Mathematical methods in Nuclear reactor Dynamics

1st Edition - January 1, 1971
Author: Ziya Akcasuh
Language: English
eBook ISBN:
9 7 8 - 0 - 3 2 3 - 1 4 9 0 8 - 2

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… Read more

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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.

Preface

Chapter 1. Kinetic Equations

1.1. Transport Equation

1.2. Feedback

1.3. Kinetic Equations

1.4. Reduced Forms of the Kinetic Equations

1.5. Simple Kinetic Models

Problems

References

Chapter 2. Point Kinetic Equations

2.1. Mathematical Preliminaries

2.2. Stationary Reactor and the Multiplication Factor

2.3. Adjoint Angular Density and Neutron Importance

2.4. Reduction of the Kinetic Equations

2.5. Alternative Derivations of the Point Kinetic Equations

2.6. Point Reactor Kinetic Equations with Feedback

2.7. Calculation of Kinetic Parameters in the Diffusion Approximation

Problems

References

Chapter 3. Exact Solutions of the Point Kinetic Equations without Feedback

3.1. Standard and Integrodifferential Forms of the Point Kinetic Equations

3.2. Inverse Method for Solving Kinetic Problems

3.3. Exact Solution of Reactor Kinetic Equations for a Known Reactivity Insertion

Problems

References

Chapter 4. Approximate Solutions of the Point Kinetic Equations without Feedback

4.1. Approximation of Constant Delayed-Neutron Production Rate

4.2. The Prompt-Jump Approximation

4.3. Gradual Reactivity Changes

4.4. Small-Amplitude Approximation (Linearization)

4.5. Logarithmic Linearization

4.6. Perturbation Analysis

4.7. The Response of a Reactor to Large Periodic Reactivity Variations

Problems

References

Chapter 5. Mathematical Description of Feedback

5.1. Feedback Kernels

5.2. Temperature Feedback

5.3. Xenon Feedback

5.4. Transfer Function of a Reactor with Feedback

5.5. Response of a Reactor with Feedback to a Large Periodic Reactivity Insertion

5.6. Equivalent Space-Independent Temperature Models

References

Chapter 6. Linear Stability Analysis

6.1. Characteristic Function and Linear Stability

6.2. Routh-Hurwitz Stability Criterion

6.3. Linear Stability Analysis of Xenon and Temperature Feedback

6.4. Pontryagin's Stability Criteria for Transcendental Equations

6.5. Nyquist Stability Criterion

6.6. Critical Power Level and the Effect of Delayed Neutrons on Linear Stability

6.7. Stability Margins

6.8. Stability of Distributed-Parameter Systems

6.9. The Theory of Linearization

Problems

References

Chapter 7. Nonlinear Stability Analysis

7.1. Concepts of Stability

7.2. General Criteria for Boundedness and Global Asymptotic Stability

7.3. Global Asymptotic Stability of Reactors with Linear Feedback

7.4. Asymptotic Stability of Reactors with a Nonlinear Feedback

7.5. Asymptotic Stability of an Integral Equation

7.6. Lyapunov's "Second Method"

7.7. The Lurie-Letov Function

7.8. The Lefschetz Criterion

7.9. Asymptotic Stability in a Finite Region

7.10. Popov Function

7.11. Criteria for Asymptotic Stability in the Frequency Domain

7.12. The Effects of Delayed Neutrons

7.13. Finite Escape Time and Boundedness

Problems

References

Index