Solution of two-point reactor kinetic equations for source-driven reflected reactors using the Green's function generation method

Abstract

The transient analysis of nuclear reactors is a very important issue from the safety point of view. The point reactor kinetics equations are extensively used in the analysis of the transient behavior of the nuclear reactors. The experimental results confirm that the dynamical behavior of the strongly reflected reactors cannot be adequately characterized by the conventional one-point reactor kinetics equations. In this study, a Green's function generation method is developed to solve the two-point reactor kinetics equations for a subcritical source-driven reflected reactor with one group of delayed neutron precursors during the reactor start-up. Moreover, the two-point reactor kinetics equations are solved using the prompt-jump approximation method and it is shown that the obtained results are in good agreement with the results obtained from the Green’s function generation method. The validity of the given methodologies is also demonstrated through comparison with asymptotic solutions.

Keywords

• Point reactor kinetics model
• Reflected reactor
• Green’s function
• Prompt jump approximation

Kaynak-güdümlü yansıyan reaktörlerin iki-nokta kinetik denklemlerinin Green fonksiyon üretim yöntemi ile çözümü

Abstract

Nükleer reaktörlerin zamana bağlı analizi güvenlik açısından çok önemli bir faktördür. Nokta reaktör kinetik denklemleri nükleer reaktörlerin zamana bağlı davranışlarının analizinde yaygın olarak kullanılmaktadır. Deneysel sonuçlar, yaygın olarak kullanılan tek nokta reaktör kinetik modelinin güçlü yansıtıcılı reaktörlerin dinamik davranışlarının tanımlanmasında yetersiz olduğunu göstermektedir. Bu çalışmada, reaktörün çalışmaya başlatılması sırasında bir grup gecikmiş nötron öncüleri içeren kritik altı kaynak güdümlü yansıtıcılı reaktörün iki nokta reaktör kinetik eşitliklerinin çözümüne yönelik bir Green fonksiyon üretim yöntemi geliştirilmiştir. Bunun yanı sıra, iki-nokta reaktör kinetik denklemlerini çözmek için ani sıçrama yaklaşım yöntemi kullanılmıştır. Sonuç olarak ani sıçrama yaklaşım yöntemi ve Green fonksiyon üretim yöntemi ile elde edilen sonuçların uyum içinde olduğu bulunmuştur. Önerilen yöntemlerin geçerliliği asimptotik çözümlerle karşılaştırılarak da doğrulanmıştır.

Keywords

• Nokta reaktör kinetik modeli
• yansıtıcılı reaktör
• Green fonksiyonu
• Ani sıçrama Yaklaşımı

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