Recent Advances on the Application of a Spectral Nodal Numerical Method for the Solution of One-Dimensional Neutron Shielding Problems

Authors

DOI:

https://doi.org/10.14295/vetor.v31i1.13473

Keywords:

Neutrons transport theory, Neutron shielding, Spectral nodal methods, Deterministic computational modelling, Computational neutronics

Abstract

In this work, it is presented the application of a spectral nodal method (coarse-mesh) in the solution of one-dimensional neutron shielding problems, in the discrete ordinates and energy multigroup formulations. This method, named Modifed Spectral Deterministic (MSD), represents a modification of the calculation structure of the neutron angular flux in the sweeping process used in the Spectral Deterministic Method (SDM). The numerical results for 3 model-problems are shown, with different dimensions, number of energy groups and types of boundary conditions in using a computational application developed in the programming language C++.

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References

J. J. Duderstadt, L. J. Hamilton et al., Nuclear reactor analysis, 1a ed. New York, USA: Wiley New York, 1976. Disponível em: https://www.wiley.com/en-us/Nuclear+Reactor+Analysis-p-9780471223634

E. E. Lewis e W. F. Miller, Computational methods of neutron transport, 1a ed. New York, USA: Wiley New York, 1993.

O. P. da Silva, “Um método de matriz resposta para cálculos de transporte multigrupos de energia na formulação de ordenadas discretas em meios não-multiplicativos,” Tese de doutorado, Programa de Pós-Graduação em Modelagem Computacional, Universidade do Estado do Rio de Janeiro, Nova Friburgo, Brasil, 2018. Disponível em: https://www.bdtd.uerj.br:8443/handle/1/13795

R. B. Libotte, “Método de malha grossa para solução numérica de problemas de blindagem de nêutrons em geometria unidimensional na formulação de ordenadas discretas com perspectivas a cálculos multidimensionais em geometria retangular,” Dissertação de mestrado, Programa de Pós-Graduação em Modelagem Computacional, Universidade do Estado do Rio de Janeiro, Nova Friburgo, Brasil, 2021. Disponível em: https://www.bdtd.uerj.br:8443/handle/1/16461

A. M. Oliva, “Método espectral determinístico para a solução de problemas de transporte de nêutrons usando a formulação das ordenadas discretas,” Tese de doutorado, Programa de Pós-Graduação em Modelagem Computacional, Universidade do Estado do Rio de Janeiro, Nova Friburgo, Brasil, 2018. Disponível em: https://www.bdtd.uerj.br:8443/handle/1/13719

R. C. de Barros e E. W. larsen, “A spectral nodal method for one-group x, y-geometry discrete ordinates problems,” Nuclear Science and Engineering, vol. 111, no. 1, pp. 34–45, 1992. Disponível em: https://doi.org/10.13182/NSE92-A23921

R. C. de Barros, “A spectral nodal method for the solution of discrete ordinates problems in one- and two-dimensional cartesian geometry,” Tese de doutorado, University of Michigan, UMICH, Ann Arbor, USA, 1990. Disponível em: https://deepblue.lib.umich.edu/handle/2027.42/105093

L. B. Barichello, L. C. Cabrera, e J. F. Prolo Filho, “An analytical approach for a nodal scheme of two-dimensional neutron transport problems,” Annals of Nuclear Energy, vol. 38, no. 6, pp. 1310–1317, 2011. Disponível em: https://doi.org/10.1016/j.anucene.2011.02.0042

G. I. Bell e S. Glasstone, Nuclear Reactor Theory, 2a ed. Washington, DC: Krieger Pub Co., 1970.

L. B. Barichello, R. D. M. Garcia, e C. E. Siewert, “A spherical harmonics solution for radiative-transfer problems with reflecting boundaries and internal sources,” Journal of Quantitative Spectroscopy and Radiative Transfer, vol. 60, pp. 247–260, 1998. Disponível em: http://repositorio.ipen.br/handle/123456789/7212

L. B. Barichello e C. E. Siewert, “A discrete ordinates solution for a non-grey model with complete frequency redistribution,” Journal of Quantitative Spectroscopy and Radiative Transfer, vol. 62, pp. 665–675, 1999. Disponível em: https://doi.org/10.1016/S0022-4073(98)00096-X

M. Benassi, R. M. Cotta, e C. E. Siewert, “The method for radiative transfer problems with reflective boundary conditions,” Journal of Quantitative Spectroscopy and Radiative Transfer, vol. 30, pp. 547–553, 1983. Disponível em: https://doi.org/10.1016/0022-4073(83)90010-9

Published

2021-11-18

How to Cite

Libotte, R., Alves Filho, H., & Silva, F. C. (2021). Recent Advances on the Application of a Spectral Nodal Numerical Method for the Solution of One-Dimensional Neutron Shielding Problems. VETOR - Journal of Exact Sciences and Engineering, 31(1), 94–103. https://doi.org/10.14295/vetor.v31i1.13473

Issue

Section

Seção Especial Energia Nuclear