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The general formulation and practical calculation of the diffusion coefficient in a lattice containing cavities; Formulation generale et calcul pratique du coefficient de diffusion dans un reseau comportant des cavites

Abstract

The calculation of diffusion coefficients in a lattice necessitates the knowledge of a correct method of weighting the free paths of the different constituents. An unambiguous definition of this weighting method is given here, based on the calculation of leakages from a zone of a reactor. The formulation obtained, which is both simple and general, reduces the calculation of diffusion coefficients to that of collision probabilities in the different media; it reveals in the expression for the radial coefficient the series of the terms of angular correlation (cross terms) recently shown by several authors. This formulation is then used to calculate the practical case of a classical type of lattice composed of a moderator and a fuel element surrounded by an empty space. Analytical and numerical comparison of the expressions obtained with those inferred from the theory of BEHRENS shows up the importance of several new terms some of which are linked with the transparency of the fuel element. Cross terms up to the second order are evaluated. A practical formulary is given at the end of the paper. (author) [French] Le calcul des coefficients de diffusion dans un reseau suppose la connaissance d'un mode de ponderation correct des libres  More>>
Authors:
Benoist, P [1] 
  1. Commissariat a l'Energie Atomique, Saclay (France).Centre d'Etudes Nucleaires
Publication Date:
Jul 01, 1959
Product Type:
Technical Report
Report Number:
CEA-R-1354
Resource Relation:
Other Information: 21 refs
Subject:
22 GENERAL STUDIES OF NUCLEAR REACTORS; ANGULAR CORRELATION; BOLTZMANN EQUATION; COLLISION PROBABILITY METHOD; CROSS SECTIONS; DIFFUSION LENGTH; HETEROGENEOUS EFFECTS; INTEGRAL CALCULUS; MEAN FREE PATH; NEUTRON DIFFUSION EQUATION; NEUTRON FLUX; NEUTRON LEAKAGE; NEUTRON TRANSPORT; REACTOR CHANNELS; REACTOR LATTICES
OSTI ID:
20942972
Research Organizations:
CEA Saclay, 91 - Gif-sur-Yvette (France)
Country of Origin:
France
Language:
French
Other Identifying Numbers:
TRN: FR07R1354096425
Availability:
Available from INIS in electronic form
Submitting Site:
FRN
Size:
55 pages
Announcement Date:
Dec 13, 2007

Citation Formats

Benoist, P. The general formulation and practical calculation of the diffusion coefficient in a lattice containing cavities; Formulation generale et calcul pratique du coefficient de diffusion dans un reseau comportant des cavites. France: N. p., 1959. Web.
Benoist, P. The general formulation and practical calculation of the diffusion coefficient in a lattice containing cavities; Formulation generale et calcul pratique du coefficient de diffusion dans un reseau comportant des cavites. France.
Benoist, P. 1959. "The general formulation and practical calculation of the diffusion coefficient in a lattice containing cavities; Formulation generale et calcul pratique du coefficient de diffusion dans un reseau comportant des cavites." France.
@misc{etde_20942972,
title = {The general formulation and practical calculation of the diffusion coefficient in a lattice containing cavities; Formulation generale et calcul pratique du coefficient de diffusion dans un reseau comportant des cavites}
author = {Benoist, P}
abstractNote = {The calculation of diffusion coefficients in a lattice necessitates the knowledge of a correct method of weighting the free paths of the different constituents. An unambiguous definition of this weighting method is given here, based on the calculation of leakages from a zone of a reactor. The formulation obtained, which is both simple and general, reduces the calculation of diffusion coefficients to that of collision probabilities in the different media; it reveals in the expression for the radial coefficient the series of the terms of angular correlation (cross terms) recently shown by several authors. This formulation is then used to calculate the practical case of a classical type of lattice composed of a moderator and a fuel element surrounded by an empty space. Analytical and numerical comparison of the expressions obtained with those inferred from the theory of BEHRENS shows up the importance of several new terms some of which are linked with the transparency of the fuel element. Cross terms up to the second order are evaluated. A practical formulary is given at the end of the paper. (author) [French] Le calcul des coefficients de diffusion dans un reseau suppose la connaissance d'un mode de ponderation correct des libres parcours des differents constituants. On definit ici sans ambiguite ce mode de ponderation a partir du calcul des fuites hors d'une zone de reacteur. La formulation obtenue, simple et generale, ramene le calcul des coefficients de diffusion a celui des probabilites de collision dans les differents milieux; elle fait apparaitre dans l'expression du coefficient radial la serie des termes de correlation angulaire (termes rectangles), mis en evidence recemment par plusieurs auteurs. Cette formulation est ensuite appliquee au calcul pratique d'un reseau classique, compose d'un moderateur et d'un element combustible entoure d'une cavite; la comparaison analytique et numerique des expressions obtenues avec celles deduites de la theorie de BEHRENS fait apparaitre l'importance de plusieurs termes nouveaux, dont certains sont lies a la transparence de l'element combustible; les termes rectangles sont calcules jusqu'a l'ordre 2. Un formulaire pratique est donne a la fin de cette etude. (auteur)}
place = {France}
year = {1959}
month = {Jul}
}