On-line cross section homogenization method for reactor core physics calculation of full-spectrum application

Abstract

The online cross section homogenization method suitable for full spectrum type reactor core physical calculation obtains a multi-group microscopic cross section library and a few-group microscopic cross section library through spatial homogenization and energy homogenization when performing assembly calculation, then performs core calculation to obtain a few-group macroscopic leakage cross section of each material, obtains a multi-group macroscopic leakage cross section through segmented interpolation; the multi-group macroscopic leakage cross section is used to correct the initial multi-group total cross section, the multi-group neutron flux density is obtained by constructing a multi-group neutron transport equation, and then the energy homogenization is performed on the initial multi-group microscopic cross section to obtain a new generation of few-group microscopic cross section, finally, the core calculation is performed again, the flux initial value is updated in the process, and the above process is repeated until convergence. The method can correct the difference between the neutron flux density and the actual core neutron flux density caused by the infinite medium assumption during assembly calculation, improve the applicability and robustness of the two-step physical calculation applied to different spectrum type core calculation, and ensure the full spectrum calculation precision.

Description

Technical Field

[0001] This invention relates to the fields of nuclear reactor core design and nuclear reactor physics calculations, and is a method for online cross-sectional homogenization correction applied to full-spectrum reactor core physics calculations. Background Technology

[0002] The design of nuclear reactors requires accurate numerical calculations. In the existing two-step calculation strategy, the minority group cross section directly affects the accuracy of core calculations. Under the two-step calculation strategy, component calculations are based on total internal reflection boundary conditions, which leads to a difference between the neutron environment calculated for components and the actual neutron environment in the core. In conventional pressurized water reactors and fast reactors, since the neutron energy spectrum of the entire reactor exhibits essentially the same characteristics, this assumption does not introduce significant deviations. However, with the increase in reactor core geometry complexity and the introduction of moderator materials, the inhomogeneity within the core is significantly enhanced, and the above assumptions no longer hold strictly, resulting in increased errors in the calculation results.

[0003] In traditional pressurized water reactor (PWR) computational programs, this problem is typically addressed through environmental effect corrections, commonly using subgrid methods and multi-assembly computations. Furthermore, advanced reactor physics software, such as the French program APOLLO3, employs coupled 0° and 45° pseudo-one-dimensional lateral calculations in core computation to handle core inhomogeneity. The Embedded Self-Shielding Calculation (ITDM) method proposed by Ivanov Boyan et al. combines whole-reactor small-group network diffusion calculations with local multi-group assembly transport calculations, considering the actual neutron environment of each fuel assembly through appropriate boundary conditions to generate effective cross-sections online. However, current international research on this problem is largely based on commercial PWR reactors, with fewer solutions for reactor core computations that address the higher geometric and spectral complexity.

[0004] Therefore, an online homogenization section correction method applicable to the entire spectrum of reactors is invented. Under the "two-step" calculation framework, the calculation error caused by the difference between the neutron flux density due to the infinite medium assumption and the actual neutron flux density in the reactor core is reduced. This is beneficial to improving the applicability and robustness of the "two-step" method for high-precision calculation of reactors of different spectrum types. Summary of the Invention

[0005] To address the shortcomings of existing technologies, the present invention aims to provide a full-spectrum applicable method for online cross-sectional homogenization of reactor core physics calculations. This method uses the leakage cross-section obtained from core calculations to correct the initial cross-section. By constructing a homogenization problem, a new neutron flux density considering the core environment is obtained, and the cross-section is corrected iteratively.

