Multi-group shielding database manufacturing and energy group structure optimization method suitable for lead-bismuth reactor

Abstract

The invention belongs to the technical field of radiation protection, and particularly relates to a multi-group shielding database manufacturing and energy group structure optimization method suitable for a lead-bismuth reactor. The method comprises the following steps: S1, manufacturing a fine group section library; s2, carrying out resonance calculation in combination with the characteristics of the lead-bismuth reactor; s3, optimizing an energy group structure; and S4, energy group merging. According to the method, particle contribution of each energy group in a 199-group neutron and 42-group photon shielding database is calculated by adopting a response contribution method in combination with reactor type characteristics of a lead-bismuth problem, energy group division is performed again through an idea of contribution equipartition, finally, an optimized 47-group neutron and 20-group photon energy group structure is obtained, a corresponding multi-group shielding database is generated, and the optimal multi-group shielding database is obtained. The lead-bismuth problem shielding calculation precision can be improved, the calculation efficiency is improved, and the calculation time is shortened.

Description

Technical Field

[0001] This invention belongs to the field of radiation protection technology, specifically relating to a method for creating a multi-group shielding database and optimizing the energy group structure applicable to lead-bismuth piles. Background Technology

[0002] Deterministic methods are one of the mainstream methods used in large-scale shielding computation. Their computational input comes from various nuclide cross-sectional information stored in a multi-group shielding database. Existing research shows that the multi-group shielding database used in deterministic methods has a significant impact on their computational accuracy and efficiency.

[0003] In water-cooled reactor shielding calculations, the BUGLE series database is commonly used as a multi-group shielding database. This database, incorporating engineering experience with water-cooled reactors, sets up two typical models: a one-dimensional pressurized water reactor and a one-dimensional boiling water reactor, from the reactor core to the outer shielding layer. Based on practical experience, it has determined the energy group structure of 47 neutron groups and 20 photon groups. With the increasing demand for high-precision, large-scale reactor shielding calculations in recent years, a series of quantitative energy group structure optimization methods have been developed based on water-cooled reactors to improve computational efficiency, including genetic algorithms, particle swarm optimization, and response contribution theory. From a feasibility perspective, genetic algorithms and particle swarm optimization are suitable for energy group structure optimization with a small number of energy groups, but the problems of large computational load and cumbersome iterative process under multi-group conditions need to be addressed. Response contribution theory has a simple principle, low computational load, and strong correlation of the optimized energy group structure, making it the most reliable, mature, and widely used energy group structure optimization method among multi-group shielding databases.

[0004] Lead-bismuth reactors use lead-bismuth alloys as coolants. Their internal components, main equipment layout, reflector design, shielding design, and mid- and photon energy spectrum distributions differ significantly from those of water-cooled reactors. The typical water-cooled reactor models set in the BUGLE series databases do not match those of lead-bismuth reactors. If the BUGLE series databases are used directly for shielding calculations of lead-bismuth reactors, the calculation accuracy will be reduced.

[0005] Therefore, it is necessary to find a method for constructing a multi-group shielding database suitable for lead-bismuth reactors, and to optimize it based on the energy group structure of the database, so as to obtain a set of highly targeted and applicable multi-group shielding databases, providing high-precision input for large-scale shielding calculations. Summary of the Invention

[0006] The technical problem solved by this invention is to provide a method for optimizing the energy group structure of a multi-group shielding database applicable to the lead-bismuth problem. Combining the stack characteristics of the lead-bismuth problem, the method uses the response contribution method to calculate the particle contributions of each energy group in the 199-group neutron and 42-group photon shielding databases. By re-dividing the energy groups using the idea of ​​equal contribution, the optimized energy group structure of 47-group neutron and 20-group photon is obtained, generating the corresponding multi-group shielding database. This method can improve the accuracy of shielding calculations for the lead-bismuth problem, increase computational efficiency, and reduce computation time.

