Nuclear reactor design method and system of fine group and subgroup based on accurate processing of resonance interference effect

Abstract

The invention belongs to the technical field of nuclear reaction, and discloses a nuclear reactor design method and system of a fine group subgroup based on a precise processing resonance interference effect, and the method comprises the following steps: S1, encrypting an energy group structure of a traditional resonance group; s2, on a relatively fine energy group structure, secondary discretization is carried out through a subgroup, so that the calculation precision equivalent to that of a superfine group method can be achieved; s3, a fine group structure of hundreds of groups is used, the thought of superfine group moderation is combined, only the resonance group is subjected to recursive solving of moderation flux through a characteristic line method, and energy group merging is only carried out in the resonance group; and S4, in combination with fast group and hot group data provided by a conventional multi-group database, performing multi-group transportation calculation by adopting a feature line method. According to the method, the resonance interference phenomenon can be accurately calculated, and the calculation precision equivalent to that of a superfine group method can be obtained through low calculation cost. Compared with a background iteration method and an interference factor method adopted by a traditional subgroup method for processing resonance interference, the method has higher precision.

Description

Technical Field

[0001] The present invention belongs to the field of nuclear reaction technology, and in particular relates to a nuclear reactor design method and system based on fine group subgroups for accurate processing of resonance interference effects. Background Art

[0002] Accurately understanding the laws of neutron reactions in reactors is an important guarantee for the safety and economy of nuclear reactors. The increasingly complex composition and geometric structure of new reactor materials pose a severe challenge to high-fidelity core physics analysis and calculation. Resonance self-screening calculations provide multiple groups of effective cross sections for neutron transport and burnup calculations, and are a key link in reactor physics calculations. Accurate calculation of resonance self-screening cross sections is an important basis for analyzing neutron behavior in reactors.

[0003] The deterministic calculation methods for the resonance self-screening effect in the world mainly include the ultrafine group method, the equivalent theory method and the subgroup method. By making extremely detailed divisions in the energy group structure, the ultrafine group method accurately describes the cross-sectional changes of the violent fluctuations of the resonance group in a way close to continuous energy, and is currently the most accurate deterministic method for resonance calculation. However, the solution of the ultrafine group equation close to continuous energy is very complicated, and the calculation efficiency is very low, which is only applicable to the calculation of single gate elements or small-scale components. The equivalent theory method establishes an equivalent relationship between uniform problems and non-uniform problems by calculating the probability of the first neutron collision. Through a series of approximate calculations, the background cross section in the actual problem is obtained, and then the effective resonance cross section is obtained by interpolating the resonance integral table in the background cross section database. However, the key to the equivalent theory method lies in the accurate approximation of the probability of the first neutron collision. Its calculation process is closely related to the geometry and materials of the actual problem, and is only applicable to the calculation of geometric structures with regular arrangements or simple material composition problems. With the development of new reactors, traditional equivalent theory is no longer applicable to refined resonance calculations. Unlike the traditional method of discretizing energy groups from the perspective of energy, the subgroup method discretizes the resonance group from the perspective of cross section, describes the change of cross section value through the subgroup cross section, and describes the probability density corresponding to the subgroup cross section through the subgroup probability. The subgroups divided by cross section size have a very small range of internal cross section changes, and the flux within the subgroup can be considered constant, so the resonance phenomenon can be described more accurately. Compared with the traditional method of grouping by energy, the subgroup method can achieve higher calculation accuracy with fewer groups. The subgroup method solves the subgroup flux by coupling the transport equation, and then merges the effective resonance cross section by combining the subgroup parameters. The subgroup transport equation has the same format as the multi-group transport equation, so it can be combined with any transport solution method. Compared with the geometric approximation of the traditional resonance calculation method, the subgroup method directly considers the influence of geometry on flux by solving the subgroup transport equation. In theory, it can handle any geometric type and has strong geometric adaptability. With the above advantages, the subgroup method has been widely used internationally.

[0004] In recent years, with the gradual development of new reactors, more complex and diverse fuel compositions and geometric arrangements have brought greater challenges to resonance calculations. The derivation process of the subgroup method is based on the assumption that there is only one resonant nuclide in the system. However, there are usually a large number of different resonant nuclides in actual reactors. The resonance peaks of various resonant nuclides overlap with each other, forming a resonance interference phenomenon. The ultrafine group method is the most accurate method in determinism to deal with the resonance interference phenomenon. However, due to the limitation of computational efficiency, this method is not suitable for actual calculations of core physics analysis. The traditional subgroup method includes the background iteration method and the interference factor method for correcting resonance interference. Both methods have been widely used, but the calculation accuracy is lower than that of the ultrafine group method. However, the ultrafine group structure is difficult to directly apply to multi-group transport calculations, and the solution of the slowing-down equation in the entire energy segment can only be carried out on a small-scale problem at the gate element level.

[0005] The technical problems brought about by existing technologies in industrial applications can be summarized as follows:

[0006] 1. Weak geometric adaptability:

[0007] The traditional equivalent theory method is closely related to the actual problem geometry when calculating the resonant self-shield cross section, and is usually only applicable to regularly arranged geometric structures. As the reactor design becomes more complex, this method is unable to cope with irregular or complex geometric structures.

[0008] Although the subgroup method can theoretically handle any geometric type, in practical applications, its computational accuracy and efficiency may still be affected for extremely complex or irregular geometric structures.

[0009] 2. Low computational efficiency:

[0010] Although the ultrafine group method can accurately describe the resonance phenomenon, the solution of the ultrafine group equation close to the continuous energy is very complicated, resulting in very low computational efficiency, and is only applicable to the calculation of single gate element or small-scale components. This is particularly insufficient in industrial applications, especially when large-scale core physics analysis is required.

[0011] Although the traditional subgroup method has improved the computational efficiency to a certain extent, when dealing with the resonance interference phenomenon, the computational accuracy of its correction methods such as the background iteration method and the interference factor method is lower than that of the ultrafine group method, and it may take multiple iterations to achieve satisfactory accuracy, thus affecting the overall computational efficiency.

[0012] 3. Insufficient calculation accuracy:

[0013] When dealing with refined resonance calculations, the equivalent theory method may lead to a decrease in calculation accuracy due to its approximate treatment of the probability of the first neutron collision, and cannot meet the needs of high-precision analysis.