[0006] To achieve the above objectives, the technical solution of the present invention is as follows: A method for online cross-sectional homogenization of reactor core physics calculations applicable to the entire spectrum includes the following steps: Step 1: Use the component program in the fast neutron reactor neutronics analysis and calculation software to calculate and generate the multi-group micro-sections after spatial homogenization, the few-group micro-sections after spatial and energy homogenization, and the multi-group macro-total cross-section of the nuclear reactor core material composed of multiple nuclides; (1) (2) (3) —Before spatial and energy homogenization i Nuclide in r Region 1 g Multigroup microsections of a group, in units of ; —After spatial homogenization, before energy homogenization i Nuclide g Multigroup microsections of a group, in units of ; —After spatial and energy homogenization i Nuclide G The small-group microscopic cross-section of a group, in units of ; —Number is The total macroscopic cross section of the core material, in units of ; x —Cross section type, , t Represents the total cross-section. a Represents the absorption cross section. s Represents the scattering cross section. f Represents the fission section; —The total cross-section of the multi-group microstructures before energy homogenization, after spatial homogenization, in units of ; -area r Volume, in units of ; — i The atomic number density of nuclides, in units of 10-1 24 cm -3 ; —The region before spatial and energy homogenization in the component program r The gGroup neutron flux density, in units of ; —In the component program, after spatial homogenization and before energy homogenization, the first... g Group neutron flux density, in units of ; Step 2: Use the core program in the fast neutron reactor neutronics analysis and calculation software to perform initial state core calculations and obtain the average minority group macroscopic leakage cross section of the nuclear reactor core material composed of multiple triangular prism segments; (4) —Number is The first core material The average small-group macroscopic leakage cross section of the group, in units of ; —Number is The total leakage reaction rate of the triangular prism segment, in units of ; —Number is The first triangular prism segment The average neutron flux density of the group, in units of ; —Number is The volume of the triangular prism segment, in units of ; L -leakage; Step 3: Perform piecewise interpolation on the average few-group macroscopic leakage cross-section of the core material of each nuclear reactor to obtain the multi-group macroscopic leakage cross-section. ; (1) For the fast neutron energy region, energy Direct mapping interpolation is used: (5) (2) For the resonant neutron energy region, energy Interpolation of the overall cross-sectional shape is used: (6) (3) For the thermal neutron energy region, energy Linear interpolation is used: (7) —Numbered as The material of the first g The multi-group macroscopic leakage cross section of the group, in units of ; , —Numbered as The material of the first G Group, No. G The average minor group macroscopic leakage cross section of group +1, in units of ;; — These represent the energy group numbers respectively. g , G, G+ Energy of 1, unit is eV ; Step 4: Correct the multi-group macro total cross section obtained in Step 1 using multi-group macro leakage cross sections; (8) —The revised number is The material of the first g The macroscopic total cross section of the group is expressed in units of... ; Step 5: For the homogeneity problem of core material construction for each nuclear reactor, the multi-group neutron transport equation under the homogeneity problem is solved using the modified multi-group macroscopic total cross section in Step 4 to obtain the multi-group neutron flux density of each material; (9) —Numbered as The material is from the first Group scattering to the first Macroscopic scattering cross section of the group, in units of ; —Numbered as The multigroup neutron flux density of the g-th group of the material, in units of ; —Numbered as Material No. Macroscopic fission cross section of the group, in units of ; —Numbered as Material No. Spectrum of group fission; —The number of neutrons produced in each fission; Step 6: Use the multi-group neutron flux density obtained in Step 5 to re-merge the energy groups of the multi-group micro-sections to obtain the corrected few-group micro-sections. Considering the corrected few-group micro-sections of the multi-group macro-leakage section, the few-group micro-sections can better reflect the real environment of the reactor core compared with the original few-group micro-sections calculated under the infinite medium assumption, which can effectively reduce the error caused by the infinite medium assumption calculation.

[0007] (10) —Revised i Nuclide g The small-group microscopic cross-section of a group, in units of Step 7: Iterative flux initial value update is adopted. The average neutron flux density of the block, the neutron surface flux density of each face in the block, the neutron corner flux density of the block, and the neutron point flux density of the block after the previous core calculation iteration are used as the initial values ​​for the next core calculation iteration. The initial value update can effectively reduce the number of subsequent iterations and speed up the calculation efficiency.

