Multi-type particle dispersion fuel online subgroup resonance self-shielding calculation method
Through a multi-type particle diffusion fuel online subgroup resonance self-screen calculation method, the calculation accuracy and efficiency problems when multiple types of particles coexist in the prior art are solved, and the stability and scope of application of calculation accuracy are expanded.
Patent Information
- Application Number
- CN202411560612.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-11-04
- Publication Date
- 2025-02-07
AI Technical Summary
In the prior art, when dealing with neutron transport calculations for multi-type particle diffusion fuels, there is a problem of high calculation accuracy but low efficiency or high efficiency but low accuracy. Especially when multiple types of particles coexist, it is difficult to accurately deal with the dual non-uniform effect. .
A multi-type particle diffusion fuel online subgroup resonance self-screen calculation method is adopted, and the subgroup macroscopic cross-sectional calculation, collision probability information and regional uniform cross-sectional calculation, fixed source problem subgroup feature line calculation, transportation correction calculation and multi-group feature Steps such as line transportation calculation eliminate the typical working condition assumptions in the production of offline subgroup parameters, and retain the microscopic information of the particles.
This method avoids the problem of calculation distortion, expands the scope of application, and ensures the stability of calculation accuracy. The calculated effective self-screen section deviation is within 5% from the Monte Carlo result, and the keff calculation average deviation is within 200pcm.
Smart Images
Figure CN119397872A_ABST
Abstract
Description
Technical Field
[0001] The invention relates to the field of nuclear reactor core design and nuclear reactor physical calculation technology, and in particular to an online subgroup resonance self-screening calculation method for multi-type particle dispersed fuel. Background Art
[0002] Dispersed particle fuel has the characteristics of strong fission product containment capacity, good irradiation stability, high thermal conductivity and inherent safety under beyond design basis accidents. It is widely used in production reactors, experimental reactors and nuclear power plants. It also has broad application prospects in ship reactors, space reactors and application fields such as marine nuclear power platforms, vehicle-mounted mobile small reactors, and deep-submersible nuclear power supplies. It is of great significance to the safety and economy of nuclear energy.
[0003] However, there is a double inhomogeneity effect in the neutron transport process of dispersed particle fuel, especially when multiple types of particles are dispersed together, the double inhomogeneity effect is more intense, and must be accurately considered in the neutron transport calculation process. For example, when the content of burnable poison particles is 5% and the particle diameter is 300μm, the impact on the characteristic value can exceed 900pcm.
[0004] The difficulty of neutron transport calculation of dispersed particle fuel lies in the calculation of resonance self-screening of multiple types of dispersed particle fuel. The existing methods that can handle the double non-uniform effect of resonance self-screening calculation of dispersed particle fuel mainly include the following:
[0005] (1) Monte Carlo method. This method uses a continuous energy point cross-section library to directly skip the resonant self-screening calculation. This method has the ability to accurately describe complex geometries and achieve accurate calculations of dispersed particle fuels in an explicit or implicit modeling manner. However, due to the huge number of fuel particles, the calculation takes a very long time. It can only be used to provide a reference solution, but it is difficult to directly apply it to scenarios that require fast calculations, such as engineering design and core analysis.
[0006] (2) Reactivity equivalent physical transformation method, also known as RPT method. The basic principle is to transform the dispersed particle fuel problem into a traditional homogeneous problem in accordance with the requirement of ensuring unchanged reactivity, and obtain the effective self-screening cross section of the dispersed particle fuel problem through resonance calculation of the homogeneous problem. This method is simple and efficient, but the reactivity of the target dispersed particle fuel problem must be known in advance, and it does not have the ability to describe the microscopic information of the particles, and cannot accurately consider the interference effect between the fuel particles and the matrix.