[0014] The accuracy of the traditional subgroup method in correcting the resonance interference phenomenon is lower than that of the ultrafine group method, which may affect the accuracy of reactor physics analysis.

[0015] In summary, the main problems of existing technologies in industrial applications include weak geometric adaptability, low computational efficiency, and insufficient computational accuracy. These problems limit the widespread application of existing technologies in complex reactor design and operation and maintenance. Therefore, it is urgent to study a new resonance calculation method that can simultaneously meet the requirements of strong geometric adaptability, high computational efficiency, and high precision. Summary of the invention

[0016] In view of the problems existing in the prior art, the present invention provides a nuclear reactor design method and system based on fine group subgroups that accurately process the resonance interference effect.

[0017] The present invention is implemented as follows: a method for designing a nuclear reactor based on a fine group of subgroups that accurately processes the resonance interference effect, comprising:

[0018] S1, encrypt the energy group structure of the traditional resonance group;

[0019] S2, on a relatively detailed energy group structure, performs secondary discretization through subgroups, enabling it to achieve a computational accuracy comparable to that of the ultrafine group method;

[0020] S3, using a fine group structure of hundreds of groups (such as the SHEM361 energy group structure), combined with the idea of ​​ultrafine group slowing down, only the resonance group is recursively solved for the slowing down flux by the characteristic line method, and the energy group merging is also only performed on the resonance group;

[0021] S4, combined with the fast group and thermal group data provided by conventional multi-group databases (such as WLUP69 or HELIOS47 energy group structures), multi-group transport calculations are performed using the characteristic line method.

[0022] Furthermore, the subgroup method transforms the continuous Riemann integral of the neutron energy spectrum with respect to energy f(E) into the Lebesgue integral f(σ) with respect to the longitudinal cross section:

[0023]

[0024] Where: min and σ max are the minimum and maximum cross sections in energy group g respectively, and p(σ) is the probability that the neutron reaction cross section value in energy group g is exactly σ.

[0025] Furthermore, the effective resonance cross section of reaction channel x can be calculated by the following formula:

[0026]

[0027] Similar to the steady-state neutron transport equation, the neutron transport equation for the i-th subgroup of the resonance group g is:

[0028]

[0029] Furthermore, for the region containing the current resonant nuclide, ∑ t',g,i It can be obtained by the following formula: For the area that does not contain the current resonant nuclide, ∑ t',g,i Then it is taken to be zero:

[0030] Σ t′,g,i =Σ t,g,i,R -(1-λ g,R )Σ s,g,i,R .

[0031] Furthermore, the equivalent single resonance group contains the subgroup parameters of all actual resonance groups. The non-resonance cross section of the group is obtained by weighted average of the resonance integral under infinite dilution conditions of each energy group:

[0032]

[0033] Where: G res is the total number of resonance groups; Δu g For the g group, RI a,g,∞ is the infinite dilution absorption resonance integral of the resonant nuclide in the gth group; for the non-resonant nuclide, RI a,g,∞ Take it as the integral value of the resonant nuclide currently being calculated in the subgroup.

[0034] Furthermore, the fine group also uses the asymptotic energy spectrum 1 / E in the fast group energy segment, and the source term of the first resonance group can be obtained through the asymptotic energy spectrum and scattering matrix of the fast group. After completing the recursive solution of the slowing flux, the fine group resonance cross section is combined according to the following formula:

[0035]

[0036] Where: x is the reaction channel type; G r It is the number of fine groups corresponding to the current resonance group energy segment in the multi-group structure.

[0037] Another object of the present invention is to provide a fine group subgroup computing system for accurately processing resonance interference effect using the nuclear reactor design method based on the fine group subgroup for accurately processing resonance interference effect, comprising:

[0038] An encryption module, used to encrypt the energy group structure of the traditional resonance group;

[0039] The secondary discretization module is used to perform secondary discretization through subgroups on a relatively detailed energy group structure, so that it can achieve a calculation accuracy comparable to that of the ultrafine group method;

[0040] The slowing flux solving module is used to use the fine group structure of hundreds of groups (such as the SHEM361 energy group structure), combined with the idea of ​​ultrafine group slowing down, to recursively solve the slowing flux only for the resonance group through the characteristic line method, and the energy group merging is also only performed on the resonance group;

[0041] The multi-group transport calculation module is used to combine the fast group and thermal group data provided by conventional multi-group databases (such as WLUP69 or HELIOS47 energy group structure) and use the characteristic line method to perform multi-group transport calculations.

[0042] Another object of the present invention is to provide a computer device, which includes a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor executes the steps of the nuclear reactor design method for fine group sub-groups based on accurate processing of resonance interference effects.

[0043] Another object of the present invention is to provide a computer-readable storage medium storing a computer program, which, when executed by a processor, enables the processor to execute the steps of the nuclear reactor design method based on fine group sub-groups that accurately process the resonance interference effect.

[0044] Another object of the present invention is to provide an information data processing terminal, which is used to implement the fine group subgroup computing system for accurately processing the resonance interference effect.

[0045] In combination with the above technical solutions and the technical problems solved, the advantages and positive effects of the technical solutions to be protected by the present invention are as follows:

[0046] First, the present invention aims at the problem of resonant interference, and proposes a fine group subgroup method to achieve the advantages of ultra-fine group accuracy and subgroup geometric adaptability. The advantages of the present invention are as follows:

[0047] 1) High calculation accuracy: The fine subgroup method can accurately calculate the resonance interference phenomenon and achieve the same calculation accuracy as the ultrafine group method at a lower calculation cost. Compared with the background iteration method and interference factor method used by the traditional subgroup method to deal with resonance interference, the fine subgroup method has higher accuracy.

[0048] 2) High computational efficiency: In order to reduce the number of times the subgroup fixed source equation is solved, this technology merges all resonance groups into an equivalent single group in the process of solving the subgroup fixed source equation, and only solves the fixed source equation for a specific subgroup section on the basis of the single resonance group. After obtaining the subgroup flux of a specific section, the escape section interpolation is used to obtain the flux of each subgroup of the actual resonance group, which improves the efficiency of subgroup resonance calculation while ensuring accuracy.

