Nuclear Engineering and Technology

Korean Nuclear Society (한국원자력학회)
권호 표지
DOI QR코드

DOI QR Code

On the numerical solution of the point reactor kinetics equations

  • Suescun-Diaz, D. (Departamento de Ciencias Exactas y Naturales, Grupo de Fisica Aplicada, Universidad Surcolombiana) ;
  • Espinosa-Paredes, G. (Area de Ingenieria en Recursos Energeticos, Universidad Autonoma Metropolitana-Iztapalapa)
  • Received : 2019.10.13
  • Accepted : 2019.11.30
  • Published : 2020.06.25
Download PDF
⟨ Previous Next ⟩

Abstract

The aim of this paper is to explore the 8th-order Adams-Bashforth-Moulton (ABM8) method in the solution of the point reactor kinetics equations. The numerical experiment considers feedback reactivity by Doppler effects, and insertions of reactivity. The Doppler effects is approximated with an adiabatic nuclear reactor that is a typical approximation. The numerical results were compared and discussed with several solution methods. The CATS method was used as a benchmark method. According with the numerical experiments results, the ABM8 method can be considered as one of the main solution method for changes reactivity relatively large.

Keywords

References

  1. Y.A. Chao, A. Attard, A resolution of the stiffness problem of reactor kinetics, Nucl. Sci. Eng. 90 (1985) 40-46. https://doi.org/10.13182/NSE85-A17429
  2. J. Sanchez, On the numerical solution of the point reactor kinetics equations by generalized Runge-Kutta methods, Nucl. Sci. Eng. 103 (1989) 94-99. https://doi.org/10.13182/NSE89-A23663
  3. A.E. Aboanber, Analytical solution of the point kinetics equations by exponential mode analysis, Prog. Nucl. Energy 42 (2003) 179-197. https://doi.org/10.1016/S0149-1970(03)80008-2
  4. L.B. Quintero, CORE: a numerical algorithm to solve the point kinetics equations, Ann. Nucl. Energy 35 (2008) 2136-2138. https://doi.org/10.1016/j.anucene.2008.07.002
  5. H. Li, W. Chen, L. Luo, Q. Zhu, A new integral method for solving the point reactor neutron kinetics equations, Ann. Nucl. Energy 36 (4) (2009) 427-432. https://doi.org/10.1016/j.anucene.2008.11.033
  6. D. McMohan, A. Pierson, A Taylor Series Solution of the Reactor Point Kinetic Equations, 2010 arXiv preprint Retrieved from arXiv: 1001.4100 http://arxiv.org/ftp/arxiv/papers/1001/1001.4100.pdf.
  7. A.A. Nahla, Taylor series method for solving the nonlinear point kinetics equations, Nucl. Eng. Des. 241 (2011) 1592-1595. https://doi.org/10.1016/j.nucengdes.2011.02.016
  8. B.D. Ganapol, A highly accurate algorithm for the solution of the point kinetics equations, Ann. Nucl. Energy 62 (2013) 564-571. https://doi.org/10.1016/j.anucene.2012.06.007
  9. H.T. Kim, Y. Park, N. Kazantzis, A.G. Parlos, F.P. Vista IV, K.T. Chong, A numerical solution to the point kinetic equations using Taylor-Lie series combined with a scaling and squaring technique, Nucl. Eng. Des. 272 (2014) 1-10. https://doi.org/10.1016/j.nucengdes.2013.12.066
  10. A. Patra, S.S. Ray, A numerical approach based on Haar wavelet operational method to solve neutron point kinetics equation involving imposed reactivity insertions, Ann. Nucl. Energy 68 (2014) 112-117. https://doi.org/10.1016/j.anucene.2014.01.008
  11. Y.M. Hamada, Trigonometric Fourier-series solutions of the point reactor kinetics equations, Nucl. Eng. Des. 281 (2015) 142-153. https://doi.org/10.1016/j.nucengdes.2014.11.017