[0008] (11) , —respectively the first generation and first n The node block number is n The G Group average neutron flux density, in units of ; , —respectively the first generation and first n The node block number is n , No. s Each surface has a discrete direction. The G Group neutron surface flux density, in units of ; , —respectively the first generation and first n The node block number is n Discrete direction is The G Group angular flux density, in units of ; , —respectively the first generation and first n The grid point number is p Discrete direction is The G Sub-point flux density in the group, in units of ; Step 8: After updating the initial values, recalculate the core using the corrected minority group microsection, and repeat steps 2 to 7 until convergence.

[0009] Compared with the prior art, the present invention has the following outstanding advantages: 1. In the method of this invention, the total leakage reaction rate of each triangular prism segment is calculated by combining the average neutron flux density and volume to obtain the small group macroscopic leakage cross section. The multi-group macroscopic leakage cross section is obtained by segmented interpolation and used to correct the multi-group macroscopic total cross section. Therefore, it can reflect the actual neutron leakage situation in the nuclear reactor core, thereby dynamically eliminating the deviation introduced by the infinite medium assumption in the calculation of the small group cross section, reducing the calculation deviation caused by the non-homogeneity of the core, and providing a new idea for high-precision calculation of reactors of various spectrum types.

[0010] 2. In the method of the present invention, the segmented interpolation method is used to expand the few leakage sections into multiple macroscopic leakage sections, which can take into account the characteristics of each section and avoid truncation errors during section expansion. Attached Figure Description

[0011] Figure 1 This is a flowchart of the online homogenization section correction method for full-spectrum reactor core calculations according to the present invention.

[0012] Figure 2 This is a schematic diagram of a reactor core layout. Detailed Implementation

[0013] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments: for Figure 2 The reactor core shown is made of stainless steel in the middle, surrounded by three layers of fuel with different enrichment levels and different material compositions, and the outermost layer is surrounded by 10 rings of graphite. This invention is used to model and calculate this reactor core.

[0014] like Figure 1 As shown, the online cross-sectional homogenization method for reactor core physics calculations applicable to the entire spectrum of this invention comprises the following steps: Step 1: Use the component program SARAX-TULIP in the fast neutron reactor neutronics analysis and calculation software to calculate and generate a small group micro-section library after spatial homogenization and energy homogenization, as well as a multi-group micro-section library after spatial homogenization, and a multi-group macroscopic total cross section of the nuclear reactor core material composed of multiple nuclides; (1) (2) (3) —Before spatial and energy homogenization i Nuclide in r Region 1 g Multigroup microsections of a group, in units of ; —After spatial homogenization, before energy homogenization i Nuclide g Multigroup microsections of a group, in units of ; —After spatial and energy homogenization i Nuclide G The small-group microscopic cross-section of a group, in units of ; —Number is The total macroscopic cross section of the core material, in units of ; x —Cross section type, , t Represents the total cross-section. a Represents the absorption cross section. s Represents the scattering cross section. f Represents the fission section; —The total cross-section of the multi-group microstructures before energy homogenization, after spatial homogenization, in units of ; -area r Volume, in units of ; — i The atomic number density of nuclides, in units of 10-1 24 cm -3 ; —The region before spatial and energy homogenization in the component program r The g Group neutron flux density, in units of ; —In the component program, after spatial homogenization and before energy homogenization, the first... g Group neutron flux density, in units of .

[0015] Step 2: Use the core program SARAX-LAVENDER in the fast neutron reactor neutronics analysis and calculation software to perform initial state core calculations and obtain the average minority group macroscopic leakage cross section of the nuclear reactor core material composed of multiple triangular prism segments; (4) —Number is The first core material The average small-group macroscopic leakage cross section of the group, in units of ; —Number is The total leakage reaction rate of the triangular prism segment, in units of ; —Number is The first triangular prism segment The average neutron flux density of the group, in units of ; —Number is The volume of the triangular prism segment, in units of ; L -leakage.

