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Space-time dependent impulse response of a subcritical cylindrical reactor; Reponse impulsionnelle spatio-temporelle d'un reacteur cylindrique en regime sous-critique

Abstract

In this paper, a new formulation of the spatial dependent impulse response of a subcritical reactor in a cylindrical geometry is proposed. An expression of the transfer function between a point source at the center of coordinates and the flux at a given point (r,z) is obtained by solving: by means of Laplace transform, the one group diffusion equation. In this transfer function, variables r and p (p being the Laplace variable) remain linked within a modified Bessel function. Taking the inverse Laplace transform is done by two different ways: - using the Mellin-Fourier method which separates variables r and t. This method makes it possible to establish that there is identity between the classical formulation and the new one. - using an inverse Laplace transform which keeps variables r and t linked. This method requires to approximate the inverse Laplace transform of the end factor. It is then possible to replace the radial harmonics modes series of the classical expression by a single function. This new formulation seems to be of particular interest when dealing with reactors of large size and lifetime. It is also interesting each time the harmonics play an important role. (author) [French] Dans le present  More>>
Authors:
Cazemajou, J [1] 
  1. Commissariat a l'Energie Atomique, Saclay (France). Centre d'Etudes Nucleaires
Publication Date:
Jul 01, 1965
Product Type:
Technical Report
Report Number:
CEA-R-2836
Resource Relation:
Other Information: 19 refs
Subject:
22 GENERAL STUDIES OF NUCLEAR REACTORS; CYLINDRICAL CONFIGURATION; DIFFUSION EQUATIONS; HARMONICS; LAPLACE TRANSFORMATION; POINT SOURCES; REACTORS; SPACE DEPENDENCE; SUBCRITICAL ASSEMBLIES; TIME DEPENDENCE; TRANSFER FUNCTIONS
OSTI ID:
20706597
Research Organizations:
CEA Saclay, 91 - Gif-sur-Yvette (France)
Country of Origin:
France
Language:
French
Other Identifying Numbers:
TRN: FR05R2836021802
Availability:
Available from INIS in electronic form
Submitting Site:
FRN
Size:
38 pages
Announcement Date:
Apr 27, 2006

Citation Formats

Cazemajou, J. Space-time dependent impulse response of a subcritical cylindrical reactor; Reponse impulsionnelle spatio-temporelle d'un reacteur cylindrique en regime sous-critique. France: N. p., 1965. Web.
Cazemajou, J. Space-time dependent impulse response of a subcritical cylindrical reactor; Reponse impulsionnelle spatio-temporelle d'un reacteur cylindrique en regime sous-critique. France.
Cazemajou, J. 1965. "Space-time dependent impulse response of a subcritical cylindrical reactor; Reponse impulsionnelle spatio-temporelle d'un reacteur cylindrique en regime sous-critique." France.
@misc{etde_20706597,
title = {Space-time dependent impulse response of a subcritical cylindrical reactor; Reponse impulsionnelle spatio-temporelle d'un reacteur cylindrique en regime sous-critique}
author = {Cazemajou, J}
abstractNote = {In this paper, a new formulation of the spatial dependent impulse response of a subcritical reactor in a cylindrical geometry is proposed. An expression of the transfer function between a point source at the center of coordinates and the flux at a given point (r,z) is obtained by solving: by means of Laplace transform, the one group diffusion equation. In this transfer function, variables r and p (p being the Laplace variable) remain linked within a modified Bessel function. Taking the inverse Laplace transform is done by two different ways: - using the Mellin-Fourier method which separates variables r and t. This method makes it possible to establish that there is identity between the classical formulation and the new one. - using an inverse Laplace transform which keeps variables r and t linked. This method requires to approximate the inverse Laplace transform of the end factor. It is then possible to replace the radial harmonics modes series of the classical expression by a single function. This new formulation seems to be of particular interest when dealing with reactors of large size and lifetime. It is also interesting each time the harmonics play an important role. (author) [French] Dans le present rapport, on propose une nouvelle formulation de la reponse impulsionnelle spatio-temporelle d'un reacteur sous-critique, en geometrie cylindrique. Une expression de la fonction de transfert entre une source ponctuelle placee au centre des coordonnees et le flux au point courant (r,z) est obtenue en resolvant, par transformation de Laplace, l'equation de la diffusion a un seul groupe d'energie. Dans cette fonction de transfert, les variables r et p (variable de Laplace) demeurent groupees dans une fonction de Bessel modifiee. Le retour a l'original est effectue de deux manieres: - la methode de Mellin-Fourier qui separe les variables r et t, permet d'etablir l'identite entre la nouvelle formulation et la formulation classique. - un original conservant les variables r et t groupees est propose qui comporte une approximation pour l'original du facteur d'extremite; cela permet de remplacer la serie des modes harmoniques radiaux de l'expression classique par une fonction unique. Cette nouvelle formulation semble particulierement interessante dans le cas des reacteurs de grandes dimensions et a grand temps de vie, ainsi que chaque fois que les harmoniques jouent un role important. (auteur)}
place = {France}
year = {1965}
month = {Jul}
}