Document Type : Research Paper
Authors
Abstract
The finite element method is applied to the spatial variables of multigroup neutron transport equation in a twodimensional cylindrical (r, z) geometry. The equation is discretized using rectangular sub regions in the (r, z) plane. The discontinuous method with the bilinear or biquadratic Lagrang's interpolating polynomials and basis functions is used in the ANSYS program. Here, the angular fluxes are allowed to be discontinued across the sub region boundaries. Some numerical calculations have been made on a real cylindrical Aristotle reactor with different fuel concentrations on the fuel rods; the results indicate that the flux and power of the heterogeneous critical reactor increase on the edges of the core in comparison with the homogeneous one.
Highlights

C. Papastefanou, “Measurement of neutron flux and albedo of water for thermal neutrons with foils of indium in a subcritical nuclear reactor,” Journal of Radio Analytical and Nuclear Chemistry, Vol. 261, 671678 (2004).

M.Y. Bettan, Samuel H. Levine, “Critical experiment to determine amount of U235 in research reactor fuel assemblies,” Annals of Nuclear Energy, Vol. 34, 159165 (2007).

E.E. Lewis, “Finite element approximation to the evenparity transport equation,” Adv. Nucl. Sci. Thechnol., Vol. 22, 565583 (1985).

Masahide Iimasaki, Masahiko OOki, “Stability analysis of linearized nuclear reactor by finite element method,” Journal of Nuclear Science and Technology, Vol. 14, 551557 (1977).

R. KhodaBakhsh, S. Behnia, O. Jahanbakhsh, “Stability analysis in nuclear reactor using lyaponov exponent,” Annals of Nuclear Energy, Vol. 35, 13701372 (2008).

M.R. Golbahar Haghighi, M. Eghtesad, P. Malekzadeh, “Coupled DQ–FE methods for two dimensional transient heat transfer analysis of functionally graded material,” Energy Conversion and Management, Vol. 49, 9951001 (2008).

P. Havu, V. Havu, M.J. Puska, R.M. Nieminen, “Nonequilibrium electron transport in twodimensional nanostructures modeled using Green’s functions and the finiteelement method,” Physical Rev. B, Vol. 69, 115325115338 (2004).

W.H. Reed, T.R. Hill, “Triangular mesh methods for neutron transport equation,” Tech. Report LAUR, Los Alamos Scientific Laboratory (1973).

T. Fujimura, “Application of finite element method to twodimensional multigroup neutron transport equation in cylindrical geometry,” Journal of Nuclear Science and Technology, Vol. 14, 541550 (1977).

E.M. Gilbert, Monte Carlo, “Finite Element and S_{n} Methods, Conf750413,” Vol. 2, VIII (1975).

H. Lin, J. ChangLung Hsieh, Ch. Shih, “Kuosheng BWR/6 stability analysis with LAPUR5 code,” Annals of Nuclear Energy, Vol. 33, 289299 (2006).

NAJIB GUESSOUS, FOUZIA HADFAT, “Analatical Nodal Methods for Diffusion Equations,” Electronic J. of Differential Equations, Conference 11, 143155 (2004).

C.M. Kang, K.F. Hansen, “Finite element methods for reactor analysis,” Nucl. Sci. 51, (1973).

D.J. Lewins, N.N. Ngcobo, “Property discontinuities in the solution of finite difference approximations to the neutron diffusion equations,” Ann. Nucl. Energy, 23, 1, 2934 (1996).

D. Ginestar, G. Verdu, V. Vidal, R. Bru, J. MunozCobo, “High order backward discretization for the neutron diffusion equation,” Ann. Nucl. Energy, Vol. 25, 4764 (1998).

Thomas Hohne, Soren Kliem, Ulrich Rohde, FrankPeter Weiss, “Boron dilution transient during natural circulation flow in PWRExpriments and CFD simulations,” Nuclear Engineering and Design, Vol. 25, 13231328 (2008).

Z.R.de Lima, F.C.da Silva, A.C.M. Alvim, “Solution of the fixed source neutron diffusion equation by using the pseudoharmonics method,” Annals of Nuclear Energy, 31, 16491666 (2004).