[0016] Step 3: Perform segmented interpolation on the average few-group macroscopic leakage cross section of the core material of each nuclear reactor to obtain the 1968-group multi-group macroscopic leakage cross section; (1) For the fast neutron energy region, energy Direct mapping interpolation is used: (5) (2) For the resonant neutron energy region, energy Interpolation of the overall cross-sectional shape is used: (6) (3) For the thermal neutron energy region, energy Linear interpolation is used: (7) —Numbered as The material of the first g The multi-group macroscopic leakage cross section of the group, in units of ; , —Numbered as The material of the first G Group, No. G The average minor group macroscopic leakage cross section of group +1, in units of ;; — These represent the energy group numbers respectively. g , G, G+ Energy of 1, unit is eV.

[0017] Step 4: Correct the multi-group macro total cross section obtained in Step 1 using multi-group macro leakage cross sections; (8) —The revised number is The material of the first g The macroscopic total cross section of the group is expressed in units of... .

[0018] Step 5: For the homogeneity problem of core material construction for each nuclear reactor, the multi-group neutron transport equation under the homogeneity problem is solved using the modified multi-group macroscopic total cross section in Step 4 to obtain the multi-group neutron flux density of each material; (9) —Numbered as The material is from the first Group scattering to the first Macroscopic scattering cross section of the group, in units of ; —Numbered as The multigroup neutron flux density of the g-th group of the material, in units of ; —Numbered as Material No. Macroscopic fission cross section of the group, in units of ; —Numbered as Material No. Spectrum of group fission; —The number of neutrons produced in each fission.

[0019] Step 6: Use the multi-group neutron flux density obtained in Step 5 to re-merge the energy groups of the multi-group microsections to obtain the corrected few-group microsections. (10) —Revised i Nuclide g The small-group microscopic cross-section of a group, in units of Step 7: Use iterative flux initial value update, and use the average neutron flux density of the block, the neutron surface flux density of each face in the block, the neutron corner flux density of the block, and the neutron point flux density of the block after the previous core calculation iteration as the initial values ​​for the next core calculation iteration. (11) , —respectively the first generation and first n The node block number is n The GGroup average neutron flux density, in units of ; , —respectively the first generation and first n The node block number is n , No. s Each surface has a discrete direction. The G Group neutron surface flux density, in units of ; , —respectively the first generation and first n The node block number is n Discrete direction is The G Group angular flux density, in units of ; , —respectively the first generation and first n The grid point number is p Discrete direction is The G Sub-point flux density in the group, in units of ; Step 8: After updating the initial values, recalculate the core using the corrected minority group microsection, and repeat steps 2 to 7 until convergence.

[0020] The effective multiplication factor calculation results are shown in Table 1. Before online homogenization, due to the significant differences in energy spectrum in different regions, the calculation results had a very large deviation, with a deviation of 1294 pcm compared to the reference solution. However, after online homogenization in this invention, the calculation deviation was greatly reduced to only 3 pcm, demonstrating high calculation accuracy.

[0021] Table 1. Results of effective proliferation factors calculated using the online homogenization method of this invention. As shown in Table 1, this invention can significantly reduce calculation errors caused by the infinite medium assumption in component calculations, thereby improving the accuracy of the calculation results. It provides a new approach to improving the applicability and robustness of the "two-step" physical calculation method and ensuring the correctness of physical calculations for different types of reactors, playing a crucial role in the design calculations of novel nuclear reactors.

