Nuclear Science and Techniques

《核技术》(英文版) ISSN 1001-8042 CN 31-1559/TL     2019 Impact factor 1.556

Nuclear Science and Techniques ›› 2019, Vol. 30 ›› Issue (11): 161 doi: 10.1007/s41365-019-0695-y

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Numerical study of scattering Legendre moments and effect of anisotropic scattering on SN shielding calculation

Cong Liu1 • Xiao-Li Hu2 • Bin Zhang1 • You Gong3 • Liang Zhang1 • Yi-Xue Chen1   

  1. 1 School of Nuclear Science and Engineering, North China Electric Power University, Beijing 102206, China
    2 China Nuclear Power Engineering Co. Ltd., Beijing 100840, China
    3 China Institute of Atomic Energy, Beijing 102413, China
  • Received:2018-11-26 Revised:2019-05-25 Accepted:2019-07-03
  • Contact: Bin Zhang E-mail:zhangbin@ncepu.edu.cn
  • Supported by:
    This work was supported by the National Natural Science Foundation of China (Nos. 11505059, 11575061) and the Fundamental Research Funds for Central Universities (No. 2017XS087).
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Cong Liu, Xiao-Li Hu, Bin Zhang, You Gong, Liang Zhang, Yi-Xue Chen. Numerical study of scattering Legendre moments and effect of anisotropic scattering on SN shielding calculation.Nuclear Science and Techniques, 2019, 30(11): 161     doi: 10.1007/s41365-019-0695-y

Abstract: In neutron and photon transport problems, anisotropic scattering is of great importance for the particle flux, especially when the angular flux has a strong forward peak in shielding analyses. The conventional Legendre expansion is widely used in discrete ordinates transport codes because of algebraic simplifications with spherical harmonics for the scattering source. However, negative cross sections caused by the finitely truncated expansion may give rise to a negative source and flux. A simple method is adopted, based on integrating functions of scattering moments, to evaluate anisotropy and convergence of expanded functions. A series of problems were designed with angular fluxes of different anisotropy, and numerical simulations were performed using the ARES transport code to study different treatments and algorithms for scattering. Results show that the diagonal transport approximation is more stable and obtains a similar accuracy with the extended approximation. A conservative fixup for the negative source could ensure particle balance and improve computational accuracy significantly for photon transport. The effect of anisotropic scattering is problem-dependent, and no distinct differences among various methods are observed for volume source problems with a continuous energy source. For beam source problems, flux results are sensitive to negative scattering functions, and strictly nonnegative cross sections need to be implemented.

Key words: Particle transport, Shielding calculation, Discrete ordinates method, Anisotropic scattering, Transport approximation, Negative source fix-up