Solutions of Reactor Point Kinetics equations with six group of delayed neutrons using Collocation method

Document Type : Full length research Paper

Authors

1 faculty of ilam university

2 Department of mathematics, Faculty of Science, Urmia University, P.O.Box:165-57153, Urmia – Iran

Abstract

In this study we have used Collocation Method (COM) as a new method in the control and dynamics of reactor fields for solution of reactor point kinetics equations in the presence of step, linear and sinusoidal reactivities with six groups delayed neutron. The calculation code has written by MATHEMATICA software. This method in addition to the low time of calculations and convergence of solutions, it has high accuracy. The results of numerical calculations by COM compared with other numerical methods show that this method is efficient and accurate. Therefore, it can be used for dynamical computing at the startup stage of the reactor.

Keywords

References

[1] A.A. Nahla, Taylor’s series method for solving the nonlinear point kinetics equations, Nuclear Engineering and Design 241 (2011) 1592–1595.
[2] A.E. Aboanber,Analytical Solution of the Point Kinetics Equations by Exponential Mode Analysis, .Progress in Nuclear Energy 42 (2003) 179-197.
[3] A.A. Nahla, Generalization of the analytical exponential model to solve the point kinetics equations of - and -moderated reactors, Nuclear Engineering and Design 238 (2008) 2648–2653.
[4] D.A.P. Palma, A.S. Martinez, A.C. Gonçalves, Analytical solution of point kinetics equations for linear reactivity variation during the start-up of a nuclear reactor, Annals of Nuclear Energy 36 (2009) 1469–1471.
[5] A.A. Nahla, Analytical solution to solve the point reactor kinetics equation, Nuclear Engineering and Design 240 (2010) 1622–1629.
[6] C.Z. Petersen, S. Dulla, M.T.M.B. Vilhena, P. Ravetto, An analytical solution of the point kinetics equations with time-variable reactivity by the decomposition method, Progress in Nuclear Energy 53 (2011) 1091-1094.
[7] S.D. Hamieh, M. Saidinezhad, Analytical solution of the point reactor kinetics equations with temperature feedback, Annals of Nuclear Energy 42 (2012) 148–152.
[8] S. Yamoah, E.H.K. Akaho, B.J.B. Nyarko, An accurate solution of point reactor neutron kinetics equations of multi-group of delayed neutrons, Annals of Nuclear Energy 54 (2013) 104–108.
[9] S.Q.B. Leite, D.A.P. Palma, M.T.d. Vilhena, B. E.J. Bodmann, Analytical representation of the solution of the point reactor kinetics equations with adaptive time step, Progress in Nuclear Energy 70 (2014) 112-118.
[10] A.E. Aboanber, Y.M. Hamada, PWS: an efficient code system for solving space-independent nuclear reactor dynamics, Annals of Nuclear Energy 29 (2002) 2159-2172.
[11] A.E. Aboanber, Y.M. Hamada, Power series solution (PWS) of nuclear reactor dynamics with Newtonian temperature feedback, Annals of Nuclear Energy 30 (2003) 1111-1122.
[12] M.E. Kinard, E.J. Allen, Efficient numerical solution of the point kinetics equations in nuclear reactor dynamics, Annals of Nuclear Energy 31 (2004) 1039-1051.
[13] K.F. Hansen, B.V. Koen, W.W. Little, Stable numerical solutions of the reactor kinetics equations, Nuclear Science and Engineering 22 (1965) 51-59.
[14] A.A. Nahla, Taylor’s series method for solving the nonlinear point kinetics equations, Nuclear Engineering and Design 241 (2011) 1592–1595.
[15] A.E. Aboanber, Stability of generalized Runge-Kutta methods for stiff kinetics coupled differential equations, Journal of Physics A: Mathematical and General 39 (2006) 1859-1876.
[16] J. Sanchez, On the numerical solution of the point reactor kinetics equations by generalized Rungee-Kutta methods, Nuclear Science and Engineering 103 (1989) 94-99.
[17] Y.C. Chao, A. Attard, A resolution of the stiffness problem of reactor kinetics, Nuclear Science and Engineering 90 (1985) 40-46.
[18] A.E. Aboanber, Stiffness treatment of differential equations for the point reactor dynamic systems, Progress in Nuclear Energy 71 (2014) 248-257.
[19] P. Ravetto, M.M. Rostagno, G. Bianchini, M. Carta, A. Dangelo,  Application of the multipoint method to the kinetics of accelerator-driven systems, Nuclear Science and Engineering 148 (2004) 79-88.
[20] S.Q.B. Leite, M.T.D. Vilhena, B.E.J. Bodmann, Solution of the point reactor kinetics equations with temperature feedback by the ITS2 method, Progress in Nuclear Energy 91 (2016) 240-249.
[21] J.P. Yan, B.Y. Guo, A Collocation Method for Initial Value Problems of Second-Order ODEs by Using Laguerre Functions, Numerical Mathematics; Theory, Method and Application 4 (2011) 283-295.
[22] E.A. Areo, R.B. Adeniyi, A Self-Starting Linear Multistep Method for direct solution of initial value problems of second order ordinary differential equations, International Journal of Pure and Applied Mathematics 82 (2013) 345-364.
[23] J.J. Duderstadt, L.J. Hamilton, Nuclear Reactor Analysis, John Wiley &Sons, USA, (1976).
Journal of Research on Many-body Systems
Volume 8, Issue 17
September 2018
Pages 67-75

Files

History

  • Receive Date: 23 August 2017
  • Revise Date: 04 February 2018
  • Accept Date: 04 March 2018

Share

How to cite

Statistics