Journal of Nuclear Science, Engineering and Technology (JONSAT)
In cooperation with the Iranian Nuclear Society

The Study of Two, Three and Four Dimensional Nonlinear Dynamics of Nuclear Fission Reactors and Effective Parameters on its Behaviour

Document Type : Research Paper

Authors

M Tajik
A Ghasemi zad
Abstract
In this research, new physical fission reactor parameters which have very sensitive effects on the qualitative behavior of a reactor, are introduced. Therefore, the two, the nonlinear dynamics of two, three and four dimensional, considering almost the effective parameters are formulated for describing nuclear fission reactor systems. Using both analytical and numerical methods, the stability and instability of the given dynamical equations and the conditions of stability are studied in these systems. We have shown that the two parameters of the mean energy residence time in fuel and coolant and also their ratios have the most qualitative effects on the dynamical behaviour of a typical nuclear fission reactor. Increasing or decreasing of these parameters from a cartain limit can lead to stability or unstability in a given system.
 

Highlights

 

  1. 1.    A.A. Harms, “Interactive nuclear kinetics and nonlinear dynamics,” Ann.nucl.Energy, 10, No.12 (1983).

 

  1. 2.    M.R. Eskandari and A. Ghasemi-Zad, “Dynamics of intrinsically safe pellet suspension reactors,” Iranian  Journal of Science and Technology, 20, No.4 (1996).

 

  1. 3.    R.K. Miller and A.N. Michel, “Ordinary differentional equation,” Academic Press. N.Y (1982).

 

  1. 4.    C.C. Bissell and Stodola, “Hurwitz and the genesis of the stability criterion,” Int. J Control 50(6), 2313-2332 (1989).

 

  1. 5.    E. Jury, “From sylvester to hurwitz: A historical review, in: stability theory,” Internat. Ser. Numer. Math., vol. 121, Birkhäuser, Basel, pp. 53-65 (1996).

 

  1. 6.    J. Sanchez, “On the numerical solution of the point reactor kinetics equation by generalized runge-kutta methods,” Nuclear Science and Engineering, 103, 94-99 (1989).

 

  1. 7.    V.N. Vedamurthy and N. Lyngar, “Numerical methods,” Vikas Publishing House, PUT.LTD (1999).

 

  1. 8.    J. Lewins, “Nuclear reactors kinetics and control,” Pergamon Press, Oxford, U.K (1978).

 

  1. 9.    D.L. Hetric, “Dynamics of nuclear reactors,” Chicago university Press, USA (1971).

 

  1. 10.              A.A. Harms, MacMaster University Reports (1990).

 

  1. 11.              D.J. Bennet and J.R. Thomson, “The elements of nuclear power,” longman Scientific & Technical (1989).

 

  1. 12.              A.A. Harms and Z. Bilanovic, “Nonlinear dynamics of three-dimensional point fission reactors,” Plenum Publishing corporation (1989).

Keywords

Nuclear Reactor
Nonlinear Dynamics
Mean Energy Residence Time
Stable
Unstable

  1.  

    1. 1.    A.A. Harms, “Interactive nuclear kinetics and nonlinear dynamics,” Ann.nucl.Energy, 10, No.12 (1983).

     

    1. 2.    M.R. Eskandari and A. Ghasemi-Zad, “Dynamics of intrinsically safe pellet suspension reactors,” Iranian  Journal of Science and Technology, 20, No.4 (1996).

     

    1. 3.    R.K. Miller and A.N. Michel, “Ordinary differentional equation,” Academic Press. N.Y (1982).

     

    1. 4.    C.C. Bissell and Stodola, “Hurwitz and the genesis of the stability criterion,” Int. J Control 50(6), 2313-2332 (1989).

     

    1. 5.    E. Jury, “From sylvester to hurwitz: A historical review, in: stability theory,” Internat. Ser. Numer. Math., vol. 121, Birkhäuser, Basel, pp. 53-65 (1996).

     

    1. 6.    J. Sanchez, “On the numerical solution of the point reactor kinetics equation by generalized runge-kutta methods,” Nuclear Science and Engineering, 103, 94-99 (1989).

     

    1. 7.    V.N. Vedamurthy and N. Lyngar, “Numerical methods,” Vikas Publishing House, PUT.LTD (1999).

     

    1. 8.    J. Lewins, “Nuclear reactors kinetics and control,” Pergamon Press, Oxford, U.K (1978).

     

    1. 9.    D.L. Hetric, “Dynamics of nuclear reactors,” Chicago university Press, USA (1971).

     

    1. 10.              A.A. Harms, MacMaster University Reports (1990).

     

    1. 11.              D.J. Bennet and J.R. Thomson, “The elements of nuclear power,” longman Scientific & Technical (1989).

     

    1. 12.              A.A. Harms and Z. Bilanovic, “Nonlinear dynamics of three-dimensional point fission reactors,” Plenum Publishing corporation (1989).

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