%0 Journal Article
%T Solution of Point Reactor Neutron Kinetics Equations with Temperature Feedback by Singularly Perturbed Method
%A Wenzhen Chen
%A Jianli Hao
%A Ling Chen
%A Haofeng Li
%J Science and Technology of Nuclear Installations
%D 2013
%I Hindawi Publishing Corporation
%R 10.1155/2013/261327
%X The singularly perturbed method (SPM) is proposed to obtain the analytical solution for the delayed supercritical process of nuclear reactor with temperature feedback and small step reactivity inserted. The relation between the reactivity and time is derived. Also, the neutron density (or power) and the average density of delayed neutron precursors as the function of reactivity are presented. The variations of neutron density (or power) and temperature with time are calculated and plotted and compared with those by accurate solution and other analytical methods. It is shown that the results by the SPM are valid and accurate in the large range and the SPM is simpler than those in the previous literature. 1. Introduction The analysis of variation of neutron density (or power) and reactivity with time under the different conditions is an important content of nuclear reactor physics or neutron kinetics [1¨C7]. Some important achievements on the supercritical transient with temperature feedback with big ( ) or small ( ) reactivity inserted have been approached through the effort of many scholars [7¨C12]. The studies on the delayed supercritical transient with small reactivity inserted and temperature feedback are introduced in the related literature [13¨C15], in which the explicit function of density (or power) and reactivity with respect to time is derived mainly with decoupling method, power prompt jump approximation, precursor prompt jump approximation, temperature prompt jump approximation [10, 16], and so forth. From the detailed analysis and comparison of the results in the early and recent literature [7, 12, 14], it is found that some results have certain limit and rather big error under the particular conditions. In present work, the variation law of power, reactivity, and precursor density with respect to time at any level of initial power is obtained by the singularly perturbed method (SPM). All the results are compared with those obtained by the numerical solution which tend to the accurate solution under very small time step size [17]. It is proved that the SPM is correct and reliable and is simpler than the analytical methods by the related literature. 2. Theoretical Derivation The point reactor neutron kinetics equations with one group of delayed neutrons are [3, 4] where is the average neutron density, is the time, is the reactivity, is the total fraction of the delayed neutron, £¿£¿is the prompt neutron lifetime, is the radioactive decay constant of delayed neutron precursor, and is the average density of delayed neutron precursor. When multiplied
%U http://www.hindawi.com/journals/stni/2013/261327/