The adjoint transport problem applied to estimate neutral particle leakage in the discrete ordinates formulations
DOI:
https://doi.org/10.15392/2319-0612.2022.1850Keywords:
neutron leakage, adjoint transport problem, discrete ordinates, spectral nodal method, energy multigroupAbstract
In source–detector problems, neutron leakage is a quantity of interest that could lead to improve shielding structures, thus reducing the dose received by humans. In this work, we apply an adjoint technique with spectral nodal methods to compute neutron leakage in multigroup one– and two–dimensional problems in the discrete ordinates (SN) formulation. The use of the adjoint technique to calculate the leakages due to various source distributions is very convenient as it is possible to run adjoint problems and store the neutron importance maps. Here we solve the homogeneous adjoint SN transport equation by considering unit outgoing adjoint flux at the boundary. In order to numerically solve slab– and X, Y–geometry problems, we use spectral nodal methods that have been widely applied and discussed in the literature. Numerical results are given to illustrate the present adjoint technique to estimate the neutron leakage for each energy group in source–detector problems. For all the test problems, the results obtained by the adjoint technique as described in this paper do agree with the results obtained by solving the analogous forward problem.
- Views: 68
- PDF Downloads: 88
Downloads
References
LEWIS, E.E.; MILLER, W.F. Computational methods of neutron transport, 1st ed., Illinois, USA: American Nuclear Society, 1993.
PRINJA, A.K.; LARSEN, E.W. General principles of neutron transport. In: CACUCI, D.G. Handbook of nuclear engineering, 1st ed., New York, USA: Springer Science + Business Media, 2010. P.427–542. DOI: https://doi.org/10.1007/978-0-387-98149-9_5
CURBELO, J.P.; DA SILVA, O.P; BARROS, R.C. An adjoint technique applied to slab–geometry source–detector problems using the generalized spectral Green’s function nodal method. Journal of Computational and Theoretical Transport, v. 47 (1–3), p. 278–99, 2018. DOI: https://doi.org/10.1080/23324309.2018.1539403
BARICHELLO, L.B.; PAZINATTO, C.B.; RUI, K. An analytical discrete ordinates nodal solution to the two–dimensional adjoint transport problem, Annals of Nuclear Energy, v. 135, p. 106959, 2020. DOI: https://doi.org/10.1016/j.anucene.2019.106959
MORAES, L.R.C.; MANSUR, R.S., MOURA, C. A.; CURBELO, J.P.; ALVES FILHO, H.; BARROS, R.C. A Response Matrix Method for Slab–Geometry Discrete Ordinates Adjoint Calculations in Energy–Dependent Neutral Particle Transport, Journal of Computational and Theoretical Transport, v. 50:3, p. 159–179, 2021. DOI: https://doi.org/10.1080/23324309.2021.1914661
CURBELO, J.P.; BARROS, R.C. A spectral nodal method for the adjoint S_N neutral particle transport equations in X,Y–geometry: Application to direct and inverse multigroup source–detector problems, Annals of Nuclear Energy, v. 150, p. 107822, 2021. DOI: https://doi.org/10.1016/j.anucene.2020.107822
MORATÓ, S.; BERNAL, A.; MIRÓ, R.; ROMAN, J.E.; VERDÚ, G. Calculation of k modes of the multi–group neutron transport equation using the discrete ordinates and Finite Difference Method. Annals of Nuclear Energy, v. 137, p. 107077, 2020. DOI: https://doi.org/10.1016/j.anucene.2019.107077
SIEWERT, C.E. A spherical–harmonics method for multigroup or non–gray radiation transport. Journal of Quantitative Spectroscopy and Radiative Transfer, v. 49 (2), p. 95–106, 1993. DOI: https://doi.org/10.1016/0022-4073(93)90050-R
CURBELO, J.P.; DA SILVA, O.P; BARROS, R.C. On the Generalization of the Response Matrix Spectral Nodal Method for Neutral Particle S_N Source–Detector Problems in Slab Geometry, Journal of Computational and Theoretical Transport, v. 50:1, p. 67–86, 2021. DOI: https://doi.org/10.1080/23324309.2021.1889604
Published
How to Cite
Issue
Section
License
Copyright (c) 2022 Brazilian Journal of Radiation Sciences
This work is licensed under a Creative Commons Attribution 4.0 International License.
Licensing: The BJRS articles are licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/