[0049] 3) High calculation resolution: The fine subgroup method can handle the spatial self-screening and edge effect phenomena of fuel rods that are difficult to handle with traditional resonance calculation methods. It can accurately provide the refined resonance cross-section distribution inside the fuel rods during the burnup process, ensuring the accurate calculation of the neutron density field and nuclear density field of the entire core.

[0050] Second, considering the technical solution as a whole or from the perspective of the product, the technical effects and advantages of the technical solution to be protected by the present invention are described in detail as follows:

[0051] Technical effects:

[0052] 1) Improved calculation accuracy of resonance cross section: The fine group subgroup method proposed in this invention can effectively deal with the resonance interference phenomenon, and the calculation accuracy reaches the level of the ultrafine group method. Compared with the traditional subgroup method, this method can more accurately describe the mutual influence between the resonance peaks, thereby improving the accuracy of the calculation results.

[0053] 2) Improved computational efficiency: The present invention uses the equivalent single resonance group subgroup flux interpolation technology to merge all resonance groups into an equivalent single group, and only solves the fixed source equation for a specific subgroup cross section, which significantly improves the computational efficiency. Compared with directly solving the subgroup transport equations of hundreds of groups, this method can obtain high-precision results at a lower computational cost.

[0054] 3) Strong geometric adaptability: The present invention directly solves the subgroup transport equation without approximating the geometry, and can handle reactor problems of any geometric type, with extremely strong geometric adaptability.

[0055] 4) High calculation resolution: This method can handle the spatial self-screening and edge effect phenomena of fuel rods that are difficult to handle with traditional resonance calculation methods, accurately provide the refined resonance cross-section distribution inside the fuel rods during the burnup process, and ensure the accurate calculation of the neutron density field and nuclear density field of the entire core.

[0056] advantage:

[0057] 1) Wide scope of application: The present invention is applicable to various types of reactors, including pressurized water reactors, boiling water reactors, fast reactors, etc., and can meet the increasingly complex reactor design and operation and maintenance requirements.

[0058] 2) High commercial value: The present invention can improve the calculation accuracy of reactor physics, provide important guarantee for reactor safety and economy, and has broad application prospects and commercial value.

[0059] 3) Strong innovation: The present invention combines the advantages of the subgroup method and the ultrafine group method, and proposes a fine group-subgroup secondary discrete strategy to more accurately handle the resonance interference effect, which is highly innovative.

[0060] Third, as auxiliary evidence of the inventiveness of the claims of the present invention, it is also reflected in the following important aspects:

[0061] (1) The expected benefits and commercial value of the technical solution of the present invention after transformation are:

[0062] 1) Improve the accuracy of reactor physics calculations: The fine group subgroup method proposed in this invention can effectively deal with the resonance interference phenomenon, and the calculation accuracy reaches the level of the ultra-fine group method. This will help improve the accuracy of reactor physics calculation results and provide important guarantees for reactor safety and economy.

[0063] 2) Reduce the risk of reactor design and operation: The present invention can help designers better understand the neutron behavior inside the reactor, thereby reducing the risk of reactor design and operation. For example, the power distribution, burnup distribution and critical safety margin of the reactor can be predicted more accurately, providing a more reliable basis for the safe operation of the reactor.

[0064] 3) Optimizing reactor design: The present invention can help designers optimize reactor design and improve the economic efficiency of the reactor. For example, the arrangement of fuel assemblies, the configuration of control rods, the flow rate of coolant and other parameters can be optimized, thereby improving the thermal efficiency of the reactor, reducing fuel consumption and extending the operating life of the reactor.

[0065] 4) Reduce reactor operating costs: The present invention can help operators better control the operating status of the reactor, thereby reducing the operating costs of the reactor. For example, parameters such as the insertion depth of the control rod, the flow rate of the coolant, and the power adjustment method can be optimized, thereby improving the thermal efficiency of the reactor, reducing fuel consumption, and reducing operating and maintenance costs.

[0066] 5) Promote the development of nuclear energy: The fine subgroup method proposed in this invention, as an advanced resonance calculation method, will provide a new solution for reactor physics analysis and calculation, and promote the further development of nuclear energy technology.

[0067] (2) The technical solution of the present invention solves a technical problem that people have been eager to solve but have never been able to solve successfully:

[0068] 1) Difficulty in accurately processing the resonance interference effect: Existing resonance calculation methods have the problem of insufficient precision when processing the resonance interference effect. Although the ultrafine group method has high precision, it has low computational efficiency and is difficult to apply to actual engineering calculations; the traditional subgroup method has high computational efficiency but low precision. The fine group subgroup method proposed in the present invention uses a secondary discrete strategy and combines the advantages of the subgroup method and the ultrafine group method. It can effectively process the resonance interference effect while ensuring computational efficiency, solving the problem that has long plagued the field of nuclear reactor physics calculations.

[0069] 2) Breaking through the bottleneck between computational efficiency and accuracy: Existing resonance calculation methods often require a trade-off between computational efficiency and accuracy. The fine subgroup method of the present invention uses the equivalent single resonance group subgroup flux interpolation technology to merge all resonance groups into an equivalent single group, and only solves the fixed source equation for a specific subgroup cross section, which significantly improves the computational efficiency while ensuring the computational accuracy, breaking through the bottleneck between computational efficiency and accuracy.

[0070] 3) Shortcomings in dealing with complex geometric structures: Existing resonance calculation methods have certain limitations in dealing with complex geometric structures. The ultrafine group method is difficult to deal with complex geometric structures, and the equivalent theory method is only applicable to regularly arranged geometric structures. The fine group subgroup method of the present invention directly solves the subgroup transport equation without approximating the geometry, and can handle reactor problems of any geometric type, making up for the shortcomings of the prior art in dealing with complex geometric structures.

