Yansıtıcılı reaktörlerin stokastik iki-nokta reaktör kinetik denklemlerinin sayısal simülasyonu

Abstract

Nokta reaktör kinetik denklemlerinin sayısal çözümleri bize nötron nüfusu ve gecikmiş nötron öncü yoğunluklarının ortalama değerlerini vermektedir. Gerçek dinamik süreç stokastik bir süreç olduğu için, nötron nüfusu ve öncü yoğunlukları zamanla rastgele dalgalanmaktadır. Bu çalışmada, harici nötron kaynağı olmayan ve altı grup gecikmiş nötron öncüsü olan güçlü yansıyan reaktörlerin dinamik davranışını analiz etmek amacıyla iki-nokta reaktör kinetik denklemleri için yeni bir stokastik model geliştirilmiştir. Bu modele karşılık gelen Itô stokastik diferansiyel denklemler sistemini türetmek için iki-nokta reaktör kinetik denklemleri üç terime ayrılır: ani nötronlar, gecikmiş nötronlar ve yansıyan nötronlar. Geri besleme etkilerinin olup ve olmadığı farklı pertürbasyon durumlarında, stokastik diferansiyel denklemler sistemi Euler-Murayama sayısal yöntemini kullanarak çözülür. Sistemin ortalama yanıtının diğer deterministik sayısal yöntemlerin sonuçlarıyla karşılaştırılabilir halde olduğu görünmektedir.

Keywords

• Reflected reactor
• Euler-Murayama Method
• Stochastic models
• Feedback effect

Numerical simulation of stochastic two-point reactor kinetics equations for reflected reactors

Abstract

Deterministic numerical solutions of point reactor kinetic equations give us the mean values of the neutron population and delayed neutron precursor concentrations, whereas the actual dynamical process is stochastic and the neutron population and precursor concentrations fluctuate randomly with time. In the present study, a novel stochastic model for two-point reactor kinetics equations is developed and used to analyze the dynamical behavior of the source-free strongly reflected reactors with six groups of delayed neutron precursors. To derive the Itô stochastic differential equations system corresponding to this model, the two-point reactor kinetics equations are separated into three terms: prompt neutrons, delayed neutrons and reflected neutrons. In the case of different perturbation scenarios, both with and without the Newtonian temperature reactivity feedback effects, this system of stochastic differential equations is solved using the Euler-Murayama numerical method. It is observed that the mean response of the system is comparable with the results of other deterministic numerical methods.

Keywords

• Reflected reactor
• Euler-Murayama Method
• Stochastic models

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