• High Power Laser and Particle Beams
  • Vol. 34, Issue 2, 026006 (2022)
Zhiyuan Feng, Kaiwen Li, Hao Luo, and Kan Wang
Author Affiliations
  • Department of Engineering Physics, Tsinghua University, Beijing 100084, China
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    DOI: 10.11884/HPLPB202234.210309 Cite this Article
    Zhiyuan Feng, Kaiwen Li, Hao Luo, Kan Wang. Micro cross-section parameterization based on RMC code[J]. High Power Laser and Particle Beams, 2022, 34(2): 026006 Copy Citation Text show less

    Abstract

    To perform realistic core calculations, few-group neutron cross-sections library by functions of burn-up and thermal hydraulics parameters should be prepared in advance. Traditional deterministic parameterization process is based on the macro cross-section. However, this method should consider the historical effect of some physical states, which increases the number of calculation branches. Thus, this paper proposes a new parameterization process based on the micro cross-section of nuclide. This method effectively eliminates the historical impact. Therefore, only burn-up and material temperature need to be considered. The calculation process is performed by RMC code. Firstly, all of material nuclides micro cross-section and nuclides density is calculated. Then, macro cross-section is obtained by the micro cross-section lib. To test the method accuracy, a self-design pressurized water reactor model is built. The test results agree well with the reference results calculated by RMC full core calculation.
    $ \displaystyle\int\limits_{{{{V}}_{{i}}}} {{\displaystyle\sum\nolimits_{{{x}},{{g}}}} {\phi _{\rm{g}}}\left( r \right){{{\rm{d}}}}V} = \displaystyle\int\limits_{{{{V}}_{{{{i}}}}}} {{\displaystyle{\bar \sum }_{{{x}},{{g}}}} \cdot {{\bar \phi }_{{g}}}\left( r \right){\rm{d}}V}{\rm{ }} \quad x = a,f,s,\cdots, \quad g = 1,2, \cdots ,G $(1)

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    $ {{{{\int}}}}_{{S_{{{ip}}}}} {J_{{g}}^u\left( r \right) \cdot {\rm{d}}S} = - \int_{{S_{{{ip}}}}} {{{\bar D}_{{g}}}\left( r \right) \cdot \frac{{\partial {{\bar \phi }_{{g}}}\left( r \right)}}{{\partial u}}{\rm{d}}S} $(2)

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    $ - \sum\limits_{p = 1}^P {\int_{{S_{{{ip}}}}} {{{\bar D}_{{g}}}\left( r \right) \cdot \nabla {{\bar \phi }_{{g}}}\left( r \right) \cdot {\rm{d}}S} } + \int_{{V_{{i}}}} {{{\bar \sum }_{{{t}},{{g}}}}{{\bar \phi }_{{g}}}\left( r \right)} = \sum\limits_{g' = 1}^G {\left( {\int_{{V_{{i}}}} {{{\bar \sum }_{{{s}},{{g}}' \to {{g}}}}{\phi _{{{g'}}}}\left( r \right){\rm{d}}V} + \frac{{{\chi _{{g}}}}}{{k{\rm_{eff}}}}\int_{{V_{{i}}}} {V{\sum\nolimits_{{{f}},{{g}}'}}} {{\bar \phi }_{{{g'}}}}\left( r \right){\rm{d}}V} \right)} $(3)

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    $ {\displaystyle\sum _{{{g}},{{j}}}} = \frac{{\displaystyle\sum\limits_{m = 1}^N {\left( {WTL_{{{g}},{{{V}}_{{i}}}}^m \cdot {{\left( {\displaystyle\sum\limits_{k = 1}^K {{N_{{{k}},{\rm{i}}}} \cdot {\sigma _{{{k}},{{j}}}}(E)} } \right)}_{{V_{{i}}}}}} \right)} }}{{\displaystyle\sum\limits_{m = 1}^N {WTL_{{{g}},{{{V}}_{{i}}}}^m} }} $(4)

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    $ {\sigma _{{{k}},{{g}},{{j}}}} = \frac{{\displaystyle\sum\limits_{m = 1}^N {\left( {WTL_{{{g}},{{{V}}_{{{{i}}}}}}^m \cdot {{\left( {{N_{{{k}},{{i}}}} \cdot {\sigma _{{{k}},{{j}}}}(E)} \right)}_{{V_{{i}}}}}} \right)} }}{{{N_{{k}}}\displaystyle\sum\limits_{m = 1}^N {WTL_{{{g}},{{{V}}_{{i}}}}^m} }} $(5)

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    $ {\displaystyle\sum\nolimits_{{{s}},{{g}}' \to {{g}}}} = \frac{{\displaystyle\int_{\Delta {{E^{'}}}} {\displaystyle\int_{\Delta {{E}}} {\displaystyle\int_{{V}} {\phi \left( {r,E'} \right) \cdot {\displaystyle\sum\nolimits_{{s}}}\left( {r,E' \to E} \right){\rm{d}}V} {\rm{d}}E} {\rm{d}}E'} }}{{\displaystyle\int_{\Delta {{E^{'}}}} {\displaystyle\int_{{V}} {\phi \left( {r,E'} \right){\rm{d}}E'{\rm{d}}V} } }} $(6)

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    $ {\sigma _{{{k}},{{s}},{{g}}' \to {{g}}}} = \frac{{\displaystyle\int_{\Delta {{E^{'}}}} {\displaystyle\int_{\Delta {{E}}} {\displaystyle\int_{{V}} {\phi \left( {r,E'} \right) \cdot {\sigma _{{{k}},{{s}}}}\left( {r,E' \to E} \right){N_{{{{{k}}}},{{i}}}}{\rm{d}}V} {\rm{d}}E} {\rm{d}}E'} }}{{{N_{{k}}}\displaystyle\int_{\Delta {{E^{'}}}} {\displaystyle\int_{{V}} {\phi \left( {r,E'} \right){\rm{d}}E'{\rm{d}}V} } }} $(7)

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    Zhiyuan Feng, Kaiwen Li, Hao Luo, Kan Wang. Micro cross-section parameterization based on RMC code[J]. High Power Laser and Particle Beams, 2022, 34(2): 026006
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