[0071] 4) Solve the problem of fuel rod space self-screening and edge effect: The existing resonance calculation method is difficult to deal with the phenomenon of fuel rod space self-screening and edge effect. The fine group subgroup method of the present invention can accurately provide the refined resonance cross-section distribution inside the fuel rod during the burnup process, ensure the accurate calculation of the neutron density field and nuclear density field of the whole core, solve the problem of fuel rod space self-screening and edge effect, and make up for the shortcomings of the existing technology in dealing with fuel rod space self-screening and edge effect. BRIEF DESCRIPTION OF THE DRAWINGS

[0072] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments of the present invention. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0073] Figure 1 It is a flow chart of a nuclear reactor design method based on fine group subgroups accurately processing resonance interference effects provided by an embodiment of the present invention;

[0074] Figure 2 It is a structural diagram of a fine group subgroup computing system for accurately processing resonance interference effects provided by an embodiment of the present invention;

[0075] Figure 3 is a schematic diagram of a subgroup structure provided by an embodiment of the present invention;

[0076] Figure 4 is a graph showing the variation trend of the escape cross sections in different regions with the cross sections of the subgroups provided by an embodiment of the present invention;

[0077] Figure 5 is an overall flow chart of a fine group subgroup calculation method provided by an embodiment of the present invention;

[0078] Figure 6 is a diagram of a single gate cell structure provided by an embodiment of the present invention;

[0079] Figure 7 Schematic diagram of the number of subgroups of the resonant fine group provided by the embodiment of the present invention; wherein (a) 235 U; (b) 238 U; (c) 239 Pu; (d) 241 Pu;

[0080] Figure 8 The UO2 example resonance group fuel rod provided by the embodiment of the present invention 235 U-section relative deviation diagram, where (a) absorption; (b) fission fraction;

[0081] Fig. 9 The example resonance group fuel rod provided by the embodiment of the present invention is 238 Schematic diagram of relative deviation of U absorption cross section. DETAILED DESCRIPTION

[0082] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0083] In view of the problems existing in the prior art, the present invention provides a nuclear reactor design method and system based on fine group sub-groups that accurately process the resonance interference effect. The present invention is described in detail below in conjunction with the accompanying drawings.

[0084] The industrial application of the above-mentioned nuclear reactor design method based on fine subgroups with accurate processing of resonance interference effects can be implemented in the following two specific areas:

[0085] ###1. Nuclear Reactor Physical Design and Analysis

[0086] Background: In nuclear reactor physics design, accurate calculation of the distribution of neutron energy spectrum and related reaction cross sections is crucial, especially when nuclear fuel contains strong resonant absorption. The resonant interference effect can significantly affect the neutron slowing down and thermalization process, thus affecting the safety and economy of the reactor.

[0087] Example: The above method is used to handle the resonant interference effect, which can accurately evaluate the neutron flux and reaction cross-section distribution in the fuel rods in nuclear fuel design. Specific applications include fuel assembly design and optimization for pressurized water reactors (PWR) and boiling water reactors (BWR). In this case, the SHEM361 energy group structure is used for fine group calculations to improve the accuracy of the simulation, while the WLUP69 or HELIOS47 energy group structure is used to process fast group and thermal group data. This calculation method can significantly improve the calculation accuracy of the reactor core design, thereby optimizing fuel utilization and improving the overall efficiency of the reactor.

[0088] ###2. Nuclear safety analysis

[0089] Background: Nuclear safety analysis requires accurate neutron transport calculations to assess the behavior of nuclear facilities under normal operation and accident conditions, especially the impact of resonant absorption effects in the fuel on parameters such as power distribution and criticality safety margin of nuclear reactors.

[0090] Embodiment: In nuclear safety analysis, the above method can be used to deal with scenarios containing resonant nuclides such as uranium 238 and plutonium 240, such as in the safety assessment of MOX (mixed oxide) fuel. Using this method, the changes in the neutron energy spectrum under accident conditions (such as the moderation conditions in the coolant loss accident) and its impact on the reactor safety parameters can be more accurately simulated, thereby providing more reliable data support for the reactor safety design and accident consequence mitigation measures.

[0091] These specific embodiments demonstrate the important application of the above-mentioned fine group subgroup calculation method in the field of nuclear energy, especially in nuclear fuel design and optimization and nuclear safety analysis, which can significantly improve the accuracy and reliability of calculations.

[0092] like Figure 1 As shown, the nuclear reactor design method based on fine group subgroups accurately processing the resonance interference effect provided by the embodiment of the present invention includes:

[0093] S1, encrypt the energy group structure of the traditional resonance group;

[0094] S2, on a relatively detailed energy group structure, performs secondary discretization through subgroups, enabling it to achieve a computational accuracy comparable to that of the ultrafine group method;

[0095] S3, using a fine group structure of hundreds of groups (such as the SHEM361 energy group structure), combined with the idea of ​​ultrafine group slowing down, only the resonance group is recursively solved for the slowing down flux by the characteristic line method, and the energy group merging is also only performed on the resonance group;

[0096] S4, combined with the fast group and thermal group data provided by conventional multi-group databases (such as WLUP69 or HELIOS47 energy group structures), multi-group transport calculations are performed using the characteristic line method.

[0097] like Figure 2 As shown, the fine group subgroup computing system for accurately processing the resonance interference effect provided by the embodiment of the present invention includes:

[0098] An encryption module, used to encrypt the energy group structure of the traditional resonance group;

[0099] The secondary discretization module is used to perform secondary discretization through subgroups on a relatively detailed energy group structure, so that it can achieve a calculation accuracy comparable to that of the ultrafine group method;

[0100] The slowing flux solving module is used to use the fine group structure of hundreds of groups (such as the SHEM361 energy group structure), combined with the idea of ​​ultrafine group slowing down, to recursively solve the slowing flux only for the resonance group through the characteristic line method, and the energy group merging is also only performed on the resonance group;

[0101] The multi-group transport calculation module is used to combine the fast group and thermal group data provided by conventional multi-group databases (such as WLUP69 or HELIOS47 energy group structure) and use the characteristic line method to perform multi-group transport calculations.

[0102] The derivation process of the traditional subgroup method is based on the assumption that there is only one resonant nuclide in the system. However, there are usually a large number of different resonant nuclides in actual reactors. The resonance peaks of various resonant nuclides overlap with each other, forming a resonance interference phenomenon. The ultrafine group method is the most accurate method in determinism to deal with the resonance interference phenomenon. However, due to the limitation of computational efficiency, this method is not suitable for the actual calculation of core physics analysis. The correction methods for resonance interference of the traditional subgroup method include the background iteration method and the interference factor method. Both methods have been widely used, but the calculation accuracy is lower than that of the ultrafine group method. This technology combines the advantages of the subgroup method and the ultrafine group method, and proposes a fine group subgroup secondary discretization strategy to more accurately deal with the resonance interference effect.

