Spectral-Nodal Deterministic Methodology for Neutron Shielding Calculations using the X, Y - geometry Multigroup Transport Equation in the Discrete Ordinates Formulation
DOI:
https://doi.org/10.14295/vetor.v31i1.13472Keywords:
Neutron Transport Theory, Shielding Calculations, Spectral Nodal MethodAbstract
In this work, we present the most recent numerical results in a nodal approach, which resulted in the development of a new numerical spectral nodal method, based on the spectral analysis of the multigroup, isotropic scattering neutron transport equations in the discrete ordinates ($S_N$) formulation for fixed-source calculations in non-multiplying media (shielding problems). The numerical results refer to simulations of typical problems from the reactor physics field, in rectangular two-dimensional Cartesian geometry, $X, Y$ geometry, and are compared with the traditional Diamond Difference ($DD$) fine-mesh method results, used as a reference, and the spectral coarse-mesh method Green's function ($SGF$) results.Downloads
References
J. M. Hammersley and D. C. Handscomb, Monte Carlo Methods. London, UK: Methuen & Co, 1964.
E. E. Lewis and W. F. Miller, Computational methods of neutron transport. Illinois, USA: American Nuclear Society, 1993.
J. J. Duderstadt and W. R. Martin, Transport Theory. New York, USA: Wiley–Interscience, 1979.
A. A. Mohamad, “Local analytical discrete ordinate method for the solution of the radiative transfer equation,” International Journal of Heat and Mass Transfer, vol. 39, no. 9, pp. 1859–1864, 1996. Available at: https://doi.org/10.1016/0017-9310(95)00282-0
C. E. Siewert, “The method for solving radiative transfer problems in plane geometry,” Astrophysics and Space Science, vol. 58, no. 2, pp. 131–137, 1978. Available at: https://doi.org/10.1007/BF00645380
A. Badruzzaman, Nodal methods in transport theory. New York, USA: Plenum Press, 1990, vol. 21, ch. 3.
R. D. Laurence, “Progress in nodal methods for the neutron diffusion and transport equations,” Progress in Nuclear Energy, vol. 17, pp. 271–301, 1986. Available at: https://doi.org/10.1016/0149-1970(86)90034-X
W. A. Menezes, “Métodos espectronodais para cálculos de partículas neutras com fonte fixa na formulação de ordenadas discretas e multigrupo de energia.” Ph.D. dissertation, Programa de Pós-Graduação em Modelagem Computacional, Universidade do Estado do Rio de Janeiro, Nova Friburgo, Brasil, 2012. Available at: http://www.bdtd.uerj.br/handle/1/13651
A. M. Oliva, “Método espectral determinístico para a solução de problemas de transporte de nêutrons usando a formulação das ordenadas discretas,” Ph.D. dissertation, Programa de Pós-Graduação em Modelagem Computacional, Universidade do Estado do Rio de Janeiro, Nova Friburgo, Brasil, 2018. Available at: https://www.bdtd.uerj.br:8443/bitstream/1/13719/1/Tese_AmauryMunozOliva.pdf
O. Da Silva, “Um método de matriz resposta para cálculos de transporte multigrupos de energia na formulação de ordenadas discretas em meios não-multiplicativos,” Ph.D. dissertation, Programa de Pós-Graduação em Modelagem Computacional, Universidade do Estado do Rio de Janeiro., Nova Friburgo, Brasil, 2018. Available at: http://www.bdtd.uerj.br/handle/1/13715
R. Barros and E. Larsen, “A numerical method for one-group slab-geometry discrete ordinates problems with no spatial truncation error,” Nuclear Science and Engineering, vol. 104, no. 3, pp. 199–208, 1990. Available at: https://doi.org/10.13182/NSE90-A23719
R. C. Barros, “A spectral nodal method for the solution of discrete ordinates problems in one and two dimensional cartesian geometry.” Ph.D. dissertation, The University of Michigan, Ann Arbor, Michigan, United States., 1990. Available at: https://deepblue.lib.umich.edu/handle/2027.42/105093
R. C. Barros and E. W. Larsen, “A spectral nodal method for one-group , X,Y-geometry discrete ordinates problems,” Nuclear Science and Engineering, vol. 111, no. 1, pp. 34–45, 1992. Available at: https://doi.org/10.13182/NSE92-A23921
R. Barros and E. Larsen, “A numerical method for multigroup slab-geometry discrete ordinates problems with no spatial truncation error,” Transport Theory and Statistical Physics, vol. 20, no. 5-6, pp. 441–462, 1991. Available at: https://doi.org/10.1080/00411459108203914
E. W. Larsen, “Spectral analysis of numerical methods for discrete-ordinates problems. i,” Transp. Theory Stat. Phys.; (United States), vol. 15:1, 1 1986. Available at: https://www.osti.gov/biblio/5871918
A. Oliva, H. Alves Filho, D. J. Silva, and C. R. García, “Computer Deterministic Modelling of Nuclear Problems using Nodal Methods,” in Proceeding Series of the Brazilian Society of Computational and Applied Mathematicsl–CNMAC 2016, ser. ISSN: 2359–0793. Gramado, RS, Brazil: Sociedade de Matemática Aplicada e Computacional(SBMAC), 2016.
——, “Spectral nodal methodology for multigroup slab-geometry discrete ordinates neutron transport problems with linearly anisotropic scattering,” in International Nuclear Atlantic Conference–INAC 2017, ser. ISBN: 978–85–99141–07–6. Belo Horizonte, MG, Brazil: Associação Brasileira de Energia Nuclear (ABEN), 2017.
——, “The spectral nodal method applied to multigroup neutron transport problems in one–dimensional geometry with fixed–source,” Progress in Nuclear Energy, vol. 105, pp. 106–113, 2018. Available at: https://doi.org/10.1016/j.pnucene.2017.12.017
K. M. Case and P. F. Zweifel, Linear transport theory., ser. Addison-Wesley series in nuclear engineering. USA: Reading, Mass., Addison-Wesley Pub. Co, 1967.
W. Menezes, H. A. Filho, and R. Barros, “Spectral green’s function nodal method for multigroup problems with anisotropic scattering in slab-geometry non-multiplying media,” Annals of Nuclear Energy, vol. 64, pp. 270–275, 2014. Available at: https://doi.org/10.1016/j.anucene.2013.09.023
A. M. Oliva, H. Alves Filho, D. J. SILVA, and C. R. García, “The spectral nodal method applied to multigroup neutron transport problems in one–dimensional geometry with fixed–source,” Progress in Nuclear Energy, vol. 105, pp. 106–113, 2018.
A. Oliva, H. Alves Filho, R. C. Barros, and J. Pérez Curbelo, “The Spectral Deterministic Method applied to neutron fixed-source discrete ordinates problems in X, Y-geometry for multigroup calculations,” in International Nuclear Atlantic Conference–INAC 2019, ser. ISBN: 978–85–99141–08–3. Santos, SP, Brazil: Associação Brasileira de Energia Nuclear (ABEN), 2019.
A. F. Dias, “Estudo e aplicação dos códigos ANISN e DOT-II em problemas de física de reatores,” Master’s thesis, Instituto de Pesquisas Energéticas e Nucleares - IPEN/CNEN-SP, SP, Brasil, 1980. Available at:
Downloads
Published
How to Cite
Issue
Section