Claims

1. A method for online cross-sectional homogenization of reactor core physics calculations applicable to the entire spectrum, characterized in that, The macroscopic leakage cross section of the multiple groups, obtained from calculations using the core program in fast neutron reactor neutronics analysis software, is used to correct the overall macroscopic cross section of the multiple groups. By constructing a homogeneous problem, the neutron flux density of the multiple groups, taking into account the core environment, is re-obtained. The microscopic cross section of the few groups is then corrected iteratively, including the following steps: Step 1: Use the component program in the fast neutron reactor neutronics analysis and calculation software to calculate and generate the multi-group micro-sections after spatial homogenization, the few-group micro-sections after spatial and energy homogenization, and the multi-group macro-total cross-section of the nuclear reactor core material composed of multiple nuclides; （1） （2） （3） —Before spatial and energy homogenization i Nuclide in r Region 1 g Multigroup microsections of a group, in units of ; —After spatial homogenization, before energy homogenization i Nuclide g Multigroup microsections of a group, in units of ; —After spatial and energy homogenization i Nuclide G The small-group microscopic cross-section of a group, in units of ; —Number is The total macroscopic cross section of the core material, in units of ; x —Cross section type, , t Represents the total cross-section. a Represents the absorption cross section. s Represents the scattering cross section. f Represents the fission section; —The total cross-section of the multi-group microstructures before energy homogenization, after spatial homogenization, in units of ; -area r Volume, in units of ; — i The atomic number density of nuclides, in units of 10-1 24 cm -3 ; —The region before spatial and energy homogenization in the component program r The g Group neutron flux density, in units of ; —In the component program, after spatial homogenization and before energy homogenization, the first g Group neutron flux density, in units of ; Step 2: Use the core program in the fast neutron reactor neutronics analysis and calculation software to perform initial state core calculations and obtain the average minority group macroscopic leakage cross section of the nuclear reactor core material composed of multiple triangular prism segments; （4） —Number is The first core material The average small-group macroscopic leakage cross section of the group, in units of ; —Number is The total leakage reaction rate of the triangular prism segment, in units of ; —Number is The first triangular prism segment The average neutron flux density of the group, in units of ; —Number is The volume of the triangular prism segment, in units of ; L -leakage; Step 3: Perform piecewise interpolation on the average few-group macroscopic leakage cross-section of the core material of each nuclear reactor to obtain the multi-group macroscopic leakage cross-section. ; (1) For the fast neutron energy region, energy Direct mapping interpolation is used: （5） (2) For the resonant neutron energy region, energy Interpolation of the overall cross-sectional shape is used: （6） (3) For the thermal neutron energy region, energy Linear interpolation is used: （7） —Numbered as The material of the first g The multi-group macroscopic leakage cross section of the group, in units of ; , —Numbered as The material of the first G Group, No. G The average minor group macroscopic leakage cross section of group +1, in units of ;; — These represent the energy group numbers respectively. g , G, G+ Energy of 1, unit is eV ; Step 4: Correct the total macroscopic cross section obtained in Step 1 using multiple macroscopic leakage cross sections; （8） —The revised number is The material of the first g The macroscopic total cross section of the group is expressed in units of... ; Step 5: For the homogeneity problem of core material construction for each nuclear reactor, the multi-group neutron transport equation under the homogeneity problem is solved using the modified multi-group macroscopic total cross section in Step 4 to obtain the multi-group neutron flux density of each material; （9） —Numbered as The material is from the first Group scattering to the first Macroscopic scattering cross section of the group, in units of ; —Numbered as The multigroup neutron flux density of the g-th group of the material, in units of ; —Numbered as Material No. Macroscopic fission cross section of the group, in units of ; —Numbered as Material No. Spectrum of group fission; —The number of neutrons produced in each fission; Step 6: Use the multi-group neutron flux density obtained in Step 5 to re-merge the energy groups of the multi-group microsections to obtain the corrected few-group microsections. （10） —Revised i Nuclide g The small-group microscopic cross-section of a group, in units of Step 7: Use iterative flux initial value update, and use the average neutron flux density of the block, the neutron surface flux density of each face in the block, the neutron corner flux density of the block, and the neutron point flux density of the block after the previous core calculation iteration as the initial values ​​for the next core calculation iteration. （11） , —respectively the first generation and first n The node block number is n The G Group average neutron flux density, in units of ; , —respectively the first generation and first n The node block number is n , No. s Each surface has a discrete direction. The G Group neutron surface flux density, in units of ; , —respectively the first generation and first n The node block number is n Discrete direction is The G Group angular flux density, in units of ; , —respectively the first generation and first n The grid point number is p Discrete direction is The G Sub-point flux density in the group, in units of ; Step 8: After updating the initial values, recalculate the core using the corrected minority group microsection, and repeat steps 2 to 7 until convergence.

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