas Telford
Page : 214 pages
File Size : 50,6 Mb
Release : 1992
Category : Technology & Engineering
ISBN : 0727716611

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Dynamics and Control in Nuclear Power Stations by British Nuclear Energy Society Pdf

This volume covers a wider view of the aspects of control of nuclear power stations by taking into consideration the plant as a whole and the protection systems employed therein. Authors with world-wide experience consider all the aspects of dynamics and control in the context of both fast and thermal power stations. The topics discussed include both the methods of development and applications within - analysis of plant behaviour, validation of mathematical models, plant testing, design and implementation of controls.

Author : Melville Clark,Kent F. Hansen
Publisher : Unknown
Page : 358 pages
File Size : 43,8 Mb
Release : 1964
Category : Technology & Engineering
ISBN : UOM:39015004451087

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Numerical Methods of Reactor Analysis by Melville Clark,Kent F. Hansen Pdf

Author : Weston M. Stacey
Publisher : John Wiley & Sons
Page : 735 pages
File Size : 54,5 Mb
Release : 2007-06-27
Category : Science
ISBN : 9783527611058

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Nuclear Reactor Physics by Weston M. Stacey Pdf

Nuclear reactor physics is the core discipline of nuclear engineering. Nuclear reactors now account for a significant portion of the electrical power generated worldwide, and new power reactors with improved fuel cycles are being developed. At the same time, the past few decades have seen an ever-increasing number of industrial, medical, military, and research applications for nuclear reactors. The second edition of this successful comprehensive textbook and reference on basic and advanced nuclear reactor physics has been completely updated, revised and enlarged to include the latest developments.

Author : A Gandini,J J Schmidt,S Ganesan
Publisher : World Scientific
Page : 1126 pages
File Size : 50,5 Mb
Release : 1995-10-24
Category : Electronic
ISBN : 9789814548649

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Nuclear Reactors-physics, Design And Safety - Proceedings Of The Workshop by A Gandini,J J Schmidt,S Ganesan Pdf

The lectures reported in these proceedings were given in the Workshop on Nuclear Reactors — Physics, Design and Safety held at the International Centre for Theoretical Physics in Trieste in 1994 by experts from leading international research institutions and industries. They have been organized in a self-consistent form with the objective of giving basic, up-dated information to scientists and engineers from developing countries in modern methods for the computation and analysis of nuclear reactors, with particular emphasis on reactor physics, design and safety.

Author : Serge Marguet
Publisher : Springer
Page : 1445 pages
File Size : 41,6 Mb
Release : 2018-02-26
Category : Science
ISBN : 9783319595603

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The Physics of Nuclear Reactors by Serge Marguet Pdf

This comprehensive volume offers readers a progressive and highly detailed introduction to the complex behavior of neutrons in general, and in the context of nuclear power generation. A compendium and handbook for nuclear engineers, a source of teaching material for academic lecturers as well as a graduate text for advanced students and other non-experts wishing to enter this field, it is based on the author’s teaching and research experience and his recognized expertise in nuclear safety. After recapping a number of points in nuclear physics, placing the theoretical notions in their historical context, the book successively reveals the latest quantitative theories concerning: • The slowing-down of neutrons in matter • The charged particles and electromagnetic rays • The calculation scheme, especially the simplification hypothesis • The concept of criticality based on chain reactions • The theory of homogeneous and heterogeneous reactors • The problem of self-shielding • The theory of the nuclear reflector, a subject largely ignored in literature • The computational methods in transport and diffusion theories Complemented by more than 400 bibliographical references, some of which are commented and annotated, and augmented by an appendix on the history of reactor physics at EDF (Electricité De France), this book is the most comprehensive and up-to-date introduction to and reference resource in neutronics and reactor theory.

Author : Jeffery Lewins
Publisher : Elsevier
Page : 282 pages
File Size : 52,8 Mb
Release : 2013-10-22
Category : Technology & Engineering
ISBN : 9781483278759

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Nuclear Reactor Kinetics and Control by Jeffery Lewins Pdf

Nuclear Reactor Kinetics and Control highlights the application of classical control methods in the frequency space to the dynamic processes of a nuclear reactor. This book contains nine chapters and begins with an introduction to some important mathematical theories related to nuclear engineering, such as the Laplace and Fourier transforms, linear system stability, and the probability theory. The succeeding chapters deal with the frequency space of classical linear design. A chapter describes a stochastic model for the “lumped reactor and presents equations that measure the departure from the mean, as well as representative experiments or applications of the theory to neutron detection. The discussion then shifts to the aspects of reliability and its consequences for safety of nuclear reactors and some techniques for nonlinear studies centered on the use of the state space and its equations in the time domain. The final chapter introduces the modern electric analogue computer and derives the patching or programming rules that can be use to find solutions to problems of interest using the analogous behavior of electric circuits. This chapter also provide examples of intrinsic interest in nuclear engineering showing the programming involved and typical results, including the slower transients of xenon poisoning and fuel burn-up. This book is intended for nuclear engineers, physicists, applied mathematicians, and nuclear engineering undergraduate and postgraduate students.