Solução das equações da cinética pontual de nêutrons via Método de Fator de Integração Implícito com fonte externa
DOI:
https://doi.org/10.15392/bjrs.v8i3.1201Keywords:
Neutron point kinetics, Integrating factor, Piecewise constant approximation, Accelerator driven systemAbstract
Os autores apresentam uma abordagem semi-analítica para obter soluções para as equações da cinética pontual de nêutrons. A reatividade dependente do tempo é aproximada por aproximação constante por partes em tempo discretizado, e o sistema de equações diferenciais é resolvido por um fator de integração. O termo de fonte externa na solução possui uma integral, que é resolvida numericamente pela interpolação de polinômios de Lagrange e uma fórmula simples de quadratura. Mesmo que a fonte externa apresente não linearidade nas equações, a metodologia é apropriada. A metodologia proposta é utilizada em casos de referência padrão e seus resultados são comparados com os da literatura.
- Views: 172
- PDF Downloads: 233
Downloads
References
ABOANBER, A. E.; HAMADA, Y. M. Power series solution (PWS) of nuclear reactor dynam-ics with newtonian temperature feedback. Annals of Nuclear Energy, p. 1111–1122, 2003.
ABOANBER, A. E. ; HAMADA, Y. M. On Pade' Approximations to the Exponential Function and Application to the Point Kinetics Equations. Progress in Nuclear Energy, v. 44, No. 4, p. 347–368, 2004.
CHAO, Y.; ATTARDT, A. A resolution of the stiffness problem of reactor kinetics. Nuclear science and engineering. p. 40–46, 2017.
DUDERSTADT J. J.; HAMILTON, L. J.Nuclear Reactor Analysis, John Wiley & Sons, New York, 1976.
GANAPOL, B. D. The refined way to solve the reactor point kinetics equations for imposed reactivity insertions. Nuclear Technology and Radiation Protection, v. 24, p. 157–166, 2009.
GANAPOL, B. D.; PICCA, P. A highly accurate benchmark for reactor point kinetics with feedback. In: 2010. Annals of Nuclear Energy, The 17th Pacific Basin Nuclear Conference: 17th PBNC: Cancun: México, 2010.
GANAPOL, B. D. A highly accurate algorithm for the solution of the point kinetics equations. Annals of Nuclear Energy, v.62, p.564–571, 2013.
SÁNCHEZ, J. On the numerical solution of the point reactor kinetics equations by generalized Runge-Kutta methods. Nuclear Science and Engineering, v. 103, p. 94–99, 1989.
QUINTERO-LEYVA, B. CORE: a numerical algorithm to solve the point kinetics equations. Annals of Nuclear Energy, v. 35, p. 2136–2138, 2008.
NAHLA, A. A. Generalization of the analytical exponential model to solve the point kinet-ics equations of Be- and D2O-moderated reactors. Nuclear Engineering and Design, v. 238, p. 2648–2653, 2008.
LI, H.; CHEN, W.; LUO, L.; ZHU, Q. A new integral method for solving the point reactor neutron kinetics equations. Annals of Nuclear Energy, v. 36, p. 427–432, 2009.
NAHLA, A. A. An efficient technique for the point reactor kinetics equations with Newto-nian temperature feedback effects. Annals of Nuclear Energy, v. 38, p. 2810–2817, 2011.
PETERSEN, C. Z.; DULLA, S.; VILHENA, M. T. B.; RAVETTO, P. An analytical solu-tion of the point kinetics equations with time-variable reactivity by the decomposition method. Progress in Nuclear Energy, v. 53, p. 1091–1094, 2011.
KINARD, M. ; ALLEN , E. Efficient numerical solution of the point kinetics equations in nuclear reactor dynamics. Annals of Nuclear Energy, v. 31, p. 1039–1051, 2004.
PICCA, P.; FURFARO, R.; GANAPOL, B. A highly accurate technique for the solution of the non-linear point kinetics equations. Annals of Nuclear Energy, v. 58, p. 43–53, 2013.
SILVA, J. J. A.; ALVIM, A. C. M. ; VILHENA, M. T. M. B. ; BODMANN, B. E. J. ; PE-TERSEN, C. Z. . On a closed-form solution of the point kinetics equations with reactivity feed-back of temperature. International Journal of Nuclear Energy, Science and Technology (Print), v. 8, p. 131-145, 2014.
TUMELERO, F.; PETERSEN, C. Z.; GONÇALVES, G. A. and SCHRAMM, M. Polyno-mial approach method to solve the neutron point kinetics equations with use of the analytic con-tinuation. KERNTECHNIK, v. 81, p. 662–670, 2016.
XOUBI, N. Neutronic design study of accelerator driven system (ADS) for Jordan subcriti-cal reactor as a neutron source for nuclear research. Applied Radiation and Isotopes, v. 131, p. 71–76, 2018.
AL QAAOD, A. A.; GULIK, V. 226Ra irradiation to produce 225Ac and 213Bi in an accelera-tor-driven system reactor. Nuclear Science and Techniques, v. 31, 44, 2020.
Published
How to Cite
Issue
Section
License
Copyright (c) 2020 Brazilian Journal of Radiation Sciences
This work is licensed under a Creative Commons Attribution 4.0 International License.
Licensing: The BJRS articles are licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/
