Neutron density calculation using the generalised adams-bashforth-moulton method

Este artículo presenta una solución numérica a las ecuaciones de cinética puntual para reactores de energía nuclear, un conjunto de siete ecuaciones diferenciales acopladas que describen la variación temporal de la densidad de neutrones y la concentración de precursores de neutrones retardados. Debi...

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Autores:: Suescún-Díaz, Daniel
Rasero, Diego
Lozano Parada, Jaime Humberto

Tipo de recurso:: Article of journal

Fecha de publicación:: 2019

Institución:: Universidad Autónoma de Occidente

Repositorio:: RED: Repositorio Educativo Digital UAO

Idioma:: eng

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dc.title.eng.fl_str_mv	Neutron density calculation using the generalised adams-bashforth-moulton method
dc.title.alternative.por.fl_str_mv	Cálculo da densidade de nêutrons usando o método generalizado de Adams-Bashforth-Moulton
dc.title.alternative.spa.fl_str_mv	Cálculo de densidad de neutrones utilizando el método generalizado de Adams-Bashforth-Moulton
title	Neutron density calculation using the generalised adams-bashforth-moulton method
spellingShingle	Neutron density calculation using the generalised adams-bashforth-moulton method Reacciones nucleares Ecuaciones diferenciales con retardo - Soluciones numéricas Nuclear reactions Delay differential equations - Numerical solutions Nuclear reactor power Nuclear density Point kinetics equations Numerical methods Densidade nuclear Potência do reator nuclear Métodos numéricos Equações da cinetica pontual
title_short	Neutron density calculation using the generalised adams-bashforth-moulton method
title_full	Neutron density calculation using the generalised adams-bashforth-moulton method
title_fullStr	Neutron density calculation using the generalised adams-bashforth-moulton method
title_full_unstemmed	Neutron density calculation using the generalised adams-bashforth-moulton method
title_sort	Neutron density calculation using the generalised adams-bashforth-moulton method
dc.creator.fl_str_mv	Suescún-Díaz, Daniel Rasero, Diego Lozano Parada, Jaime Humberto
dc.contributor.author.spa.fl_str_mv	Suescún-Díaz, Daniel Rasero, Diego Lozano Parada, Jaime Humberto
dc.subject.armarc.spa.fl_str_mv	Reacciones nucleares Ecuaciones diferenciales con retardo - Soluciones numéricas
topic	Reacciones nucleares Ecuaciones diferenciales con retardo - Soluciones numéricas Nuclear reactions Delay differential equations - Numerical solutions Nuclear reactor power Nuclear density Point kinetics equations Numerical methods Densidade nuclear Potência do reator nuclear Métodos numéricos Equações da cinetica pontual
dc.subject.armarc.eng.fl_str_mv	Nuclear reactions Delay differential equations - Numerical solutions
dc.subject.proposal.eng.fl_str_mv	Nuclear reactor power Nuclear density Point kinetics equations Numerical methods
dc.subject.proposal.por.fl_str_mv	Densidade nuclear Potência do reator nuclear Métodos numéricos Equações da cinetica pontual
description	Este artículo presenta una solución numérica a las ecuaciones de cinética puntual para reactores de energía nuclear, un conjunto de siete ecuaciones diferenciales acopladas que describen la variación temporal de la densidad de neutrones y la concentración de precursores de neutrones retardados. Debido a la naturaleza del sistema, proponemos resolver numéricamente las ecuaciones de cinética de puntos mediante la implementación de los métodos de Adams-Bashforth y de Adams-Moulton, que son esquemas predictores-correctores con sus respectivos modificadores para aumentar la precisión. El método propuesto se probó computacionalmente para diferentes formas de reactividad con hasta seis grupos de precursores de neutrones retardados. Este método se utilizó en una publicación reciente para resolver el problema inverso de encontrar la reactividad. Adicionalmente, se muestra que también se puede utilizar para el cálculo de la energía nuclear, que es simple y fácil de implementar, y que produce buenos resultados en comparación con los de la literatura para la densidad de población de neutrones y la concentración de precursores de neutrones retardados
