A New Equivalence Theory Method for Treating Doubly Heterogeneous Fuel  I. Theory
Abstract
A new methodology has been developed to treat resonance selfshielding in doubly heterogeneous very high temperature gascooled reactor systems in which the fuel compact region of a reactor lattice consists of small fuel grains dispersed in a graphite matrix. This new method first homogenizes the fuel grain and matrix materials using an analytically derived disadvantage factor from a tworegion problem with equivalence theory and intermediate resonance method. This disadvantage factor accounts for spatial selfshielding effects inside each grain within the framework of an infinite array of grains. Then the homogenized fuel compact is selfshielded using a Bondarenko method to account for interactions between the fuel compact regions in the fuel lattice. In the final form of the equations for actual implementations, the doubleheterogeneity effects are accounted for by simply using a modified definition of a background cross section, which includes geometry parameters and cross sections for both the grain and fuel compact regions. With the new method, the doubly heterogeneous resonance selfshielding effect can be treated easily even with legacy codes programmed only for a singly heterogeneous system by simple modifications in the background cross section for resonance integral interpolations. This paper presents a detailed derivation of the new methodmore »
 Authors:
 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
 Ulsan National Institute of Science and Technology (UNIST), Uljugun (South Korea)
 Publication Date:
 Research Org.:
 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1223634
 Grant/Contract Number:
 AC0500OR22725
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Nuclear Science and Engineering
 Additional Journal Information:
 Journal Volume: 180; Journal Issue: 1; Journal ID: ISSN 00295639
 Publisher:
 American Nuclear Society  Taylor & Francis
 Country of Publication:
 United States
 Language:
 English
 Subject:
 22 GENERAL STUDIES OF NUCLEAR REACTORS
Citation Formats
Williams, Mark L., Lee, Deokjung, and Choi, Sooyoung. A New Equivalence Theory Method for Treating Doubly Heterogeneous Fuel  I. Theory. United States: N. p., 2015.
Web. doi:10.13182/NSE1468.
Williams, Mark L., Lee, Deokjung, & Choi, Sooyoung. A New Equivalence Theory Method for Treating Doubly Heterogeneous Fuel  I. Theory. United States. doi:10.13182/NSE1468.
Williams, Mark L., Lee, Deokjung, and Choi, Sooyoung. 2015.
"A New Equivalence Theory Method for Treating Doubly Heterogeneous Fuel  I. Theory". United States.
doi:10.13182/NSE1468. https://www.osti.gov/servlets/purl/1223634.
@article{osti_1223634,
title = {A New Equivalence Theory Method for Treating Doubly Heterogeneous Fuel  I. Theory},
author = {Williams, Mark L. and Lee, Deokjung and Choi, Sooyoung},
abstractNote = {A new methodology has been developed to treat resonance selfshielding in doubly heterogeneous very high temperature gascooled reactor systems in which the fuel compact region of a reactor lattice consists of small fuel grains dispersed in a graphite matrix. This new method first homogenizes the fuel grain and matrix materials using an analytically derived disadvantage factor from a tworegion problem with equivalence theory and intermediate resonance method. This disadvantage factor accounts for spatial selfshielding effects inside each grain within the framework of an infinite array of grains. Then the homogenized fuel compact is selfshielded using a Bondarenko method to account for interactions between the fuel compact regions in the fuel lattice. In the final form of the equations for actual implementations, the doubleheterogeneity effects are accounted for by simply using a modified definition of a background cross section, which includes geometry parameters and cross sections for both the grain and fuel compact regions. With the new method, the doubly heterogeneous resonance selfshielding effect can be treated easily even with legacy codes programmed only for a singly heterogeneous system by simple modifications in the background cross section for resonance integral interpolations. This paper presents a detailed derivation of the new method and a sensitivity study of doubleheterogeneity parameters introduced during the derivation. The implementation of the method and verification results for various test cases are presented in the companion paper.},
doi = {10.13182/NSE1468},
journal = {Nuclear Science and Engineering},
number = 1,
volume = 180,
place = {United States},
year = 2015,
month = 3
}
Web of Science

A new methodology has been developed recently to treat resonance selfshielding in systems for which the fuel compact region of a reactor lattice consists of small fuel grains dispersed in a graphite matrix. The theoretical development adopts equivalence theory in both micro and macrolevel heterogeneities to provide approximate analytical expressions for the shielded cross sections, which may be interpolated from a table of resonance integrals or Bondarenko factors using a modified background cross section as the interpolation parameter. This paper describes the first implementation of the theoretical equations in a reactor analysis code. In order to reduce discrepancies caused bymore »Cited by 2

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A new raytracing method for the calculation of collision probabilities within arbitrary threedimensional geometries has been developed. This method is used to discretize the neutron transport equation for the heterogenous rectangular cells containing zones of mixed cylindrical and rectangular geometry. For multicell applications, the interface current (IC) method provides the coupling between cells. The solution to the IC equations over multicell domains consisting of rectangular threedimensional cells is improved by using an alternative direction implicit scheme with variational acceleration. Results indicate comparisons of this technique with SHETAN for simple geometries and the analysis of a threedimensional extension of a twodimensionalmore »