[0103] The equivalent approximation of the resonance cross section by the traditional resonance group structure is not rigorous. In fact, there are still extremely violent resonance peak fluctuations within the resonance group of the common multi-group structure, and the effective resonance cross sections of different problems vary greatly. Under the condition of resonance interference, it is difficult to fully reflect the resonance peak change trend of different resonance nuclides by discretizing the conventional resonance group with only a few subgroups. Therefore, a more feasible method is to encrypt the energy group structure of the traditional resonance group. On the relatively detailed energy group structure, the subgroup is used for secondary discretization so that it can achieve the same calculation accuracy as the ultrafine group method. The fine group subgroup method uses a fine group structure of hundreds of groups (such as the SHEM361 energy group structure), combined with the idea of ​​ultrafine group slowing down, and only recursively solves the slowing down flux for the resonance group through the characteristic line method, and the energy group merging is also only performed on the resonance group. Finally, combined with the fast group and thermal group data provided by the conventional multi-group database (such as the WLUP69 or HELIOS47 energy group structure), the characteristic line method is used for multi-group transport calculations. The specific calculation method is as follows:

[0104] First, the resonance group is divided into several subgroups according to the cross-section value, as shown in 3. The cross-section variation within the subgroup is small, so the flux variation range within the same subgroup is much smaller than that of the traditional resonance group. Compared with the energy group structure of the ultrafine group, the subgroup method can accurately discretize the resonance group through several subgroups, which has higher computational efficiency.

[0105] From 3, we can see that the same subgroup cross section range may correspond to different energy intervals, so the energy within the same subgroup is not continuous. The subgroup method transforms the continuous Riemann integral f(E) of the neutron energy spectrum to the energy into the Lebesgue integral f(σ) of the longitudinal cross section, as shown in formula (1):

[0106]

[0107] Where: min and σ max are the minimum and maximum cross sections in energy group g respectively, and p(σ) is the probability that the neutron reaction cross section value in energy group g is exactly σ.

[0108] Compared with the drastic change of f(E) with energy, f(σ) is approximately inversely proportional to the cross section, and the integral calculation is simpler. Fewer discrete points can be used to calculate the integral value, and each discrete point is a subgroup. The subgroup cross section is the average cross section value of the subgroup, and the subgroup probability reflects the proportion of each energy interval of the subgroup to the total energy interval of the resonance group. The subgroup cross section, subgroup probability and subgroup flux of the same subgroup are all constants, so formula (1) can be simplified to formula (2):

[0109]

[0110] Where: g,i is the subgroup cross section; pg,i is the subgroup probability; g,i is the subgroup flux; I is the number of subgroups.

[0111] According to the definition of subgroup probability, the sum of all subgroup probabilities should be equal to 1. The subgroup cross section and subgroup probability are collectively referred to as subgroup parameters. Equation (2) transforms the continuous integral of flux over energy into a discrete product group with respect to subgroup parameters. From a mathematical point of view, the range of subgroup cross section is not limited to σ min ~σ max , and the subgroup probability no longer corresponds to the energy range in the actual sense. Combined with equation (1), the effective resonance cross section of reaction channel x can be calculated by equation (3):

[0112]

[0113] Similar to the steady-state neutron transport equation, the neutron transport equation of the i-th subgroup of the resonance group g can be expressed as follows:

[0114]

[0115] The subgroup flux is obtained by solving equation (3) through the transport module, and then substituted into equation (2) to obtain the effective resonance cross section. The neutron energy spectrum of the actual problem can be calculated through the subgroup transport equation, and the resonance self-screening calculation can be performed for any geometric problem.

[0116] The purpose of resonance calculation is to obtain the effective resonance cross section. As can be seen from formula (2), the effective resonance cross section is only related to the relative size of the subgroup flux in the current resonance group. Therefore, it is only necessary to obtain the subgroup energy spectrum shape in the current resonance group to merge and obtain the effective resonance cross section of the group, without the need to accurately calculate the subgroup flux distribution between the resonance groups. Combined with the idea of ​​neutron slowing, for the i-th subgroup of the g-th energy group, its subgroup transport equation can be expressed as:

[0117]

[0118] The source term shown in equation (5) is no longer related to the flux of other subgroups, so the transport equation of each subgroup can be solved independently without iterative calculation of inter-group scattering source terms. Therefore, (5) can be further simplified as:

[0119]

[0120] For the region containing the current resonant nuclide, ∑ t',g,i It can be obtained by formula (7). For the area that does not contain the current resonant nuclide, ∑ t',g,i Then take it as zero.

[0121] Σ t′,g,i =Σ t,g,i,R -(1-λ g,R )Σs,g,i,R (7)

[0122] From equation (6), we can see that the source term of the subgroup transport equation is independent of the flux, and its value is fixed during the solution process. Therefore, the subgroup transport equation can be equivalent to a fixed source equation. The subgroup fixed source equation only needs to be calculated independently in each subgroup, without the need for loop iteration between different subgroups. After obtaining the subgroup flux, the cross section of the resonance zone can be calculated by equation (3).

[0123] However, directly solving the subgroup transport equations of the hundreds of groups mentioned above is too inefficient and must be optimized to improve efficiency. The subgroup cross sections of different resonance groups vary greatly, while the potential scattering cross section changes little, and the intermediate resonance factor is also mainly related to the resonant nuclear mass. At the same time, since the source term of the subgroup fixed source equation is only the scattering source, the potential scattering cross section of the moderator and the intermediate resonance approximation factor remain almost constant. Therefore, for the subgroup fixed source equations of different resonance groups, the source term on the right side of equation (6) changes very little, and it can be considered that all resonance groups share the same source term. If two subgroups have similar subgroup cross sections, the two fixed source equations only need to be solved once. Based on this idea, this section proposes an equivalent single resonance group subgroup fixed source interpolation method to equate all resonance groups to one group. The equivalent single resonance group contains the subgroup parameters of all actual resonance groups. The non-resonance cross section of the group is obtained by the weighted average of the resonance integral under the infinite dilution conditions of each energy group, as shown in equation (8):

[0124]

[0125] Where: G res is the total number of resonance groups; Δu g For the g group, RI a,g,∞ is the infinite dilution absorption resonance integral of the resonant nuclide in the gth group; for the non-resonant nuclide, RI a,g,∞ Take it as the integral value of the resonant nuclide currently being calculated in the subgroup.

