Nuclear reactor analysis duderstadt pdf free download

Nuclear Reactor Analysis James J. Duderstadt Louis J. Author: James J. All rights reserved. Published simultaneously in Canada. N o part of this book may be reproduced by any means, nor transmitted, nor translated into a machine language without the written permission of the publisher. Includes bibliographical references and index. Nuclear reactors—Design and construction. Nuclear engineering. Nuclear fission. Hamilton, Louis J. D77 Ang University of Illinois Donald S.

William Lambe R. Steidel, Jr. White Cornell University Civil Engineering—Structures To Anne and Jacqueline vii Preface The maturation of the nuclear power industry, accompanied by a redirection in emphasis from research and development to the large-scale installation of nuclear power systems, has induced a corresponding change in the growing demand for well-trained nuclear engineers. Earlier laboratory needs for research-oriented Ph.

Most universities are rapidly reorienting their own nuclear engineering programs in response to these changes. Of central importance in such programs are those introductory courses in nuclear reactor analysis that first introduce the nuclear engineering student to the basis scientific principles of nuclear fission chain reactions and lay a foundation for the subsequent application of these principles to the nuclear design and analysis of reactor cores. Although several excellent texts have been written on the subject of nuclear reactor theory, we have found both the material and orientation of existing treatments somewhat outdated for today's nuclear engineering student.

For example, the availability of large fast digital computers has had a very strong influence on the analytical techniques used in modern nuclear reactor design. In most cases such modern methods of reactor analysis bear little resemblance to the precomputer techniques of earlier years. And yet most existing texts on nuclear reactor theory dwell quite heavily on these outdated techniques, stressing analytical methods to the near exclusion of numerical techniques and digital computation.

Furthermore most introductory texts on nuclear reactor theory present a rather narrow view of nuclear reactor analysis by concentrating only on the behavior of the neutron population in the reactor core. However the neutronics analysis of a reactor core cannot be divorced from other nonnuclear aspects of core analysis such as thermal-hydraulics, structural design, or economic considerations. In any ix XV practical design study, the interplay between these various facets of reactor analysis must be taken into account, and this should be reflected in modern nuclear engineering education programs.

We have attempted to write a reactor analysis text more tailored to the needs of the modern nuclear engineering student. In particular, we have tried to introduce 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.

This goal has led to a very considerable emphasis on numerical methods suitable for digital computation. We have also stressed throughout this development 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.

Finally, we have included illustrations of the various concepts that we develop by considering a number of more practical problems arising in the nuclear design of various types of power reactors. The text has been organized into four parts. In Part 1 we present a relatively elementary and qualitative discussion of the basic concepts involved in nuclear fission chain reactions, inducing a brief review of the relevant nuclear physics and a survey of modern power reactors.

In Part 2 we develop in some detail a particularly simple and useful model of nuclear reactor behavior by assuming that the neutrons sustaining the fission chain reaction diffuse from point to point in the reactor in such a way that their energy and direction ol motion can be ignored one-speed diffusion theory.

In Part 3 we generalize this model to develop the primary tool of nuclear reactor analysis, multigroup diffusion theory. In Part 4 we illustrate these methods of nuclear reactor analysis by considering several important applications in nuclear reactor design. We include a wide variety of problems to further illustrate these concepts, since we have learned by past experience that such problems are essential for and adequate understanding of nuclear reactor theory.

The degree of difficulty spanned by the problems is enormous, ranging from simple formula substitution to problems requiring extensive outside reading by the student. Since most universities have at their disposal large time-sharing computer systems, we have not hesitated to include problems that require rudimentary programming experience as well as access to digital computers.

Also, since more and more nuclear engineering programs have access to libraries of the more common reactor design computer codes, we also include problems utilizing such codes.

It is our hope that the volume and variety of problems are sufficient to provide the instructor with the opportunity to select those problems most appropriate to this particular needs. The same broad scope also characterizes the material included in the text.

We have attempted to prepare a text suitable for a wide variety of students, including not only senior-year B. Hence the text has been written with the intent of providing suitable material for a student with only a modest background in modern physics and applied mathematics, such as would be included in the curriculum of most undergraduate engineering or science students.

