Control rod super cell model building method based on reaction rate conservation

Abstract

This invention discloses a method for establishing a control rod supercell model based on reaction rate conservation, applicable to the field of high-fidelity physics calculations for nuclear reactors. This model does not require the inclusion of the fuel region. First, the control rods are independently geometrically modeled. Based on escape probability conservation, non-rod-shaped geometric control rods are equivalent to one-dimensional rod-shaped equivalent control rods. Considering the moderator arrangement around the control rods, a modified moderator equivalent geometry conforming to the actual geometry is constructed. Combining the precise control rod geometry and the modified equivalent geometry, a fuel-free supercell model is constructed, establishing a bidirectional mapping between this model and the core physics calculation grid. The effective self-screen cross-section of the control rod is obtained using the ultrafine group method, and updated to all corresponding calculation grids according to the mapping relationship. This invention overcomes the limitation of traditional methods requiring the inclusion of surrounding fuel, enabling flexible handling of resonant self-screen calculations for complex geometrically strong absorbing control rods, simplifying the control rod supercell model, and improving the neutronics calculation accuracy of complex geometric small reactors.

Description

Technical Field

[0001] This invention relates to the field of nuclear reactor physics calculation technology, specifically to a method for establishing a super-gate model for calculating the resonant self-shielding effect of strong absorbing control rods in a complex geometric miniature reactor in the high-fidelity physics calculation program NECP-X. Background Technology

[0002] Strong absorbers, such as control rods and flammable poison rods, are crucial for controlling reactivity in nuclear reactors. In small reactors with limited space, where the chemical control system is removed, a large number and variety of flammable poison rods and control rods are often installed. Due to the strong resonant self-shielding effect of strong absorbers, proper handling of resonant self-shielding calculations is essential to achieving high neutronics calculation accuracy in small reactors with complex geometries.

[0003] The cross-section of resonant nuclides is highly irregular in the resonance energy region, varying drastically with energy. Furthermore, resonance self-shielding calculations are influenced by factors such as geometry, materials, and temperature specific to the problem, making resonance calculations a crucial step in nuclear reactor physics calculations. Existing methods, such as equivalence theory, cannot accurately handle the resonance effect of strong absorbers. Therefore, supergate methods need to be considered for resonance self-shielding calculations of strong absorbers.

[0004] The basic idea of ​​the super-enclosure method is to use the strong absorber as the center of the one-dimensional equivalent model for resonance calculation, and then treat the surrounding elements, including moderator materials, as an additional layer outside the strong absorber. This ensures that the energy spectrum of the one-dimensional equivalent model is close to that of the strong absorber in the real problem, thus obtaining the accurate effective self-shielding cross-section of the strong absorber. However, the one-dimensional equivalent model set by the general super-enclosure method is often composed of strong absorber material from the inside out, followed by surrounding material layers. This fixed structure cannot universally handle strong absorbers arranged in special locations or with unique structures.

[0005] In the high-fidelity physics computation program NECP-X, a super-gate method based on the ultrafine group method is employed to handle the resonance self-shielding effect of strong absorbers. This method can construct a more accurate one-dimensional equivalent model for resonance calculation that closely approximates the actual problem, based on the fine structure of the strong absorber and the arrangement around the control rods. In the one-dimensional equivalent model, the structure of the control rods is consistent with the actual problem, and the construction of the outer additional layer fully considers the influence of the surrounding structural materials, especially the moderator. For the one-dimensional equivalent model, when calculating the effective self-shielding cross section based on the ultrafine group method, the resonance energy region is divided very finely. An ultrafine group moderation equation is established in each energy region, and a fine neutron energy spectrum is obtained by solving the equation, thus yielding the accurate effective self-shielding cross section of the control rods.

[0006] However, existing supercell methods based on ultrafine groups still have the following limitations when constructing equivalent geometry: ① Must include ambient fuel (e.g.) Figure 1 As shown): Traditional supercell models are built on modules, with the control rods located by default inside the fuel assembly, surrounded by a fuel region. However, in some advanced reactor designs, such as hexagonal cores, the control rods may be placed at corner positions (e.g., Figure 2 (As shown). At this point, there may be no fuel around the control rod, only structural materials such as moderators. Traditional methods cannot construct an accurate supercell model because they must include the surrounding fuel, causing the program to fail to perform calculations.