publishDate	2019
dc.date.issued.none.fl_str_mv	2019-11-20
dc.date.accessioned.none.fl_str_mv	2021-11-11T15:27:17Z
dc.date.available.none.fl_str_mv	2021-11-11T15:27:17Z
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dc.relation.citationedition.spa.fl_str_mv	Volumen 24, número 3 (2019)
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dc.relation.cites.eng.fl_str_mv	Suescún Díaz, D., Rasero Causil, D.A., Lozano Parada, J.H. (2019). Neutron Density Calculation Using the Generalised Adams-Bashforth-Moulton Method. Universitas Scientiarum. Pontificia Universidad Javeriana. (Vol. 24 (3), pp. 543-563, 2019. doi: 10.11144/Javeriana.SC24-3.ndcu
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dc.relation.references.none.fl_str_mv	[1] Chao YA, Attard A. A resolution of the stiffness problem of reactor kinetics, Nuclear Science and Engineering, 90(1):40-46, 1985. doi: 10.13182/NSE85-A17429 [2] Sánchez J. On the numerical solution of the point reactor kinetics equations by generalized Runge-Kutta methods, Nuclear Science and Engineering, 103: 94-99, 1989. doi: 10.13182/NSE89-A23663 [3] Aboanber AE, Nahla AA. Solution of the point kinetics equations in the presence of Newtonian temperature feedback by Padé approximation via the analytical inversion method, Journal of Physics A: Mathematical and General, 35(45):9609-9627, 2002b. doi: 10.1088/0305-4470/35/45/309 [4] Aboanber AE, Nahla AA. Generalization of the analytical inverse method for the solution of point kinetics equations, Journal of Physics A: Mathematical and General, 35(14): 3245-3263, 2002a. doi: 10.1088/0305-4470/35/14/307 [5] Aboanber AE. Analytical solution of the point kinetics equations by exponential mode analysis, Progress in Nuclear Energy, 42(2): 179-197, 2003. doi: 10.1016/s0140-6701(03)82201-4 [6] Kinard, M.; Allen, E. J.: Efficient numerical solution of the point kinetics equations in nuclear reactor dynamics, Annals of Nuclear Energy, 31(9): 1039-1051, 2004. doi: 10.1016/j.anucene.2003.12.008 [7] Quintero LB. CORE: a numerical algorithm to solve the point kinetics equations, Annals of Nuclear Energy, 35(11): 2136-2138, 2008. doi: 10.1016/j.anucene.2008.07.002 [8] Li H, Chen W, Luo L, Zhu Q. A new integral method for solving the point reactor neutron kinetics equations, Annals of Nuclear Energy, 36(4): 427-432, 2009. doi: 10.1016/j.anucene.2008.11.033 [9] Nahla, A. A.: Taylor series method for solving the nonlinear point kinetics equations, Nuclear Engineering and Design, 241(5): 1592-1595, 2011. doi: 10.1016/j.nucengdes.2011.02.016 [10] Hamada, Y. M.: Generalized power series method with step size control for neutron kinetics equations, Nuclear Engineering and Design, 241(8): 3032-3041, 2011. doi: 10.1016/j.nucengdes.2011.05.006 [11] Hamada YM. Confirmation of accuracy of generalized power series method for the solution of point kinetics equations with feedback, Annals of Nuclear Energy, 55: 184-193, 2013. doi: 10.1016/j.anucene.2012.12.013 [12] Ganapol BD. A highly accurate algorithm for the solution of the point kinetics equations, Annals of Nuclear Energy, 62: 564- 571, 2013. doi: 10.1016/j.anucene.2012.06.007 [13] Picca P, Furfaro R, Ganapol B. A highly accurate technique for the solution of the non-linear point kinetics equations, Annals of Nuclear Energy, 58: 43-53, 2013. doi: 10.1016/j.anucene.2013.03.004 [14] Salah A. Hassan SA. Samia.: The Analytical Algorithm for the Differential Transform Method to Solution of the Reactor Point kinetics Equations, World Applied Sciences Journal, 27(3):367-370, 2013. doi: 10.5829/idosi.wasj.2013.27.03.1601 [15] Kim HT, Park Y, Kazantzis