Numerical-analytical solutions of the fractional point kinetic model with Caputo derivatives

被引：8

作者：

Polo-Labarrios, M. A. ^{[1
,2
]}

Godinez, F. A. ^{[3
,4
]}

Quezada-Garcia, S. ^{[2
]}

机构：

[1] Univ Iberoamer, Dept Fis & Matemat, Prolongac Paseo Reforma 880, Lomas De Santa Fe 01219, Cd De Mexico, Mexico

[2] Univ Nacl Autonoma Mexico, Fac Ingn, Dept Sistemas Energet, Av Univ 3000,Ciudad Univ, Coyoacon 04510, Ciudad De Mexic, Mexico

[3] UNAM, Inst Ingn, Univ Nacl Autonoma Mexico, Ciudad De Mexico 04510, Mexico

[4] Univ Nacl Autonoma Mexico, Polo Univ Tecnol Avanzada, Via Innovac 410,Km 10 PIIT, Nuevo Leon 66629, Mexico

来源：

ANNALS OF NUCLEAR ENERGY | 2022年 / 166卷

关键词：

Reactor dynamics; Fractional neutron point kinetic equations; Anomalous diffusion exponent; Caputo fractional derivative; Laplace Transform method; Chebyshev polynomials; NUCLEAR-REACTOR; START-UP; EQUATION; FINITE; SCHEME;

D O I：

10.1016/j.anucene.2021.108745

中图分类号：

TL [原子能技术]; O571 [原子核物理学];

学科分类号：

0827 ; 082701 ;

摘要：

Novel solutions to the fractional neutron point kinetic equations in terms of Caputo derivatives are obtained for three different cases: 1) constant reactivity; 2) cold startup process of a Pressurized Water Reactor; and 3) start-up of a nuclear reactor. Numerical-analytical solutions for the first and second cases are achieved via Laplace transform technique with Talbot's method for the numerical inversion of the transformed equations. Analytical solutions for the third case are constructed by a collocation method using Chebyshev polynomials. The solutions predict inertia effects observed as a growth in neutron density up to reaching a peak and then a gradual decrease followed by a series of oscillations until reaching a steady state. This behavior, on the one hand, is accentuated as the fractional order decreases, and on the other hand, it is reconciled with the fact that the propagation speed of the neutrons within the reactor is finite. (C) 2021 Elsevier Ltd. All rights reserved.

引用

页数：14