[0007] ② Difficulty in obtaining information on non-rod-shaped control rods: For non-rod-shaped control rods arranged in special locations or with special geometries, it is difficult to obtain their accurate geometric and material information, resulting in unreasonable one-dimensional equivalent geometry and inaccurate effective self-shield cross sections obtained by solving the ultrafine group slowing equation.

[0008] ③ Lack of optimization of equivalent geometric parameters: Traditional methods often simply adopt volume conservation when equivaling surrounding materials, without considering the optimization of the moderator radius by the conservation of Dankov factor, resulting in a large deviation between the equivalent geometry and the actual geometry.

[0009] Therefore, a method for establishing a control rod supercell model based on reaction rate conservation is needed. This method should be able to overcome the limitation of having to include the surrounding fuel, flexibly handle the resonance calculation of strong absorbing control rods with arbitrary positions and geometries, accurately obtain information about the surrounding moderators, and improve the calculation accuracy through reasonable geometric corrections. Summary of the Invention

[0010] The purpose of this invention is to overcome the problem that existing technologies cannot calculate complex control rod arrangements and geometries, and to provide a method for establishing a control rod supercell model based on reaction rate conservation. This method addresses the limitations of traditional supercell models, which must include surrounding fuel, the difficulty in obtaining information on non-rod-shaped control rods, and the lack of optimization of equivalent geometric parameters, thereby improving the calculation accuracy of the resonant self-shielding effect of strong absorbing control rods under complex geometries.

[0011] To achieve the above objectives, the present invention adopts the following technical solution: A method for establishing a control rod supergate model based on reaction rate conservation, used for calculating the resonant self-screen of a strong absorbing control rod with a complex control rod arrangement, includes the following steps: Step 1: Model the control rods as independent geometric entities, reserving positions for them within the assembly. Read the geometric and material information of the core to be calculated, the material information of the control rods, and the independently defined radial and axial precise geometric information of the control rods. This independent modeling method is not dependent on the assembly's mesh generation or cell size limitations, and can accurately describe control rods at arbitrary locations and with arbitrary geometry, ensuring that the control rod structure remains consistent with the actual problem and avoiding geometric distortion caused by module segmentation in traditional methods.

[0012] Step 2: Extract the precise radial layered structure and axial segmented structure of the control rod from the independently defined precise radial and axial geometric information. If the control rod is non-rod-shaped, it is equivalent to a one-dimensional rod-shaped equivalent control rod based on the escape probability conservation. This solves the problem of difficulty in obtaining information about non-rod-shaped control rods in traditional methods.

[0013] Step 3: Obtain material information around the control rod according to the preset search range, excluding fuel and only including the moderator, and specify the material zone number in the surrounding module. Equip the material zones around the control rod with volume weights to obtain the equivalent one-dimensional radial geometry of the surrounding material layer. This equivalence process effectively considers the spatial interference effect caused by the surrounding structure. The equivalent material parameters are calculated using the following formula: (1) (2) In the formula: — Equivalent mass density; — Equivalent nucleon density; — For the first The volume of the material within the search area; — refers to mass density; — For the first Type of material The nucleon density of a nuclide.

[0014] Step 4: Correct the equivalent one-dimensional radial geometry of the surrounding material layers constructed in Step 3. For the optimal radius of the outermost moderator layer, specifically, traverse different moderator radii to construct a series of equivalent super-cell models, ensuring that the Dankoff factor of the equivalent super-cell model is conserved from the actual Dankoff factor. Compare the effective self-shielding cross-section with the results calculated using a high-precision Monte Carlo program. The conclusion is that the optimal moderator radius corresponds to the case where the radius of the moderator layer is tangent to the next layer of material (such as the cladding). The one-dimensional equivalent geometry most closely approximates the actual physical layout and effectively guarantees the conservation of the Dankoff factor. Thus, the corrected equivalent one-dimensional radial geometry of the surrounding layers is obtained.

[0015] Step 5: Combine the one-dimensional rod-shaped equivalent control rod obtained in Step 2 with the corrected one-dimensional radial geometry of the surrounding layers obtained in Step 4 to construct a one-dimensional equivalent super-cell resonance calculation model for resonance calculation. This model does not include fuel and is suitable for complex control rod arrangement problems.

[0016] Step 6: Establish a bidirectional mapping relationship between each material region in the one-dimensional equivalent super-gate resonance calculation model and the corresponding material region mesh in the actual physical calculation model. Accurately write back the calculated multi-group cross sections to the calculation mesh to ensure that the resonance group cross sections in all material region meshes corresponding to the control rod are updated.

