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Critical Enrichment Calculation of Spherical Reactor- ZPR-III Model Using Lyapunov Exponent

Document Type : Research Paper

Authors

Abstract

By considering the chaos theory, the condition for stability of nuclear reactor is studied. By considering the enrichment fuel as a control parameter, the lyapunov exponent is used for the study of the critical condition. This study, as an example, will focus on the special type of spherical ZPR-III nuclear reactor.

Highlights

  1. G.V. Durga Prasad, Manmohan Pandey, “Stability analysis and nonlinear of natural circulation boiling water reactors,” Nuclear Engineering and Design 238, 229 (2008).

     

  2. J. Morales-Sandoval, A. Hernandez-Solis, “Global physical and numerical stability of a nuclear reactor core,” Ann.Nucl. Energy 321, 666 (2005).

 

  1. Pankaj Wahi, Vivek Kumawat, “Nonlinear stability analysis of a reduced order model of nuclear reactors: A parametric study relevant to the advanced heavy water point reactor,” Nuclear Engineering and Design 241, 134 (2011).

 

  1. J.D. Lewins, E.N. Ngcobo, “Property discontinuities in the solution of finite difference approximations to the neutron diffusion equation,” Ann. Nucl. Energy  23, 29 (1996).

 

  1. J. Koclas, “Comparisons of the different approximations leading to mesh centered finite differences starting from the analytic nodal method,” Ann. Nucl. Energy 25, 821 (1998).

 

  1. S. Cavdar, H.A. Ozgener, “A finite element/boundary element hybrid method for 2-D neutron diffusion calculations,” Ann. Nucl. Energy 31, 1555 (2004).

 

  1. S.T. Liu, “Nuclear fission and spatial chaos,” Chaos, Solitons & Fractals 30, 462 (2006).

 

  1. R. Uddin, “Turning points and sub- and supercritical bifurcations in a simple BWR model,” Nucl. Eng. and Design 236, 267 (2006).

 

  1. H. Konno, S. Kanemoto, Y. Takeuchi, “Theory of stochastic bifurcation in BWRS and applications,” Progress in Nucl. Energy 43, 201 (2003).

 

  1. K. Kaneko, “Clustering, coding, switching, hierarchical ordering, and control in a network of chaotic elements,” Phys. D: Nonlinear Phenomena. 41, 137 (1990).

 

  1. K. Kaneko, “Chaotic traveling waves in a coupled map lattice,” Phys. D: Nonlinear Phenomena. 68, 299 (1993).

  2. T. Suzudo, “Applaication of nonlinear dynamical descriptor to BWR stability analysis,” Progress in Nucl. Energy 43, 217 (2003).

 

  1. Hiroshi Shibata, “Fluctuation of mean Lyapunov exponent for a coupled map lattice model,” Physica A 284, 124 (2000).

 

  1. K.M. Case, P.M. Zweifel, “Linear transport theory,” Addison-wesely, Massachusetts, (1967).

 

  1. R. khoda-bakhsh, S. Behnia, O. Jahanbkhsh, “A novel lyapunov exponent approach for stability analysis of the simple nuclear reactor,” Iranian Physical Journal, 3-1, 36-41 (2009).

 

  1. J.J. Duderstat, L.J. Hamilton, “Nuclear Reactor Anaysis,” Wiley, New York, (1976).

 

  1. G.I. Bell, S. Glasstone, “Nuclear reactor theory,” Van Nostrand Reinhold Company, New York (1970).

 

  1. German G. Theler, Fabian J. Bonetto, “On the stability of the point reactor kinetics equations,” Nuclear Engineering and Design 240, 1443 (2010).

 

  1. L.G. Vulkov, A.A. Samarskii, P.N. Vabishchevich, “Finite difference methods: theory and applications,” Nova Science Publishers, Samarskii (1999).

 

  1. Kazoo Azekura and Kunitoshi Kurihara, “High-order finite difference nodal method for neutron diffusion equation,” Nuclear Scince and Technology, 28, 285 (1991).

 

  1. S.T. Strogatz, “Nonlinear dynamics and chaos,” Perseus Books Publishing, L.L.C. (1994).

 

  1. E. Ott, “Chaos in dynamical systems,” Cambridge University Press (1993).

 

  1. M.A. Jafarizadeh, S. Behnia, M. Foroutan, “Hierarchy of piecewise non-linear maps with non-ergodic behaviour,” J. Phys. A: Math, Gen. 37, 9403 (2004).

 

  1. M.M.R. Williams, “A method for solving a stochastic eigenvalue problem applied to criticality,” Ann. Nucl. Energy 37, 894 (2010).

 

  1. B.L. Kirk, “Overviw of Monte Carlo radiation transport codes,” Radiation Measurements 45, 1318 (2010).

 

  1. S. Behnia, M. Panahi, A. Mobaraki, A. Akhshani, “A novel approach for the potential parameters selection of Peyrarad-Bishop model,” Physics Letters A 375, 1092 (2011).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  1. H. Shibata, “Fluctuation of mean Lyapunov exponent for turbulence,” Physica A 292, 175 (2001).

 

  1. R. Khoda-Bakhsh, S. Behnia, O. Jahanbkhsh, “Stability analysis in nuclear reactor using Lyapunov exponent,” Ann. Nucl. Energy 35, 1370 (2008).

