A numerical validation between the neutron transport and diffusion theories for a spatial kinetics problem

Autores/as

  • Rodrigo Zanette Instituto Federal de Educação, Ciência e Tecnologia Sul-rio-grandense , Instituto Federal de Educação, Ciência e Tecnologia Sul-rio-grandense
  • Liliane Basso Barichello Universidade Federal do Rio Grande do Sul image/svg+xml
  • Claudio Zen Petersen Universidade Federal de Pelotas image/svg+xml

DOI:

https://doi.org/10.15392/2319-0612.2024.2361

Palabras clave:

neutron transport theory, neutron diffusion theory, comparative analysis, K dominant eigenvalue

Resumen

In this paper, a comparative analysis of numerical results of the neutron transport and diffusion theories for steady-state and transient multigroup problems is presented. The neutron transport equation is known as the one that best describes the behavior of the neutron population in a nuclear reactor. However, due to the difficulty of working with its complete form, other models are considered as approximations to this equation. One such approximation is the neutron diffusion equation, which uses the Fick's Law. It is well known, however, that the diffusion model may not work well under specific conditions. The objective of this work is to establish a quantitative comparison of numerical results obtained for the K dominant eigenvalue and for the scalar fluxes from the two theories and to analyze the influence of the model on the results.

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Referencias

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GANAPOL, B. D. Analytical Benchmarks for Nuclear Engineering Applications Case Studies in Neutron Transport Theory. Paris: OECD Publishing, 2008.

ZANETTE, R.; BARICHELLO, L. B.; PETERSEN, C. Z. A study on the solution of the spatial kinetics equations in the neutron diffusion theory. Progress in Nuclear Energy, v. 145, p. 104113, 2022.

AMERICAN NUCLEAR SOCIETY. National Energy Software Center: Benchmark problem book. Illinois: ANL-7416, Supplement 3, 1985.

ZANETTE, R.; BARICHELLO, L. B.; PETERSEN, C. Z. Cálculo de criticalidade pela teoria de difusão de nêutrons: uma análise comparativa de aproximação da densidade de corrente. REMAT: Revista Eletrônica da Matemática, v. 6, n. 2, p. e4006, 2020.

BANFIELD, J. E. Semi-Implicit Direct Kinetics Methodology for Deterministic, Time-Dependent, Three-Dimensional, and Fine-Energy Neutron Transport Solutions. PhD diss., University of Tennessee, 2013.

GINESTAR, D.; VERDÚ, G; VIDAL, V.; BRU, R.; MARÍN, J.; MUÑOZ-COBO, J. L. High order backward discretization of the neutron diffusion equation. Annals of Nuclear Energy, v. 25, p. 47–64, 1998.

Publicado

2024-05-17

Número

Sección

Articles

Cómo citar

A numerical validation between the neutron transport and diffusion theories for a spatial kinetics problem. Brazilian Journal of Radiation Sciences (BJRS), Rio de Janeiro, Brazil, v. 12, n. 2, p. e2361, 2024. DOI: 10.15392/2319-0612.2024.2361. Disponível em: https://bjrs.org.br/revista/index.php/REVISTA/article/view/2361. Acesso em: 17 jul. 2025.