[0007] The technical solution adopted in this invention is as follows:

[0008] A method for constructing a multi-group shielding database and optimizing the energy group structure for lead-bismuth reactors includes the following steps:

[0009] S1. Creation of the fine group section library;

[0010] S2. Resonance calculations combining lead-bismuth pile characteristics;

[0011] S3, Energy Group Structure Optimization;

[0012] S4, can be grouped.

[0013] In S1, the nuclear data processing program Atlas is used to generate a fine group cross-section library of 199 neutron groups and 42 photons in MATXS format, based on the neutron evaluation nuclear database and the photon-atom evaluation nuclear database.

[0014] Using the nuclear data processing program Atlas, based on the neutron evaluation nuclear database, fine group neutron cross-section data and fine group photon generation cross-section data were obtained through resonance reconstruction and linearization, Doppler broadening, calculation of effective self-screen cross-section in indistinguishable resonance region, thermal neutron scattering calculation, and fine group cross-section calculation.

[0015] Based on the photon-atom evaluation nuclear database, the fine-group photon-atom reaction cross section is obtained through cross section linearization and fine-group cross section calculation.

[0016] The fine-group neutron cross section, photon generation cross section, and fine-group photon-atom reaction cross section are stored in MATXS format.

[0017] In S2, a one-dimensional typical model of the lead-bismuth reactor is established radially outward from the reactor core. Resonance calculations are performed on the nuclides included in the model. After calculation, new fine group cross-section data are obtained. The original cross-section data is replaced with the new cross-section data, and the fine group cross-section library of 199 group neutrons and 42 group photons is updated.

[0018] If the nuclide is a non-resonance nuclide, the Bondarenko iterative method is used in the full-energy region; if the nuclide is a resonance nuclide, the ultrafine group method is used in the resonance energy region, and the Bondarenko iterative method is used in the other energy regions.

[0019] In S3, based on the response contribution theory and a typical one-dimensional lead-bismuth pile model, the forward and conjugate neutron transport equations are solved using a pre-built 199-group neutron fine-group cross-section library. The source strength of the forward neutron transport equation is filled in according to the source distribution in the typical model, and the source strength of the conjugate neutron transport equation is defined as the important response function of the detector for different energy ranges. The neutron angular flux and conjugate neutron angular flux are solved for the two equations respectively. The total neutron contribution in each energy range of the fast, hyperthermal, and hot regions is statistically analyzed, and the contribution is evenly distributed in each energy range to determine the optimized energy group structure.

[0020] In S3,

[0021] The solution to the forward transport equation is:

[0022]

[0023] In the formula: Ω represents the direction of neutron motion; ψ g (r,Ω) represents the neutron angular flux of energy group g at position r, in the direction of motion Ω, and in cm. -2 ·s -1 );Σ t,g (r) represents the total neutron cross section of energy group g at position r, in cm. -1 );Σ s,g→g' (r,Ω'→Ω) represents the neutron scattering cross section at position r, with the direction of motion from Ω to Ω', from energy group g to g', in cm. -1 );q g (r,Ω) represents the neutron source intensity of energy group g at position r, in the direction of motion Ω, and in cm. -3 ·s -1 );

[0024] The conjugate transport equation corresponding to the above equation is:

[0025]

[0026] In the formula This represents the conjugate neutron angular flux of energy group g at position r, in the direction of motion Ω, and in units of (cm). -2 ·s -1 ); This represents the conjugate neutron source intensity of energy group g at position r, in the direction of motion Ω, and in cm. -3 ·s -1 );

[0027] According to the definition of the conjugate equation, we know that:

[0028]

[0029] The contribution value of each energy group is defined as follows:

[0030]

[0031] In the formula C g This represents the contribution of neutrons to energy group g, expressed in s. -1 The contribution values ​​in each energy segment of the fast, superheated, and hot regions will be calculated separately. The contribution will be evenly distributed in each energy segment to divide the boundaries of the multi-group neutron energy groups, thus obtaining the optimized multi-group neutron energy group structure.

