Improved Neutron Leakage Treatment on Nodal Expansion Method for PWR Reactors
For a quick and accurate calculation of spatial neutron
distribution in nuclear power reactors 3D nodal codes are usually
used aiming at solving the neutron diffusion equation for a given
reactor core geometry and material composition. These codes use a
second order polynomial to represent the transverse leakage term. In
this work, a nodal method based on the well known nodal expansion
method (NEM), developed at COPPE, making use of this polynomial
expansion was modified to treat the transverse leakage term for the
external surfaces of peripheral reflector nodes.
The proposed method was implemented into a computational
system which, besides solving the diffusion equation, also solves the
burnup equations governing the gradual changes in material
compositions of the core due to fuel depletion. Results confirm the
effectiveness of this modified treatment of peripheral nodes for
practical purposes in PWR reactors.
[1] W. M. Stacey, Nuclear Reactor Physics, Wiley-VCH, Weinheim,
Germany (2004)
[2] H. Finnemann, F. Benneritz and M. R. Wagner, "Interface current
techniques for multidimensional reactor calculations" Atomkernenergie
30, 123 (1977)
[3] F. C. Silva, A. C. M. Alvim and A. S. Martinez, "An Alternative Solver
for the Nodal Expansion Method Equations" PHYSOR 2010 - Advances
in Reactor Physics to Power the Nuclear Renaissance, Pittsburgh,
Pennsylvania, USA (2010)
[4] A. S. Martinez, V. Pereira and F. C. da Silva, "A system for the
prediction and determination of subcritical multiplication condition"
Kerntechinik 64, 230 (1999)
[5] M. R. Wagner, K. Koebke and H. J. Winter, "A nonlinear extension of
the nodal expansion method" Proceedings of ANS/ENS International
Topical Meeting, Munich, Germany, 2, 43 (1981)
[6] H. D. Fischer and H. Finnemann, "The Nodal Integration Method - A
Diverse Solver for Neutron Diffusion problems" Atomkernenergie-
Kerntechnik, 30, 229 (1981)
[7] H. K. Joo, C. H. Kim, J. M. Noh and S. Kim, "A Semi-Analytic
Multigroup Nodal Method" Annals of Nuclear Energy, 26, 699 (1999)
[8] B. Christensen, "Three-dimensional static and dynamic reactor
calculations by the nodal expansion method" RISO National Laboratory
DK-4000, Roskild, Denmark (1985)
[9] A. C. M. Alvim, F. C. Silva and A. S. Martinez, "Depletion Calculation
for a Nodal Reactor Physics Code" ICONE 18 - 18th International
Conference on Nuclear Engineering, Xi'an, China (2010)
[1] W. M. Stacey, Nuclear Reactor Physics, Wiley-VCH, Weinheim,
Germany (2004)
[2] H. Finnemann, F. Benneritz and M. R. Wagner, "Interface current
techniques for multidimensional reactor calculations" Atomkernenergie
30, 123 (1977)
[3] F. C. Silva, A. C. M. Alvim and A. S. Martinez, "An Alternative Solver
for the Nodal Expansion Method Equations" PHYSOR 2010 - Advances
in Reactor Physics to Power the Nuclear Renaissance, Pittsburgh,
Pennsylvania, USA (2010)
[4] A. S. Martinez, V. Pereira and F. C. da Silva, "A system for the
prediction and determination of subcritical multiplication condition"
Kerntechinik 64, 230 (1999)
[5] M. R. Wagner, K. Koebke and H. J. Winter, "A nonlinear extension of
the nodal expansion method" Proceedings of ANS/ENS International
Topical Meeting, Munich, Germany, 2, 43 (1981)
[6] H. D. Fischer and H. Finnemann, "The Nodal Integration Method - A
Diverse Solver for Neutron Diffusion problems" Atomkernenergie-
Kerntechnik, 30, 229 (1981)
[7] H. K. Joo, C. H. Kim, J. M. Noh and S. Kim, "A Semi-Analytic
Multigroup Nodal Method" Annals of Nuclear Energy, 26, 699 (1999)
[8] B. Christensen, "Three-dimensional static and dynamic reactor
calculations by the nodal expansion method" RISO National Laboratory
DK-4000, Roskild, Denmark (1985)
[9] A. C. M. Alvim, F. C. Silva and A. S. Martinez, "Depletion Calculation
for a Nodal Reactor Physics Code" ICONE 18 - 18th International
Conference on Nuclear Engineering, Xi'an, China (2010)
@article{"International Journal of Engineering, Mathematical and Physical Sciences:61450", author = "Antonio Carlos Marques Alvim and Fernando Carvalho da Silva and Aquilino Senra Martinez", title = "Improved Neutron Leakage Treatment on Nodal Expansion Method for PWR Reactors", abstract = "For a quick and accurate calculation of spatial neutron
distribution in nuclear power reactors 3D nodal codes are usually
used aiming at solving the neutron diffusion equation for a given
reactor core geometry and material composition. These codes use a
second order polynomial to represent the transverse leakage term. In
this work, a nodal method based on the well known nodal expansion
method (NEM), developed at COPPE, making use of this polynomial
expansion was modified to treat the transverse leakage term for the
external surfaces of peripheral reflector nodes.
The proposed method was implemented into a computational
system which, besides solving the diffusion equation, also solves the
burnup equations governing the gradual changes in material
compositions of the core due to fuel depletion. Results confirm the
effectiveness of this modified treatment of peripheral nodes for
practical purposes in PWR reactors.", keywords = "Transverse leakage, nodal expansion method, power
density, PWR reactors", volume = "6", number = "3", pages = "330-4", }