Nuclear Engineering and Technology

Korean Nuclear Society (한국원자력학회)
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A variational nodal formulation for multi-dimensional unstructured neutron diffusion problems

  • Qizheng Sun (School of Nuclear Science and Engineering, Shanghai Jiao Tong University) ;
  • Wei Xiao (School of Nuclear Science and Engineering, Shanghai Jiao Tong University) ;
  • Xiangyue Li (School of Nuclear Science and Engineering, Shanghai Jiao Tong University) ;
  • Han Yin (School of Nuclear Science and Engineering, Shanghai Jiao Tong University) ;
  • Tengfei Zhang (School of Nuclear Science and Engineering, Shanghai Jiao Tong University) ;
  • Xiaojing Liu (School of Nuclear Science and Engineering, Shanghai Jiao Tong University)
  • Received : 2022.11.06
  • Accepted : 2023.02.14
  • Published : 2023.06.25
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Abstract

A variational nodal method (VNM) with unstructured-mesh is presented for solving steady-state and dynamic neutron diffusion equations. Orthogonal polynomials are employed for spatial discretization, and the stiffness confinement method (SCM) is implemented for temporal discretization. Coordinate transformation relations are derived to map unstructured triangular nodes to a standard node. Methods for constructing triangular prism space trial functions and identifying unique nodes are elaborated. Additionally, the partitioned matrix (PM) and generalized partitioned matrix (GPM) methods are proposed to accelerate the within-group and power iterations. Neutron diffusion problems with different fuel assembly geometries validate the method. With less than 5 pcm eigenvalue (keff) error and 1% relative power error, the accuracy is comparable to reference methods. In addition, a test case based on the kilowatt heat pipe reactor, KRUSTY, is created, simulated, and evaluated to illustrate the method's precision and geometrical flexibility. The Dodds problem with a step transient perturbation proves that the SCM allows for sufficiently accurate power predictions even with a large time-step of approximately 0.1 s. In addition, combining the PM and GPM results in a speedup ratio of 2-3.

Keywords

Acknowledgement

This research is supported by the National Key R&D Program of China [2020YFB1901900] and the National Natural Science Foundation of China [12175138, U20B2011].

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