[0032] In step S4, the photon energy spectrum of each material region in the typical one-dimensional lead-bismuth pile model in S2 is calculated using the Monte Carlo method. This energy spectrum is used as the weight spectrum of the merged energy group. Based on the optimized energy group structure in S3, the fine group cross-section data obtained in S2 is merged to obtain multi-group cross-section data, and a multi-group shielding database is created.

[0033] The beneficial effects of this invention are:

[0034] (1) The present invention provides a method for optimizing the energy group structure of a multi-group shielded database applicable to the lead-bismuth problem. This method can solve the problem of insufficient accuracy of existing multi-group shielded databases in dividing the energy group structure of the lead-bismuth problem, and significantly improves the calculation accuracy. It has potential engineering and economic value.

[0035] (2) The present invention provides a method for optimizing the energy group structure of a multi-group shielding database applicable to the lead-bismuth problem. The method uses the response contribution method to calculate the particle contribution of each energy group in the 199-group neutron and 42-group photon shielding databases. The energy groups are re-divided by the idea of ​​equal contribution. The energy groups are merged according to the energy group structure of the 47-group neutron and 20-group photon. The optimized multi-group shielding database can improve the computational efficiency and reduce the computation time. Attached Figure Description

[0036] To more clearly illustrate the embodiments of the present invention, the accompanying drawings used in describing the embodiments of the present invention will be briefly described below. Obviously, the drawings described below are merely some embodiments recorded in the present invention. Those skilled in the art can derive other drawings from the following drawings without any creative effort.

[0037] Figure 1 Example of a typical one-dimensional lead-bismuth pile model.

[0038] Figure 2 An example of the neutron contribution distribution in the optimized energy group structure. Detailed Implementation

[0039] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the protection scope of the present invention.

[0040] In the description of this invention, it should be noted that the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., refer to the orientation or positional relationship shown in the accompanying drawings, and are used only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0041] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or a connection through an intermediate medium; and they can refer to the internal communication between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0042] This invention provides a method for constructing a multi-group shielding database and optimizing the energy group structure of lead-bismuth reactors, comprising the following steps:

[0043] like Figure 1 As shown, a lead-bismuth reactor layout is assumed. The structures arranged radially outward from the reactor core are, in order: reactor core, control rods, reflector layer, internal shielding layer, enclosure, lead-bismuth coolant, and pressure vessel.

[0044] The fine group cross-section database was created using the nuclear data processing program Atlas, based on the neutron evaluation nuclear database and the photon-atom evaluation nuclear database, to generate a fine group cross-section database of 199 neutron groups and 42 photons in MATXS format.

[0045] Resonance calculations combining lead-bismuth pile characteristics: such as Figure 1 As shown, a typical one-dimensional lead-bismuth reactor model is established radially outward from the reactor core. Resonance calculations are performed on the nuclides included in the model. After calculation, new fine group cross-section data are obtained. The original cross-section data are replaced with the new cross-section data to update the fine group cross-section library of group 199 neutrons and group 42 photons.

[0046] Energy group structure optimization: Based on response contribution theory, Figure 1 A typical model of a one-dimensional lead-bismuth pile was used, employing a pre-built 199-group neutron fine-group cross-section library, to solve the forward and conjugate neutron transport equations. The source strength for the forward neutron transport equation was filled in according to the source distribution in the typical model, while the source strength for the conjugate neutron transport equation was defined as the important response function of detectors in different energy ranges. The neutron angular flux and conjugate neutron angular flux were solved for the two equations respectively, and the 199-group neutron contribution value was calculated using formulas. The total neutron contribution value in each energy range of the fast, hyperthermal, and hot regions was statistically analyzed, and the contribution was evenly distributed within each energy range to determine the optimized energy group structure, such as... Figure 2 As shown.