  12. M.A. Razak, K. Devan, T. Sathiyasheela, The modified exponential time differencing (ETD) method for solving the reactor point kinetics equations, Ann. Nucl. Energy 76 (2015) 193-199. https://doi.org/10.1016/j.anucene.2014.09.020
  13. A.A. Nahla, Numerical treatment for the point reactor kinetics equations using theta method, eigenvalues and eigenvectors, Prog. Nucl. Energy 85 (2015) 756-763. https://doi.org/10.1016/j.pnucene.2015.09.008
  14. D.D. Suescun, P.M. Narvaez, P.H. Lozano, Calculation of nuclear reactivity using the generalised Adams-Bashforth-Moulton predictor-corrector method, Kerntechnik 81 (2016) 86-93. https://doi.org/10.3139/124.110591
  15. D.D. Suescun, C.D. Rasero, P.H. Lozano, Adams-Bashforth-Moulton method with Savitzky-Golay filter to reduce reactivity fluctuations, Kerntechnik 82 (2017) 674-677. https://doi.org/10.3139/124.110842
  16. C. Yun, P. Xingjie, L. Qing, W. Kan, A numerical solution to the nonlinear point kinetics equations using Magnus expansion, Ann. Nucl. Energy 89 (2016) 84-89. https://doi.org/10.1016/j.anucene.2015.11.021
  17. A.E. Aboanber, Y.M. Hamada, Power series solution (PWS) of nuclear reactor dynamics with Newtonian temperature feedback, Ann. Nucl. Energy 30 (2003) 1111-1122. https://doi.org/10.1016/S0306-4549(03)00033-1
  18. M. Kinard, E.J. Allen, Efficient numerical solution of the point kinetics equations in nuclear reactor dynamics, Ann. Nucl. Energy 31 (2004) 1039-1051. https://doi.org/10.1016/j.anucene.2003.12.008
  19. A.A. Nahla, Analytical solution to solve the point reactor kinetics equations, Nucl. Eng. Des. 240 (2010) 1622-1629. https://doi.org/10.1016/j.nucengdes.2010.03.003
  20. A.A. Nahla, An efficient technique for the point reactor kinetics equations with Newtonian temperature feedback effects, Ann. Nucl. Energy 38 (2011) 2810-2817. https://doi.org/10.1016/j.anucene.2011.08.021
  21. B. Ganapol, P. Picca, A. Previti, D. Mostacci, The solution of the point kinetics equations via converged accelerated Taylor series (CATS), in: Advances in Reactor Physics-Linking Research, Industry and Education (PHYSOR 2012), Knoxville, Tennessee, USA, April 15-20, 2012, 2012.
  22. P. Picca, R. Furfaro, B.D. Ganapol, A highly accurate technique for the solution of the non-linear point kinetics equations, Ann. Nucl. Energy 58 (2013) 43-53. https://doi.org/10.1016/j.anucene.2013.03.004
  23. S.Q.B. Leite, M.T. de Vilhena, B.E. Bodmann, Solution of the point reactor kinetics equations with temperature feedback by the ITS2 method, Prog. Nucl. Energy 91 (2016) 240-249. https://doi.org/10.1016/j.pnucene.2016.05.001
  24. J.J. Duderstadt, L.J. Hamilton, Nuclear Reactor Analysis, John Wiley and Sons Inc, New York, USA, 1976.
  25. D.L. Hetrick, Dynamics of Nuclear Reactors, University of Chicago Press, Chicago and London, 1971.
  26. J.C. Butcher, Numerical Methods for Ordinary Differential Equations, second ed., John Wiley & Sons Ltd, 2008.
  27. T.M. Sutton, B.N. Aviles, Diffusion theory methods for spatial kinetics calculations, Prog. Nucl. Energy 30 (1996) 119-182. https://doi.org/10.1016/0149-1970(95)00082-U
  28. B. Ganapol, Numerical Data provided by B, D. Ganapol, 2009.

Cited by

  1. An efficient exponential representation for solving the two-energy group point telegraph kinetics model vol.166, 2020, https://doi.org/10.1016/j.anucene.2021.108698