N, Parlos A, Vista IV F, Chong KT. A numerical solution to the point kinetic equations using Taylor-Lie series combined with a scaling and squaring technique, Nuclear Engineering and Design, 272: 1-10, 2014. doi: 10.1016/j.nucengdes.2013.12.066 [16] Patra A, Ray SS. A numerical approach based on Haar wavelet operational method to solve neutron point kinetics equation involving imposed reactivity insertions, Annals of Nuclear Energy, 68: 112-117, 2014. doi: 10.1016/j.anucene.2014.01.008 [17] Leite QB, Palma AP, Vilhena MT, Bodmann EJ. Analytical representation of the solution of the point reactor kinetics equations with adaptive time step, Progress in Nuclear Energy, 70: 112-118, 2014. doi: 10.1016/j.pnucene.2013.07.008 [18] Hamada YM. Trigonometric Fourier-series solutions of the point reactor kinetics equations. Nuclear Engineering and Design, 281: 142-153, 2015. doi: 10.1016/j.nucengdes.2014.11.017 [19] Razak MA, Devan K, Sathiyasheela T. The modified exponential time differencing (ETD) method for solving the reactor point kinetics equations, Annals of Nuclear Energy, 76: 193-199, 2015. doi: 10.1016/j.anucene.2014.09.020 [20] Nahla AA. Numerical treatment for the point reactor kinetics equations using theta method, eigenvalues and eigenvectors, Progress in Nuclear Energy, 85: 756-763, 2015. doi: 10.1016/j.pnucene.2015.09.008 [21] Suescún DD, Narváez PM, Lozano PH. Calculation of Nuclear Reactivity Using the Generalised Adams Bashforth-Moulton Predictor-Corrector Method, Kerntechnik, 81(1): 86-93, 2016. doi: 10.3139/124.110591 [22] Yun C, Xingjie P, Qing L, Kan W. A numerical solution to the nonlinear point kinetics equations using Magnus expansion, Annals of Nuclear Energy, 89: 84-89, 2016. doi: 10.1016/j.anucene.2015.11.021 [23] Duderstadt JJ, Hamilton LJ. Nuclear Reactor Analysis, second ed. John Wiley & Sons Inc., New York, 1976
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spelling	Suescún-Díaz, Daniel29eca95d98db655eeb1ef3f95c2c66e9Rasero, Diego86c039a30c118baf0a30fff759f3096eLozano Parada, Jaime Humberto5e37d5ded4625c6929b3fb6a8753c3502021-11-11T15:27:17Z2021-11-11T15:27:17Z2019-11-201227483https://hdl.handle.net/10614/13432Este artículo presenta una solución numérica a las ecuaciones de cinética puntual para reactores de energía nuclear, un conjunto de siete ecuaciones diferenciales acopladas que describen la variación temporal de la densidad de neutrones y la concentración de precursores de neutrones retardados. Debido a la naturaleza del sistema, proponemos resolver numéricamente las ecuaciones de cinética de puntos mediante la implementación de los métodos de Adams-Bashforth y de Adams-Moulton, que son esquemas predictores-correctores con sus respectivos modificadores para aumentar la precisión. El método propuesto se probó computacionalmente para diferentes formas de reactividad con hasta seis grupos de precursores de neutrones retardados. Este método se utilizó en una publicación reciente para resolver el problema inverso de encontrar la reactividad. Adicionalmente, se muestra que también se puede utilizar para el cálculo de la energía nuclear, que es simple y fácil de implementar, y que produce buenos resultados en comparación con los de la literatura para la densidad de población de neutrones y la concentración de precursores de neutrones retardadosThis paper presents a numerical solution to the equations of point kinetics for nuclear power reactors, a set of seven coupled differential equations that describe the temporal variation of neutron density and the concentration of delayed neutron precursors. Due to the nature of the system, we propose to numerically solve the point kinetics equations by implementing the Adams-Bashforth and Adams-Moulton methods, which are predictor-corrector schemes with their respective modifiers to increase precision. The proposed method was tested computationally for different forms of reactivity