Solución Numérica de la Reactividad en Reactores Nucleares
DOI:
https://doi.org/10.22517/23447214.25438Keywords:
Reactor nuclear, reactividad nuclear, formula Euler-Maclaurin, densidad de neutrones, simulación numérica, números de Bernoulli.Abstract
La reactividad nuclear y la densidad de la población de neutrones son los parámetros más significativos al momento de cuantificar y describir físicamente el comportamiento de un reactor nuclear. Conocer el valor de la reactividad con suficiente precisión permite realizar el control y la operación segura de un reactor nuclear. Existen varios enfoques y métodos para calcular la reactividad reportados en la literatura. Sin embargo, en este artículo se propone usar la fórmula de Euler-Maclaurin para la solución numérica de la reactividad mediante la ecuación inversa de la cinética puntual que ha sido un modelo clave en el diseño de medidores de reactividad digital. Considerando la aproximación de una integral como una suma, en el desarrollo de la expansión de la integral continua en una versión discreta y tomando en cuenta únicamente los tres primeros números de Bernoulli y una aproximación que reduce las derivadas de mayor orden, es posible deducir un modelo que permite el cálculo de la reactividad nuclear en función de la densidad de la población de neutrones y de las constantes física en reactores térmicos que usan uranio como combustible nuclear.
Downloads
References
M. Stacey, Nuclear Reactor Physics 3e. Weinheim, Germany: Wiley-VCH Verlag GmbH & Co. KGaA, 2018. doi: 10.1002/9783527812318
Y. Shimazu, Y. Nakano, Y. Tahara, and T. Okayama, “Development of a Compact Digital Reactivity Meter and a Reactor Physics Data Processor.,” Nucl Technol, vol. 77, no. 3, pp. 247–254, 1987, doi: 10.13182/NT87-A33964
J. E. Hoogenboom and A. R. van der Sluijs, “Neutron source strength determination for on-line reactivity measurements,” Ann Nucl Energy, vol. 15, no. 12, pp. 553–559, 1988, doi: 10.1016/0306-4549(88)90059-X
S. E. Binney and A. J. M. Bakir, “Design and development of a personal-computer-based reactivity meter for a research reactor,” Nucl Technol, vol. 85, no. 1, pp. 12–21, 1989, doi: 10.13182/NT89-A34223
S. A. Ansari, “Development of on-line reactivity meter for nuclear reactors,” IEEE Trans Nucl Sci, vol. 38, no. 4, pp. 946–952, Aug. 1991, doi: 10.1109/23.83857
A. Kitano, M. Itagaki, and M. Narita, “Memorial-Index-Based Inverse Kinetics Method for Continuous Measurement of Reactivity and Source Strength,” J Nucl Sci Technol, vol. 37, no. 1, pp. 53–59, Jan. 2000, doi: 10.1080/18811248.2000.9714866
H. Malmir and N. Vosoughi, “On-line reactivity calculation using Lagrange method,” Ann Nucl Energy, vol. 62, pp. 463–467, 2013, doi: 10.1016/j.anucene.2013.07.006
D. Suescún-Díaz, J. A. Rodríguez-Sarasty, and J. H. Figueroa-Jiménez, “Reactivity calculation using the Euler–Maclaurin formula,” Ann Nucl Energy, vol. 53, pp. 104–108, Mar. 2013, doi: 10.1016/j.anucene.2012.09.026
D. Suescún-Díaz, M. C. Ibarguen-Gonzalez, and J. H. Figueroa-Jiménez, “Hamming generalized corrector for reactivity calculation,” Kerntechnik, vol. 79, no. 3, pp. 219–225, Jun. 2014, doi: 10.3139/124.110423
M. Mohideen Abdul Razak and N. Rathinasamy, “Haar wavelet for solving the inverse point kinetics equations and estimation of feedback reactivity coefficient under background noise,” Nuclear Engineering and Design, vol. 335, pp. 202–209, Aug. 2018, doi: 10.1016/j.nucengdes.2018.04.022
P. Picca and R. Furfaro, “Reactivity determination using the hybrid transport point kinetics and the area method,” Ann Nucl Energy, vol. 114, pp. 191–197, 2018, doi: 10.1016/j.anucene.2017.12.019
N. Chentre, P. Saracco, S. Dulla, and P. Ravetto, “On the prompt time eigenvalue estimation for subcritical multiplying systems,” Ann Nucl Energy, vol. 132, pp. 172–180, 2019, doi: 10.1016/j.anucene.2019.04.030
D. Suescún-Díaz, G. Ule-Duque, and F. H. Escobar, “Novel approach to solving the inverse equation of point kinetics by the Bernoulli number generalisation method,” J Nucl Sci Technol, vol. 57, no. 8, pp. 989–999, 2020, doi: 10.1080/00223131.2020.1742813
J. J. Duderstadt and L. J. Hamilton, Nuclear Reactor Analysis, Second ed. New York: John Wiley & Sons Inc, 1976.
Y. K. Kwok, Applied Complex Variables for Scientists and Engineers. Cambridge University Press, 2010. doi: 10.1017/CBO9780511844690
S. Haykin and B. Van Veen, Signals and Systems. New York: Wiley, 2005.
D. Suescún Díaz, A. Senra Martinez, and F. Carvalho Da Silva, “Calculation of reactivity using a finite impulse response filter,” Ann Nucl Energy, vol. 35, no. 3, pp. 472–477, 2008, doi: 10.1016/j.anucene.2007.07.002
Downloads
-
Vistas(Views): 9
- PDF (Español (España)) Descargas(Downloads): 14
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 Scientia et Technica
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Copyrights
The journal is free open access. The papers are published under the Creative Commons Attribution / Attribution-NonCommercial-NoDerivatives 4.0 International - CC BY-NC-ND 4.0 license. For this reason, the author or authors of a manuscript accepted for publication will yield all the economic rights to the Universidad Tecnológica of Pereira free of charge, taking into account the following:
In the event that the submitted manuscript is accepted for publication, the authors must grant permission to the journal, in unlimited time, to reproduce, to edit, distribute, exhibit and publish anywhere, either by means printed, electronic, databases, repositories, optical discs, Internet or any other required medium. In all cases, the journal preserves the obligation to respect, the moral rights of the authors, contained in article 30 of Law 23 of 1982 of the Government Colombian.
The transferors using ASSIGNMENT OF PATRIMONIAL RIGHTS letter declare that all the material that is part of the article is entirely free of copyright. Therefore, the authors are responsible for any litigation or related claim to intellectual property rights. They exonerate of all responsibility to the Universidad Tecnológica of Pereira (publishing entity) and the Scientia et Technica journal. Likewise, the authors accept that the work presented will be distributed in free open access, safeguarding copyright under the Creative Commons Attribution / Recognition-NonCommercial-NoDerivatives 4.0 International - https://creativecommons.org/licenses/by-nc-nd/4.0/deed.es license.