Foundations in Applied Nuclear Engineering Analysis

Glenn E Sjoden

• Publisher: WSPC
• Year: 2015
• eBook ISBN: 9789814630955
• Edition: 2
• Topic: Technology & Engineering
• Subtopic: Mathematical & Computational Physics
• Index: Technology & Engineering

Foundations in Applied Nuclear Engineering Analysis (2nd Edition) covers a fast-paced one semester course to address concepts of modeling in mathematics, engineering analysis, and computational problem solving needed in subjects such as radiation interactions, heat transfer, reactor physics, radiation transport, numerical modeling, etc., for success in a nuclear engineering/medical physics curriculum. While certain topics are covered tangentially, others are covered in depth to target on the appropriate amalgam of topics for success in navigating nuclear-related disciplines. Software examples and programming are used throughout the book, since computational capabilities are essential for new engineers.

The book contains a array of topics that cover the essential subjects expected for students to successfully navigate into nuclear-related disciplines. The text assumes that students have familiarity with undergraduate mathematics and physics, and are ready to apply those skills to problems in nuclear engineering. Applications and problem sets are directed toward problems in nuclear science. Software examples using Mathematica software are used in the text.

This text was developed as part of a very applied course in mathematical physics methods for nuclear engineers. The course in Nuclear Engineering Analysis that follows this text began at the University of Florida; the 2nd edition was released while at the Georgia Institute of Technology.

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Readership: Students of Nuclear Engineering; advanced undergraduate students familiar with undergraduate mathematics and physics.
Readership: Students of Nuclear Engineering; advanced undergraduate students familiar with undergraduate mathematics and physics.
Key Features:

• New in this edition are expanded fundamentals of nuclear physics principles, essential elements of parallel programming, more coverage of basic probability principles and distributions, limits of detection, expanded presentations of applications highlighting real world examples in nuclear science and medical physics, including counting, detection, mixing, criticality safety, flow induced vibration, anisotropic Legendre moments for cross sections, and introductory transport theory and diffusion theory with numerics

Chapter 1

Nuclear Engineering Analysis

Nuclear engineering analysis is a very broad subject title. Nuclear engineering and medical physics are disciplines that are ultimately very applied; while the “pure sciences” are often afforded the luxury of only considering hypothetical problems, nuclear engineers must respond to delivering real engineering systems to benefit humanity, e.g. providing nuclear power, advanced imaging devices, curing cancer, and the like. Therefore, nuclear engineers must design systems and devices that are based on nuclear interactions using subatomic particles that are not detectable by the ordinary human senses.

A fundamental and practical understanding of mathematics and physics must synergistically be employed to be effective as a nuclear engineer or medical physicist. The successful nuclear engineer must be adaptable, and able to create appropriate mathematical models, so that those models may be used to answer questions and solve real engineering problems. How does one achieve this? The answer is education, training, hard work, and practice.

In most cases, the inherent complexity of the systems involved in nuclear related disciplines require computation. Models are often implemented as computer programs; almost every “real” problem in nuclear engineering requires the use of a computer in some manner, and programming skills among any variety of languages and tools is essential. It is envisioned that users of this text will be assigned problems that involve computation, particularly as progress through the material culminates in solving partial differential equations.

Origins of Nuclear Engineering

Nuclear Engineering began its historical roots in 450 B.C. Greece, where Democritus argued that substances were ultimately composed of small, indivisible particles that he labeled “atoms.” In 1869, Russian chemist Mendeleev organized these elements of particular atoms into a table that grouped them by their physical properties and characteristics called “the periodic table of the elements”. Much work was advanced over time so that in the early 20^th Century, and nuclear fission was discovered by Hahn & Strassman in 1939, where Barium and Krypton resulted from bombarding neutrons into Uranium, a conclusion reached with counsel from scientist Lise Meitner.

An American named William Arnold, visiting Otto Frisch to view a confirmatory experiment, recalled that “binary fission” was a biology term describing when one Bacterium divides into two… hence “nuclear fission” came from liberating energy by splitting the atom, and with it, nuclear engineering was born. (P.260–266 Rhodes, “Making of the A-bomb”).

Nuclear energy always invokes “mysterious wonder” from many, since its initial release was a result of the then very secret “Manhattan Project” and atom bomb development during World War II. For many years and into present day, nuclear energy and engineering principles maintain a “mystery quality” due to an association with nuclear weapons. Granted, the awesome amount of energy release possible from fission and subsequent weapons development during the Cold War to present day furthered this image; an example of weapons developed is given in the following figure.

