Calculation of coupling coefficients for equations of multipoint kinetics
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ulation of Coupling Coefficients for Equations of Multipoint Kinetics M. V. Ioannisian National Research Center Kurchatov Institute, pl. Kurchatova 1, Moscow, 123182 Russia email: [email protected] Received March 21, 2011
Abstract—The multipoint kinetics equations for fission reaction rate are developed. The algorithm for com putation of coupling coefficients is implemented within the MCU5 code. Results from approbation of the method using the model problem and experimental data are presented. Keywords: multipoint kinetics, theory of coupled reactors, Monte Carlo method, coupling coefficients. DOI: 10.1134/S1063778813130048
INTRODUCTION The contemporary stage of development of nuclear power engineering is characterized by the growth of its share in the total volume of energy production, by the tendency to increase the unit capacity of individual power units, and by the search for ways of creating more efficient and reliable nuclear energy sources with enhanced resource and safety. To provide the needs of the evolving nuclear power engineering, further cre ation and improvement of methods for calculation and design of complicated power systems with nuclear fuel are necessary. The high cost of development of a project for a nuclear power plant (NPP) and its creation and also the long time of its construction make the task of developing modeling codes (solving many problems of optimizing new objects, reducing the time and cost of their creation, enhancing the reliability and safety at the design stage) extremely urgent. One of problems in designing is a problem on spa tial kinetics. Solving the transport equation with spacetime dependence is today one of the most diffi cult problems of reactor physics. Until now, this prob lem has still not been fully resolved, though substantial efforts are being applied to find methods for its solu tion with the use of modern computer resources and mathematical methods. This work is devoted to this problem. A combined approach is proposed which is based on using a system of singlepoint kinetics equations written for an aggre gate of subdomains. Each equation contains the terms of exchange with the remaining subdomains. The concepts of theory of coupled reactors first for mulated by R. Avery in 1959 [1] underlie the proposed method. The term “coupled system” itself means that a fraction of neutrons in each of the multiplying sub domains of a reactor are emitted as a result of fission
events caused by neutrons generated in other subdo mains of the reactor. The system is described using integral parameters characterizing individual subdo mains and couplings between them. It should be noted that the Avery equations were derived on the basis of a phenomenological approach. Works appeared in subsequent years in which attempts were made to give their theoretical substantiation. For that period, the work by M. Komata [2] was most interesting, in which the author demonstrated the pos sibility of deducing the Avery equations based on the kinetic theory by using the Green’s fun
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