J.J. Duderstadt & L.J. Hamilton, “Nuclear Reactor Analysis,” John Wiley & Sons, New York (1976).

S. Cavda, H.A. Ozgener, “A finite element/boundary element hybrid method for 2D neutron diffusion calculations,” Annals of Nuclear Energy, Vol. 31, 15551582 (2004).

M. Aasadzadeh, “A finite element method for the neutron transport equation in an infinite cylindrical domain,” Siam J. Numer. Anal. Vol. 35, 12991314 (1998).

J.J.W. van der Vegt, J.J. Sudirham, “A space–time discontinuous Galerkin method for the timedependent Oseen equations,” Applied Numerical Mathematics, Vol. 58, 18921917 (2008).

S.K. Tomar, J.J.W. van der vegt, “A Runge–Kutta discontinuous Galerkin method for linear freesurface gravity waves using high order velocity recovery,” Computer Methods in Applied Mechanics and Engineering, Vol. 196, 19841996 (2007).

J.J. Sudirham, J.J.W. van der Vegt, R.M.J. van Damme, “Space–time discontinuous Galerkin method for advection–diffusion problems on timedependent domains,” Applied Numerical Mathemaics, Vol. 56, 14911415 (2006).

N. Vosoughi, A. Salehi, M. Shahriari, “Discrete Formulation for TwoDimensional Multigroup Neutron Diffusion Equations,” Annals of Nuclear Energy, Vol. 31, 231253 (2003).

H.A. Ozgener, B. Ozgener, “A multiregion boundary element method for multigroup neutron diffusion calculations,” Ann. Nucl. Energy, Vol. 28, 581616 (2001).

J.R. Lamarsh, “Introduction to nuclear engineering,” AddisonWesley Publishing Company, New York (1975).

Ron T. Ackroyd, “Finite Element Methods for Particle Transport: Applications to Reactor and Radiation Physics,” (1997).

S. Charalambous, “Experiments in atomic and nuclear physics,” P. Ziti, Thessaloniki, Greece (1983).

ANSYS Version 11. User Manual. ANSYS, Inc. Software Products. Pennsylvania (2007).

R. KhodaBakhsh, S. Behnia, O. Jahanbakhsh, “Simulation of criticality of a homogeneous reactor using Finite Element Method,”University of Urmia (1906).
Keywords

C. Papastefanou, “Measurement of neutron flux and albedo of water for thermal neutrons with foils of indium in a subcritical nuclear reactor,” Journal of Radio Analytical and Nuclear Chemistry, Vol. 261, 671678 (2004).

M.Y. Bettan, Samuel H. Levine, “Critical experiment to determine amount of U235 in research reactor fuel assemblies,” Annals of Nuclear Energy, Vol. 34, 159165 (2007).

E.E. Lewis, “Finite element approximation to the evenparity transport equation,” Adv. Nucl. Sci. Thechnol., Vol. 22, 565583 (1985).

Masahide Iimasaki, Masahiko OOki, “Stability analysis of linearized nuclear reactor by finite element method,” Journal of Nuclear Science and Technology, Vol. 14, 551557 (1977).

R. KhodaBakhsh, S. Behnia, O. Jahanbakhsh, “Stability analysis in nuclear reactor using lyaponov exponent,” Annals of Nuclear Energy, Vol. 35, 13701372 (2008).

M.R. Golbahar Haghighi, M. Eghtesad, P. Malekzadeh, “Coupled DQ–FE methods for two dimensional transient heat transfer analysis of functionally graded material,” Energy Conversion and Management, Vol. 49, 9951001 (2008).

P. Havu, V. Havu, M.J. Puska, R.M. Nieminen, “Nonequilibrium electron transport in twodimensional nanostructures modeled using Green’s functions and the finiteelement method,” Physical Rev. B, Vol. 69, 115325115338 (2004).

W.H. Reed, T.R. Hill, “Triangular mesh methods for neutron transport equation,” Tech. Report LAUR, Los Alamos Scientific Laboratory (1973).