[0126] According to equation (8), the scattering source term of the equivalent single resonance group can be calculated. Since the source terms of the fixed source equations of each subgroup are the same, the subgroup flux obtained by solving is directly negatively correlated with the subgroup removal term. Therefore, it is only necessary to solve the fixed source equation for a specific subgroup cross section, and the flux corresponding to other subgroup cross sections can be obtained by interpolating the adjacent subgroup cross sections.

[0127] For most subgroups, the removed term and source term of the subgroup fixed source equation are very close in value, so the subgroup flux obtained by transport calculation is close to 1, which is not suitable for interpolation of the subgroup flux directly through the subgroup cross section. The larger the subgroup cross section, the smaller the probability of neutrons escaping without any reaction in the subgroup. Under non-uniform conditions, due to the spatial self-screening effect, the probability of neutron escape is not only related to the subgroup cross section, but also to the position of the neutron in the fuel rod. In order to comprehensively reflect the influence of cross section and space, for the resonant nuclide R, the neutron escape cross section is defined as shown in formula (9):

[0128]

[0129] Compared with the subgroup flux, the escape cross section can more significantly reflect the influence of the subgroup cross section and spatial position on the neutron reaction. Taking a single cell as an example, if its fuel rod is divided into five concentric rings of equal volume, and a series of subgroup cross sections σ of different sizes are t' That is, by calculating the subgroup fixed source equation, the escape cross section of each region can be obtained as σ t' The changing relationship, such as Figure 4 As shown in Figure 2, the average escape cross section of the fuel rod subgroup changes very little with the subgroup cross section value. As the subgroup cross section increases, the average escape cross section shows only a slight downward trend. However, for the radial rings of the fuel rod, the fine distribution of the escape cross section shows obvious changes, especially at the outermost part of the fuel rod. The escape cross section is 10~10 4 The change is most dramatic when b is between 10 and 10. 4 The subgroup cross section of b and the escape cross section are almost constant. Therefore, in order to describe the neutron behavior under different subgroup cross section conditions, the value of the equivalent subgroup cross section should be concentrated in the range of 10~10 4 b. By ln(σ t' ) interpolation calculation is used to obtain the actual subgroup escape cross section, and then the actual subgroup flux can be inferred according to formula (9), and finally the effective resonance cross section is calculated by formula (3).

[0130] By repeating the above process, the effective resonance cross section of all fine groups can be obtained.

[0131] Since the fine group structure of hundreds of groups is not suitable for multi-group transport calculations, similar to the ultrafine group method, the fine group subgroup calculation also performs group processing on the resonance group. Compared with the narrow width of the ultrafine group, the width of the fine group does not meet the requirement of being much smaller than the mean free path of the neutron. Neutrons may collide multiple times in the fine group, so the collision probability recursive relationship of the ultrafine group is not applicable to the fine group structure. However, since the number of fine groups is much smaller than the order of magnitude of the tens of universal groups of the ultrafine group, when calculating the scattering source of the slowdown equation, it can be calculated directly based on the fine group scattering matrix, as shown in equation (8):

[0132]

[0133] Where: t,g,l is the total cross section of the g-th subgroup of nuclide l; ∑ s,g'→g,l is the scattering cross section from the g'th group to the gth group.

[0134] Equation (8) also establishes a recursive expression for solving the slowing flux group by group. The other energy group variables of the source term of the equation all come from the upstream resonance group or the fast group. Therefore, only the slowing flux of the first resonance group needs to be obtained, and the slowing equation of the downstream resonance group can be recursively solved, and the slowing equation of each resonance group is a fixed source equation. Similar to the ultrafine group method, the fine group also uses the asymptotic energy spectrum 1 / E in the fast group energy segment. The source term of the first resonance group can be obtained through the asymptotic energy spectrum and scattering matrix of the fast group. After completing the recursive solution of the slowing flux, the fine group resonance cross section is grouped according to equation (9).

[0135]

[0136] Where: x is the reaction channel type; G r It is the number of fine groups corresponding to the current resonance group energy segment in the multi-group structure.

[0137] At this point, the effective resonance cross section of all resonance groups can be obtained. The overall calculation flow chart is as follows: Figure 5 shown.

[0138] Example

[0139] The implementation case selected a single-element problem of 6.5wt% enriched PWR UO2 new material and its burnup depth of 60GWd / t. The geometric structure of the problem is as follows Figure 6 As shown, the fuel rod, cladding radius and grid element half-side length are 0.412, 0.476 and 0.6325 cm respectively. The resonant nuclides contained in the fuel rod are 235 U and 238 U; The main resonant nuclides included under the burnup condition are 235 U. 238 U. 239 Pu, 240 Pu, 241 Pu and 241 Am et al. Due to the edge effect, the nucleon density of Pu isotopes under burnup conditions increases outward along the radius of the fuel rod; the cladding material is natural zirconium, the moderator is cold water, and the calculated temperature is 300K.

[0140] The fine group subgroup method is used to calculate the fine group cross section and the merged multi-group effective resonance cross section of the above problem. First, according to the fine group structure (taking the SHEM361 energy group structure as an example), each fine group resonance group is further divided into subgroup structures. The number of subgroups in most resonance groups is 2 to 3. For energy groups with sufficient energy discreteness or unclear resonance peaks, the number of subgroups can be taken as 1. The number of subgroups of each nuclide on the fine group structure is as follows: Figure 7 shown.

[0141] Then, the subgroup flux of each subgroup in all subgroups needs to be calculated. According to the traditional method, 235 U. 238 U. 239 Pu and 241 The total number of Pu subgroups in the resonance fine group is 611, 475, 540 and 553 respectively. The traditional method needs to solve the fixed source equation for each subgroup, which is very computationally intensive. This technology proposes an equivalent single resonance group subgroup flux interpolation calculation. Each resonance nuclide only needs to solve 8 subgroup fixed source equations, which greatly reduces the computational complexity.