To this end, much of the early material is presented in an essentially self-contained fashion. In such cases we provide numerous references to supplement our treatment. Certainly the entirety of the material presented would be overwhelming for a one- or even two-term course. We have distributed the material among three terms at Michigan. Rather we have sought to provide a text sufficiently flexible for a wide variety of applications. Hence we do not apologize for the scope and occasionally more rugged terrain covered by the text, since the instructor can always choose a less demanding route by selecting an appropriate subset of this material.

The units employed in this text are the International System of Units SI , their derivatives, and several non-SI units such as the electronvolt or the barn which are recognized by the International Organization for Standardization for use in special fields. Unfortunately, the vast majority of nuclear engineering literature published in the United States prior to makes use of British units. To assist the reader in coordinating this literature with the SI units used in this text, we have included brief tables of the appropriate conversion factors in Appendix I.

As with any text at this level, very little of the material presented has originated with the authors, but rather has been accumulated and assimilated from an enormous variety of sources, some published, many unpublished.

We generally attempt to present material in the fashion we have found most successful from our own teaching experience, frequently sacrificing originality for effectiveness of presentation. Throughout the text we attempt to acknowledge the sources of our material. However, we would particularly like to acknowledge the impact made upon this work by several of our associates.

In presentation, we have chosen to utilize the very appealing pedagogical approach of P. Zweifel by introducing as much of reactor analysis as possible within the one-speed diffusion approximation before continuing to discuss neutron energy-dependence.

Our attempts to relate the basic concepts of nuclear reactor theory to practical reactor analysis have relied heavily upon numerous discussions, lecture materials, admonitions, and advice of Harvey Graves, Jr.

Price, Jr. Turinsky, as well as scores of other students who have suffered, sweated, and occasionally cursed their way through the many sets of lecture notes which led to this text. It is particularly important to acknowledge the considerable assistance provided by other staff members at Michigan including A. Osborn, Fred Shure, and George C. Also we should acknowledge that much of the motivation and inspiration for this effort originated at Caltech with Harold Lurie and Noel Corngold and at Berkeley with Virgil Schrock.

But, above all, we would like to thank William Kerr, without whose continued encouragement and support this work would have never been completed. We also wish to express our gratitude to Miss Pam Hale for her Herculean xii efforts and cryptographic abilities in helping prepare the various drafts and manuscripts which led to this text. James J. Louis J. VI II. Some Useful Nuclear Data I.

Some Useful Mathematical Formulas C. Introduction II. Properties of the Dirac S-Function A. Alternative Representations B. Properties C. Derivatives D. Some Properties of Special Functions E. Scalar Products II. Some Definitions II. Matrix Algebra G. An Introduction to Laplace Transforms I. Since that time an extensive worldwide effort has been directed toward nuclear reactor research and development in an attempt to harness the enormous energy contained within the atomic nucleus for the peaceful generation of power.

Nuclear reactors have evolved from an embryonic research tool into the mammoth electrical generating units that drive hundreds of central-station power plants around the world today.

The recent shortage of fossil fuels has made it quite apparent that nuclear fission reactors will play a dominant role in meeting man's energy requirements for decades to come. For some time electrical utilities have been ordering and installing nuclear plants in preference to fossil-fueled units.

Such plants are truly enormous in size, typically generating over MWe megawatts-electric of electrical power enough to supply the electrical power needs of a city of , people and costing more than half a billion dollars. The motivation for such a staggering commitment to nuclear power involves a number of factors that include not only the very significant economic and operational advantages exhibited by nuclear plants over conventional sources of power, but their substantially lower environmental impact and vastly larger fuel resources as well.

Until at least A. However the massive practical implementation of such alternatives, if proven feasible, could probably not occur until after the turn of the century since experience has shown that it takes several decades to shift the energy industry from one type of fuel to another, 2 due both to the long operating lifetime of existing power machinery and the long lead times needed to redirect manufacturing capability. Hence nuclear fission power will probably be the dominant new source of electrical power during the productive lifetimes of the present generation of engineering students.

This restricted definition may offend that segment of the nuclear community involved in nuclear fusion research, but since even a prototype nuclear fusion reactor seems several years down the road, no confusion should result. In such a device, neutrons are used to induce nuclear fission reactions in heavy nuclei.