[0017] Step 7: Based on the ultrafine group method, establish ultrafine group moderation equations for each energy region. Solve the equations to obtain a refined neutron energy spectrum, and obtain the radial distribution of fine group neutron flux in the control rod and its surrounding material region. ,in Radial coordinates, It is the energy of a neutron.

[0018] Step 8: Based on the conservation of reaction rate, the neutron flux distribution of the fine group is determined. Ultrafine group cross-section of the control rod material region By performing weighted merging, the effective self-shielding multigroup cross section of the control rod material region on the resonant energy group is obtained. The merging formula is: (3) (4) In the formula: — This represents the energy range of the first energy group; — This represents the average neutron flux within the material region of the control rod; — This refers to the total volume of the control rod material region; — This is a spatial position vector; — For volume infinitesimal elements; Step 9: According to the bidirectional mapping relationship, assign the effective self-screen multi-group cross-sections. Update the mesh to all material regions corresponding to the control rods for use in subsequent full-core physics calculations.

[0019] The proposed super-cell model only includes the control rod body and surrounding moderator material, eliminating the need for a fuel region. Therefore, it is applicable to control rods at any location, especially corner control rods that cannot be calculated using traditional methods. Furthermore, based on the conservation of escape probability, it equates non-rod-shaped control rods to one-dimensional equivalent rods. This significantly enhances the model's computational capabilities for complex control rod arrangements and geometries in hexagonal reactor cores.

[0020] Independent control rod geometry modeling is performed to obtain accurate geometry, unaffected by the traditional method of identifying control rod material regions from modules, thus avoiding geometric distortion. Based on the conservation of escape probability, non-rod-shaped control rods are equivalent to one-dimensional rod-shaped equivalent control rods, solving the problem that traditional methods cannot calculate complex geometric control rods with non-rod-shaped geometry. By searching the surrounding structural material region, without the need for surrounding fuel cells, accurate geometric and material information around the control rod can be obtained, solving the problem of difficulty in obtaining information around the control rod in special locations, effectively improving the accuracy of resonance self-screen calculation. By optimizing the moderator layer radius, the one-dimensional equivalent geometry is made closer to the actual physical layout, reasonably considering the spatial interference effect caused by surrounding cells. Verification examples show that this optimization can ensure the program is calculable and effectively increase the coefficient (K). eff The deviation is only -13.6 pcm. The ultrafine group method is used to finely partition the resonance energy region, and the slowing equation is established to solve the fine energy spectrum, which can accurately handle the resonance self-shielding effect caused by the drastic changes in neutron flux in the resonance energy range of the control rods. By establishing independent control rod modeling and mapping with the component material region, it is ensured that the effective cross-section can be accurately updated to all relevant meshes, guaranteeing reaction rate conservation and improving the overall accuracy of neutronics calculations. Attached Figure Description

[0021] Figure 1 This is a schematic diagram of the traditional supergate method.

[0022] Figure 2 This is a schematic diagram of a method for placing circular control rod supergrid elements at the corners of a module in a hexagonal core.

[0023] Figure 3 This is a flowchart illustrating the construction process of the novel control rod super-gate model of this invention. Detailed Implementation

[0024] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments: This invention is based on the high-fidelity physics calculation program NECP-X. First, an input card is filled out, where the radial and axial information of the control rods are defined separately. The program reads the geometry and material information of the reactor core to be calculated from the input card. If the control rod is a non-rod-shaped geometry, based on the conservation of escape probability, it is equivalent to a one-dimensional rod-shaped equivalent control rod. Material information around the control rod is obtained according to a preset search range, excluding the fuel zone. The material zone around the control rod is equivalently weighted by volume to obtain the equivalent one-dimensional radial geometry of the surrounding material layer. Given the optimal radius of the moderator layer, the corrected equivalent one-dimensional radial geometry of the surrounding layer is obtained. One-dimensional radial geometry is obtained by combining the precise geometric information of the control rod with the corrected equivalent one-dimensional radial geometry to obtain a one-dimensional equivalent supergate resonance calculation model for resonance calculation. A bidirectional mapping relationship is established between each material region in the one-dimensional equivalent supergate resonance calculation model and the corresponding material region mesh in the actual physical calculation model. The one-dimensional supergate equivalent model is solved based on ultrafine groups to obtain the fine group neutron flux distribution. Based on the conservation of reaction rate, the effective self-shielded multigroup cross section of the control rod material region on the resonance energy group is obtained. The obtained effective self-shielded multigroup cross section is updated to the material region mesh corresponding to the control rod for subsequent calculations.

