Nuclear Reactor Kinetics and Control (eBook)

Jeffery Lewins (Autor)

eBook Download: PDF | EPUB

2013 | 1. Auflage
278 Seiten
Elsevier Science (Verlag)
978-1-4832-7875-9 (ISBN)

Infos

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 "e;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.

Textauszug

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 problems at the end of this and subsequent chapters will help to consolidate the material and will also introduce new ideas for which there is no space in the main text. Thus the problems vary in difficulty and some are open-ended topics with no concise examination-room answer. For some, as in real life, not all the data necessary to answer the problem are available in the problem statement or even within the cover of this book.

Subsequent chapters are sufficiently well contained, it is hoped, to be read independently, but they follow a natural order perhaps in starting with the neutronics equations and the data appropriate to them for low power reactor behaviour. Chapter 3 provides a range of solutions for these low power cases before extending consideration in Chapter 4 to normal operational behaviour of the system at power, using the linear and frequency domain methods.

Up to this point, the emphasis is largely quantitative and analytical. Chapter 5, however, is largely qualitative in describing the major reactor systems now in commercial use. Chapters 6 and 7 turn to a range of matters whose connecting theme is that of randomness where probability considerations are paramount whether this is a study of the correlation in stochastic processes within the reactor itself or of the safety and reliability of the control system. In Chapter 8 we return to analytical methods for the study of safety and startup problems in a nonlinear description of reactor behaviour in the time dependent state space.

In Chapter 9 analogue computing is introduced since for the nuclear engineering student we envisage using this text it is a natural place to acquaint him with this method of solving a range of equations, a technique that enables us to illustrate the method with a number of important cases in nuclear engineering. That digital computers are not given the same prominence is quite the opposite of decrying their importance to reactor kinetics and control; on the contrary, there is not enough space in such a text to give full coverage to the role of digital computers for both numerical analysis and data handling in reactor control, and we are relieved by the thought that this must of itself form a major part of any current engineering training. Implications for direct digital control (DDC) are touched upon in Chapter 6.

Very largely, this text covers “lumped” kinetics behaviour and not space dependent behaviour. It might even be sufficient reason to say that a full space and energy dependent treatment is too difficult or too long for such a text, but there are two more rationalisations that can be advanced to justify the limitation further. The first is that one has to start somewhere and it is logical to start by a treatment that takes the reactor “as a whole” whether this is a pedagogic viewpoint or whether this is a starting point for more elaborate treatments to extend the spatial treatment in some consistent fashion without jumping immediately into partial integro-differential equations in seven-dimensional Boltzmann space and all the rest of it. Secondly, whatever elaborate models are found necessary in particular cases, the techniques will require testing; one battery of tests requires elaborate codes to reduce to known solutions in special cases. The kinetics and control engineer must at least pass through the stage of developing his “feel” for the discipline from specialised, albeit idealised, cases that he can manipulate analytically. That there should be such an intermediate stage is perhaps well demonstrated by comparing the excellent introductory book by Tyror and Vaughan(8) with the review of dynamic safety codes for light water reactors (9). Knowles (13) may also be helpful as a short introduction to the place of a power station in a utility grid system, with special reference to nuclear power. Henry (14) and Weisman (15) provide excellent texts on reactor theory and design methods.

Laplace and Fourier Transforms

Much of the analysis of reactor kinetics and control can be done in the form of systems of ordinary differential equations, i.e. equations and their boundary conditions, for dependent variables x1, x2, etc., dependent on the independent variable time t. By suitably defining , etc., these can always be written as sets of first order equations, n such equations implying an nth order system since elimination in the other direction would produce a single nth order equation. Thus

(1.1)

There is an implication in this notation that the system is linear, but in general the coefficients aii′ might be functions of the xi′. In the simplest case the...

Produkt-Details

• Erscheint lt. Verlag: 22.10.2013
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Physik / Astronomie
• Themenwelt: Technik ► Maschinenbau
• ISBN-10: 1-4832-7875-1 / 1483278751
• ISBN-13: 978-1-4832-7875-9 / 9781483278759