“Grable” 280 mm howitzer nuclear cannon test, Nevada Test Site (US Govt image)

Modern applications of nuclear engineering are focused primarily on power and medical applications, as noted. For nuclear power generation, most of these involve reactor design. While a nuclear weapon is a device designed to release nuclear energy using an uncontrolled fission chain reaction, a nuclear reactor is a device in which nuclear energy from fission is released in a controlled manner using fission neutrons as the fission chain carrier.

The principal subatomic particles are the proton (charge of +1, 1.007277 amu, where 1 amu = 1.66054 E-27 kg = 1/12 of a carbon atom), the neutron (neutral charge, 1.008665 amu), and the electron (charge of −1, 5.4858E-4 amu). The operation of a reactor relies on the fate of subatomic particles (neutrons) released in the reactor as a consequence of fission. Fission is brought about by neutron irradiation of fissile materials; when a neutron is absorbed by a fissile nucleus, this results in an unstable excited nucleus that splits into two smaller, more stable pieces while liberating typically 2 to 3 new neutrons in each fission, which then go on to further sustain the chain reaction or leak out. Not counting the neutrons, the two large halves or “fission fragments” are often radioactive. Therefore, neutrons interact with nuclei in the reactor system and serve as a “fission chain carrier,” governing how the fission reactions continue. Therefore, understanding “neutronics,” or neutron balance in a reactor, is a fundamental principle of “Reactor Physics,” and we will expand upon this late in the text, where we will consider the neutron transport and diffusion problem for some fundamental scenarios.

Nuclear Applications

Nuclear fission reactors can produce power for electricity generation,

generation for fuel cell based transportation, nuclear driven propulsion in ships and submarines, and even space travel, including nuclear rocket engines, compact nuclear power systems, etc. Medical devices use nuclear reactions include linear accelerators of various types where radioactive particles are used to kill cancer cells in humans, and generate isotopes used in diagnosis, imaging, and cancer treatment.

Work to support applications in nuclear energy and medical applications requires a wide range of applied mathematics, which was the motivation for writing this text… students need to be exposed to a variety of applications to reinforce their ability to be problem solvers! To be good at problem solving, for nuclear applications, this usually involves some type of computing and computer programming; so we briefly discuss this in the next section.

Computer Programming

Computer programming plays several important roles in nuclear engineering analysis: modeling problems, exploring new ideas, automating well-known techniques, and creating new tools for other engineers. A programming language is a tool for creating computer programs. As engineers, we should be aware of each tool’s strengths so that we can choose the right tool for each job. In this book, a few programming languages are noted: Mathematica, TK-Solver, and FORTRAN or C. Programming is an essential tool for nuclear engineers; mastering this in a variety of forms yields new and profound understanding of the physics.

Mathematica is an advanced commercial programming language with built-in support for common tasks in science, engineering, and mathematics. Mathematica is particularly well-suited to trying out new ideas or profiling your homework. This tool is expensive, but worth the price (especially with a student version discount).

TK-Solver is a useful tool for modeling engineering problems and solving systems of equations. One advantage of TK-Solver is that it is often possible to model new systems without doing any new programming. Variables can be interchangeably mixed at will as input or output, and therefore TK-Solver models can be readily used as “design optimization” tools.

FORTRAN or C languages are often used for programs that need to be fast, such as for neutron transport simulators. You may need to know FORTRAN if you are trying to improve processing data from a “legacy” nuclear application, because FORTRAN has always been popular among nuclear engineers; many codes that have been “nuclear certified” in FORTRAN may never be re-written in other languages, since certification in a new language is cost-prohibitive. Therefore, it is envisioned that FORTRAN will be alive and well in the foreseeable future simply due to its widespread (and certified) use in the nuclear industry. Message Passing Interface (MPI) libraries have enabled FORTRAN and C codes to be readily parallelized on multiprocesso...

Table of contents

• Cover Page
• Title
• Copyright
• Dedication
• Preface to Second Edition
• About the Author
• Contents
• Chapter 1: Nuclear Engineering Analysis
• Chapter 2: Essentials of Probability
• Chapter 3: Introduction to Numerical Concepts and Applications
• Chapter 4: Fundamentals of Complex Numbers
• Chapter 5: Methods for Solving Ordinary Differential Equations
• Chapter 6: Applications of Power Series
• Chapter 7: Methods of Solving DEs with Variable Coefficients
• Chapter 8: Vectors, Matrices, and Linear Systems
• Chapter 9: Gram–Schmidt Orthogonalization and Fourier Series
• Chapter 10: Applied Solution Methods—Part 1
• Chapter 11: Applied Solution Methods—Part 2: PDEs and Heat Transfer
• Chapter 12: Applied Solution Methods—Part 3: Neutronics
• Chapter 13: Numerical Solution of Partial Differential Equations
• Appendix: Selected Problems; Sets I–V
• Bibliography
• Index