A Group Collapse Method Of Coarse Group Macroscopic Cross Sections For Shielding Calculations

Shielding calculations are the theoretical foundation and technical support for the design of reactor nuclear facilities,equipment safety evaluation,and radiation evaluation of employees.The discrete ordinates method(SN)uses a multigroup approximation to discretize the energy variable.High-precision multi group macroscopic cross-section data are crucial for SN transport calculations.Hyperfine energy group structures can result in a multiplication of computational resources and computational time costs,and shielding calculations often make them into a narrow energy group.The group collapse method is based on the concept of "reaction rate preservation",which requires the exact fine-group energy spectrum.Since this quantity is not known a priori,an approximate fine-group flux must be used,which unavoidably results in a loss of accuracy,and affects the accuracy and reliability of the broad-group cross sections.In problems with the introducing errors in the weighting function during the group collapse process,we propose a group collapse method for broad group macroscopic cross sections to improve their accuracy and allow for fewer groups to better reflect the fine group solution.To process multigroup microscopic cross sections of nuclides and obtain the problem-dependent multigroup macroscopic cross sections,the multigroup macroscopic cross-section generation module is independently de veloped,which provides a basis for the implementation of the coarse group collapse method.The legender moments of flux are added as the weighting function for the standard group collapse method,which does not account for angular variations,to increase the accuracy of the scattering cross-section matrix.The on-the-fly(OTF)group collapse method builds four piecewise linear functions to expand the broad group transport calculation results to fine group energy structure,and obtain a new OTF weighting function by modifying the initial weighting function.Then re-collapse the fine group cross sections to the broad group structures,which effectively reduces the errors introduced by the broad group cross sections while ensuring calculation efficiency.Numerical results show that for self-designed single nuclide one-dimensional sphere problems,the multigroup macroscopic cross-section generation module can effectively handle the resonance self-shielding effects of various nuclides,and the results are consistent with MCNP reference results.For the ill-Fe shielding benchmark experiment,the multi-group macroscopic cross-section generation module obtains calculation results close to TRANSX2.15 and is in good agreement with experimental values.In one-dimensional plate problems,UO2,water,and stainless steel are used as shielding materials.For the UO2 and stainless steel problems,the OTF group collapse method has the same computational accuracy as the consistent PN collapse method.For the water problem,the consistent PN group collapse method has better computational accuracy,and the OTF group collapse method is better than the standard grouping method.For the typical pressurized water reactor shielding problem,the OTF group collapse method shows good computational accuracy,and the consistent PN group collapse method has higher accuracy in areas with strong anisotropic scattering.This research helps alleviate errors introduced in the group collapse process and provides a reference for selecting group collapse methods in reactor shielding calculations,with certain application prospects in engineering.