On a point kinetic with explicit presence of neutron poisons: reactivity decomposition according to long time scales
DOI:
https://doi.org/10.14393/BEJOM-v4-2023-68618Palavras-chave:
Difusão de nêutrons, Venenos de nêutrons, Método da decomposição de Adomian, Cinética de curta e longa escala de tempo, Combustível nuclear reutilizadoResumo
The present work consists of deducing the point kinetics model considering neutron absorber poisons from the neutron diffusion equation. When considering poisons products, the non-linear system has different orders of magnitude in short and long time scales. The first one represents operational reactor control, whereas the second is due to the change of the chemical composition of the nuclear fuel as a result of burn-up. This represents a first step in a new direction, as it shows how we arrived at the extension of the point kinetics model considering Xenon-135 and Samarium-149 poisons. The non-linear system is solved using the Adomian decomposition method that expands the non-linear terms into an infinite series, obtaining a recursive system, where the recursion initialization is a homogeneous linear equation and the subsequent recursion steps consider the non-linear contributions as source terms constructed from previous recursion steps. The formulation of the source terms of the decomposition method is shown. In order to demonstrate the robustness of the current approach to this type of problem, case studies are presented where nuclear fuel uses reused elements up to third generation, taking a step in a new direction where poisons are already present in the reactor initially.
Downloads
Referências
ADOMIAN, G. A review of the decomposition method in applied mathematics. Journal of Mathematical Analysis and Aplicationsv. 135, p. 501–544, 1988.
ADOMIAN, G. Solving frontier problems of physics: the decomposition method, USA, Kluwer academic Publishers, 1994.
BIAZAR, J.; SHAFIOF, S. M. A simple algorithm for calculating adomian polynomials. Int. J. Contemp. Math. Sciences, v. 20, p. 975–982, 2007.
BOYCE, W. E.; DIPRIMA, R. C.Elementary Differential Equations and Boundary Value Problems. USA, John Wiley & Sons Inc., 2001.
BUZANO, M. L.; CORNO, S. E. C. I. A new procedure for integrating the pointkinetic equations for fission reactors. Applied Mathematics and Computation, v.29, p. 5–19, 1995.
CACUCCI, D. G. Handbook of nuclear engineering, Germany, Springer, 2010.
DOE, F. H.Nuclear Physics and Reactor Theory, USA, U.S. Department of Energy Washington, 2013.
ESPINOSA, C.E.; BODMANN, B.E.J.; VILHENA, M.T. On the Neutron Point Kinetic Equation with Reactivity Decomposition Based on Two Time Scales. In: Constanda, C., Dalla Riva, M., Lamberti, P., Musolino, P. Integral Methods in Scienceand Engineering, v. 2, Birkhäuser, 2017. Cham. https://doi.org/10.1007/978-3-319-59387-6_7
ESPINOSA, C. E. Modelagem e Simulação dos venenos no combustível nuclearem cenário com duas escalas de tempo. Tese de Doutorado – UFRGS, Porto Ale-gre, 2016.
PAGANIN, T.; BODMANN, B.; VILHENA, M. T. M. On a point kinetic model fornuclear reactors considering the variation in fuel composition. Progress in NuclearEnergy, v. 118, p. 103-134, 2020.
PETERSEN, C. Z.; DULLA, S.; VILHENA, M. T. M.; RAVETTO, P. An analytical solution of the point kinetics equations with time-variable reactivity by the decomposition method. Progress in Nuclear Energy, p. 1–4. 2011.
REUSS, P.Neutron Physics, France, EDP Sciences, 2008.
DA SILVA, M. W.; LEITE, S. B.; VILHENA, M. T.; BODMANN, B.On an analytical representation for the solution of the neutron point kinetics equation free of stiffness. Annals of Nuclear Energy, v. 71, p. 97–102, 2014.
DA SILVA, M. W.; VASQUES, R.; VILHENA, M. T.; BODMANN, B. On an analytical representation for the solution of the neutron point kinetics equation free of stiffness. Annals of Nuclear Energy, v. 97, p. 47–52. 2016.
GLASSTONE, S. Nuclear Reactor Theory, New York, Van Nostrand Reinhold Company, 1970.
LAMARSH, J.R. Introduction to Nuclear Reactor Theory, New York, Addison Wesley Publishing, 1966.
SCHAUN, N.B.; TUMELERO F.; PETERSEN, C. Z. Influence of the main neutron absorbers poisons coupled to the Point Kinetics model by the Rosenbrock’s method. Brazilian Journal of Radiation Sciences, p. 01-19. 2022.
ZIYA, A.; LELLOUCHE G.S.; SHOTKIN, L.M. Mathematical Methods in Nuclear Reactor Dynamics, USA, Academic Press, 1971.
Downloads
Publicado
Como Citar
Edição
Seção
Licença
Copyright (c) 2023 BRAZILIAN ELECTRONIC JOURNAL OF MATHEMATICS
Este trabalho está licenciado sob uma licença Creative Commons Attribution-NonCommercial 4.0 International License.
- Os artigos publicados são licenciados sob a versão CreativeCommons CCBY-NC/4.0. Ao enviar o material para publicação, os autores estarão automaticamente abrindo mão de seus direitos autorais, concordando com as diretrizes editoriais do periódico e assumindo que o texto foi devidamente revisado. A submissão simultânea de artigos a outras revistas é proibida, e, é também proibida a tradução de artigos publicados no periódico para outro idioma sem a devida autorização.
