A Review of Nonlinear Reactor Dynamics Problems
Author : Jack Chernick
Publisher :
Page : 16 pages
File Size : 31,3 MB
Release : 1962
Category : Nuclear reactor kinetics
ISBN :
Author : Jack Chernick
Publisher :
Page : 16 pages
File Size : 31,3 MB
Release : 1962
Category : Nuclear reactor kinetics
ISBN :
Author : Jack Chernick
Publisher :
Page : 210 pages
File Size : 27,4 MB
Release : 1973
Category : Nuclear reactors
ISBN :
Author : Mahmoud Ahmad Salehi
Publisher :
Page : 624 pages
File Size : 37,8 MB
Release : 1983
Category :
ISBN :
Author : Richard Allen Olsen
Publisher :
Page : 122 pages
File Size : 24,60 MB
Release : 1975
Category : Mechanical engineering
ISBN :
The solution of the nonlinear two-dimensional reactor dynamics equation subjected to prompt feedback conditions using the finite element technique leads to a matrix formulation. The task of this thesis is the development of computational techniques which allow the problem to be solved for large systems. Specifically, these techniques are: (1) the treatment of the nonlinearity on the element level, (2) the compacting of the sparce matrices to include only non-zero terms, and (3) the construction of a new computer code based on the Crank-Nicolson formulation for the solution of differential equations. To support the theory presented, test problems were solved by the original method, the linearized technique, and the Crank-Nicolson treatment. The results were analyzed and compared graphically. All three of the innovations developed in this thesis appear to be useful tools for solving nonlinear time dependent differential equations.
Author : Ziya Akcasuh
Publisher : Elsevier
Page : 473 pages
File Size : 30,94 MB
Release : 2012-12-02
Category : Science
ISBN : 0323149081
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.
Author : Vishwesh Vyawahare
Publisher : Springer
Page : 210 pages
File Size : 27,57 MB
Release : 2018-02-03
Category : Technology & Engineering
ISBN : 9811075875
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.
Author :
Publisher :
Page : 0 pages
File Size : 34,42 MB
Release : 1976
Category :
ISBN :
This work examines the three-dimensional dynamic response of a nonlinear fast reactor with temperature-dependent feedback and delayed neutrons when subjected to uniform and local disturbances. The finite element method was employed to reduce the partial differential reactor equation to a system of ordinary differential equations which can be numerically integrated. A program for the numerical solution of large sparse systems of stiff differential equations developed by Franke and based on Gear's method solved the reduced neutron dynamics equation. Although a study of convergence by refining element mesh sizes was not carried out, the crude finite element mesh utilized yielded the correct trend of neutron dynamic behavior. (Author).
Author :
Publisher :
Page : 1124 pages
File Size : 43,12 MB
Release : 1987
Category : Aeronautics
ISBN :
Author : Eulogio Conception Bermudes
Publisher :
Page : 160 pages
File Size : 16,73 MB
Release : 1976
Category : Mechanical engineering
ISBN :
This work examines the three-dimensional dynamic response of a nonlinear fast reactor with temperature-dependent feedback and delayed neutrons when subjected to uniform and local disturbances. The finite element method was employed to reduce the partial differential reactor equation to a system of ordinary differential equations which can be numerically integrated. A program for the numerical solution of large sparse systems of stiff differential equations developed by Franke and based on Gear's method solved the reduced neutron dynamics equation. Although a study of convergence by refining element mesh sizes was not carried out, the crude finite element mesh utilized yielded the correct trend of neutron dynamic behavior. (Author).
Author :
Publisher :
Page : 616 pages
File Size : 19,50 MB
Release :
Category : Nuclear engineering
ISBN :