 

  1. J.L. Meem, “Two group reactor theory,” Gordon and Breach Science Publishers. New York (1964).

Keywords

References

  1. G.V. Durga Prasad, Manmohan Pandey, “Stability analysis and nonlinear of natural circulation boiling water reactors,” Nuclear Engineering and Design 238, 229 (2008).

     

  2. J. Morales-Sandoval, A. Hernandez-Solis, “Global physical and numerical stability of a nuclear reactor core,” Ann.Nucl. Energy 321, 666 (2005).

 

  1. Pankaj Wahi, Vivek Kumawat, “Nonlinear stability analysis of a reduced order model of nuclear reactors: A parametric study relevant to the advanced heavy water point reactor,” Nuclear Engineering and Design 241, 134 (2011).

 

  1. J.D. Lewins, E.N. Ngcobo, “Property discontinuities in the solution of finite difference approximations to the neutron diffusion equation,” Ann. Nucl. Energy  23, 29 (1996).

 

  1. J. Koclas, “Comparisons of the different approximations leading to mesh centered finite differences starting from the analytic nodal method,” Ann. Nucl. Energy 25, 821 (1998).

 

  1. S. Cavdar, H.A. Ozgener, “A finite element/boundary element hybrid method for 2-D neutron diffusion calculations,” Ann. Nucl. Energy 31, 1555 (2004).

 

  1. S.T. Liu, “Nuclear fission and spatial chaos,” Chaos, Solitons & Fractals 30, 462 (2006).

 

  1. R. Uddin, “Turning points and sub- and supercritical bifurcations in a simple BWR model,” Nucl. Eng. and Design 236, 267 (2006).

 

  1. H. Konno, S. Kanemoto, Y. Takeuchi, “Theory of stochastic bifurcation in BWRS and applications,” Progress in Nucl. Energy 43, 201 (2003).

 

  1. K. Kaneko, “Clustering, coding, switching, hierarchical ordering, and control in a network of chaotic elements,” Phys. D: Nonlinear Phenomena. 41, 137 (1990).

 

  1. K. Kaneko, “Chaotic traveling waves in a coupled map lattice,” Phys. D: Nonlinear Phenomena. 68, 299 (1993).

  2. T. Suzudo, “Applaication of nonlinear dynamical descriptor to BWR stability analysis,” Progress in Nucl. Energy 43, 217 (2003).

 

  1. Hiroshi Shibata, “Fluctuation of mean Lyapunov exponent for a coupled map lattice model,” Physica A 284, 124 (2000).

 

  1. K.M. Case, P.M. Zweifel, “Linear transport theory,” Addison-wesely, Massachusetts, (1967).

 

  1. R. khoda-bakhsh, S. Behnia, O. Jahanbkhsh, “A novel lyapunov exponent approach for stability analysis of the simple nuclear reactor,” Iranian Physical Journal, 3-1, 36-41 (2009).

 

  1. J.J. Duderstat, L.J. Hamilton, “Nuclear Reactor Anaysis,” Wiley, New York, (1976).

 

  1. G.I. Bell, S. Glasstone, “Nuclear reactor theory,” Van Nostrand Reinhold Company, New York (1970).

 

  1. German G. Theler, Fabian J. Bonetto, “On the stability of the point reactor kinetics equations,” Nuclear Engineering and Design 240, 1443 (2010).

 

  1. L.G. Vulkov, A.A. Samarskii, P.N. Vabishchevich, “Finite difference methods: theory and applications,” Nova Science Publishers, Samarskii (1999).

 

  1. Kazoo Azekura and Kunitoshi Kurihara, “High-order finite difference nodal method for neutron diffusion equation,” Nuclear Scince and Technology, 28, 285 (1991).

 

  1. S.T. Strogatz, “Nonlinear dynamics and chaos,” Perseus Books Publishing, L.L.C. (1994).

 

  1. E. Ott, “Chaos in dynamical systems,” Cambridge University Press (1993).

 

  1. M.A. Jafarizadeh, S. Behnia, M. Foroutan, “Hierarchy of piecewise non-linear maps with non-ergodic behaviour,” J. Phys. A: Math, Gen. 37, 9403 (2004).

 

  1. M.M.R. Williams, “A method for solving a stochastic eigenvalue problem applied to criticality,” Ann. Nucl. Energy 37, 894 (2010).

 

  1. B.L. Kirk, “Overviw of Monte Carlo radiation transport codes,” Radiation Measurements 45, 1318 (2010).

 

  1. S. Behnia, M. Panahi, A. Mobaraki, A. Akhshani, “A novel approach for the potential parameters selection of Peyrarad-Bishop model,” Physics Letters A 375, 1092 (2011).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  1. H. Shibata, “Fluctuation of mean Lyapunov exponent for turbulence,” Physica A 292, 175 (2001).

 

  1. R. Khoda-Bakhsh, S. Behnia, O. Jahanbkhsh, “Stability analysis in nuclear reactor using Lyapunov exponent,” Ann. Nucl. Energy 35, 1370 (2008).

 

  1. J.L. Meem, “Two group reactor theory,” Gordon and Breach Science Publishers. New York (1964).

Journal of Nuclear Science, Engineering and Technology (JONSAT)
Volume 33, Issue 2 - Serial Number 60
September 2012
Pages 31-39
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