[0025] The following example uses NECP-X to calculate a complex circular fuel assembly, including hafnium (Hf) control rods located at the corners (e.g.) Figure 2 As shown, a novel method for establishing a control rod super-gate element model is described, such as... Figure 3 As shown, the specific steps include: Step 1: Model the control rods as independent geometric entities. Define the radial and axial information of the control rods, as well as their position within the assembly, in the input card. After completing the modeling of fuel and other materials, and filling in the calculation conditions, the program reads the geometry and material information of the reactor core to be calculated from the input card, the material parameters of the control rods, and the independently defined precise radial and axial geometric information of the control rods. It then establishes a mapping relationship between the independently defined control rod geometry and the material region mesh in the module. This modeling is independent of the mesh generation or cell size limitations of the fuel assembly and can accurately describe control rods in any position and with any geometry, ensuring that the structure of the control rods remains consistent with the actual problem.

[0026] Step 2: Extract the precise radial layered structure and axial segmented structure of the control rod from the independently defined control rod geometry information. If the control rod is non-rod-shaped, based on the escape probability conservation, it is equivalent to a one-dimensional rod-shaped equivalent control rod. This step accurately obtains the precise geometric and material information of the control rod, solving the problem of difficulty in obtaining information for non-rod-shaped control rods using traditional methods.

[0027] Step 3: Obtain material information around the control rod according to the preset search range, excluding fuel and only including the moderator, and specify the material zone number in the surrounding module. Equip the material zones around the control rod with volume weights to obtain the equivalent one-dimensional radial geometry of the surrounding material layer. This equivalence process effectively considers the spatial interference effect caused by the surrounding structure. The equivalent material parameters are calculated using the following formula: (1) (2) In the formula: — Equivalent mass density; — Equivalent nucleon density; — For the first The volume of the material within the search area; — refers to mass density; — For the first Type of material The nucleon density of a nuclide.

[0028] Step 4: Correct the equivalent one-dimensional radial geometry of the surrounding material layers constructed in Step 3. For the outermost moderator layer, a series of super-cell models are constructed by traversing different moderator radii, ensuring that the Dankoff factor of the equivalent super-cell model is conserved from the actual Dankoff factor. The effective self-shielding cross-section is calculated and compared with the results calculated by the high-precision Monte Carlo program. The conclusion is that the optimal moderator radius corresponds to the case where the radius of the moderator layer is tangent to the next layer of material (such as the cladding). The one-dimensional equivalent geometry is closest to the actual physical layout and can effectively guarantee the conservation of the Dankoff factor. Thus, the corrected equivalent one-dimensional radial geometry of the surrounding layers is obtained.

[0029] Step 5: Combine the one-dimensional rod-shaped equivalent control rod obtained in Step 2 with the corrected one-dimensional radial geometry of the surrounding layers obtained in Step 4 to construct a one-dimensional equivalent super-grid resonance calculation model for resonance calculation. This model does not include fuel and is suitable for complex control rod arrangement problems.

[0030] Step 6: Establish a bidirectional mapping relationship between each material region in the one-dimensional equivalent super-gate resonance calculation model and the corresponding material region mesh in the actual physical calculation model. Accurately write back the calculated multi-group cross sections to the calculation mesh to ensure that the resonance group cross sections in all material region meshes corresponding to the control rod are updated.

[0031] Step 7: Based on the ultrafine group method, establish ultrafine group moderation equations for each energy region. Solve the equations to obtain a refined neutron energy spectrum, and obtain the radial distribution of fine group neutron flux in the control rod and its surrounding material region. ,in Radial coordinates, It is the energy of a neutron.

[0032] Step 8: Based on the conservation of reaction rate, the neutron flux distribution of the fine group is determined. Ultrafine group cross-section of the control rod material region By performing weighted merging, the effective self-shielding multigroup cross section of the control rod material region on the resonant energy group is obtained. The merging formula is: (3) (4) In the formula: — This represents the energy range of the first energy group; — This represents the average neutron flux within the material region of the control rod; — This refers to the total volume of the control rod material region; — This is a spatial position vector; — For volume infinitesimal elements; Step 9: According to the bidirectional mapping relationship, assign the effective self-screen multi-group cross-sections. Update the mesh to all material regions corresponding to the control rods for use in subsequent full-core physics calculations.