These nuclei fission into lighter nuclei fission products , accompanied by the release of energy some MeV per event plus several additional neutrons. These fission neutrons can then be utilized to induce still further fission reactions, thereby inducing a chain of fission events. In a very narrow sense then, a nuclear reactor is simply a sufficiently large mass of appropriately fissile material e. Indeed a small sphere of U metal slightly over 8 cm in radius could support such a chain reaction and hence would be classified as a nuclear reactor.

However a modern power reactor is a considerably more complex beast. It must not only contain a lattice of very carefully refined and fabricated nuclear fuel, but must as well provide for cooling this fuel during the course of the chain reaction as fission energy is released, while maintaining the fuel in a very precise geometrical arrangement with appropriate structural materials. Furthermore some mechanism must be provided to control the chain reaction, shield the surroundings of the reactor from the intense nuclear radiation generated during the fission reactions, and provide for replacing nuclear fuel assemblies when the fission chain reaction has depleted their concentration of fissile nuclei.

If the reactor is to produce power in a useful fashion, it must also be designed to operate both economically and safely. Such engineering constraints render the actual nuclear configuration quite complex indeed as a quick glance ahead to the illustrations in Chapter 3 will indicate.

Nuclear reactors have been used for over 30 years in a variety of applications. They are particularly valuable tools for nuclear research since they produce copious amounts of nuclear radiation, primarily in the form of neutrons and gamma rays. Such radiation can be used to probe the microscopic structure and dynamics of matter neutron or gamma spectroscopy. Reactors can use the same scheme to produce nuclear fuel from nonfissile materials. For example, U can be irradiated by neutrons in a reactor and transmuted into the nuclear fuel Pu.

This is the process utilized to "breed" fuel in the fast breeder reactors currently being developed for commercial application in the next decade. Small, compact reactors have been used for propulsion in submarines, ships, aircraft, and rocket vehicles. Indeed the present generation of light water reactors used in nuclear power plants are little more than the very big younger brothers of the propulsion reactors used in nuclear submarines.

Reactors can also be utilized as small, compact sources of long-term power, such as in remote polar research stations or in orbiting satellites. Yet by far the most significant application of nuclear fission reactors is in large, central station power plants. A nuclear power plant is actually very similar to a fossil-fueled power plant, except that it replaces the coal or oil-fired boiler by a nuclear reactor, which generates heat by sustaining a fission chain reaction in a suitable lattice of fuel material.

Of course, there are some dramatic differences between a nuclear reactor and, say, a coal-fired boiler. However the useful quantity produced by each is high temperature, high pressure steam that can then be used to run turbogenerators and produce electricity. At the center of a modern nuclear plant is the nuclear steam supply system NSSS , composed of the nuclear reactor, its associated coolant piping and pumps, and the heat exchangers "steam generators" in which water is turned into steam.

A further glance at the illustrations in Chapter 3 will provide the reader with some idea of these components. The remainder of the power plant is rather conventional. Yet we must not let the apparent similarities between nuclear and fossil-fueled power plants overshadow the very significant differences between the two systems.

For example, in a nuclear plant sufficient fuel must be inserted into the reactor core to allow operation for very long periods of time typically one year. The nuclear fuel cycle itself is extremely complex, involving fuel refining, fabrication, reprocessing after utilization in the reactor, and eventually the disposal of radioactive fuel wastes.

The safety aspects of nuclear plants are also quite different, since one must be concerned with avoiding possible radiological hazards. Furthermore the licensing required by a nuclear plant before construction or operation demands a level of sophisticated analysis totally alien to fossil-fueled plant design. Furthermore it is the low fuel costs of the NSSS that are responsible for the economic advantages presently enjoyed by nuclear power generation.

The principal component of the NSSS is, of course, the nuclear reactor itself. A rather wide variety of nuclear reactors are in operation today or have been proposed for future development. Reactor types can be characterized by a number of features. Yet another common distinction refers to the type of coolant used in the reactor. In the United States, and indeed throughout the world, the most popular of the present generation of reactors, the light water reactor LWR uses ordinary water as a coolant.

Such reactors operate at very high pressures approximately bar in order to achieve high operating temperatures while maintaining the water in its liquid phase. If the water is allowed to boil in the core, the reactor is referred to as a boiling water reactor BWR , while if the system pressure is kept sufficiently high to prevent bulk boiling bar , the reactor is known as a pressurized water reactor PWR.