with up to six groups of delayed neutron precursors. This method was used in a recent publication to solve the inverse problem of finding the reactivity. In this work, it is shown that it can also be used for the calculation of nuclear power, that it is simple and easy to implement, and that it produces good results when compared with those in the literature for neutron population density and concentration of delayed neutron precursorsEste artigo apresenta uma solução numérica para as equações da cinética pontual para reatores de energia nuclear, um conjunto de sete equações diferenciais acopladas que descrevem a variação temporal da densidade de nêutrons e concentração de precursores de nêutrons atrasados. Devido à natureza do sistema, propomos resolver numericamente as equações da cinética pontual implementando os métodos de Adams-Bashforth e de Adams-Moulton, que são esquemas preditores-corretores com seus respectivos modificadores para aumentar a precisão. O método proposto foi testado computacionalmente para diferentes formas da reatividade com até seis grupos de precursores de nêutrons atrasados. Este método foi usado em uma publicação recente para resolver o problema inverso de encontrar a reatividade. Além disso, mostra-se que também pode ser utilizado para o cálculo da potência nuclear, que é simples e fácil de implementar e que produz bons resultados quando comparado com os da literatura para densidade populacional de nêutrons e concentração de precursores de nêutrons atrasados21 páginasapplication/pdfengPrograma Editorial Pontificia Universidad JaverianaBogotáDerechos reservado - Editorial Pontificia Universidad Javerianahttps://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessAtribución-NoComercial-SinDerivadas 4.0 Internacional (CC BY-NC-ND 4.0)http://purl.org/coar/access_right/c_abf2Neutron density calculation using the generalised adams-bashforth-moulton methodCálculo da densidade de nêutrons usando o método generalizado de Adams-Bashforth-MoultonCálculo de densidad de neutrones utilizando el método generalizado de Adams-Bashforth-MoultonArtículo de revistahttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1Textinfo:eu-repo/semantics/articlehttp://purl.org/redcol/resource_type/ARTinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/version/c_970fb48d4fbd8a85Reacciones nuclearesEcuaciones diferenciales con retardo - Soluciones numéricasNuclear reactionsDelay differential equations - Numerical solutionsNuclear reactor powerNuclear densityPoint kinetics equationsNumerical methodsDensidade nuclearPotência do reator nuclearMétodos numéricosEquações da cinetica pontualVolumen 24, número 3 (2019)563354324Suescún Díaz, D., Rasero Causil, D.A., Lozano Parada, J.H. (2019). Neutron Density Calculation Using the Generalised Adams-Bashforth-Moulton Method. Universitas Scientiarum. Pontificia Universidad Javeriana. (Vol. 24 (3), pp. 543-563, 2019. doi: 10.11144/Javeriana.SC24-3.ndcuUniversitas Scientiarum[1] Chao YA, Attard A. A resolution of the stiffness problem of reactor kinetics, Nuclear Science and Engineering, 90(1):40-46, 1985. doi: 10.13182/NSE85-A17429[2] Sánchez J. On the numerical solution of the point reactor kinetics equations by generalized Runge-Kutta methods, Nuclear Science and Engineering, 103: 94-99, 1989. doi: 10.13182/NSE89-A23663[3] Aboanber AE, Nahla AA. Solution of the point kinetics equations in the presence of Newtonian temperature feedback by Padé approximation via the analytical inversion method, Journal of Physics A: Mathematical and General, 35(45):9609-9627, 2002b. doi: 10.1088/0305-4470/35/45/309[4] Aboanber AE, Nahla AA. Generalization of the analytical inverse method for the solution of point kinetics equations, Journal of Physics A: Mathematical and General, 35(14): 3245-3263, 2002a. doi: 10.1088/0305-4470/35/14/307[5] Aboanber AE. Analytical solution of the point kinetics equations by exponential