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首页> 外文期刊>Annals of nuclear energy >On an analytical representation for the solution of the neutron point kinetics equation free of stiffness
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On an analytical representation for the solution of the neutron point kinetics equation free of stiffness

机译：关于无刚度的中子点动力学方程解的解析表示

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摘要

In this work, we report on an analytical representation for the solution of the neutron point kinetics equation, free of stiffness and assuming that reactivity is a continuous or sectionally continuous function of time. To this end, we cast the point kinetics equation in a first order linear differential equation. Next, we split the corresponding matrix into a diagonal matrix plus a matrix that contains the remaining terms. Expanding the neutron density and the delayed neutron precursor concentrations in a truncated series allows one to construct a recursive system in form of a first order matrix differential equation with source. The initialization of the recursion procedure is of diagonal form and has no source but satisfies the initial conditions. The remaining equations are subject to null initial conditions and include the time-dependent diagonal elements together with the off-diagonal elements as a source term. The solution is obtained in an analytical representation which may be evaluated for any time value, because it is free of stiffness. We present numerical simulations and comparisons against results from the literature for a constant, a step, a ramp, a quadratic, and a sine shaped reactivity function.
机译：在这项工作中，我们报告中子点动力学方程解的解析表示形式，其中不包括刚度，并假设反应性是时间的连续或部分连续函数。为此，我们将点动力学方程式转化为一阶线性微分方程式。接下来，我们将相应的矩阵拆分为对角矩阵以及包含其余项的矩阵。以截断序列的形式扩展中子密度和延迟的中子前驱物浓度，使人们可以构造具有源的一阶矩阵微分方程形式的递归系统。递归过程的初始化是对角线形式，没有源，但满足初始条件。其余方程式均受零初始条件的约束，并且包括与时间相关的对角线元素以及非对角线元素作为源项。该解决方案以解析表示形式获得，该解决方案可以不受任何时间值的影响，因为它没有刚度。我们针对常数，阶跃，斜率，二次方和正弦形反应性函数提供了数值模拟和与文献结果的比较。

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  • 来源
    《Annals of nuclear energy》 |2014年第9期|97-102|共6页
  • 作者

    M. Wollmann da Silva; S. Bogado Leite; M.T. Vilhena; B.E.J. Bodmann;

  • 作者单位

    Programa de Pos-Graduacao em Engenharia Mecanica, Universidade Federal do Rio Grande do Sul, Rua Sarmento Leite 425, 2° Andar, CEP: 90.050-170, Porto Alegre, RS, Brazil;

    Comissao Nacional de Energia Nuclear (CNEN/SEDE), Rua General Severiano 90, CEP: 22.291-901, Rio de Janeiro, RJ, Brazil;

    Programa de Pos-Graduacao em Engenharia Mecanica, Universidade Federal do Rio Grande do Sul, Rua Sarmento Leite 425, 2° Andar, CEP: 90.050-170, Porto Alegre, RS, Brazil;

    Programa de Pos-Graduacao em Engenharia Mecanica, Universidade Federal do Rio Grande do Sul, Rua Sarmento Leite 425, 2° Andar, CEP: 90.050-170, Porto Alegre, RS, Brazil;

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  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Point kinetics; Decomposition method; Free of stiffness;

    机译：点动力学;分解方法;没有僵硬;

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