Such reactors have benefited from a well-developed technology and performance experience achieved in the nuclear submarine program. A very similar type of reactor uses heavy water D 2 0 either under high pressure as a primary coolant or simply to facilitate the fission chain reaction.

This particular concept has certain nuclear advantages that allow it to utilize lowenrichment uranium fuels including natural uranium. Power reactors can also utilize gases as coolants. A particularly attractive recent design is the high-temperature gas-cooled reactor HTGR manufactured in the United States which uses high-pressure helium. Related gas-cooled reactors include the pebble-bed concept and the advanced gas cooled reactors AGR under development in Germany and the United Kingdom, respectively.

All of the above reactor types can be classified as thermal reactors since their fission chain reactions are maintained by low-energy neutrons. Such reactors comprise most of the world's nuclear generating capacity today, and of these the LWR is most common.

It is generally agreed that the LWR will continue to dominate the nuclear power industry until well into the s, although its market may tend to be eroded somewhat by the successful development of the H T G R or advanced heavy water reactors.

However as we will see in the next chapter, there is strong incentive to develop a fast reactor which will breed new fuel while producing power, thereby greatly reducing nuclear fuel costs. Such fast breeder reactors may be cooled by either liquid metals [the liquid metal-cooled fast breeder reactor LMFBR ] or by helium [the gas-cooled fast breeder reactor GCFR ].

Although fast breeder reactors are not expected to make an appreciable impact on the nuclear power generation market until after , their development is actively being pursued throughout the world today.

Numerous other types of reactors have been proposed and studied—some even involving such exotic concepts as liquid or gaseous fuels. Although much of the analysis presented in this text is applicable to such reactors, our dominant concern is with the solid-fuel reactors cooled by either water, sodium, or helium, since these will comprise the vast majority of the power reactors installed during the next several decades.

In the early days of the reactor industry a nuclear engineer was usually regarded as a Ph. Today, however, nuclear engineers are needed not only by research laboratories and reactor manufacturers to develop and design nuclear reactors, but also by the electrical utilities who buy and operate the nuclear power plants, and by the engineering companies who build the power plants and service them during their operating lifetimes. Hence an understanding of core physics is not sufficient for today's nuclear engineer.

He must also learn how to interface his specialized knowledge of nuclear reactor theory with the myriad of other engineering demands made upon a nuclear power reactor and with a variety of other disciplines, including mechanical, electrical, and civil engineering, metallurgy, and even economics and politics , just as specialists of these other disciplines must learn to interact with nuclear engineers. In this sense, he must recognize that the nuclear analysis of a reactor is only one facet to be considered in nuclear power engineering.

To study and master it outside of the context of these other disciplines would be highly inadvisable. In the same sense, those electrical, mechanical, or structural engineers who find themselves involved in various aspects of nuclear power station design as ever increasing numbers are will also find some knowledge of nuclear reactor theory useful in the understanding of nuclear components and interfacing with nuclear design.

Future nuclear engineers must face and solve complex problems such as those involved in nuclear reactor safety, environmental impact assessment, nuclear power plant reliability, and the nuclear fuel cycle, which span an enormous range of disciplines. They must always be concerned with the economic design, construction, and operation of nuclear plants consistent with safety and environmental constraints. An increasing number of nuclear engineers will find themselves concerned with activities such as quality assurance and component standardization as the nuclear industry continues to grow and mature, and of course all of these problems must be confronted and handled in the public arena.

SCOPE OF THE TEXT Our goal in this text is to develop in detail the underlying theory of nuclear fission reactors in a manner accessible to both prospective nuclear engineering students and those engineers from other disciplines who wish to gain some exposure to nuclear reactor engineering. In every instance we attempt to begin with the fundamental scientific principles governing nuclear fission chain reactions and then carry these fundamental concepts through to the level of realistic engineering applications in nuclear reactor design.

During this development we continually stress the interplay between the nuclear analysis of a reactor core and the parallel nonnuclear design considerations that must accompany it in any realistic nuclear reactor analysis.

We must admit a certain preoccupation with nuclear power reactors simply because most nuclear engineers will find themselves involved in the nuclear power industry.

