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

Year 2020, , 181 - 192, 18.12.2020

Bahram Rashidian Maleki

https://doi.org/10.33484/sinopfbd.759521

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

References

• Polo-Labarrios, M. A., & Espinosa-Paredes, G. 2012. Application of the fractional neutron point kinetic equation: Start-up of a nuclear reactor. Annals of Nuclear Energy, 46: 37-42
• Polo-Labarrios, M. A., & Espinosa-Paredes, G. 2012. Numerical analysis of startup PWR with fractional neutron point kinetic equation. Progress in Nuclear Energy, 60: 38-46.
• Sathiyasheela, T. 2010. Inhomogeneous point kinetics equations and the source contribution. Nuclear engineering and design, 240(12): 4083-4090.
• Henry, A. F. 1975. Nuclear Reactor Analysis. MIT Press, Cambridge, MA.
• Duderstadt, J. J. 1976. Nuclear reactor analysis. Wiley.
• Goluoglu S, Dodds HL, 2001. A time-dependent, three-dimensional neutron transport methodology. Nuclear Science and Engineering, 139(3): 248-261.
• Ball TA, 2017. The Inverse Kinetics Method and Its Application to the Annular Core Research Reactor. MSc. Thesis, The University of New Mexico.
• Spriggs, G. D., Busch, R. D., & Williams, J. G. 1997. Two-region kinetic model for reflected reactors. Annals of Nuclear Energy, 24(3): 205-250.
• Aboanber, A. E., & Nahla, A. A. 2018. Mathematical treatment for two-point reactor kinetics model of reflected systems. Progress in Nuclear Energy, 105: 287-293.
• Wang, X., Huff, K. D., Aufiero, M., Peterson, P. F., & Fratoni, M. 2016, June. Coupled reactor kinetics and heat transfer model for fluoride salt-cooled high-temperature reactor transient analysis. In International Conference on Nuclear Engineering (Vol. 50053, p. V005T15A055). American Society of Mechanical Engineers.
• Avery, R. 1958. Theory of coupled reactors (No. A/CONF. 15/P/1858). Argonne National Lab., Lemont, Ill.
• Cohn, C. E. 1962. Reflected-reactor kinetics. Nuclear Science and Engineering, 13(1): 12-17.
• Van Dam, H. 1996. Inhour equation and kinetic distortion in a two-point reactor kinetic model. Annals of Nuclear Energy, 23(14): 1127-1142.
• Aboanber, A. E., & El Mhlawy, A. M. 2009. Solution of two-point kinetics equations for reflected reactors using Analytical Inversion Method (AIM). Progress in Nuclear Energy, 51(1): 155-162.
• Aboanber, A. E., & El Mhlawy, A. M. 2008. A new version of the reflected core inhour equation and its solution. Nuclear engineering and design, 238(7): 1670-1680.
• Aboanber, A. E. 2009. Exact solution for the non-linear two point kinetic model of reflected reactors. Progress in Nuclear Energy, 51(6-7): 719-726.
• Holschuh, T. V., Marcum, W. R., & Palmer, T. S. 2017. One-group analytical solution to two-region reactor kinetic model. Annals of Nuclear Energy, 99: 199-205.
• Pázsit, I. 1996. On the kinetic response of a reactor with delayed neutrons. Annals of Nuclear Energy (Oxford), 23(4-5): 407-412.
• Almenas, K., & Lee, R. 2012. Nuclear engineering: an introduction. Springer Science & Business Media.
• Oka, Y., & Suzuki, K. 2013. Nuclear Reactor Kinetics and Plant Control (Vol. 10, pp. 978-4). Tokyo: Springer.