[0142] The subgroup fluxes in the fine group are calculated and merged to obtain the effective resonance cross section of the fine group. Then, the fine group slowing down flux of the above problem is solved by the slowing down equation. Taking the HELIOS47 energy group structure as an example, the fine group resonance cross section can be merged into 16 resonance groups in the 47 group structure.

[0143] For new UO2 material, Figure 8 and Fig. 9 The above methods are given respectively 235 U and 238 The relative calculation deviation of the average absorption cross section of the fuel rod of U. In the figure, the method is FSM, and its calculation results are compared with the traditional subgroup local iteration method (BIM), the interference factor method (RIFM), and the most accurate ultra-fine group (UFG) method. The fine group subgroup method has higher accuracy and is more accurate. 235 U absorption cross section, fission fraction and 238 The maximum calculated deviations of the U absorption cross sections are 1.01%, 0.98% and 1.17% respectively, and the root mean square deviations are 0.52%, 0.48% and 0.49% respectively. 235 The calculation of U absorption cross section and fission fraction is more accurate, with maximum deviations of 0.68% and 1.31% and root mean square deviations of 0.26% and 0.54% respectively, which are similar to the above two methods. 238 The calculation deviation of U is large, and the absorption cross section of each resonance group is generally overestimated, with the maximum deviation reaching 6.2% and the root mean square deviation being 2.4%. The calculation accuracy of the background iteration method for both resonance nuclides is low, especially for 235U, the calculation deviation increases significantly in the energy group with dense resonance peaks, the maximum deviation of the absorption cross section and the fission share reaches 27.6% and 32.7%, and the root mean square deviation is 8.25% and 8.54%, respectively. 238 The calculated absorption cross section of U also has large deviations, with the maximum deviation and root mean square deviation being 7.18% and 2.02% respectively. Overall, the ultrafine group method and the fine group subgroup method have good 235 U and 238 U has a high calculation accuracy; the interference factor method has a high 235 U calculation accuracy is high, but 238 The U resonance cross section is significantly overestimated; the background iteration method has low calculation accuracy for both resonance nuclides. Compared with the tens of thousands of energy groups of the ultrafine group, the fine group subgroup method proposed in the present invention is obviously more efficient.

[0144] In order to verify the radial space self-screening phenomenon of fuel rods under the condition of resonant interference, Fig. 9 The results of the above methods in the energy ranges of 6.48-7.34eV and 13.71-29.02eV are given. 238 Relative deviation distribution of U absorption cross section along the radial direction. Both the ultrafine group method and the fine group subgroup method have high accuracy. The calculation deviation of most radial regions in the two energy segments is within ±1%. The maximum deviation occurs at the outermost side of the fuel rod and remains within 1.5%. The background iteration method and the interference factor method both overestimate the absorption cross section inside the fuel rod, while the calculated value at the outermost ring of the fuel rod is significantly smaller. The maximum radial deviations of the background iteration method for the two energy segments are 3.72% and 5.89%, respectively, and the interference factor method is 10.17% and 10.03%, respectively. Both methods cannot accurately handle the spatial self-screening phenomenon. Compared with the average cross section of the fuel rod, the calculation accuracy of the radial cross section distribution by the interference factor method is significantly reduced. In summary, the ultrafine group method and the fine group subgroup method have high calculation accuracy for the average cross section and radial cross section distribution of UO2 rods, and compared with the calculation scale of tens of thousands of ultrafine groups, the fine group subgroup method significantly reduces the calculation cost.

[0145] An application embodiment of the present invention provides a computer device, which includes a memory and a processor. The memory stores a computer program. When the computer program is executed by the processor, the processor executes the steps of a fine group subgroup calculation method for processing resonance interference effects.

[0146] An application embodiment of the present invention provides a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, the processor executes the steps of a fine group subgroup calculation method for processing resonance interference effects.

[0147] The application embodiment of the present invention provides an information data processing terminal, which is used to implement a fine group subgroup computing system for accurately processing the resonance interference effect.

[0148] 2. Application Examples: In order to prove the creativity and technical value of the technical solution of the present invention, this section provides application examples of the technical solution of the claims on specific products or related technologies.

[0149] The nuclear reactor design method and system based on fine group subgroups for accurate processing of resonance interference effects provided by the present invention can be applied to the following products or related technologies:

[0150] 1) Nuclear reactor design and analysis software: Integrating the method of the present invention into nuclear reactor design and analysis software can significantly improve the calculation accuracy and efficiency of the software, and provide more reliable technical support for reactor design and operation.

[0151] 2) Nuclear reactor safety analysis software: Integrating the method of the present invention into nuclear reactor safety analysis software can more accurately predict the consequences of reactor accidents and provide more reliable technical support for reactor safety analysis.

[0152] 3) Nuclear reactor economic analysis software: Integrating the method of the present invention into the nuclear reactor economic analysis software can more accurately evaluate the economic benefits of the reactor and provide more reliable technical support for the reactor economic analysis.

[0153] 4) Nuclear reactor operation optimization software: Integrating the method of the present invention into nuclear reactor operation optimization software can help operators better control the operating status of the reactor, optimize the operating parameters of the reactor, and improve the economic benefits of the reactor.

[0154] 5) Nuclear reactor teaching and training software: Integrating the method of the present invention into nuclear reactor teaching and training software can help students and trainers better understand the principles and methods of nuclear reactor physics calculations and improve their professional knowledge and skills.

[0155] 6) Nuclear data evaluation and processing software: Applying the method of the present invention to nuclear data evaluation and processing software can improve the accuracy and efficiency of nuclear data evaluation and processing, and provide more reliable data support for the development of nuclear energy technology.

[0156] 7) Nuclear reactor material research: Applying the method of the present invention to nuclear reactor material research can more accurately evaluate the resonance characteristics of the material and provide more reliable technical support for the design and development of new nuclear reactor materials.

[0157] It should be noted that the embodiments of the present invention can be implemented by hardware, software, or a combination of software and hardware. The hardware part can be implemented using dedicated logic; the software part can be stored in a memory and executed by an appropriate instruction execution system, such as a microprocessor or dedicated design hardware. A person of ordinary skill in the art will appreciate that the above-mentioned devices and methods can be implemented using computer executable instructions and / or contained in a processor control code, such as a carrier medium such as a disk, CD or DVDROM, a programmable memory such as a read-only memory (firmware), or a data carrier such as an optical or electronic signal carrier. Such code is provided on the carrier medium. The device and its modules of the present invention can be implemented by hardware circuits such as very large-scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, etc., or programmable hardware devices such as field programmable gate arrays, programmable logic devices, etc., can also be implemented by software executed by various types of processors, and can also be implemented by a combination of the above-mentioned hardware circuits and software, such as firmware.

