Nuclear Reactor Kinetics and Control

Jeffery Lewins

• Publisher: Pergamon
• Year: 2013
• Print ISBN: 9780080216829
• eBook ISBN: 9781483278759
• Topic: Technology & Engineering
• Subtopic: Mechanical Engineering
• Index: Technology & Engineering

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.

CHAPTER 1

Introductory Review

Publisher Summary

This chapter discusses that nuclear power reactors are an established part of an advanced industrial economy and are found in many parts of the world. They offer, on the one hand, a source of power, particularly, electrical power, whose raw materials in the form of uranium ores are cheap and have a correspondingly smaller impact on the environment than fossil fuels. By contrast, the release of nuclear energy is accompanied by intense and long-lasting radiation whose containment is of fundamental importance. Much of the analysis of reactor kinetics and control can be done in the form of systems of ordinary differential equations. The Laplace transform is a technique to replace the operation of integration with an operation of algebraic manipulation, rather like logarithms replace multiplication by a process of addition in the logarithmic transform space. The one-sided Laplace transform of a function of time is defined via an integral over all time, which has the effect of replacing time dependence with dependence on a new or transform variable.

Nuclear power reactors are an established part of an advanced industrial economy and are to be found in many parts of the world. They offer, on the one hand, a source of power, particularly electrical power, whose raw materials in the form of uranium ores are cheap and have a correspondingly smaller impact on the environment in their winning than fossil fuels. On the other hand, the release of nuclear energy is accompanied by intense and long-lasting radiation whose containment is of fundamental importance. Thus the control of nuclear reactors, the subject of this text, is a matter not only for the day-to-day operation of plant in an efficient manner but also for the study of possible fault conditions, the specification of control systems of adequate reliability and the analysis of experimental information that may have a direct or indirect bearing on these matters.

This book is written as a text therefore in that part of nuclear engineering that can be called reactor kinetics and control with a view to a reasonably broad coverage. It goes beyond an elementary introduction to the subject written in qualitative terms, but it is neither a specialist monograph on the analysis of some specific aspect nor will it substitute for professional experience and practice. Rather it attempts to prepare the student using this book to make good use of subsequent experience.

The remainder of this first chapter is devoted to a review of some but by no means all of the preparatory material utilised in the subsequent chapters. The well-prepared reader will have studied differential calculus through linear differential equations and no review is attempted here. He will also, we hope, have had a course in automatic control and will have taken (or at least be taking simultaneously) a course in reactor physics to understand the conventional diffusion theory description, in multi-group theory, of the distribution of neutrons and the specification of a self-sustaining or critical reactor. It is desirable, too, that he is prepared in heat transfer, enough to appreciate the basic engineering design of a reactor as a plant for turning fission energy into electrical energy, and is taking a practical course in instrumentation.

Readers coming to the book at different levels of preparation will make use of the review material in different ways. For the expert it will serve only to establish notation and nomenclature if this is needed at all. The reader who is seriously underprepared will find that the review material is necessarily condensed and to that extent indigestible; he is advised, however, to “ruminate” upon it before he rushes past the hors d’ouvres to the tastier menu in subsequent chapters lest it provokes indigestion if consumed too quickly. Our “average” reader we suppose to be taking a final year in a degree course in nuclear engineering and will be able to proceed steadily through all the chapters.

The elements to be reviewed here cover the treatment of systems of ordinary differential equations using Laplace and Fourier transforms and the subsequent analysis on the frequency space to determine stability and transient response, particularly under automatic control with feedback, using the methods of Nyquist, Bode and Evans. We also review the fundamentals of probability theory with a view to their employment in chapters 6 and 7. While everyone has had some exposure to the ideas of probability, there is still much to be desired in the understanding brought to this deep subject, and the review material is specifically directed to areas where mistakes may be prevalent.

Exercises and p...

Table of contents

• Cover image
• Title page
• Table of Contents
• Other Pergamon Titles of Interest
• Copyright
• Dedication
• ERRATA
• Preface
• Acknowledgements
• Chapter 1: Introductory Review
• Chapter 2: Neutron and Precursor Equations
• Chapter 3: Elementary Solutions of the Kinetics Equations at Low Power
• Chapter 4: Linear Reactor Process Dynamics with Feedback
• Chapter 5: Power Reactor Control Systems
• Chapter 6: Fluctuations and Reactor Noise
• Chapter 7: Safety and Reliability
• Chapter 8: Nonlinear Systems; Stability and Control
• Chapter 9: Analogue Computing
• Index
• Inside Back Cover