[0007] (3) Defect factor method. The core idea is to convert the dispersed particle fuel problem into a traditional single inhomogeneous problem by solving the ultrafine group slowing-down equation. The effective self-screening cross section of the dispersed particle fuel problem is obtained through the resonance calculation of the single inhomogeneous problem. This method is easy to implement and has high computational efficiency, but it also has no ability to describe the microscopic information of particles and is difficult to accurately handle the coexistence of multiple types of particles.
[0008] (4) Sanchez-Pomraning method based on ultrafine groups. The basic principle is to establish an update equation for the neutron flux density of dispersed particle fuel based on the Markov chain hypothesis, which can describe the neutron flux distribution of each layer inside the dispersed particles in detail. The ultrafine group method is used for resonant self-screening calculations. It has the ability to describe the microscopic information of particles and process multiple types of particles, and has high calculation accuracy. However, because the neutron transport calculation of the ultrafine group is very time-consuming, the calculation efficiency of this method is obviously not high.
[0009] (5) Offline subgroup method based on the Sanchez-Pomraning method. The basic principle is to design a series of benchmark problems based on specific problems, and then fit and make an offline subgroup library through ultra-fine group calculation. Its advantage is high calculation accuracy. However, due to the typical working condition assumption in the offline subgroup parameter making process, there is a problem of calculation distortion when it is far from the typical working condition.
[0010] In summary, the existing methods either have high calculation accuracy but low calculation efficiency; or have high calculation efficiency but low calculation accuracy. Summary of the invention
[0011] In order to solve the problems existing in the above-mentioned prior art, the purpose of the present invention is to propose an online subgroup resonance self-screening calculation method for multi-type particle dispersed fuel, which eliminates the typical operating condition assumption in the offline subgroup parameter production process, avoids the problem of calculation distortion when far away from the typical operating condition, expands the scope of application, and ensures the stability of calculation accuracy within the scope of application. It also retains the microscopic information of the particles in the transport calculation and fuel consumption calculation, and can handle the problem of coexistence of multiple types of dispersed particles.
[0012] In order to achieve the above object, the present invention adopts the following technical solution:
[0013] A method for calculating online subgroup resonance self-screening of multi-type particle dispersed fuels comprises the following steps:
[0014] 1) Subgroup macroscopic cross section calculation: Based on the multi-group database, the optimal subgroup parameters are generated online through the pada approximation. The subgroup macroscopic cross sections of the matrix and each layer of the dispersed particles in the dispersed particle fuel area are merged and solved through the subgroup microscopic cross sections and the corresponding nuclear number density;
[0015] 2) Calculation of collision probability information and regional uniform cross section: Using the volume fraction of the matrix and particle layer in the dispersed particle fuel zone and the subgroup macroscopic cross section, the initial equivalent homogenized subgroup macroscopic cross section of the dispersed particle fuel zone is solved. By iterating the update equation group of the cross section in the dispersed particle fuel zone, the equivalent homogenized subgroup macroscopic cross section after convergence of the dispersed particle fuel zone and the collision probability information of each dispersed particle layer and the matrix in the dispersed particle fuel zone are obtained;
[0016] 3) Calculation of subgroup characteristic lines for fixed source problems: By solving the subgroup characteristic line transport equation, the average standard flux of the matrix, each layer of dispersed particles and the dispersed particle fuel area in the dispersed particle fuel area is obtained, and the multi-group microscopic effective self-screening cross section is solved by subgroup merging. The multi-group microscopic effective self-screening cross section when multiple resonance nuclides coexist is corrected by the resonance interference factor method, and finally the multi-group macroscopic effective self-screening cross section of each layer of dispersed particles is solved;
[0017] 4) Transport correction calculation: For nuclides with strong anisotropic scattering, the multi-group macroscopic total cross section and self-scattering cross section of each layer of the dispersed particles are corrected according to the first-order neutron flux moment of each dispersed particle fuel zone. Based on the corrected cross section information, the update equation group of the cross section in the dispersed particle fuel zone is iterated to solve the equivalent homogenized multi-group macroscopic cross section and collision probability information after convergence in the dispersed particle fuel zone;
[0018] 5) Multi-group characteristic line transport calculation: The multi-group macroscopic cross sections of each layer and matrix of the dispersed particle fuel region, the regional equivalent homogenized multi-group macroscopic cross sections, the initial and converged collision probabilities, the escape probability, the weakened escape probability, and the normalization coefficient are passed to the characteristic line transport solver for iterative solution of the transport equation to obtain the converged dispersed particle layered flux and the characteristic value of the dispersed particle fuel system;
[0019] 1)6) Calculation of fuel consumption of dispersed particle fuel: The estimated correction method is used to perform detailed fuel consumption calculation of dispersed particle fuel partitioning and particle stratification. The fuel consumption calculation retains the stratified fuel consumption information of each particle layer.
