Vyawahare / Nataraj Fractional-order Modeling of Nuclear Reactor: From Subdiffusive Neutron Transport to Control-oriented Models

A Systematic Approach
1. Auflage 2018
ISBN: 978-981-10-7587-2
Verlag: Springer Nature Singapore
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 210 Seiten

This book addresses the topic of fractional-order modeling of nuclear reactors. Approaching neutron transport in the reactor core as anomalous diffusion, specifically subdiffusion, it starts with the development of fractional-order neutron telegraph equations. Using a systematic approach, the book then examines the development and analysis of various fractional-order models representing nuclear reactor dynamics, ultimately leading to the fractional-order linear and nonlinear control-oriented models. The book utilizes the mathematical tool of fractional calculus, the calculus of derivatives and integrals with arbitrary non-integer orders (real or complex), which has recently been found to provide a more compact and realistic representation to the dynamics of diverse physical systems.Including extensive simulation results and discussing important issues related to the fractional-order modeling of nuclear reactors, the book offers a valuable resource for students and researchers working in the areas of fractional-order modeling and control and nuclear reactor modeling.

Vishwesh A. Vyawahare is a faculty in the Department of Electronics Engineering at Ramrao Adik Institute of Technology, Nerul, Navi Mumbai, India. He received his Master of Engineering degree in Control Systems from the Government College of Engineering, Pune, India in 2004, followed by a PhD in Systems and Control Engineering from the Indian Institute of Technology Bombay, Mumbai, India, in 2012. His doctoral work focused on the fractional-order modeling of nuclear reactors. His current research areas include modeling and control using fractional-order, complex-order and variable-order calculus. Paluri S. V. Nataraj is a faculty in the Systems and Control Engineering Group at the Indian Institute of Technology Bombay (IIT Bombay), Mumbai, India. He received his PhD in Process Dynamics and Control from the Indian Institute of Technology Madras, Chennai, India in 1987. He subsequently worked at the CAD Centre at IIT Bombay for one and a half years before joining the Systems and Control Engineering Group at IIT Bombay in 1988, where he has been involved in teaching and research for the past 28 years. His current research interests are in the areas of fractional-order modeling and control, global optimization, parallel computing, reliable computing, and robust control.

Autoren/Hrsg.

Vyawahare, Vishwesh

Nataraj, Paluri S. V.