This will be particularly apparent in the examples we have chosen to discuss and the problems we have emphasized. And although our principal target is the prospective nuclear engineer, we would hope that engineers from other disciplines would also find this text useful as an introduction to the concepts involved in nuclear reactor analysis. The present text develops in four progressive stages. Part 1 presents a very brief introduction to those concepts from nuclear physics relevant to nuclear fission reactors.

These topics include not only a consideration of the nuclear fission process itself, but also a consideration of the various ways in which neutrons, which act as the carrier of the chain reaction, interact with nuclei in the reactor core.

We next consider from a qualitative viewpoint the general concepts involved in studying nuclear chain reactions. Part 1 ends with an overview of nuclear reactor engineering, including a consideration of the various types of modern nuclear reactors, their principal components, and a qualitative discussion of nuclear reactor design.

Parts are intended to develop the fundamental scientific principles underlying nuclear reactor analysis and to apply these principles for derivation of the most common analytical tools used in contemporary reactor design. By way of illustration, these tools are then applied to analyze several of the more common and significant problems facing nuclear engineers. Part 2 develops the mathematical theory of neutron transport in a reactor.

It begins with the most general description based on the neutron transport equation and briefly and very qualitatively reviews the standard approximations to this equation. After this brief discussion, we turn quickly to the development of the simplest nontrivial model of a nuclear fission reactor, that based upon one-speed neutron diffusion theory.

This model is used to analyze both the steady state and time-dependent behavior of nuclear reactors, since although the model has very limited validity in practical reactor analysis, it does illustrate most of the concepts as well as the calculational techniques used in actual reactor design.

In Part 3, we develop the principal tool of modern nuclear reactor design, the multigroup diffusion model. Particular attention is devoted to the calculation of the multigroup constants appearing in these equations, as well as to the practical numerical solution of the equations themselves.

In Part 4, we attempt to give an overview of the methods used in nuclear reactor core design. In particular, we consider the application of the concepts and tools developed in the earlier sections to a variety of problems faced by the nuclear engineer, including criticality calculations, the determination of core power distributions and thermal-hydraulics analysis, burnup and control studies, and fuelloading requirements.

While certainly incomplete, we do feel that the problems we have chosen to examine are representative of those encountered in nuclear reactor design and serve to illustrate the concepts developed in the earlier chapters of the text. These reports provide a very comprehensive survey of the growth of the nuclear power industry.

Chauncey Starr, Sci. Little, Inc. David J. Rose, Science , A n Assessment of Accident Risks in U. Most current information concerning the nuclear power industry appears in a number of journal publications. Although the number of journals appearing in the field of nuclear science and engineering is quite voluminous, a brief list of journals of more general interest would include: Nuclear Engineering International Europressatom : A British journal distinguished by its elaborate, multicolored diagrams of nuclear power plants.

Nuclear Industry Atomic Industrial Forum : A monthly news magazine written more from the viewpoint of the consumer of nuclear power products—namely, the electrical utilities. Nuclear News American Nuclear Society : A monthly news magazine published by the American Nuclear Society, the principal technical organization of nuclear engineering in the United States.

Atomic Energy Commission : A journal highlighting recent developments in the field of nuclear reactor safety. Nuclear Science and Engineering American Nuclear Society : The principal technical research journal of nuclear engineering. Other more research-oriented journals in the field of nuclear science and engineering include: Annals of Nuclear Science and Engineering formerly Journal of Nuclear Energy Pergamon, New York.

Nuclear Technology American Nuclear Society. Soviet Atomic Energy Consultant's Bureau. References on nuclear reactor theory include: Bell, G. Henry, Allan F. Press, Cambridge, Mass. Glasstone, S. Lamarsh, J. Lamarsh, John R. Nuclear Physics and Reactor Theory. Nuclear Reactor Physics, Second Edition.

Elementary Introduction to Nuclear Reactor Physics. Nuclear Forensic Analysis. Chemical Reactor Analysis and Design , 3rd Edition. Chemical Reactor Analysis and Design Fundamentals. Reactor Physics. Chemical Reactor Design. Recommend Documents. Henry I. Nuclear Reactor Theory The continuity condition given above could also have been deduced in the course of deriving the transport equation.

Nuclear Reactor Physics Weston M. Stacey Nuclear R Nuclear reactor physics Weston M. It is designed to be appr Your name. Close Send.