[0033] To compute complex circular fuel assemblies, including hafnium (Hf) control rods located at the corners (such as... Figure 2 Taking the example shown, this invention is used for calculations based on NECP-X. When modeling the circular component, it is modeled using hexagonal modules. Control rods are arranged outside the circular component and distributed at each corner of the hexagonal modules. The effective amplification coefficient and the nuclide micro-absorption cross-section are calculated and statistically obtained using the Monte Carlo program MCX.

[0034] Table 1 gives the effective multiplier coefficient (K) for hafnium control rods. eff As a result, calculations using this invention confirmed that the radius of the moderator-controlled layer is the optimal radius. The deviation between the NECP-X calculation results and the reference solution is only -13.6 pcm, demonstrating high accuracy.

[0035] Table 1 Effective Value-Added Factor (K) for Hafnium Control Rod Assembly Problems eff )result The calculation results show that, compared with the Monte Carlo program MCX, the component problem can be calculated normally and with better accuracy by using the model of the present invention, which proves the effectiveness and high accuracy of the present invention.

[0036] The innovation of this invention lies in solving the problem that the program cannot calculate complex control rod arrangements (such as corner control rods of hexagonal components) and strong absorbing control rods with complex geometry. It breaks through the limitation of traditional methods that must include surrounding fuel, and can flexibly handle the resonant self-screen calculation of strong absorbing control rods with complex geometry. It simplifies the control rod super-cell model and improves the neutronics calculation accuracy of small stacks with complex geometry.

Claims

1. A method for establishing a control rod supergate model based on reaction rate conservation, characterized in that: Calculation of resonant self-screen for strong absorbing control rods in complex control rod arrangements includes the following steps: Step 1: Read the geometric and material information of the core to be calculated, the material information of the control rods, and the independently defined radial and axial precise geometric information of the control rods. This modeling does not depend on the meshing of the components or the cell size limitations. Step 2: Extract the precise radial layered structure and axial segmented structure of the control rod from the independently defined precise radial and axial geometric information of the control rod. If the control rod is a non-rod geometry, based on the conservation of escape probability, it is equivalent to a one-dimensional rod equivalent control rod. Step 3: Obtain material information around the control rod according to the preset search range, excluding fuel and only including the moderator. Specify the material zone number in the surrounding module, and perform equivalent material parameters of the material zone around the control rod according to volume weight to obtain the equivalent one-dimensional radial geometry of the surrounding material layer. Step 4: Correct the equivalent one-dimensional radial geometry of the surrounding material layer constructed in Step 3. The optimal radius of the moderator layer corresponds to the case where the radius of the moderator layer is tangent to the next layer of material, which can effectively ensure the conservation of the Dankov factor, and thus obtain the corrected equivalent one-dimensional radial geometry of the surrounding layer. Step 5: Combine the one-dimensional rod-shaped equivalent control rod obtained in Step 2 with the corrected one-dimensional radial geometry of the surrounding layers obtained in Step 4 to construct a one-dimensional equivalent super-gate resonance calculation model for resonance calculation. Step 6: Establish a bidirectional mapping relationship between each material region in the one-dimensional equivalent super-gate resonance calculation model and the corresponding material region mesh in the actual physical calculation model; Step 7: Based on the ultrafine group method, establish ultrafine group moderation equations for each energy region. Solve the equations to obtain a refined neutron energy spectrum, and obtain the radial distribution of fine group neutron flux in the control rod and its surrounding material region. ,in Radial coordinates, Neutron energy; Step 8: Based on the conservation of reaction rate, the neutron flux distribution of the fine group is determined. Ultrafine group cross-section of the control rod material region By performing weighted merging, the effective self-shielding multigroup cross section of the control rod material region on the resonant energy group is obtained. The merging formula is: (1) (2) In the formula: — This represents the energy range of the first energy group; — This represents the average neutron flux within the material region of the control rod; — This refers to the total volume of the control rod material region; — This is a spatial position vector; — It is a volume infinitesimal element; Step 9: According to the bidirectional mapping relationship described in Step 6, map the effective self-screen multi-group cross-section. Update the mesh to all material regions corresponding to the control rods for use in subsequent full-core physics calculations.

2. The method for establishing a control rod supergate model based on reaction rate conservation according to claim 1, characterized in that: In step 3, the material parameters of the material region surrounding the control rod are equivalently calculated using the following formula with volume weights: (1) (2) In the formula: — Equivalent mass density; — Equivalent nucleon density; — For the first The volume of the material within the search area; — refers to mass density; — For the first Type of material The nucleon density of a nuclide.

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