T. Fujimura, “Application of finite element method to twodimensional multigroup neutron transport equation in cylindrical geometry,” Journal of Nuclear Science and Technology, Vol. 14, 541550 (1977).

E.M. Gilbert, Monte Carlo, “Finite Element and S_{n} Methods, Conf750413,” Vol. 2, VIII (1975).

H. Lin, J. ChangLung Hsieh, Ch. Shih, “Kuosheng BWR/6 stability analysis with LAPUR5 code,” Annals of Nuclear Energy, Vol. 33, 289299 (2006).

NAJIB GUESSOUS, FOUZIA HADFAT, “Analatical Nodal Methods for Diffusion Equations,” Electronic J. of Differential Equations, Conference 11, 143155 (2004).

C.M. Kang, K.F. Hansen, “Finite element methods for reactor analysis,” Nucl. Sci. 51, (1973).

D.J. Lewins, N.N. Ngcobo, “Property discontinuities in the solution of finite difference approximations to the neutron diffusion equations,” Ann. Nucl. Energy, 23, 1, 2934 (1996).

D. Ginestar, G. Verdu, V. Vidal, R. Bru, J. MunozCobo, “High order backward discretization for the neutron diffusion equation,” Ann. Nucl. Energy, Vol. 25, 4764 (1998).

Thomas Hohne, Soren Kliem, Ulrich Rohde, FrankPeter Weiss, “Boron dilution transient during natural circulation flow in PWRExpriments and CFD simulations,” Nuclear Engineering and Design, Vol. 25, 13231328 (2008).

Z.R.de Lima, F.C.da Silva, A.C.M. Alvim, “Solution of the fixed source neutron diffusion equation by using the pseudoharmonics method,” Annals of Nuclear Energy, 31, 16491666 (2004).

J.J. Duderstadt & L.J. Hamilton, “Nuclear Reactor Analysis,” John Wiley & Sons, New York (1976).

S. Cavda, H.A. Ozgener, “A finite element/boundary element hybrid method for 2D neutron diffusion calculations,” Annals of Nuclear Energy, Vol. 31, 15551582 (2004).

M. Aasadzadeh, “A finite element method for the neutron transport equation in an infinite cylindrical domain,” Siam J. Numer. Anal. Vol. 35, 12991314 (1998).

J.J.W. van der Vegt, J.J. Sudirham, “A space–time discontinuous Galerkin method for the timedependent Oseen equations,” Applied Numerical Mathematics, Vol. 58, 18921917 (2008).

S.K. Tomar, J.J.W. van der vegt, “A Runge–Kutta discontinuous Galerkin method for linear freesurface gravity waves using high order velocity recovery,” Computer Methods in Applied Mechanics and Engineering, Vol. 196, 19841996 (2007).

J.J. Sudirham, J.J.W. van der Vegt, R.M.J. van Damme, “Space–time discontinuous Galerkin method for advection–diffusion problems on timedependent domains,” Applied Numerical Mathemaics, Vol. 56, 14911415 (2006).

N. Vosoughi, A. Salehi, M. Shahriari, “Discrete Formulation for TwoDimensional Multigroup Neutron Diffusion Equations,” Annals of Nuclear Energy, Vol. 31, 231253 (2003).

H.A. Ozgener, B. Ozgener, “A multiregion boundary element method for multigroup neutron diffusion calculations,” Ann. Nucl. Energy, Vol. 28, 581616 (2001).

J.R. Lamarsh, “Introduction to nuclear engineering,” AddisonWesley Publishing Company, New York (1975).

Ron T. Ackroyd, “Finite Element Methods for Particle Transport: Applications to Reactor and Radiation Physics,” (1997).

S. Charalambous, “Experiments in atomic and nuclear physics,” P. Ziti, Thessaloniki, Greece (1983).

ANSYS Version 11. User Manual. ANSYS, Inc. Software Products. Pennsylvania (2007).

R. KhodaBakhsh, S. Behnia, O. Jahanbakhsh, “Simulation of criticality of a homogeneous reactor using Finite Element Method,”University of Urmia (1906).