[0158] The above description is only a specific implementation mode of the present invention, but the protection scope of the present invention is not limited thereto. Any modifications, equivalent substitutions and improvements made by any technician familiar with the technical field within the technical scope disclosed by the present invention and within the spirit and principle of the present invention should be covered by the protection scope of the present invention.

Claims

1. A method for designing a nuclear reactor based on fine subgroups of accurately processing resonance interference effects, characterized in that: include: S1, encrypt the energy group structure of the traditional resonance group; S2, on a relatively detailed energy group structure, performs secondary discretization through subgroups, enabling it to achieve a computational accuracy comparable to that of the ultrafine group method; S3, using a fine group structure of hundreds of groups, combined with the idea of ​​ultrafine group slowing down, only the resonance group is recursively solved for the slowing down flux through the characteristic line method, and the energy group merging is also only performed on the resonance group; S4, combined with the fast group and hot group data provided by the conventional multi-group database, uses the characteristic line method to perform multi-group transport calculations.

2. The method for designing a nuclear reactor based on a fine subgroup of a precise processing of the resonance interference effect as claimed in claim 1, characterized in that: The subgroup method transforms the continuous Riemann integral f(E) of the neutron energy spectrum into the Lebesgue integral f(σ) of the longitudinal cross section: Where: min and σ max are the minimum and maximum cross sections in energy group g respectively, and p(σ) is the probability that the neutron reaction cross section value in energy group g is exactly σ.

3. The method for designing a nuclear reactor based on a fine subgroup of a precise processing of the resonance interference effect as claimed in claim 1, characterized in that: The effective resonance cross section of reaction channel x can be calculated by the following formula: Similar to the steady-state neutron transport equation, the neutron transport equation for the i-th subgroup of the resonance group g is:

4. The method for designing a nuclear reactor based on a fine subgroup of a precise processing of the resonance interference effect as claimed in claim 1, characterized in that: For the region containing the current resonant nuclide, ∑ t',g,i It can be obtained by the following formula: For the area that does not contain the current resonant nuclide, ∑ t',g,i Then it is taken to be zero: S t′,g,i =S t,g,i,R -(1-l g,R )S s,g,i,R 。 5. The method for designing a nuclear reactor based on a fine subgroup of a precise processing of the resonance interference effect as claimed in claim 1, characterized in that: The equivalent single resonance group contains the subgroup parameters of all actual resonance groups. The non-resonance cross section of the group is obtained by weighted average of the resonance integral under infinite dilution conditions of each energy group: Where: G res is the total number of resonance groups; Δu g For the g group, RI a,g,∞ is the infinite dilution absorption resonance integral of the resonant nuclide in the gth group; for the non-resonant nuclide, RI a,g,∞ Take it as the integral value of the resonant nuclide currently being calculated in the subgroup.

6. The method for designing a nuclear reactor based on a fine subgroup of a precise processing of the resonance interference effect as claimed in claim 1, characterized in that: The fine group also uses the asymptotic energy spectrum 1 / E in the fast group energy segment. The source term of the first resonance group can be obtained through the asymptotic energy spectrum and scattering matrix of the fast group. After completing the recursive solution of the slowing flux, the fine group resonance cross section is combined according to the following formula: Where: x is the reaction channel type; G r It is the number of fine groups corresponding to the current resonance group energy segment in the multi-group structure.

7. A fine group subgroup computing system for accurately processing resonance interference effect using a nuclear reactor design method based on a fine group subgroup for accurately processing resonance interference effect as claimed in any one of claims 1 to 6, characterized in that: include: An encryption module, used to encrypt the energy group structure of the traditional resonance group; The secondary discretization module is used to perform secondary discretization through subgroups on a relatively detailed energy group structure, so that it can achieve a calculation accuracy comparable to that of the ultrafine group method; The slowing down flux solving module is used to use the fine group structure of hundreds of groups, combined with the idea of ​​ultra-fine group slowing down, to recursively solve the slowing down flux only for the resonance group through the characteristic line method, and the energy group merging is also only performed on the resonance group; The multi-group transport calculation module is used to combine the fast group and hot group data provided by the conventional multi-group database and use the characteristic line method to perform multi-group transport calculations.

8. A method for processing resonance interference effects for nuclear reactor physical design and analysis based on the method of claim 1, characterized in that: The following steps are involved: The resonance groups in the reactor are refined and grouped by using a multi-group structure, and the secondary discretization is performed on a relatively detailed energy group structure by using a subgroup method to improve the calculation accuracy. Using the fine group structure of hundreds of groups combined with the idea of ​​ultra-fine group slowing down, the slowing down flux is recursively solved only for the resonance group through the characteristic line method, and the energy group merging is only performed in the resonance group; Combined with the fast group and hot group data provided by the conventional multi-group database, multi-group transport calculations are performed using the characteristic line method; The method is applied to the design and optimization of fuel assemblies of pressurized water reactors or boiling water reactors, and optimizes fuel utilization and improves the overall efficiency of the reactor by improving the calculation accuracy of the reactor core design.

9. A method for processing resonance interference effect for nuclear safety analysis based on the method of claim 1, characterized in that: The following steps are involved: The resonant nuclides in nuclear facilities are divided into fine groups using a multi-group structure, and the Riemann integral of the neutron energy spectrum over energy is converted into the Lebesgue integral of the cross section through the subgroup method to deal with scenarios with strong resonant absorption. The slowing flux of the resonance group is recursively solved using the fine group structure and characteristic line method, and the source term of the resonance group is obtained by combining the asymptotic energy spectrum of the fast group and the scattering matrix. The processing results are applied to the safety analysis of nuclear reactors under accident conditions, especially in the safety assessment of MOX fuel, to provide accurate simulation results of neutron spectrum changes under accident conditions and their impact on reactor safety parameters, providing data support for reactor safety design and accident consequence mitigation measures.

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