[0020] Compared with the prior art, the present invention has the following advantages:
[0021] Compared with the traditional offline subgroup method, the online subgroup resonance self-screening calculation method of multi-type particle dispersed fuel in the present invention does not need to design a benchmark problem specifically for a specific problem to make a subgroup parameter library for a specific problem, thus avoiding the calculation distortion caused by typical working condition assumptions, expanding the scope of application, and ensuring the stability of calculation accuracy. The verification results show that the effective self-screening cross section calculated by the method of the present invention is within 5% of the Monte Carlo result, and k eff The average calculation deviation is within 200pcm. Compared with the traditional offline subgroup method, this online method avoids the calculation distortion caused by typical working condition assumptions, expands the scope of application, and ensures the stability of calculation accuracy. BRIEF DESCRIPTION OF THE DRAWINGS
[0022] Figure 1 This is a flow chart of the online subgroup resonance self-screening calculation method for multi-type particle dispersed fuel of the present invention.
[0023] Figure 2Schematic diagram of the double-type particle calculation example of plate-shaped dispersed particle fuel grid element.
[0024] Figure 3 The nuclides in the double-type particle example of the plate-like dispersed particle fuel grid element 235 The effective self-screen cross section of U, where (a) is the total cross section, (b) is the scattering cross section, (c) is the fission cross section, and (d) is the absorption cross section.
[0025] Figure 4 The nuclides in the double-type particle example of the plate-like dispersed particle fuel grid element 238 The effective self-screen cross section of U, where (a) is the total cross section, (b) is the scattering cross section, and (c) is the absorption cross section.
[0026] Figure 5 This is a graph showing the burnup results for a dual-type particle example of a plate-shaped dispersed particle fuel grid element. DETAILED DESCRIPTION
[0027] The present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments.
[0028] like Figure 1 As shown, the method for calculating the online subgroup resonance self-screening of multi-type particle dispersed fuel of the present invention comprises the following steps:
[0029] 1. Subgroup macroscopic cross-section calculation
[0030] Based on the multi-group database, the optimal subgroup parameters are generated online through the pada approximation. The subgroup macroscopic cross sections of the matrix and each layer of the dispersed particles in the dispersed particle fuel zone are merged and solved through the subgroup microscopic cross sections and the corresponding nuclear number density.
[0031] 2. Collision probability information and regional uniform cross-section calculation
[0032] The volume fraction of dispersed particle i in the kth layer of dispersed particle type i is calculated by The volume fraction of the kth layer of dispersed particles i in all particle types is p ik , the total cross section of the matrix subgroup Σ0 and the macroscopic cross section of the subgroup of the kth layer of particle i Σ ik , solve the initial equivalent homogenized subgroup macroscopic cross section of the dispersed particle fuel zone, and iterate the update equation group of the cross section in the dispersed particle fuel zone to obtain the equivalent homogenized subgroup macroscopic cross section after convergence of the dispersed particle fuel zone, the collision probability and escape probability of each layer of dispersed particles with the matrix in the dispersed particle fuel zone, and other information.
