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.
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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
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