mode analysis, Progress in Nuclear Energy, 42(2): 179-197, 2003. doi: 10.1016/s0140-6701(03)82201-4[6] Kinard, M.; Allen, E. J.: Efficient numerical solution of the point kinetics equations in nuclear reactor dynamics, Annals of Nuclear Energy, 31(9): 1039-1051, 2004. doi: 10.1016/j.anucene.2003.12.008[7] Quintero LB. CORE: a numerical algorithm to solve the point kinetics equations, Annals of Nuclear Energy, 35(11): 2136-2138, 2008. doi: 10.1016/j.anucene.2008.07.002[8] Li H, Chen W, Luo L, Zhu Q. A new integral method for solving the point reactor neutron kinetics equations, Annals of Nuclear Energy, 36(4): 427-432, 2009. doi: 10.1016/j.anucene.2008.11.033[9] Nahla, A. A.: Taylor series method for solving the nonlinear point kinetics equations, Nuclear Engineering and Design, 241(5): 1592-1595, 2011. doi: 10.1016/j.nucengdes.2011.02.016[10] Hamada, Y. M.: Generalized power series method with step size control for neutron kinetics equations, Nuclear Engineering and Design, 241(8): 3032-3041, 2011. doi: 10.1016/j.nucengdes.2011.05.006[11] Hamada YM. Confirmation of accuracy of generalized power series method for the solution of point kinetics equations with feedback, Annals of Nuclear Energy, 55: 184-193, 2013. doi: 10.1016/j.anucene.2012.12.013[12] Ganapol BD. A highly accurate algorithm for the solution of the point kinetics equations, Annals of Nuclear Energy, 62: 564- 571, 2013. doi: 10.1016/j.anucene.2012.06.007[13] Picca P, Furfaro R, Ganapol B. A highly accurate technique for the solution of the non-linear point kinetics equations, Annals of Nuclear Energy, 58: 43-53, 2013. doi: 10.1016/j.anucene.2013.03.004[14] Salah A. Hassan SA. Samia.: The Analytical Algorithm for the Differential Transform Method to Solution of the Reactor Point kinetics Equations, World Applied Sciences Journal, 27(3):367-370, 2013. doi: 10.5829/idosi.wasj.2013.27.03.1601[15] Kim HT, Park Y, Kazantzis N, Parlos A, Vista IV F, Chong KT. A numerical solution to the point kinetic equations using Taylor-Lie series combined with a scaling and squaring technique, Nuclear Engineering and Design, 272: 1-10, 2014. doi: 10.1016/j.nucengdes.2013.12.066[16] Patra A, Ray SS. A numerical approach based on Haar wavelet operational method to solve neutron point kinetics equation involving imposed reactivity insertions, Annals of Nuclear Energy, 68: 112-117, 2014. doi: 10.1016/j.anucene.2014.01.008[17] Leite QB, Palma AP, Vilhena MT, Bodmann EJ. Analytical representation of the solution of the point reactor kinetics equations with adaptive time step, Progress in Nuclear Energy, 70: 112-118, 2014. doi: 10.1016/j.pnucene.2013.07.008[18] Hamada YM. Trigonometric Fourier-series solutions of the point reactor kinetics equations. Nuclear Engineering and Design, 281: 142-153, 2015. doi: 10.1016/j.nucengdes.2014.11.017[19] Razak MA, Devan K, Sathiyasheela T. The modified exponential time differencing (ETD) method for solving the reactor point kinetics equations, Annals of Nuclear Energy, 76: 193-199, 2015. doi: 10.1016/j.anucene.2014.09.020[20] Nahla AA. Numerical treatment for the point reactor kinetics equations using theta method, eigenvalues and eigenvectors, Progress in Nuclear Energy, 85: 756-763, 2015. doi: 10.1016/j.pnucene.2015.09.008[21] Suescún DD, Narváez PM, Lozano PH. Calculation of Nuclear Reactivity Using the Generalised Adams Bashforth-Moulton Predictor-Corrector Method, Kerntechnik, 81(1): 86-93, 2016. doi: 10.3139/124.110591[22] Yun C, Xingjie P, Qing L, Kan W. A numerical solution to the nonlinear point kinetics equations using Magnus expansion, Annals of Nuclear Energy, 89: 84-89, 2016. doi: 10.1016/j.anucene.2015.11.021[23] Duderstadt JJ, Hamilton LJ. Nuclear Reactor Analysis, second ed. 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Neutron density calculation using the generalised adams-bashforth-moulton method

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