NEUTRON POINT KINETICS MODEL WITH A DISTRIBUTED-ORDER FRACTIONAL DERIVATIVE

F. A. Godã Nez, G. Fernã Ndez-Anaya, S. Quezada-Garcã A, L. A. Quezada-Tã‰llez and M. A. Polo-Labarrios
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F. A. Godã Nez: Universidad Nacional Autónoma de México, Instituto de Ingeniería, Departamento de Sistemas Mecánicos, Energéticos y de Transporte, Avenida Universidad 3000, Ciudad Universitaria, Coyoacán 04510 Ciudad de México, México†Unidad de Investigación y Tecnología Aplicadas, Universidad Nacional Autónoma de México, Vía de la Innovación No. 410, Autopista Monterrey-Aeropuerto km. 10 PIIT, Apodaca 66629, Nuevo León, México
G. Fernã Ndez-Anaya: ��Departamento de Física y Matemáticas, Universidad Iberoamericana Ciudad de México Prolongación, Paseo de Reforma 880, Lomas de Santa Fe 01219, Ciudad de México, México
S. Quezada-Garcã A: �Universidad Nacional Autónoma de México, Facultad de Ingeniería, Departamento de Sistemas Energéticos, Avendia Universidad 3000, Ciudad Universitaria, Coyoacán 04510, Ciudad de México, México
L. A. Quezada-Tã‰llez: �Escuela Superior de Apan, UAEH. Carretera Apan-Calpulalpan km. 8, Colonia Chimalpa Tlalayote, Apan, 43900, Hidalgo, México
M. A. Polo-Labarrios: ��Departamento de Física y Matemáticas, Universidad Iberoamericana Ciudad de México Prolongación, Paseo de Reforma 880, Lomas de Santa Fe 01219, Ciudad de México, México§Universidad Nacional Autónoma de México, Facultad de Ingeniería, Departamento de Sistemas Energéticos, Avendia Universidad 3000, Ciudad Universitaria, Coyoacán 04510, Ciudad de México, México∥à rea de Ingeniería en Recursos Energéticos, Universidad Autónoma Metropolitana-Iztapalapa Avenida, Ferrocarril San Rafael Atlixco 186, Colonia Leyes de Reforma 1era, Sección Iztapalapa, 09310, Ciudad de México, México

FRACTALS (fractals), 2024, vol. 32, issue 06, 1-18

Abstract: In this paper, the solutions of an extended form of the Fractional-order Neutron Point Kinetics (FNPK) equation in terms of Caputo-time derivatives of the same order are investigated. Instead of using a Caputo derivative, a distributed-order fractional derivative in the Caputo sense was employed in the term of the FNPK equation which is multiplied by the reactivity. This term plays an important role in the description of neutron kinetics during the start-up, shutdown, and steady-state processes in nuclear reactors. The extended (DFNPK) model was solved using the beta, normal, bimodal and Dirac delta distributions to investigate their effect on the transient state solutions of the neutron density. Regardless of the distribution used, the most significant finding is that a destabilizing effect on the neutron density is induced when the mode (or the instant of application of the Dirac delta) of the distribution tends to one while maintaining the orders of the Caputo-time derivatives constant. What defines the destabilizing effect are large magnitude oscillations, a rapid decay, and an oscillation-free steady state with a monotonic increase that is parallel to but somewhat above the trend determined by the FNPK equation. The extended model is anticipated to be effective for modeling neutron density dispersion in a highly heterogeneous medium that may be described using distributed derivatives.

Keywords: Neutron Point Kinetic; Distributed-Order Fractional Derivative; Beta Distribution; Normal Distribution; Bimodal Distribution; Dirac Delta Distribution (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0218348X24501068

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