Inhaltsverzeichnis

1;Preface;6
2;Acknowledgements;9
3;Contents;11
4;About the Authors;14
5;Acronyms;15
6;1 Fractional Calculus;16
6.1;1.1 Introduction;16
6.2;1.2 Special Functions in Fractional Calculus;18
6.2.1;1.2.1 Gamma Function;18
6.2.2;1.2.2 Mittag-Leffler Function;18
6.3;1.3 Fractional-order Integrals and Derivatives: Definitions;20
6.4;1.4 Fractional-order Differential Equations;23
6.5;1.5 Fractional-order Systems;24
6.6;1.6 Chapter Summary;25
7;2 Introduction to Nuclear Reactor Modeling;26
7.1;2.1 Introduction;26
7.2;2.2 Nuclear Reactor Theory;27
7.3;2.3 Slab Reactor;28
7.4;2.4 Mathematical Modeling of Nuclear Reactor;29
7.4.1;2.4.1 Modeling of Neutron Transport;29
7.4.2;2.4.2 Point Reactor Kinetics Model;32
7.4.3;2.4.3 Modeling of Large Commercial Reactors;34
7.4.4;2.4.4 Modeling Neutron Transport as Random Walk;34
7.5;2.5 Anomalous Diffusion;35
7.5.1;2.5.1 Continuous-Time Random Walk;36
7.6;2.6 Fractional Calculus Applications in Nuclear Reactor Theory;37
7.6.1;2.6.1 Analysis of FO Neutron Transport Equation;38
7.6.2;2.6.2 FO Modeling of Neutron Transport and Analysis of Nuclear Reactor;38
7.6.3;2.6.3 Development and Analysis of FO Point Reactor Kinetics Model;39
7.6.4;2.6.4 Design of FO Controller for Nuclear Reactor;40
7.7;2.7 Chapter Summary;41
8;3 Development and Analysis of Fractional-order Neutron Telegraph Equation;42
8.1;3.1 Introduction;42
8.2;3.2 Motivation;44
8.3;3.3 Derivation of FO Neutron Telegraph Equation Model;46
8.4;3.4 Analysis of Mean-Squared Displacement;49
8.4.1;3.4.1 General Diffusion Case;50
8.4.2;3.4.2 IO Neutron Diffusion Equation (INDE);52
8.4.3;3.4.3 IO Neutron Telegraph Equation (INTE);52
8.4.4;3.4.4 FO Neutron Diffusion Equation (FNDE);53
8.4.5;3.4.5 FO Neutron Telegraph Equation (FNTE);57
8.4.6;3.4.6 FO Neutron Telegraph Equation by Paredes (PNTE);61
8.5;3.5 Solution Using Separation of Variables Method;63
8.5.1;3.5.1 Solution of IO Neutron Diffusion Equation;65
8.5.2;3.5.2 Solution of IO Neutron Telegraph Equation;67
8.5.3;3.5.3 Solution of FO Neutron Diffusion Equation;71
8.5.4;3.5.4 Solution of FO Neutron Telegraph Equation;76
8.6;3.6 Chapter Summary;86
9;4 Development and Analysis of Fractional-order Point Reactor Kinetics Model;87
9.1;4.1 Introduction;87
9.2;4.2 Point Reactor Kinetics Model;88
9.2.1;4.2.1 Survey of FPRK Models;89
9.2.2;4.2.2 Steps for Development of Point Reactor Kinetics Model;89
9.3;4.3 Derivation of FPRK Model;90
9.3.1;4.3.1 Observations;90
9.3.2;4.3.2 Separation of Variables Method for FO Neutron Diffusion Equation;90
9.3.3;4.3.3 Longtime Behavior;92
9.3.4;4.3.4 Derivation;94
9.3.5;4.3.5 Discussion;97
9.4;4.4 Solution of FPRK Model with One Effective Delayed Group;97
9.5;4.5 Chapter Summary;105
10;5 Further Developments Using Fractional-order Point Reactor Kinetics Model;106
10.1;5.1 Introduction;106
10.2;5.2 Fractional Inhour Equation;107
10.3;5.3 Inverse FPRK Model;112
10.3.1;5.3.1 Reactivity Insertion for Exponential Rise of Power;114
10.3.2;5.3.2 Reactivity Insertion for Sinusoidal Power Variation;116
10.3.3;5.3.3 Reactivity After a Positive Power Transient;120
10.4;5.4 Constant Delayed Neutron Production Rate Approximation;122
10.5;5.5 Prompt Jump Approximation;127
10.6;5.6 Zero Power Transfer Function of the Reactor;129
10.6.1;5.6.1 Derivation of ZPFTF Using the Small Amplitude Approximation;130
10.6.2;5.6.2 Analysis of ZPFTF with One Effective Delayed Group;132
10.7;5.7 Chapter Summary;135
11;6 Development and Analysis of Fractional-order Point Reactor Kinetics Models with Reactivity Feedback;137
11.1;6.1 Introduction;137
11.2;6.2 Modeling of Reactivity Feedback in a Reactor;139
11.2.1;6.2.1 Reactivity Feedback Mechanism;139
11.2.2;6.2.2 Models of Temperature Feedback of Reactivity;141
11.3;6.3 Fractional-order Nordheim--Fuchs Model;143
11.4;6.4 FPRK Model with Reactivity Feedback (Below Prompt Critical);152
11.4.1;6.4.1 Step Reactivity Insertion;154
11.4.2;6.4.2 Sinusoidal Reactivity Insertion;158
11.5;6.5 Linearized FO Model with Reactivity Feedback;162
11.6;6.6 Chapter Summary;176
12;7 Development and Analysis of Fractional-order Two-Group Models and Fractional-order Nodal Model;179
12.1;7.1 Introduction;179
12.2;7.2 IO Two-Group Diffusion Model;182
12.3;7.3 Fractional-order Two-Group Telegraph-Subdiffusion Model;184
12.3.1;7.3.1 Motivation;184
12.3.2;7.3.2 Derivation;185
12.4;7.4 Fractional-order Two-Group Subdiffusion Model;188
12.5;7.5 Fractional-order Nodal Model;189
12.6;7.6 Chapter Summary;192
13;Appendix Fractional Second-order Adams--Bashforth--Moulton (ABM) Method;194
14;References;196
15;Index;209