[0047] Energy group merging: Calculation using the Monte Carlo method Figure 1 The photon energy spectra of each material region in a typical one-dimensional lead-bismuth pile model are used as the weight spectrum of the merged energy group. The optimized energy group structure is used to merge the fine group cross-sectional data to obtain multi-group cross-sectional data, and a multi-group shielding database is created.

[0048] Example 1

[0049] This invention provides a method for constructing a multi-group shielding database and optimizing the energy group structure of lead-bismuth reactors, comprising the following steps:

[0050] S1. Creation of the Fine Group Section Library

[0051] The creation of the multi-group shielding database begins with the evaluation nucleus database, which stores continuous energy cross-section data of various nuclides obtained through theory or experiment. This data is publicly available from major domestic and international institutions, but it cannot be directly applied to shielding calculation software and requires data processing.

[0052] Advanced nuclear data processing programs such as Atlas and NJOY were employed. Based on the neutron evaluation nuclear database, fine-group neutron cross-section data and fine-group photon generation cross-section data were obtained through resonance reconstruction and linearization, Doppler broadening, calculation of the effective self-screen cross-section in the indistinguishable resonance region, thermal neutron scattering calculation, and fine-group cross-section calculation. Based on the photon-atom evaluation nuclear database, the fine-group photon-atom reaction cross-section was obtained through cross-section linearization and fine-group cross-section calculation. Finally, the fine-group neutron cross-section, photon generation cross-section, and fine-group photon-atom reaction cross-section were stored in MATXS format.

[0053] The MATXS format is a specific format that includes the identifiers, temperatures, energy group structures, and cross-sectional data of each nuclide. In this embodiment, the nuclide types stored in the MATXS format cross-sectional library include all nuclides in the evaluation nuclide database. The temperatures are determined based on the actual lead-bismuth pile temperature, and the energy group structures are selected as the fine group structures of group 199 neutrons and group 42 photons.

[0054] S2. Resonance calculations combining lead-bismuth pile characteristics

[0055] The one-dimensional structural dimensions and materials of a lead-bismuth reactor (LDBR) from the core to the outer shielding layer were identified, mainly including the core, reflector, shroud, lead-bismuth coolant, and shielding layer. Based on this arrangement, a typical one-dimensional LBR model was established. Using the fine-group cross-section data obtained in S1, resonance calculations were performed on the nuclides included in the model. If the nuclide was non-resonant, the Bondarenko iteration method was used in the full-energy region; if the nuclide was resonant, the ultrafine-group method was used in the resonant energy region, and the Bondarenko iteration method was used in the remaining energy regions.

[0056] After resonance calculation, new fine group cross-section data of nuclides are obtained. The cross-section data of the corresponding nuclides in S1 are replaced with the new cross-section data, and the fine group cross-section library of group 199 neutrons and group 42 photons is updated.

[0057] S3, Energy Group Structure Optimization

[0058] To improve the computational efficiency of shielding large-scale or complex geometric problems, it is necessary to perform energy group merging to reduce the number of energy groups in the fine group cross-section data of S2. To obtain an energy group structure suitable for lead-bismuth piles after energy group merging, this embodiment selects the energy group structure in S2 as the initial energy group structure based on response contribution theory. Using a typical one-dimensional lead-bismuth pile model established in S2, the forward and conjugate neutron transport equations are solved to optimize the energy group structure.

[0059] The solution to the forward transport equation is:

[0060]

[0061] In the formula: Ω represents the direction of neutron motion; ψ g (r,Ω) represents the neutron angular flux of energy group g at position r, in the direction of motion Ω, and in cm. -2 ·s -1 );Σ t,g (r) represents the total neutron cross section of energy group g at position r, in cm. -1 );Σ s,g→g' (r,Ω'→Ω) represents the neutron scattering cross section at position r, with the direction of motion from Ω to Ω', from energy group g to g', in cm. -1 );q g (r, Ω The expression represents the neutron source intensity of energy group g at position r, in the direction of motion Ω, and in cm. -3 ·s -1 );

[0062] The conjugate transport equation corresponding to the above equation is:

[0063]

[0064] In the formula This represents the conjugate neutron angular flux of energy group g at position r, in the direction of motion Ω, and in units of (cm). -2 ·s -1 ); This represents the conjugate neutron source intensity of energy group g at position r, in the direction of motion Ω, and in cm. -3 ·s -1 ).

