Rigorous derivation for P2 anisotropic scattering source for hexagonal core analysis

Abstract

DeCART has treated the anisotropic scattering source by introducing the Ushio equation. This equation generates the neutron angular moments by simply using the Legendre polynomials just for the x- and y-directions. Therefore, the number of angular moments is always 2, which is independent of the anisotropic scattering order. This shows good agreement for rectangular geometry, but it is not applicable to the hexagonal core due to the power asymmetry problem. To overcome this problem, rigorous derivation was performed for the scattering order 2, and the solution was examined for assembly benchmark problems by comparing it with the Ushio treatment. The new treatment showed trivial improvements in the eigenvalue and pin power distribution for the normal assemblies without a control rod. However, for the rodded problems, the new treatment showed a slightly large improvement about 100 pcm in eigenvalue and about 0.2% in pin power distribution. Also, the new treatment overcomes the pin power asymmetry problem in hexagonal benchmarks. Therefore, it is concluded that the new derived P2 anisotropic scattering treatment works well for both the rectangular and hexagonal problems and overcomes the power asymmetry problem of the old method.