[0033] 3. Calculation of subgroup characteristic lines for fixed source problem
[0034] By solving the subgroup characteristic line transport equation, the average standard flux of the matrix, each layer of dispersed particles and the dispersed particle fuel zone in the dispersed particle fuel zone is obtained. The multi-group microscopic effective self-screening cross section is solved by subgroup merging. The resonance interference factor method is used to correct the multi-group microscopic effective self-screening cross section when multiple resonance nuclides coexist. Finally, the multi-group macroscopic effective self-screening cross section of each layer of dispersed particles is obtained.
[0035] 4. Transport correction calculation
[0036] For nuclides with strong anisotropic scattering (C, H, O and D), the multi-group macroscopic total cross section and multi-group macroscopic self-scattering cross section of each particle layer are corrected according to the first-order neutron flux moment of each diffuse particle fuel zone. Subsequently, according to the corrected multi-group macroscopic total cross section and multi-group macroscopic scattering cross section of each particle layer and matrix in the diffuse particle fuel zone, the equivalent homogenized multi-group macroscopic cross section and collision probability information after convergence in the diffuse particle fuel zone are solved by iterating the update equation of the cross section in the diffuse particle fuel zone.
[0037] 5. Transport calculation of multiple characteristic lines
[0038] According to the multi-group macroscopic cross-sections of each layer of particles and the matrix, the regional equivalent homogenized multi-group macroscopic cross-sections, the initial and converged collision probabilities, the escape probability, the weakened escape probability, the normalization coefficient and other parameters, they are passed to the characteristic line transport solver by writing into the file and then reading it for iterative solution of the transport equation.
[0039] 1) Solve the fission source terms of the particles and matrix in each dispersed particle fuel zone, and solve the equivalent fission source term of the dispersed particle fuel zone;
[0040] 2) Solve the scattering source terms of particles and matrix in the diffuse particle fuel region, and solve the equivalent scattering source terms in the diffuse particle fuel region;
[0041] 3) Solve the asymptotic flux and obtain the equivalent source term;
[0042] 4) Characteristic line scanning, solve the contribution of the angular flux of the flat source area, the line segment angular flux and the contribution of the angular flux of the area to the intermediate variable of the standard flux in turn, and finally obtain the standard flux of the regional matrix;
[0043] 5) After the inner iteration converges, solve the standard flux of each layer of particles;
[0044] 6) Repeat the solution process from 1) to 5) until the flux iteration converges.
[0045] 7) Solve the equivalent standard flux of the dispersed particle fuel area. Store the standard flux of each layer and matrix of the particles, as well as the equivalent standard flux of the dispersed particle fuel area, for subsequent fuel consumption calculations.
[0046] 6. Calculation of fuel consumption of dispersed particle fuel
[0047] Use the estimated correction method to perform fine burnup calculations for dispersed particle fuel partitions and particle stratification; process the material and nuclide information after burnup, and regenerate the material information of the next burnup calculation card based on the burnup nuclides and resonance nuclide labels in the area. Perform the next burnup calculation by reading the Dep.xml card until the burnup is completed.
[0048] Verification algorithm Figure 2 As shown, the plate-shaped dispersed particle fuel grid element contains both fuel particles and combustible poison particles. The outer FSR area is filled with H2O, and the inner dispersed particle fuel area: the matrix is filled with natural Zrnat, the diameter of UO2 particles is 150μm, the diameter of B4C particles is 80μm, the volume filling rate of UO2 is 20%, the volume filling rate of B4C is 1%, and the fuel enrichment is 20%.
[0049] Nuclide 235 The calculation results of the effective self-screening cross section of U are shown in Figure 3 Compared with the Serpent reference solution, the deviations of the numerical calculation results of the effective self-screen cross sections in all energy groups are within 2.0%; the maximum deviation of the total cross section is -1.56%, the maximum deviation of the scattering cross section is -0.13%, the maximum deviation of the fission cross section is -1.99%, and the maximum deviation of the absorption cross section is -1.90%.