[0065] According to the definition of the conjugate equation, we know that:

[0066]

[0067] In the above formula, any value of the conjugate neutron source strength can satisfy the above conjugate condition. In this embodiment, the conjugate neutron source strength is defined as a response function important to detectors in different energy ranges. The neutron energy group structure of group 199 in 2) is divided into three energy segments: the energy range above 0.1 MeV is the fast region, the energy range below 0.1 MeV and above 5 eV is the ultrathermal region, and the energy range below 5 eV is the hot region. For the fast region energy group, a value sensitive to this energy range is selected. 63 Cu(n,α) detector 54 Fe(n,p) detector 58 Ni(n,p) detector, 46 Ti(n,p) detector, 237 Np(n,f) detector and 238 For the U(n,f) detector, the normalized response cross-sections of the above detectors are summed to obtain the response function of the fast energy group. For the ultrathermal and thermal energy regions, [further details are needed]. 56 The Fe(n,r) detector response cross section is used as the response function.

[0068] The contribution value of each energy group is defined as follows:

[0069]

[0070] In the formula C g This represents the contribution of neutrons to energy group g, expressed in s. -1 The contribution values ​​in each energy segment of the fast, superheated, and hot regions will be calculated separately. The contribution will be evenly distributed in each energy segment to delineate the boundaries of the multi-group neutron energy groups, thus obtaining the optimized multi-group neutron energy group structure.

[0071] S4 can be grouped and merged.

[0072] The photon energy spectrum of each material region in the typical one-dimensional lead-bismuth pile model in S2 was calculated using the Monte Carlo method. This energy spectrum was used as the weight spectrum of the merged energy group. Based on the optimized energy group structure in S3, the fine group cross-section data obtained in S2 were merged to obtain multi-group cross-section data, and a multi-group shielding database was created.

[0073] While those skilled in the art will recognize that the present invention is not limited to the details of the exemplary embodiments described above, and that it can be implemented in other specific forms without departing from the spirit or essential characteristics of the invention, the embodiments should be considered illustrative and non-limiting in all respects. The scope of the invention is defined by the appended claims rather than the foregoing description, and therefore all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

[0074] Furthermore, it should be understood that although the present invention is described according to embodiments, not every embodiment contains only one independent technical solution. This way of describing the specification is only for clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A method for constructing a multi-group shielding database and optimizing the energy group structure for lead-bismuth reactors, characterized in that, Includes the following steps: S1. Creation of the fine group section library; S2. Resonance calculations combining lead-bismuth pile characteristics; S3, Energy Group Structure Optimization; S4, can be grouped.

2. The method for constructing a multi-group shielding database and optimizing the energy group structure for lead-bismuth reactors according to claim 1, characterized in that, In S1, the nuclear data processing program Atlas is used to generate a fine group cross-section library of 199 neutron groups and 42 photons in MATXS format, based on the neutron evaluation nuclear database and the photon-atom evaluation nuclear database.

3. The method for constructing a multi-group shielding database and optimizing the energy group structure for lead-bismuth reactors according to claim 2, characterized in that, Using the nuclear data processing program Atlas, based on the neutron evaluation nuclear database, fine group neutron cross-section data and fine group photon generation cross-section data were obtained through resonance reconstruction and linearization, Doppler broadening, calculation of effective self-screen cross-section in indistinguishable resonance region, thermal neutron scattering calculation, and fine group cross-section calculation.

4. The method for constructing a multi-group shielding database and optimizing the energy group structure for lead-bismuth reactors according to claim 3, characterized in that, Based on the photon-atom evaluation nuclear database, the fine-group photon-atom reaction cross section is obtained through cross section linearization and fine-group cross section calculation.

