Adjoint Neutron Flux Calculation Technique Based on Improved Variational Nodal Method

Liang Boning; Wu Hongchun; Li Yunzhao

doi:10.13832/j.jnpe.2023.02.0024

Volume 44 Issue 2

Apr. 2023

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Liang Boning, Wu Hongchun, Li Yunzhao. Adjoint Neutron Flux Calculation Technique Based on Improved Variational Nodal Method[J]. Nuclear Power Engineering, 2023, 44(2): 24-29. doi: 10.13832/j.jnpe.2023.02.0024

Citation:

Liang Boning, Wu Hongchun, Li Yunzhao. Adjoint Neutron Flux Calculation Technique Based on Improved Variational Nodal Method[J]. Nuclear Power Engineering, 2023, 44(2): 24-29. doi: 10.13832/j.jnpe.2023.02.0024

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Adjoint Neutron Flux Calculation Technique Based on Improved Variational Nodal Method

doi: 10.13832/j.jnpe.2023.02.0024

1.
China Institute for Radiation Protection, Taiyuan, 030006, China
2.
Xi’an Jiaotong University, Xi’an, 710049, China

Received Date: 2022-04-24
Accepted Date: 2022-06-13
Rev Recd Date: 2022-06-13
Publish Date: 2023-04-15

Abstract

Abstract

The adjoint neutron flux is of great significance for nuclear safety and detector calculation in pressurized water reactor (PWR). However, existing nodal methods would cause a big error due to heterogeneous nodes, including heterogeneous cross sections and discontinuity factors, which will appear frequently with the control rod moving. In this paper, an improved variational nodal method (VNM) is proposed to reduce the error. It determines the continuous conditions for adjoint nodal methods that are different from forward equation. Unlike traditional VNM, which establishes a functional method globally, this paper establishes a functional method for each node. It constructs a multiplier term with a heterogeneous discontinuity factor to explicitly deal with the adjoint neutron flux with surface discontinuity. Apart from the expansions of adjoint neutron flux, cross section and surface partial neutron current densities, the surface discontinuity factor (DF) is also expanded into pieces-wise orthogonal polynomials to construct the nodal response matrixes. The numerical results of the BEAVRS benchmark problem with heterogeneous nodes existing demonstrate that compared with the traditional VNM, the improved VNM can reduce the error by two orders of magnitude for the adjoint neutron flux in fuel area and the adjoint effective multiplication factor, which can help realize high accuracy calculation for the inner product of forward and adjoint neutron flux.
- PWR,
- Heterogeneous node,
- VNM,
- Adjoint neutron flux

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References(13)

References

[1]	李富,罗征培. 不连续因子理论下扩散差分方程的共轭计算[J]. 核动力工程,1998, 19(6): 485-489.
[2]	DULLA S, MUND E H, RAVETTO P. The quasi-static method revisited[J]. Progress in Nuclear Energy, 2008, 50(8): 908-920. doi: 10.1016/j.pnucene.2008.04.009
[3]	CARON D, DULLA S, RAVETTO P. New aspects in the implementation of the quasi-static method for the solution of neutron diffusion problems in the framework of a nodal method[J]. Annals of Nuclear Energy, 2016, 87: 34-48. doi: 10.1016/j.anucene.2015.02.035
[4]	杜柄. 三维时空扩散中子动力学快速计算方法及外源驱动次临界系统中子学动力研究[D]. 西安: 西安交通大学, 2012.
[5]	ROHDE U, KLIEM S, GRUNDMANN U, et al. The reactor dynamics code DYN3D – models, validation and applications[J]. Progress in Nuclear Energy, 2016, 89: 170-190. doi: 10.1016/j.pnucene.2016.02.013
[6]	李富,王亚奇,罗征培. 节块格林函数法的微扰计算[J]. 核动力工程,1999, 20(2): 103-105.
[7]	DOWNAR T, XU Y, SEKER V. Theory manual for the PARCS kinetics core simulator module[M]. Michigan: University of Michig, 2010: 89-92.
[8]	PALMIOTTI G, LEWIS E E, CARRICO C B. VARIANT: VARIational Anisotropic Nodal Transport for multidimensional Cartesian and hexagonal geometry calculation: ANL-95/40[R]. Argonne, IL, USA: Argonne National Laboratory, 1995.
[9]	ZHANG T F, WU H C, CAO L Z, et al. An improved variational nodal method for the solution of the three-dimensional steady-state multi-group neutron transport equation[J]. Nuclear Engineering and Design, 2018, 337: 419-427. doi: 10.1016/j.nucengdes.2018.07.009
[10]	ZHANG T F, ZHU L, WU H C, et al. Development and validation of high flux engineering test reactor fuel management platform HEFT[J]. Atomic Energy Science and Technology, 2013, 47(S1): 467-471.
[11]	KOBAYASHI K. Boundary condition for the adjoint flux corresponding to the flux discontinuity of the nodal diffusion equation in the perturbation theory[J]. Journal of Nuclear Science and Technology, 1998, 35(1): 20-25. doi: 10.1080/18811248.1998.9733815
[12]	LIANG B N, WU H C, LI Y Z. Adaptive expansion order for diffusion variational nodal method[J]. Annals of Nuclear Energy, 2018, 117: 114-130. doi: 10.1016/j.anucene.2018.03.019
[13]	梁博宁,吴宏春,李云召. 控制棒尖齿效应中非均匀不连续因子处理技术[J]. 核动力工程,2020, 41(6): 31-35. doi: 10.13832/j.jnpe.2020.06.0031