[0050] Nuclide 238 The calculation results of the effective self-screening cross section of U are shown in Figure 4 Compared with the Serpent reference solution, the deviation of the numerical calculation results of the effective self-screening cross section under all energy groups is within 7.0%; the maximum deviation of the total cross section is -4.08%, the maximum deviation of the scattering cross section is -3.30%, and the maximum deviation of the absorption cross section is -6.91% (the 23rd group, the absorption cross section is small, the relative deviation is <1). This shows that the function of the online subgroup resonance self-screening calculation of multi-type particle dispersed fuel is correct and the numerical accuracy is good.
[0051] At the same time, the fuel consumption calculation results are as follows Figure 5 As shown, within the entire life cycle (0-70MW / kg), the calculated deviation from the Serpent eigenvalue is between -169 and 100pcm, and the results are in good agreement, indicating that the online subgroup resonance self-screening calculation of multi-type particle dispersed fuel has good accuracy at different burnup depths. This method eliminates the typical operating condition assumption in the offline subgroup parameter production process, avoids the problem of calculation distortion when far away from the typical operating condition, expands the scope of application, and ensures the stability of the calculation accuracy within the scope of application.
Claims
1. A method for calculating the online subgroup resonance self-screening of multi-type particle dispersed fuel, characterized by: The steps include: 1) Subgroup macroscopic cross section calculation: Based on the multi-group database, the optimal subgroup parameters are generated online through the pada approximation. The subgroup macroscopic cross sections of the matrix and each layer of the dispersed particles in the dispersed particle fuel area are merged and solved through the subgroup microscopic cross sections and the corresponding nuclear number density; 2) Calculation of collision probability information and regional uniform cross section: Using the volume fraction of the matrix and particle layer in the dispersed particle fuel zone and the subgroup macroscopic cross section, the initial equivalent homogenized subgroup macroscopic cross section of the dispersed particle fuel zone is solved. By iterating the update equation group of the cross section in the dispersed particle fuel zone, the equivalent homogenized subgroup macroscopic cross section after convergence of the dispersed particle fuel zone and the collision probability information of each dispersed particle layer and the matrix in the dispersed particle fuel zone are obtained; 3) Calculation of subgroup characteristic lines for fixed source problems: By solving the subgroup characteristic line transport equation, the average standard flux of the matrix, each layer of dispersed particles and the dispersed particle fuel area in the dispersed particle fuel area is obtained, and the multi-group microscopic effective self-screening cross section is solved by subgroup merging. The multi-group microscopic effective self-screening cross section when multiple resonance nuclides coexist is corrected by the resonance interference factor method, and finally the multi-group macroscopic effective self-screening cross section of each layer of dispersed particles is solved; 4) Transport correction calculation: For nuclides with strong anisotropic scattering, the multi-group macroscopic total cross section and self-scattering cross section of each layer of the dispersed particles are corrected according to the first-order neutron flux moment of each dispersed particle fuel zone. Based on the corrected cross section information, the update equation group of the cross section in the dispersed particle fuel zone is iterated to solve the equivalent homogenized multi-group macroscopic cross section and collision probability information after convergence in the dispersed particle fuel zone; 5) Multi-group characteristic line transport calculation: The multi-group macroscopic cross sections of each layer and matrix of the dispersed particle fuel region, the regional equivalent homogenized multi-group macroscopic cross sections, the initial and converged collision probabilities, the escape probability, the weakened escape probability, and the normalization coefficient are passed to the characteristic line transport solver for iterative solution of the transport equation to obtain the converged dispersed particle layered flux and the characteristic value of the dispersed particle fuel system; 6) Calculation of fuel consumption of dispersed particle fuel: The estimated correction method is used to perform detailed fuel consumption calculation of dispersed particle fuel partitioning and particle stratification. The fuel consumption calculation retains the stratified fuel consumption information of each particle layer.