5. The method for constructing a multi-group shielding database and optimizing the energy group structure for lead-bismuth reactors according to claim 4, characterized in that, The fine-group neutron cross section, photon generation cross section, and fine-group photon-atom reaction cross section are stored in MATXS format.

6. The method for constructing a multi-group shielding database and optimizing the energy group structure for lead-bismuth reactors according to claim 5, characterized in that, In S2, a one-dimensional typical model of the lead-bismuth reactor is established radially outward from the reactor core. Resonance calculations are performed on the nuclides included in the model. After calculation, new fine group cross-section data are obtained. The original cross-section data is replaced with the new cross-section data, and the fine group cross-section library of 199 group neutrons and 42 group photons is updated.

7. The method for constructing a multi-group shielding database and optimizing the energy group structure for lead-bismuth reactors according to claim 6, characterized in that, If the nuclide is a non-resonance nuclide, the Bondarenko iterative method is used in the full-energy region; if the nuclide is a resonance nuclide, the ultrafine group method is used in the resonance energy region, and the Bondarenko iterative method is used in the other energy regions.

8. The method for constructing a multi-group shielding database and optimizing the energy group structure for lead-bismuth reactors according to claim 7, characterized in that, In S3, based on the response contribution theory and a typical one-dimensional lead-bismuth pile model, the forward and conjugate neutron transport equations are solved using a pre-built 199-group neutron fine-group cross-section library. The source strength of the forward neutron transport equation is filled in according to the source distribution in the typical model, and the source strength of the conjugate neutron transport equation is defined as the important response function of the detector for different energy ranges. The neutron angular flux and conjugate neutron angular flux are solved for the two equations respectively. The total neutron contribution in each energy range of the fast, hyperthermal, and hot regions is statistically analyzed, and the contribution is evenly distributed in each energy range to determine the optimized energy group structure.

9. The method for constructing a multi-group shielding database and optimizing the energy group structure for lead-bismuth reactors according to claim 8, characterized in that, In S3, The solution to the forward transport equation is: In the formula: Ω represents the direction of neutron motion; ψ g (r,Ω) represents the neutron angular flux of energy group g at position r, in the direction of motion Ω, and in cm. -2 ·s -1 );Σ t,g (r) represents the total neutron cross section of energy group g at position r, in cm. -1 );Σ s,g→g' (r,Ω'→Ω) represents the neutron scattering cross section at position r, with the direction of motion from Ω to Ω', from energy group g to g', in cm. -1 );q g (r,Ω) represents the neutron source intensity of energy group g at position r, in the direction of motion Ω, and in cm. -3 ·s -1 ); The conjugate transport equation corresponding to the above equation is: In the formula This represents the conjugate neutron angular flux of energy group g at position r, in the direction of motion Ω, and in units of (cm). -2 ·s -1 ); This represents the conjugate neutron source intensity of energy group g at position r, in the direction of motion Ω, and in cm. -3 ·s -1 ); According to the definition of the conjugate equation, we know that: The contribution value of each energy group is defined as follows: In the formula C g This represents the contribution of neutrons to energy group g, expressed in s. -1 The contribution values ​​in each energy segment of the fast region, superheated region, and hot region will be calculated separately. The contribution will be evenly distributed in each energy segment to divide the boundaries of the multi-group neutron energy group and obtain the optimized multi-group neutron energy group structure.

10. The method for constructing a multi-group shielding database and optimizing the energy group structure for lead-bismuth reactors according to claim 9, characterized in that, In step S4, the photon energy spectrum of each material region in the typical one-dimensional lead-bismuth pile model in S2 is calculated using the Monte Carlo method. This energy spectrum is used as the weight spectrum of the merged energy group. Based on the optimized energy group structure in S3, the fine group cross-section data obtained in S2 is merged to obtain multi-group cross-section data, and a multi-group shielding database is created.

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