Open AccessCONVERGENCE OF TRANSPORT SOLUTIONS FOR THIN SLAB CELLS
Author(s) -
D. Meneghetti
Publication year - 1961
Language(s) - English
Resource type - Reports
DOI - 10.2172/4073517
Subject(s) - flux (metallurgy) , spherical harmonics , eigenvalues and eigenvectors , harmonics , anisotropy , slab , physics , mathematical analysis , convergence (economics) , computational physics , geometry , mathematics , chemistry , optics , quantum mechanics , organic chemistry , voltage , geophysics , economics , economic growth
Reported DSN calculations of reactivity worths of heterogeneities in ZPR- III fast critical assemblies, caused by use of various fuel plate and diluent thicknesses, have shown the necessity for high-order approximations to obtain convergence of flux shape and eigenvalue. Convergence properties of solutions for a simplified two-region, oneenergy-group, repetitive slab cell having regional thicknesses and regional cross sections representative of those encountered in some energy -groups of the previous threegroup study are compared for DSN (N = 2, 4, 8, 16), singlespherical harmonics, PN (N = 1, 3,...., 11, 13), and double spherical harmonics, DPN (N = 1, 2, 3, 4, 5), solutions for the case of a spatially constant unit source density in the alternate regions of the cell. Analogous uncollided flux solutions and an integral transport solution for uncollided flux showing effects of contributions of sources in neighboring cells upon the solution are obtained. As the angular width of the anisotropic flux component occurs predominantly in the region about mu = 0, the "shape" of the spatial flux is largely determined by at most a few nearestneighbor source regions, and the anisotropic component is largely the anisotropic component of the uncollided flux. Use of either a discrete ordinate method in which the quadrature angles and weights are assigned on the basis of an uncollided angular- flux estimate or an integral transport method in which the angular integration is accurately carried out is suggested for more effective convergence. For such quasi-homogeneous cells a simple hand-calculational method is presented in which the spatial flux "shape" is first obtained from an uncollided flux analysis, using an integral transport treatment requiring at most a few nearest neighbor regions and arising from "effective" regional source levels, based upon the constant flux of an equivalent homogeneous cell, which include the elastic scattering sources as well as the "actual" sources. The "level" of the uncollided flux "shape" is sdjusted by a constant flux term to satisfy the neutron inventory requirement of total absorptions equal total "actual" sources. For multigroup solution the energy groups may be analogously treated independently by employing "effective" and "actual" regional source levels for each group based upon homogeneous cell multigroup flux levels. (auth